1 <?xml version="1.0"?>
2 <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
3 <archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
4 	<author>Biancani, Giuseppe</author>
5 	<title>Aristotelis loca mathematica</title>
6 	<date>1615</date>
7 	<place>Bologna</place>
8 	<translator/>
9 	<lang>la</lang>
10 	<cvs_file>bianc_locam_01_la_1615</cvs_file>
11 	<cvs_version/>
12 	<locator>0000000009.xml</locator>
13 </info>      <text>          <front>                           	<pb/><section><p type="head">
14 
15 <s>ARISTOTELIS<lb/>LOCA MATHEMATICA<lb/>Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/>&amp; explicata.</s></p><p type="head">
16 
17 <s><emph type="italics"/>Aristotelic&aelig; videlicet expo&longs;itionis complementum <lb/>hactenus de&longs;ideratum.<emph.end type="italics"/></s></p><p type="head">
18 
19 <s>Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/><expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s></p><p type="head">
20 
21 <s><emph type="italics"/>Authore IOSEPHO BLANCANO Bononien&longs;i &egrave; Societate Ie&longs;u, <lb/>Mathematicarum in Gymna&longs;io Parmen&longs;i Profe&longs;&longs;ore.<emph.end type="italics"/></s></p><p type="head">
22 
23 <s>Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum<lb/>PETRVMFRANCISCVM MALASPINAM<lb/>Aedificiorum Marchionem, apud C&aelig;&longs;. <!-- REMOVE S-->Maie&longs;tatem <lb/>pro Sereni&longs;s. <!-- REMOVE S-->Parmen&longs;ium Duce Legatum.</s>
24 
25 
26 
27 </p><p type="head">
28 
29 <s>BONONI&AElig; M. <!-- REMOVE S-->D C. <!-- KEEP S--><!-- REMOVE S-->X V.<!-- KEEP S--></s>
30 
31 
32 
33 </p><p type="head">
34 
35 <s>Apud Bartholom&aelig;um Cochium. <!-- KEEP S--></s>
36 
37 <s>Superiorum permi&longs;&longs;u.</s></p><p type="head">
38 
39 <s>Sumptibus Hieronymi Tamburini.</s></p><pb/><pb pagenum="3"/>
40 </section>
41 <section><p type="head"><s>ILLVSTRISSIMO <lb/>AC NOBILISSIMO<lb/>PETROFRANCISCO <lb/>MALASPINAE<lb/>&AElig;DIFICIORVM MARCHIONI.</s></p><p type="main">
42 
43 <s><emph type="italics"/>En tandem Illustri&szlig;. <!-- REMOVE S-->Marchio opus no&shy;<lb/>strum de Locis Mathematicis apud Ari&shy;<lb/>stotelem, vn&agrave; cum Tractatione de natura <lb/>&longs;cientiarum Mathematicarum, necnon <lb/>Clarorum Mathematicor&ubreve; Chronologia; <lb/>quod tibi Mec&oelig;nati meo munificenti&longs;simo iure merit&ograve; <lb/>dicare, ac &longs;ub clari&szlig;imi tui nominis patrocinio in lucem <lb/>dare con&longs;titui. </s>
44 
45 
46 
47 <s>prim&ugrave;m quidem, vt mei perpetui erga te <lb/>amoris, &amp; ob&longs;eruanti&aelig; hoc vnum &longs;altem specimen exta&shy;<lb/>ret: t&ugrave;m vt idoneum, &aelig;quumque propo&longs;it&aelig; rei iudicem <lb/>nanci&longs;cerer. </s>
48 
49 <s>c&ugrave;m enim adiu&longs;tum arbitr&ubreve; duo poti&szlig;im&ugrave;m <lb/>requirantur, rerum &longs;cilicet cognitio, atque prudentia, quem <lb/>te rei, de qua agitur peritiorem, quemu&egrave; prudentiorem <lb/>inuenire potuerim? </s>
50 
51 <s>tu enim c&ugrave;m Phy&longs;iologi&aelig;, ac Mathe&shy;<lb/>maticarum omnium Encyclop&aelig;diam mirum in modum<emph.end type="italics"/><pb pagenum="4"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>per&longs;ua&longs;i&longs;ti, vt Archimedis, &amp; Apollonij admirandis, ac <lb/>&longs;ubtili&szlig;imis Demon&longs;trationibus detinearis. </s>
52 
53 <s>Quanta por&shy;<lb/>r&ograve; in rebus agendis prudentia valeas, toti pen&egrave; Europ&aelig; <lb/>innotuit, c&ugrave;m pro no&longs;tris Sereni&szlig;. <!-- REMOVE S-->Ducibus, non &longs;ol&ugrave;m ad <lb/>omnes fer&egrave; Itali&aelig;, atque Germani&aelig; Principes, ver&ugrave;m etiam <lb/>ad C&aelig;&longs;aream Maie&longs;tatem rebus f&oelig;liciter ge&longs;tis Legatus <lb/>decim&ugrave;m extiteris; ac dem&ugrave;m &agrave; Sereni&szlig;. <!-- REMOVE S-->Duce Ranutio <lb/>inter primarios de Rep. <!-- KEEP S--></s>
54 
55 
56 
57 
58 
59 <s>Con&longs;iliorum Authores ad&longs;citus <lb/>fueris. </s>
60 
61 <s>C&aelig;ter&ugrave;m in Clarorum Mathematicorum Chro&shy;<lb/>nologia perlegenda, &longs;&aelig;pi&szlig;im&egrave; tibi nobili&szlig;imi &aelig;qu&egrave;, ac do&shy;<lb/>cti&szlig;imi Viri, tui omnino per&longs;imiles occurrent, quod tibi <lb/>nonni&longs;i grati&szlig;imum accidere po&longs;&longs;e arbitror. </s>
62 
63 <s>Complectere <lb/>igitur ea benignitate, atque clementia, qua &longs;oles no&longs;tra stu&shy;<lb/>dia promouere, mea h&aelig;c quantulacumque munu&longs;cula. <lb/></s>
64 
65 <s>qu&aelig; &longs;i tibi accepta e&longs;&longs;e intellexero, iam tandem ma&shy;<lb/>ximorum munerum loco habenda e&longs;&longs;e cen&longs;e&shy;<lb/>bo. </s>
66 
67 <s>incolumem tibi, ac f&oelig;licem D. Opt. <lb/><!-- REMOVE S-->Max. <!-- REMOVE S-->long&aelig;uitatem tueatur. <lb/></s>
68 
69 
70 
71 
72 
73 <s>Vale.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
74 
75 <s><emph type="italics"/>Parm&aelig; Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/><!-- KEEP S--></s></p></section><pb pagenum="5"/><section><p type="head">
76 
77 <s>Liber de &longs;e ip&longs;o.</s></p><p type="head">
78 
79 <s><emph type="italics"/>Nec di&longs;cet Lector me &longs;olo interprete totum, <lb/>Nec &longs;ine me totum di&longs;cet Aristotelem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
80 
81 <s>Ego Iordanus Ca&longs;&longs;ini Pr&aelig;po&longs;itus Prouincialis Prouinci&aelig; Venet&aelig; Societatis <lb/>Ie&longs;u, ex auctoritate Adm. <!-- REMOVE S-->Reuer. <!-- REMOVE S-->P. nc&longs;tro Pr&aelig;po&longs;iti Generalis P. <!-- REMOVE S-->Claudij <lb/>Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. <!-- REMOVE S-->Io&longs;ephi Blancani eiu&longs;dem <lb/>Societatis, quod in&longs;cribitur, Ari&longs;t. Loca Mathematica ex vniuer&longs;is ip&longs;ius <lb/>operibus collecta, &amp; explicata, &agrave; deputatis Patribus recognitum, &amp; ap&shy;<lb/>probatum typis mandari po&longs;&longs;it. </s>
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 <s>Parm&aelig; die 15. Ianuarij 1615.</s></p><p type="main">
92 
93 <s><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/><!-- REMOVE S-->Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s></p><p type="main">
94 
95 
96 
97 <s>&amp; Reuerendi&longs;s. <!-- REMOVE S-->Archiepi&longs;c. <!-- REMOVE S-->Bonon</s>
98 
99 
100 
101 </p><p type="main">
102 
103 <s>Imprimatur</s></p><p type="main">
104 
105 <s>Fr. <!-- REMOVE S-->Hieronymus Onuphrius pro Reuerendi&longs;s. <!-- REMOVE S-->P. <!-- REMOVE S-->Inqui&longs;itore Bonon.</s>
106 
107 
108 
109 
110 
111 </p></section><pb pagenum="6"/><section><p type="head">
112 
113 <s>LECTORI.</s></p><p type="main">
114 
115 <s>Qvod pri&longs;cis olim temporibus (humani&longs;&longs;ime Lector) &longs;um&shy;<lb/>mi duo Philo&longs;ophi, Philippus Mendeus, ac Theon Smyr&shy;<lb/>n&aelig;us in Platonis Dialogis egregi&egrave; perfecerunt, vt videli&shy;<lb/>cet qu&aelig; pa&longs;&longs;im &longs;ummus hic Philo&longs;ophus de Mathemati&shy;<lb/>cis &longs;cripta reliquit, eadem ip&longs;a ab illis &longs;electa, &amp; in vnum <lb/>qua&longs;i corpus redacta lucubrationibus illu&longs;trarent: idem ego quoque in <lb/>Ari&longs;totelis operibus efficere &longs;um conatus, vt qu&aelig; de Mathematicis re&shy;<lb/>bus in vniuer&longs;is eiu&longs;dem monumentis &longs;par&longs;a leguntur, eadem in vnum <lb/>&agrave; me collecta, &amp; explicata ijs Philo&longs;ophi&aelig; &longs;tudio&longs;is maxime &longs;eruirent, <lb/>qui pri&longs;ca illa con&longs;uetudine relicta, Mathematicarum omnium ignari <lb/>non &longs;ine graui &longs;tudiorum &longs;uorum detrimento Philo&longs;ophi&aelig; curriculum <lb/>aggrediuntur. </s>
116 
117 <s>Vt autem huius operis nece&longs;&longs;itas, <expan abbr="vari&aelig;&qacute;">vari&aelig;que</expan>; vtilitates pla&shy;<lb/>nius cogno&longs;cantur oper&aelig;pretium erit initio illius cau&longs;as exponere; qu&aelig; <lb/>me poti&longs;&longs;imum ad illud con&longs;cribendum compulerunt, quarum</s></p><p type="main">
118 
119 <s>Prima &longs;it, quod h&aelig;c Ari&longs;t. 
120 
121 loca Mathematica, qu&aelig; quidem fer&egrave; 408. <lb/>numerantur, pe&longs;&longs;im&egrave; latinis literis con&longs;ignata &longs;unt v&longs;que ade&ograve;, vt Ari&shy;<lb/>&longs;totelem ip&longs;um, vel inuitum (quod po&longs;tea multis in locis planum fiet) in <lb/>ab&longs;urdi&longs;&longs;ima errata &longs;&aelig;pi&longs;&longs;im&egrave; compellant.</s></p><p type="main">
122 
123 <s>Secunda, qu&ograve;d plurima huiu&longs;modi loca &agrave; nemine, quod &longs;ciam, adhuc <lb/>declarata in tenebris magno no&longs;trorum malo delite&longs;cunt: cuiu&longs;modi <lb/>&longs;unt ad &longs;exaginta problemata, libellus de lineis in &longs;ecabilibus, libellus <lb/>de mundo, &longs;i tamen Ari&longs;totelis e&longs;t, &amp; Mechanic&aelig; qu&aelig;&longs;tiones, quamuis <lb/>enim Picolomineus in eas paraphra&longs;im ediderit, loca tamen earum dif&shy;<lb/>ficiliora non &longs;atis illu&longs;trauit. </s>
124 
125 <s>Vt autem dixi 408. in vniuer&longs;um loca mi&shy;<lb/>nim&ugrave;m numerantur, quibus illud Platonis in&longs;criptum e&longs;t <foreign lang="greek">agaiome/trhtos <lb/>udei/s eisi/to</foreign>; &amp; in quibus Mathematic&aelig; di&longs;ciplin&aelig; rudes, &amp; imperiti, quem <lb/>&longs;equuntur ducem Ari&longs;t. 
126 
127 eum &longs;&aelig;pe de&longs;erere non &longs;ine turpi dedecoris no&shy;<lb/>ta coguntur; quo fit vt exempla illa Mathematica lucem rebus aliquan&shy;<lb/>do allatura, tenebras cimmerijs, vt aiunt vmbris cra&longs;&longs;iores ij&longs;dem <lb/>obducant.</s></p><p type="main">
128 
129 <s>Tertia, quia Gr&aelig;cieorumdem locorum commentatores breuiter, &amp; <lb/>ob&longs;cur&egrave; admodum ea, qu&aelig; ad Mathematicum &longs;pectant, attingunt, hoc <lb/>enim ab ip&longs;is <expan abbr="cert&utilde;">certum</expan> ponitur, I ectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/>Philo &longs;ophorum, Mathematicis imbutum; at ver&ograve; no&longs;tra &aelig;tate magna <lb/>cum Philo&longs;ophi&aelig; iactura, quamplurimi earumdem di&longs;ciplinarum de&longs;ti&shy;<lb/>tuti pr&aelig;&longs;idijs, ne Gr&aelig;corum quidem Interpretum explanationes, ne&shy;<lb/>dum Ari&longs;t. 
130 
131 ob&longs;cur&egrave; dicta intelligunt.</s></p><pb pagenum="7"/><p type="main">
132 
133 <s>Quarta. </s>
134 
135 <s>Adde, quod etiam &longs;i quis leuiter &longs;it erudito illo Mathemati&shy;<lb/>corum puluere con&longs;per&longs;us, ade&ograve; tamen peruer&longs;a e&longs;t eorumdem Gr&aelig;co&shy;<lb/>rum in Latinum tran&longs;latio, <expan abbr="tanta&qacute;">tantaque</expan>; figurarum, qu&aelig; nece&longs;&longs;ari&aelig; erant <lb/>confu&longs;io, &amp; deprauatio, vt nec abeo, qui &longs;it Mathematicarum &longs;cientia <lb/>excultus, &longs;ine magno labore percipi po&longs;&longs;int. </s>
136 
137 <s>Quin etiam figur&aelig; ill&aelig;, qu&aelig; <lb/>omnino nece&longs;&longs;ari&aelig; &longs;unt ob Scriptorum, &amp; Typographorum in&longs;citiam, <lb/>aut inertiam pluribus in locis de&longs;iderantur. </s>
138 
139 <s>Latini ver&ograve; multo minus, <lb/>qu&agrave;m Gr&aelig;ci Mathematic&aelig; periti, qua ratione eadem loca pertractaue&shy;<lb/>rint, facilius e&longs;t conijcere, qu&agrave;m vt dici oporteat.</s></p><p type="main">
140 
141 <s>Quinta. </s>
142 
143 <s>Ex his omnibus in aliud incommodum, vel maximum Phi&shy;<lb/>lo&longs;ophi quidam incidebant; aut enim horum locorum expo&longs;itionem ta&shy;<lb/>citi declinabant: aut eam minime nece&longs;&longs;ariam ad Ari&longs;t. 
144 
145 percipiendam <lb/>&longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;&shy;<lb/>&longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s>
146 
147 <s>Eorum ver&ograve; nonnulli eorumdem <lb/>locorum expo&longs;itionem audacter nimis aggrediebantur, <expan abbr="atq;">atque</expan> hinc pueri&shy;<lb/>les ill&aelig;, ac ridicul&aelig; expo&longs;itiones pa&longs;&longs;im audit&aelig;, cuiu&longs;modi e&longs;t illa, quan&shy;<lb/>do Ari&longs;toteles ait, quod illi frequenti&longs;&longs;imum e&longs;t, omnis triangulus ha&shy;<lb/>bet tres; nihil aliud &longs;ignificari volunt, qu&agrave;m omnem triangulum habe&shy;<lb/>re tres angulos. </s>
148 
149 <s>quod &longs;i dicat, omnis triangulus habet tres &aelig;quales duo&shy;<lb/>busrectis: hic h&aelig;rent, hinc anguntur: <expan abbr="cumq;">cumque</expan> ex his angu&longs;tijs, ac tricis <lb/>&longs;e minim&egrave; expedire valeant, aurea verba illa, quibus ingentes &longs;apienti&aelig; <lb/>the&longs;auri continentur, alto &longs;ilentij velo contegere Mathematicarum eos <lb/>cogit in&longs;citia: vnde illud, quod Gr&aelig;c&aelig; lingu&aelig; imperitis mutata oratio&shy;<lb/>ne acclamandum illis foret, Mathematicum e&longs;t, non legitur. </s>
150 
151 <s>Nec mi&shy;<lb/>nus elegans illa altera expo&longs;itio; Diametrum e&longs;le incommen&longs;urabilem <lb/>co&longs;t&aelig;; quod &longs;&aelig;pe apud Ari&longs;t. 
152 
153 legentibus occurrit, nihil aliud &longs;ibi velle, <lb/>quam Diametrum e&longs;&longs;e longiorem co&longs;ta, quam quidem a&longs;ymetri&aelig; huius <lb/>ignorantiam Plato de legibus dial. </s>
154 
155 <s>7. non hominum, &longs;ed &longs;uum, <expan abbr="peco-rumq;">peco&shy;<lb/>rumque</expan> appellare non dubitauit. </s>
156 
157 <s>Quid illa? </s>
158 
159 <s>cum Ari&longs;t. 
160 
161 ait duo cubi, cu&shy;<lb/>bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in&shy;<lb/>uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/></s>
162 
163 <s>Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. <!-- REMOVE S-->15. qu&agrave;m &longs;e Mathematicis, <lb/>reliqui&longs;que Philo&longs;ophis irridendum pr&aelig;bet dum &agrave; permutata propor&shy;<lb/>tione putat &longs;erect&egrave; in hunc modum pluribus apud ip&longs;um verbis explica&shy;<lb/>tum, argumentari,</s>
164 
165 </p><p type="main">
166 
167 <s><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/>It a voluntas antiqua ad effectum antiquum. <lb/></s>
168 
169 <s>Ergo permutatim, vt &longs;e habebit voluntas noua ad effectum <lb/>antiquum, ita voluntas antiqua ad effectum nouum.<emph.end type="italics"/></s></p><p type="main">
170 
171 <s><expan abbr="Spectat&utilde;">Spectatum</expan> admi&longs;&longs;i rilum teneatis amici? </s>
172 
173 <s>nego, ait; qui&longs;piam con&longs;equen&shy;<pb pagenum="8"/>tiam, non enim hoc e&longs;t argumentari &agrave; permutata ratione, deberet enim <lb/>inferre, &longs;ic, ergo ita &longs;e habebit voluntas noua ad antiquam, quemad&shy;<lb/>modum effectus nouus ad antiquum. </s>
174 
175 <s>qu&aelig; vitio&longs;a argumentatio quan&shy;<lb/>tumuis l&aelig;uis &longs;it, &amp; manife&longs;ta, quo&longs;dam tamen magni nominis philo&longs;o&shy;<lb/>phantes ade&ograve; tor&longs;it, vt adhuc torqueat.</s></p><p type="main">
176 
177 <s>Quanta autem mi&longs;eratione digni, qui public&egrave; aliquando apud &longs;uos <lb/>auditores totam Per&longs;pectiuam, qua nihil iucundius e&longs;t, de medio tolle&shy;<lb/>re conati &longs;unt, propterea quod ill&aelig; vi&longs;uales line&aelig;, illi anguli, ill&aelig; pyra&shy;<lb/>mides, aut coni, quibus vi&longs;io perficitur nullibi extarent, &longs;ed e&longs;&longs;ent vana <lb/>qu&aelig;dam opticorum figmenta. </s>
178 
179 <s>Qu&igrave; ver&ograve; fieri potuit, vt non aduerterint <lb/>i&longs;ti &longs;e Ari&longs;toteli &longs;uo manife&longs;te repugnare, qui &longs;&aelig;pius de lineis vi&longs;ualibus <lb/>per&longs;pectiuum pertractare a&longs;&longs;erit, <expan abbr="di&longs;crimen&qacute;">di&longs;crimenque</expan>; inter lineam phy&longs;icam, &amp; <lb/>opticam a&longs;&longs;ignat, <expan abbr="ip&longs;ius&qacute;">ip&longs;iusque</expan>; optices tanquam ver&aelig; &longs;cienti&aelig; mentionem <lb/>&longs;&aelig;pius facit.</s></p><p type="main">
180 
181 <s>Alij ex altera parte contra A&longs;tronomos in &longs;urgunt, eccentricos, <expan abbr="atq;">atque</expan> <lb/>epiciclos omnes de c&oelig;lo detrahere cupientes. </s>
182 
183 <s>Verum id i&longs;ti nulla ex&shy;<lb/>pre&longs;&longs;a nedum probabili ratione faciunt, fals&ograve; exi&longs;timantes A&longs;tronomos <lb/>admirandam illam C&oelig;lorum fabricam a&longs;&longs;erere, non autem &longs;upponere: <lb/>&longs;ed a&longs;tronomi illam &longs;upponunt, <expan abbr="eam&qacute;">eamque</expan>; propterea hypothe&longs;im <expan abbr="appell&atilde;t">appellant</expan>, <lb/>non a&longs;&longs;erunt. </s>
184 
185 <s>Quod &longs;i aliqua probabili ratione id facerent, vti nonnulli <lb/>ex recentioribus, quorum Ticho Coripheus e&longs;t, laudandi potius, quam <lb/>vituperandi e&longs;&longs;ent. </s>
186 
187 <s>Impugnant <expan abbr="itaq;">itaque</expan> a&longs;tronomachi i&longs;ti hypothe&longs;im pro <lb/>a&longs;&longs;ertione; <expan abbr="tales&qacute;">talesque</expan>; &longs;&aelig;p&egrave; hi &longs;unt, vt non &longs;atis intelligant, quid &longs;it Aequa&shy;<lb/>tor, aut Zodiacus, ne dum quid Epiciclus, aut Eccentricus. </s>
188 
189 <s>Nec defuit <lb/>qui viginti duo argumenta excogitarit, <expan abbr="atq;">atque</expan> in medium protulerit, qui&shy;<lb/>bus contra A&longs;tronomos probare conatus e&longs;t, nullo modo Solem, aut <lb/>Lunam moueri po&longs;&longs;e motibus contrarijs, ide&longs;t, ab oriente in <expan abbr="occid&etilde;tem">occidentem</expan> <lb/>motu diurno, &amp; proprio ab occidente in orientem. </s>
190 
191 <s>Sed exi&longs;timandum <lb/>e&longs;t <expan abbr="i&longs;t&utilde;">i&longs;tum</expan> Lunam nouam &agrave; Sole quotidie magis, ac magis ver&longs;us orientem <lb/>recedere, nunquam animaduerti&longs;&longs;e; ab ea enim hanc motuum concor&shy;<lb/>diam didici&longs;&longs;et.</s></p><p type="main">
192 
193 <s>Quid tandem <expan abbr="dic&etilde;dum">dicendum</expan> de quodam magni nominis Philo&longs;opho, om&shy;<lb/>nium tamen <expan abbr="Mathematicar&utilde;">Mathematicarum</expan> experte, qui in publica di&longs;putatione axio&shy;<lb/>ma illud Mathematicum, omne totum e&longs;t maius &longs;ua parte, in &longs;en&longs;u in <lb/>quo &agrave; Mathematicis effertur negare non erubuit, e&ograve;, quod in infinito, <lb/>vt aiebat non concederetur ab omnibus. </s>
194 
195 <s>&longs;cilicet non intelligebat ma&shy;<lb/>thematicum tantummodo tractare de Quantitate finita, ac terminata, <lb/>in qua axioma pr&aelig;dictum ab omnibus conceditur. </s>
196 
197 <s>Neque vero hic <lb/>nonnullorum infen&longs;us in Mathematicas animus quieuit, verum etiam <lb/>c&ograve; progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien&shy;<pb pagenum="9"/>tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu&shy;<lb/>gnante, expungere conati &longs;int; <expan abbr="idq;">idque</expan> ne&longs;cio an vlla alia de cau&longs;a egerint, <lb/>qu&agrave;m quod eas non &longs;atis calerent; non &longs;ecus <expan abbr="atq;">atque</expan> Ae&longs;opica illa Vulpes, <lb/>qu&aelig; cum cauda mutilata e&longs;&longs;et, caudarum mutilationem reliquis vulpi&shy;<lb/>bus vafr&egrave; per&longs;uadere conabatur. </s>
198 
199 <s>Verum enim ver&ograve; optim&egrave; &longs;cio, ea, <lb/>qu&ecedil; hactenus dicta &longs;unt non in omnes no&longs;tri temporis Philo&longs;ophos qua&shy;<lb/>drare, cum non pauci hodie quoque &longs;int, qui more antiquorum Mathe&shy;<lb/>maticis &longs;uffulti, optim&egrave; &longs;uis &longs;tudijs con&longs;ulentes, reliquam Philo&longs;ophiam <lb/>non &longs;ine magno compendio aggrediuntur. </s>
200 
201 <s>Quo fit, vt c&aelig;teros ageo&shy;<lb/>metretos ita antecellant, vt eorum Magi&longs;tri appellari po&longs;&longs;int, &amp; <expan abbr="debe&atilde;t">debeant</expan>; <lb/>tales fuerunt in primis Vicomercatus, Cardanus, Zabarella, Toletus, <lb/>Bonamicus, &amp; alij, quibus paulo antiquiores fuerunt D. Tho. <!-- REMOVE S-->&amp; Scotus, <lb/>Hiomnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o&shy;<lb/>phantes excelluerint, nemo e&longs;t qui non nouerit. </s>
202 
203 
204 
205 <s>Illud hoc loco minim&egrave; <lb/>tacendum, Iacobum Zabarellam in &longs;uis logic&aelig; commentarijs te&longs;tari &longs;e <lb/>bis &longs;umma diligentia totum Euclidem perlegi&longs;&longs;e, vt perfect&egrave; Ari&longs;t. 
206 
207 de <lb/>demon&longs;tratione &longs;ententiam a&longs;&longs;equi po&longs;&longs;et.</s></p><p type="main">
208 
209 <s>Hi ridiculas illas, ac pueriles expo&longs;itiones &longs;uperius allatas minim&egrave; <lb/>effutierunt, neque reliquis &longs;upra recen&longs;itis incommodis obnoxij fue&shy;<lb/>runt, quibus magno etiam cum dedecore alij Mathematicarum ope ca&shy;<lb/>rentes afficiuntur.</s></p><p type="main">
210 
211 <s>In horum igitur gratiam operam diligenter dedi, vt quantum in me <lb/>e&longs;&longs;et damna &agrave; me &longs;upra enarrata aliqua ex parte re&longs;arcirem. </s>
212 
213 <s>Quaprop&shy;<lb/>ter loca h&aelig;c mathematica num rect&egrave; e&longs;&longs;ent &egrave; gr&aelig;co in latinum tran&longs;lata <lb/>diligenter prius expendi. </s>
214 
215 <s>Deinde claritate, qu&agrave;m potui max ma eadem <lb/>loca interpretatus &longs;um, &amp; in horum, de quibus dixi gratiam, qu&aelig;dam <lb/>fan&egrave; tenuia pro&longs;equutus &longs;um, qu&aelig; alioquin libenter omi&longs;i&longs;&longs;em. </s>
216 
217 <s>Tum fi&shy;<lb/>guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s>
218 
219 <s>Hocigitur <lb/>mo&longs;tro qualicunque labore poterit qui&longs;que omnia illa facile intelligere, <lb/><expan abbr="atq;">atque</expan> enumerata incommoda euitare, vnum tantummodo &agrave; Lectore ma&shy;<lb/>thematicarum experte requiram, vt principia &longs;altem illa, &longs;cilicet defini&shy;<lb/>tiones, po&longs;tulata, &amp; axiomata, qu&aelig; prim&ograve; Euclideis libro pr&aelig;ponuntur, <lb/>diligenter prius perlegat cum illa &longs;ua per&longs;picuitate ommbus &longs;int obuia; <lb/>c&aelig;tera ego explicanda recipio. </s>
220 
221 <s>Obiter etiam auctaria nonnulla partim <lb/>mathematica, partim naturalia in&longs;erui, qu&aelig; ob nouitatem, ac pulchri&shy;<lb/>cudinem grata Lectori, atque iucunda fore exi&longs;timaui.</s></p><p type="main">
222 
223 <s>Sciat pr&aelig;terea Lector no&longs;trum in&longs;titutum e&longs;&longs;e loca h&aelig;c mathemati&shy;<lb/>ca, quatenus mathematica &longs;unt declarare, &longs;iue ea &longs;upplere, qu&aelig; ex ma&shy;<lb/>thematicis petenda e&longs;&longs;ent: reliqua autem me tantum attingere, quan&shy;<lb/>tum harum rerum cum illis connexio po&longs;tulat.</s></p><pb pagenum="10"/><p type="main">
224 
225 <s>His omnibus placuit appendices opportune nonnullas addere, qua&shy;<lb/>rum prima de natura mathematicarum &longs;cientiarum: altera, qua omnes <lb/>demon&longs;trationes primi libri Euclidis breuiter ad Logicam normam ex&shy;<lb/>penduntur, vt pateat, quonam demon&longs;trationis genere <expan abbr="c&etilde;&longs;eri">cen&longs;eri</expan> <expan abbr="vnaqu&ecedil;q;">vnaqu&ecedil;que</expan> <lb/>debeat, &amp; ex illis de c&aelig;teris iudicium fiat. </s>
226 
227 <s>Tandem in gratiam etiam <lb/>Mathematicorum tertiam appendicem appendi, qua omnia loca Ari&longs;t. <lb/><!-- REMOVE S-->Geometrica ad Euclidis ordinem referuntur; vnde &amp; ip&longs;i ad &longs;uas pr&ecedil;le&shy;<lb/>ctiones exornandas aliquid &longs;ubinde depromere queant.</s>
228 
229 </p><p type="main">
230 
231 <s>Fruere igitur amice Lector hoc no&longs;tro qualiquali labore, quo ad ple&shy;<lb/>nam totius Ari&longs;t. 
232 
233 intelligentiam, cui adhuc mathematicarum ignoratio <lb/>ob&longs;titit peruenire tandem po&longs;&longs;is: <expan abbr="illud&qacute;">illudque</expan>; experiaris, quod optimus qui&shy;<lb/>dam Philo&longs;ophus, cum totum hunc librum perlegi&longs;&longs;et, effatus e&longs;t, vide&shy;<lb/>licet, opus hoc <emph type="italics"/>Aristot elic&aelig; expo&longs;itionis complementum ad hanc v&longs;que <lb/>diem de&longs;ideratum<emph.end type="italics"/> iure ac merit&ograve; nuncupari po&longs;&longs;e.</s></p><p type="main">
234 
235 <s>Illud demum tanquam parergon addam, quod ego his elucubran&shy;<lb/>dis experientia didici, ad veram &longs;cilicet, ac perfectam to&shy;<lb/>tius Ari&longs;totelis intelligentiam lingu&aelig; in primis <lb/>gr&aelig;c&aelig;, necnon mathematicarum om&shy;<lb/>nium di&longs;ciplinarum haud medio&shy;<lb/>crem cognitionem ne&shy;<lb/>ce&longs;&longs;ariam e&longs;&longs;e. <lb/></s>
236 
237 <s>Vale.<!-- KEEP S--></s></p></section><pb pagenum="11"/><section><p type="head">
238 
239 <s>Pr&ecedil;cipua qu&ecedil;dam, aut noua, autre&longs;taurata, <lb/>qu&aelig; obiter pertractantur.<lb/><arrow.to.target n="table1"/></s></p><table><table.target id="table1"/><row><cell><emph type="italics"/>1<emph.end type="italics"/></cell><cell><emph type="italics"/>De re&longs;olutione. numero marginali.<emph.end type="italics"/></cell><cell><emph type="italics"/>4<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>2<emph.end type="italics"/></cell><cell><emph type="italics"/>De figuris vacuum replentibus, vbi Aristotelis, &amp; expo-&longs;itorum erratum aperitur. num.<emph.end type="italics"/></cell><cell><emph type="italics"/>121<emph.end type="italics"/></cell></row><row><cell/><cell><emph type="italics"/>Inibi, Apum mirabilis qu&aelig;dam in cellis &longs;uis hexagonis   constituendis indu&longs;tria detegitur. num.<emph.end type="italics"/></cell><cell><emph type="italics"/>120<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>3<emph.end type="italics"/></cell><cell><emph type="italics"/>De ijs, qu&aelig; aqu&aelig; in&longs;ident, vn&agrave; cum noua demonstratione problema-tis illius Archimedis, quo metallorum mixtionem indi&longs;&longs;oluta Co-rona, explorauit. in additione. ante num.<emph.end type="italics"/></cell><cell><emph type="italics"/>124<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>4<emph.end type="italics"/></cell><cell><emph type="italics"/>De Cometa, recentiorum &longs;ententia. num.<emph.end type="italics"/></cell><cell><emph type="italics"/>136<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>5<emph.end type="italics"/></cell><cell><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></cell><cell><emph type="italics"/>148<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>6<emph.end type="italics"/></cell><cell><emph type="italics"/>De Terr&aelig; rotunditate, ac mundi duratione.<emph.end type="italics"/></cell><cell><emph type="italics"/>151<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>7<emph.end type="italics"/></cell><cell><emph type="italics"/>De Iride. in additione.<emph.end type="italics"/></cell><cell><emph type="italics"/>181<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>8<emph.end type="italics"/></cell><cell><emph type="italics"/>Scytala quid.<emph.end type="italics"/></cell><cell><emph type="italics"/>250<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>9<emph.end type="italics"/></cell><cell><emph type="italics"/>Securis antiqua qu&aelig;, &amp; qua ratione fieret.<emph.end type="italics"/></cell><cell><emph type="italics"/>258<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>10<emph.end type="italics"/></cell><cell><emph type="italics"/>Statera antiqua qu&aelig;,<emph.end type="italics"/></cell><cell><emph type="italics"/>259<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>11<emph.end type="italics"/></cell><cell><emph type="italics"/>De Ae&longs;tu Maris.<emph.end type="italics"/></cell><cell><emph type="italics"/>272<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>12<emph.end type="italics"/></cell><cell><emph type="italics"/>Araneorum indu&longs;tria nuper patefacta: vbi Democritus contra Ari&longs;t.   defenditur.<emph.end type="italics"/></cell><cell><emph type="italics"/>293<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>13<emph.end type="italics"/></cell><cell><emph type="italics"/>De Lucis figuratione, &amp; rerum &longs;imulacris in ob&longs;curo loco.<emph.end type="italics"/></cell><cell><emph type="italics"/>345<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>14<emph.end type="italics"/></cell><cell><emph type="italics"/>De Pupilla oculi.<emph.end type="italics"/></cell><cell><emph type="italics"/>408<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>15<emph.end type="italics"/></cell><cell><emph type="italics"/>De Mathematicarum natura. prop&egrave; finem operis.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>16<emph.end type="italics"/></cell><cell><emph type="italics"/>Clarorum Mathematicorum Chronologia, in fine operis.<emph.end type="italics"/></cell><cell/></row></table></section><pb pagenum="12"/><section><p type="head">
240 
241 <s><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
242 
243 <s><emph type="italics"/>Qu&aelig; in hoc opere explicantur, iuxta ordine librorum <lb/>ip&longs;ius ex vulgata editione Lugdunen&longs;i.<emph.end type="italics"/></s></p><p type="head">
244 
245 <s>In Pr&aelig;dicamentis.</s></p><p type="main">
246 
247 <s><emph type="italics"/>Gapite s. </s>
248 
249 <s>de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s></p><p type="main">
250 
251 <s><emph type="italics"/>Cap. 
252 
253 de Priori, vbi de Principijs Mathematicarum,<emph.end type="italics"/></s></p><p type="main">
254 
255 <s><emph type="italics"/>Cap. 
256 
257 de Motu, vbi de Gnomone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
258 
259 <s>In Primo Priorum Re&longs;olutoriorum.</s></p><p type="main">
260 
261 <s><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s></p><p type="main">
262 
263 <s><emph type="italics"/>Cap. 
264 
265 23. &longs;ect 1. libri 1. de Incommen &longs;ur abilibus.<emph.end type="italics"/></s></p><p type="main">
266 
267 <s><emph type="italics"/>Cap. 
268 
269 24. &longs;ecti 1. lib. 
270 
271 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
272 
273 <s><emph type="italics"/>Cap. 
274 
275 2. &longs;ect 2. lib. 
276 
277 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
278 
279 <s><emph type="italics"/>Cap. 
280 
281 3. &longs;ecti 2. lib. 
282 
283 1. de Incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main">
284 
285 <s><emph type="italics"/>Cap. 
286 
287 1. &longs;ecti 3. lib. 
288 
289 1. de eo, quod est, omnis triangulus habet tres angulos &aelig;quales <lb/>&aelig;quales duobus rectis: Aequalitas Geometrica, qu&aelig;.<emph.end type="italics"/></s></p><p type="main">
290 
291 <s><emph type="italics"/>Cap. 
292 
293 eodem, de exemplis, quibus vtuntar Geometr&aelig;.<emph.end type="italics"/></s></p><p type="head">
294 
295 <s>In &longs;ecundo Priorum Re&longs;ol.<!-- REMOVE S--><emph type="italics"/>Cap. 
296 
297 21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s></p><p type="main">
298 
299 <s><emph type="italics"/>Cap. 
300 
301 eodem. </s>
302 
303 <s>de Paralellis, &amp; de triangulo.<emph.end type="italics"/></s></p><p type="main">
304 
305 <s><emph type="italics"/>Cap. 
306 
307 26. Quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
308 
309 <s><emph type="italics"/>Cap. 
310 
311 31. de Abductione.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
312 
313 <s><emph type="italics"/>Cap. 
314 
315 codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
316 
317 <s>In primo Po&longs;teriorum.</s></p><p type="main">
318 
319 <s><emph type="italics"/>Textu primo, De Pr&aelig;cognitis Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
320 
321 <s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
322 
323 <s><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s>
324 
325 <s>Item De Mathematicarum Principijs.<emph.end type="italics"/></s></p><p type="main">
326 
327 <s><emph type="italics"/>T. eodem, De Indiui&longs;ibilitate vnitatis.<emph.end type="italics"/></s></p><p type="main">
328 
329 <s><emph type="italics"/>T. 9. De Puncto, &amp; linea. </s>
330 
331 <s>Item de recto, &amp; circulari. </s>
332 
333 <s>Item de numero pari, impari;<lb/>primo, &amp; compo&longs;ito; &aelig;quilatero, &amp; altera parte longiore.<emph.end type="italics"/></s></p><p type="main">
334 
335 <s><emph type="italics"/>T. 11. Line&aelig; punctum inest per &longs;e, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
336 
337 <s><emph type="italics"/>T. 13. De Parallelis. <!-- KEEP S--></s>
338 
339 <s>De I&longs;o&longs;cele. </s>
340 
341 <s>De Alterna Proportione, <lb/>Item quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
342 
343 <s><emph type="italics"/>T. 14. De ij&longs;aem cum pr&aelig;cedentibus.<emph.end type="italics"/></s></p><p type="main">
344 
345 <s><emph type="italics"/>T. 20. Magnitudines euadunt numeri. </s>
346 
347 <s>Item, quod non duo cubi cubus. </s>
348 
349 <s>Item de <lb/>Mathematicis &longs;ubalternatis.<emph.end type="italics"/></s></p><p type="main">
350 
351 <s><emph type="italics"/>T. 23. Quadratura circuli &longs;ecundum Bry&longs;onem. </s>
352 
353 <s>Item per&longs;ectam illam e&longs;&longs;e Demon&shy;<lb/>&longs;trationem, qua Geometr&aelig; o&longs;tendunt, quod Omnis triangulus habet tres, &amp; c. <lb/><!-- KEEP S--></s>
354 
355 <s>Per&longs;pectinam, &amp; Mechanicam &longs;ubalternari Geometri&aelig;, Mu&longs;icam, Arithmetic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
356 
357 <s><emph type="italics"/>T. 24. De numero pari, impari, quodrangulo, cubo. </s>
358 
359 <s>In Geometria quid irrationale, <lb/>refrangi, concurrere. </s>
360 
361 <s>Quid Astronomia con&longs;ideret.<emph.end type="italics"/></s></p><p type="main">
362 
363 <s><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s></p><p type="main">
364 
365 <s><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/><!-- KEEP S--></s></p><pb pagenum="13"/><p type="main">
366 
367 <s><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. <!-- KEEP S--></s>
368 
369 <s>Item quid multiplicata propor&shy;<lb/>tio. </s>
370 
371 <s>Quid C&aelig;neus dixerit. </s>
372 
373 <s>Cur Affectiones Mathematicor&ubreve; maxim&egrave; <expan abbr="conuert&atilde;tur">conuertantur</expan>.<emph.end type="italics"/></s></p><p type="main">
374 
375 <s><emph type="italics"/>T. 30. De Lun&aelig; &longs;ph&aelig;ricitate. </s>
376 
377 <s>Quid &longs;tereometria. </s>
378 
379 <s>&amp; De &longs;ubalternatione, &amp;c. </s>
380 
381 <s>&amp; Ma&shy;<lb/>thematicorum e&longs;t &longs;cire Propter quid: &longs;en&longs;itiuorum ver&ograve; &longs;cire Quod.<emph.end type="italics"/></s></p><p type="main">
382 
383 <s><emph type="italics"/>T. 37. I&longs;o&longs;celes, &amp; Scalenum habere tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="main">
384 
385 <s><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
386 
387 <s><emph type="italics"/>T. 39. Habere tres angulos &aelig;quales, &amp;c. </s>
388 
389 <s>Item, quod omnis figura habet &longs;uos angu&shy;<lb/>los externos &aelig;quales quatuor tantum rectis.<emph.end type="italics"/></s></p><p type="main">
390 
391 <s><emph type="italics"/>T. 43. Triangulum tres &aelig;quales, &amp;c. </s>
392 
393 <s>De Eclyp&longs;i.<emph.end type="italics"/></s></p><p type="main">
394 
395 <s><emph type="italics"/>De combu&longs;tione per refractionem ex &longs;ph&aelig;ra vitrea. </s>
396 
397 <s>De principijs &longs;cientiarum.<emph.end type="italics"/></s></p><p type="main">
398 
399 <s><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head">
400 
401 <s>In 2. Po&longs;teriorum.</s></p><p type="main">
402 
403 <s><emph type="italics"/>T. 1. Aequalitas, &amp; in&aelig;qualitas. </s>
404 
405 <s>Terram e&longs;&longs;e in medio mundi ab A&longs;tronomis per&shy;<lb/>fect&egrave; demon&longs;tratur. </s>
406 
407 <s>Item Quid con&longs;onantia.<emph.end type="italics"/></s></p><p type="main">
408 
409 <s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp;c. </s>
410 
411 <s>Item de Definitionibus Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
412 
413 <s><emph type="italics"/>T. 7. Geometra, qu&aelig;dam accipit, qu&aelig;dam demon&longs;trat.<emph.end type="italics"/></s></p><p type="main">
414 
415 <s><emph type="italics"/>T. 11. Angulum in &longs;emicirculo rectum e&longs;&longs;e probari &agrave; Geometra per cau&longs;am materia&shy;<lb/>lem. </s>
416 
417 <s>Zabarella correctus.<emph.end type="italics"/></s></p><p type="main">
418 
419 <s><emph type="italics"/>T. 24. Echo, Imago &egrave; &longs;peculo, Iris.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
420 
421 <s><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s></p><p type="head">
422 
423 <s>In primo lib. <!-- REMOVE S-->Topicorum.</s>
424 
425 </p><p type="main">
426 
427 <s><emph type="italics"/>Cap. 
428 
429 13. Diameter est incommen&longs;urabilis. </s>
430 
431 <s>Vox acuta velox, cur. </s>
432 
433 <s>&amp;c. </s>
434 
435 <s>Colores in <lb/>Mu&longs;ica, qui. </s>
436 
437 <s>tria genera veteris Mu&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="head">
438 
439 <s>In 4. libro.</s></p><p type="main">
440 
441 <s><emph type="italics"/>Cap. 
442 
443 1. loco 1. line&aelig; in&longs;ecabiles.<emph.end type="italics"/></s></p><p type="head">
444 
445 <s>In 6. libro.</s></p><p type="main">
446 
447 <s><emph type="italics"/>Cap. 
448 
449 2. loco 32. Definitio line&aelig;.<emph.end type="italics"/></s></p><p type="head">
450 
451 <s>In 8. libro.</s></p><p type="main">
452 
453 <s><emph type="italics"/>Cap. 
454 
455 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
456 
457 <s><emph type="italics"/>Cap. 
458 
459 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s></p><p type="head">
460 
461 <s>In Elenchorum lib. 
462 
463 1.<!-- KEEP S--></s></p><p type="main">
464 
465 <s><emph type="italics"/>Cap. 
466 
467 10. Quid P&longs;eudographia. </s>
468 
469 <s>Quadraturarur&longs;us Hippocratis, &amp; Bry&longs;enis. </s>
470 
471 <s>Mathe&shy;<lb/>matic&aelig; non contentio&longs;&aelig;. </s>
472 
473 <s>Quadratio Antiphontis.<emph.end type="italics"/></s></p><p type="head">
474 
475 <s>Ex 1. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">
476 
477 <s><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, &amp; Antiphontis.<emph.end type="italics"/></s></p><p type="head">
478 
479 <s>Ex 2. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">
480 
481 <s><emph type="italics"/>T. 20. Quatenus Per&longs;pectmus con&longs;ideret lineam.<emph.end type="italics"/></s></p><p type="main">
482 
483 <s><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
484 
485 <s><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes babere cau&longs;am, qu&aelig; reducitur ad defini&shy;<lb/>tionem.<emph.end type="italics"/></s></p><p type="main">
486 
487 <s><emph type="italics"/>T. 8. Denece&longs;&longs;ario, quod e&longs;t in Mathematicis. <!-- KEEP S--></s>
488 
489 <s>&amp; omnis triangulus habet tres an&shy;<lb/>gulos, &amp;c.<emph.end type="italics"/></s></p><p type="head">
490 
491 <s>Ex 3. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">
492 
493 <s><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s></p><p type="main">
494 
495 <s><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
496 
497 <s><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/><!-- KEEP S--></s></p><pb pagenum="14"/><p type="head">
498 
499 <s>Ex 4. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">
500 
501 <s><emph type="italics"/>T. 120. De commen&longs;urab. </s>
502 
503 <s>&amp; incommen&longs;.<emph.end type="italics"/></s></p><p type="head">
504 
505 <s>Ex 5. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">
506 
507 <s><emph type="italics"/>T. 6. De chordis, graui, acuta; media, &amp; vltima.<emph.end type="italics"/></s></p><p type="head">
508 
509 <s>Ex 8. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">
510 
511 <s><emph type="italics"/>T. 15. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="head">
512 
513 <s>Ex 1. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
514 
515 <s><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s></p><p type="main">
516 
517 <s><emph type="italics"/>T. 36. Ratione vtitur lineari; vt probet mundum e&longs;&longs;e finitum.<emph.end type="italics"/></s></p><p type="main">
518 
519 <s><emph type="italics"/>T. 48. Commen&longs;urab. <!-- REMOVE S-->&amp; incommen&longs;urab. </s>
520 
521 
522 
523 <s>quid.<emph.end type="italics"/></s></p><p type="main">
524 
525 <s><emph type="italics"/>T. 119. Omnis triangulus habet tres, &amp;c. </s>
526 
527 <s>Item de commen&longs;urabili.<emph.end type="italics"/></s></p><p type="head">
528 
529 <s>Ex 2. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
530 
531 <s><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, qu&igrave;.<emph.end type="italics"/></s></p><p type="main">
532 
533 <s><emph type="italics"/>T. 25. Ordo figurarum planarum.<emph.end type="italics"/></s></p><p type="main">
534 
535 <s><emph type="italics"/>T. 31. Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam.<emph.end type="italics"/></s></p><p type="main">
536 
537 <s><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s>
538 
539 <s>Recentiorum ob&longs;eruationes.<emph.end type="italics"/></s></p><p type="main">
540 
541 <s><emph type="italics"/>T. 57. De ordine C&oelig;lorum ex &longs;ententia A&longs;tronomorum.<emph.end type="italics"/></s></p><p type="main">
542 
543 <s><emph type="italics"/>T. 59. De rotunditate Lun&aelig;, bis.<emph.end type="italics"/></s></p><p type="main">
544 
545 <s><emph type="italics"/>T. 107. Centrum duplex grauit: &amp; molis. </s>
546 
547 <s>Qua ratione grauia ad mundi centrum <lb/>aptarentur.<emph.end type="italics"/></s></p><p type="main">
548 
549 <s><emph type="italics"/>T. 109. Terram e&longs;&longs;e rotundam. </s>
550 
551 <s>alio item modo.<emph.end type="italics"/></s></p><p type="main">
552 
553 <s><emph type="italics"/>T. 110. Terram e&longs;&longs;e paruam re&longs;pectu C&oelig;li.<emph.end type="italics"/></s></p><p type="main">
554 
555 <s><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s></p><p type="main">
556 
557 <s><emph type="italics"/>T. 112. De quantitate Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
558 
559 <s>Ex 3. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
560 
561 <s><emph type="italics"/>T. 40. Vt componatur &longs;ph&aelig;ra.<emph.end type="italics"/></s></p><p type="main">
562 
563 <s><emph type="italics"/>T. 66. Omne corpus diui&longs;ibile.<emph.end type="italics"/></s></p><p type="main">
564 
565 <s><emph type="italics"/>T. 66. Qu&aelig;nam planarum figurarum totum &longs;patium repleant. </s>
566 
567 <s>Hinc de admirabili <lb/>Apum mgenio.<emph.end type="italics"/></s></p><p type="main">
568 
569 <s><emph type="italics"/>T. eodem. </s>
570 
571 <s>Num plures Pyramides locum replere valeant, vbi Ari&longs;totiles, &amp; omnes <lb/>expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s></p><p type="main">
572 
573 <s><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s></p><p type="head">
574 
575 <s>Ex 4. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
576 
577 <s><emph type="italics"/>T. 33. Extare centrum Mundi, qu&ograve; grauia tendunt, &agrave; quo leuia abeant.<emph.end type="italics"/></s></p><p type="main">
578 
579 <s><emph type="italics"/>T. 44. &amp; <expan abbr="&longs;eq.">&longs;eque</expan> Cur qu&aelig;dam grautora qu&agrave;m aqua, &longs;upernatent.<emph.end type="italics"/></s></p><p type="head">
580 
581 <s>Ex 2. de Generatione, &amp; Corruptione.<!-- KEEP S--></s></p><p type="main">
582 
583 <s><emph type="italics"/>Tex. 56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s></p><p type="head">
584 
585 <s>Ex 1. Meteororum.<!-- KEEP S--></s></p><p type="main">
586 
587 <s><emph type="italics"/>Summa prima cap. 
588 
589 3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s></p><p type="main">
590 
591 <s><emph type="italics"/>Cap. 
592 
593 eodem. </s>
594 
595 <s>De magnitudine A&longs;trorum.<emph.end type="italics"/></s></p><p type="main">
596 
597 <s><emph type="italics"/>Cap. 
598 
599 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
600 
601 <s><emph type="italics"/>Summa 2. cap. 
602 
603 3. de Mercurij stella. </s>
604 
605 <s>Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
606 
607 <s><emph type="italics"/>Cap. 
608 
609 5. De Magnitudine Solis, &amp; de vmbra Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
610 
611 <s><emph type="italics"/>Cap. 
612 
613 5. De Glaxia.<emph.end type="italics"/></s></p><p type="main">
614 
615 <s><emph type="italics"/>Cap. 
616 
617 6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde <lb/>aperitur.<emph.end type="italics"/></s></p><pb pagenum="15"/><p type="main">
618 
619 <s><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>
620 
621 <s>Mare extraneum, quod. </s>
622 
623 <s>Errata qu&aelig;&shy;<lb/>dam veterum Geographorum, &amp; Ari&longs;t. 
624 
625 corriguntur. </s>
626 
627 <s>Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s></p><p type="main">
628 
629 <s><emph type="italics"/>Cap. 
630 
631 2. De permutatione Aquarum, &amp; continentis. </s>
632 
633 <s>Noua ob&longs;eruatio de rotundi&shy;<lb/>tate Terr&aelig;, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s></p><p type="head">
634 
635 <s>Ex 2. Meteororum.<!-- KEEP S--></s></p><p type="main">
636 
637 <s><emph type="italics"/>Summa 1. cap. 
638 
639 1. De Marirubro.<emph.end type="italics"/></s></p><p type="main">
640 
641 <s><emph type="italics"/>Summa 2. cap. 
642 
643 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s></p><p type="main">
644 
645 <s><emph type="italics"/>Cap. 
646 
647 eodem, De Canicula. </s>
648 
649 <s>De Zonis temperatis. </s>
650 
651 <s>Corona Ariadn&aelig;. </s>
652 
653 <s>Zonam torridam <lb/>fals&ograve; putabant inho&longs;pitalem. </s>
654 
655 <s>cur habitabilis.<emph.end type="italics"/></s></p><p type="main">
656 
657 <s><emph type="italics"/>Cap. 
658 
659 3. De Ventorum&longs;itu.<emph.end type="italics"/></s></p><p type="head">
660 
661 <s>Ex 3. Meteor.<!-- KEEP S--></s></p><p type="main">
662 
663 <s><emph type="italics"/>Summa 2. cap. 
664 
665 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;iratio.<emph.end type="italics"/></s></p><p type="main">
666 
667 <s><emph type="italics"/>Cap. 
668 
669 4. De Iridis figura Mathematica demon&longs;tratio, &longs;ed deficiens. </s>
670 
671 <s>Noua de eadem <lb/>tractatio.<emph.end type="italics"/></s></p><p type="main">
672 
673 <s><emph type="italics"/>Cap. 
674 
675 5. De Parelio. <!-- KEEP S--></s>
676 
677 <s>Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s></p><p type="head">
678 
679 <s>Ex 1. De Anima.<!-- KEEP S--></s></p><p type="main">
680 
681 <s><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>
682 
683 <s>&amp; omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">
684 
685 <s><emph type="italics"/>T. 13. Sph&aelig;ra planum tangit in puncto.<emph.end type="italics"/></s></p><p type="head">
686 
687 <s>Ex 2. De Anima.<!-- KEEP S--></s></p><p type="main">
688 
689 <s><emph type="italics"/>T. 12. D finitioncm formalem, &amp; cau&longs;alem explicat exemplo Quadrationis Geo&shy;<lb/>metric&aelig;.<emph.end type="italics"/></s></p><p type="main">
690 
691 <s><emph type="italics"/>T. 86. Acutum, &amp; Graue, vt differant.<emph.end type="italics"/></s></p><p type="main">
692 
693 <s><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s></p><p type="head">
694 
695 <s>Ex 3. De Anima.<!-- KEEP S--></s></p><p type="main">
696 
697 <s><emph type="italics"/>T. 21. Incommen&longs;urabile.<emph.end type="italics"/></s></p><p type="main">
698 
699 <s><emph type="italics"/>T. 25. Indiui&longs;ibilia e&longs;&longs;e priuationes.<emph.end type="italics"/></s></p><p type="main">
700 
701 <s><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s></p><p type="head">
702 
703 <s>Ex lib. <!-- REMOVE S-->De Sen&longs;u.</s>
704 
705 </p><p type="main">
706 
707 <s><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
708 
709 <s><emph type="italics"/>Cap. 
710 
711 8. Nete. </s>
712 
713 <s>Diapa&longs;on. <!-- KEEP S--></s>
714 
715 <s>Diapen&longs;e.<emph.end type="italics"/></s></p><p type="head">
716 
717 <s>Ex lib. <!-- REMOVE S-->De Memoria, &amp; Rem.<!-- KEEP S--></s>
718 
719 </p><p type="main">
720 
721 <s><emph type="italics"/>Cap. 
722 
723 1. Omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">
724 
725 <s><emph type="italics"/>Cap. 
726 
727 3. Mathemata facile remini&longs;cibilia.<emph.end type="italics"/></s></p><p type="head">
728 
729 <s>Ex lib. <!-- REMOVE S-->De Somnijs.<!-- KEEP S--></s>
730 
731 </p><p type="main">
732 
733 <s><emph type="italics"/>Cap. 
734 
735 2. Terra, cur nauigantibus moueri videatur.<emph.end type="italics"/></s></p><p type="main">
736 
737 <s><emph type="italics"/>Cap. 
738 
739 3. Cur Oculus digito dimotus res geminatas videat.<emph.end type="italics"/></s></p><p type="head">
740 
741 <s>Ex 1. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
742 
743 <s><emph type="italics"/>Cap. 
744 
745 1. Initium Mathematicarum ab Aegyptiorum Saterdotibus. </s>
746 
747 <s>Item, Automata, <lb/>qu&aelig; &longs;olstitia. </s>
748 
749 <s>Diameter incommen&longs;.<emph.end type="italics"/></s></p><p type="main">
750 
751 <s><emph type="italics"/>Summa 2. cap. 
752 
753 3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s></p><p type="main">
754 
755 <s><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s></p><p type="head">
756 
757 <s>Ex 2. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
758 
759 <s><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s></p><p type="head">
760 
761 <s>Ex 3. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
762 
763 <s><emph type="italics"/>Tex. <!-- KEEP S--></s>
764 
765 <s>Mathematicas puras carere cau&longs;is efficiente, &amp; finali. </s>
766 
767 <s>Ariftippus, vt Mathe&shy;<lb/>maticas &longs;ugillaret. </s>
768 
769 <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main">
770 
771 <s><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head">
772 
773 <s>Ex 4. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
774 
775 <s><emph type="italics"/>T. 4. Qu&aelig; &longs;int prim&aelig;, &amp; qu&aelig; &longs;ecund&aelig; inter Mathematicas.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
776 
777 <s><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head">
778 
779 <s>Ex 5. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
780 
781 <s><emph type="italics"/>T. 2. Exemplum cau&longs;&aelig; formalis ex Diapa&longs;on. <!-- KEEP S--></s>
782 
783 <s>Qu&aelig; &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s></p><p type="main">
784 
785 <s><emph type="italics"/>T. 3. Qu&aelig; &longs;it Materia in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
786 
787 <s><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s></p><p type="main">
788 
789 <s><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
790 
791 <s><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>
792 
793 <s>Quid potentia vnius line&aelig;.<emph.end type="italics"/></s></p><p type="main">
794 
795 <s><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head">
796 
797 <s>Ex 6. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
798 
799 <s><emph type="italics"/>T. 1. Principia, elementa, &amp; cau&longs;&aelig; in Mathem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
800 
801 <s><emph type="italics"/>T. 8. Diameter. </s>
802 
803 <s>commen&longs;urab.<emph.end type="italics"/></s></p><p type="main">
804 
805 <s><emph type="italics"/>T. 20. De&longs;criptiones. </s>
806 
807 <s>Omnis triangulus habet tres, &amp;c. </s>
808 
809 <s>Cur Angulus in &longs;emicir&shy;<lb/>culo rectus.<emph.end type="italics"/></s></p><p type="main">
810 
811 <s><emph type="italics"/>T. 22. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="head">
812 
813 <s>Ex 10. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
814 
815 <s><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>
816 
817 <s>Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
818 
819 <s><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s>
820 
821 <s>Diuer&longs;um in Math. quid.<emph.end type="italics"/></s></p><p type="head">
822 
823 <s>Ex 11. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
824 
825 <s><emph type="italics"/>Cap. 
826 
827 2. Ortus punctorum, linearum, &longs;uperficierum.<emph.end type="italics"/></s></p><p type="head">
828 
829 <s>Ex 12. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
830 
831 <s><emph type="italics"/>T. 44. Peculiari&longs;&longs;imam Philo&longs;ophiam, Mathematicorum videlicet, A&longs;tronomiam <lb/>pluralitatem C&oelig;lorum docere.<emph.end type="italics"/></s></p><p type="main">
832 
833 <s><emph type="italics"/>T. 45. Numerus orbium c&oelig;le&longs;t ium &longs;ecundum Eudoxum.<emph.end type="italics"/></s></p><p type="main">
834 
835 <s><emph type="italics"/>T. 46. Itidem ex Eudoxo.<emph.end type="italics"/></s></p><p type="main">
836 
837 <s><emph type="italics"/>T. 47. Orbium c&oelig;le&longs;tium numerus, &amp; fabrica ex Calippo.<emph.end type="italics"/></s></p><p type="head">
838 
839 <s>Ex 13. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">
840 
841 <s><emph type="italics"/>Cap. 
842 
843 3. Qua ratione Mathematici tractant de Bono.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
844 
845 <s>In Mechanicas Qu&aelig;&longs;tiones.</s></p><p type="main">
846 
847 <s><emph type="italics"/>Cap. 
848 
849 1. Qu&aelig; &longs;it Mechanica facultas.<emph.end type="italics"/></s></p><p type="main">
850 
851 <s><emph type="italics"/>Cap. 
852 
853 2. De Admirandis circuli.<emph.end type="italics"/></s></p><p type="main">
854 
855 <s><emph type="italics"/>Qu&aelig;&longs;tio 1. De Libra. <!-- KEEP S--></s>
856 
857 <s>cur maior, exactior. </s>
858 
859 <s>inibi Ari&longs;t. 
860 
861 lap&longs;us.<emph.end type="italics"/></s></p><p type="main">
862 
863 <s><emph type="italics"/>Qu&aelig;&longs;t. 2. Duplex Libra. <!-- KEEP S--></s>
864 
865 <s>Piccolomineus reiectus.<emph.end type="italics"/></s></p><p type="main">
866 
867 <s><emph type="italics"/>Qu&aelig;&longs;t. 3. De Vecte.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
868 
869 <s><emph type="italics"/>Qu&aelig;&longs;t. 4. De Remo; Petri Non&yuml; in Arist. 
870 
871 correctio.<emph.end type="italics"/></s></p><p type="main">
872 
873 <s><emph type="italics"/>Qu&aelig;&longs;t. 5. De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
874 
875 <s><emph type="italics"/>Qu&aelig;&longs;t. 6. De Antenna.<emph.end type="italics"/></s></p><p type="main">
876 
877 <s><emph type="italics"/>Qu&aelig;&longs;t. 8 De Rota.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
878 
879 <s><emph type="italics"/>Qu&aelig;&longs;t. 9. De Trochlea, &amp; Scytali. </s>
880 
881 <s>figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s></p><p type="main">
882 
883 <s><emph type="italics"/>Qu&aelig;&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s></p><p type="main">
884 
885 <s><emph type="italics"/>Q&ugrave;&aelig;&longs;t. <!-- REMOVE S-->11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s>
886 
887 </p><p type="main">
888 
889 <s><emph type="italics"/>Qu&aelig;&longs;t. 13. De lugo. </s>
890 
891 <s>De Succula.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
892 
893 <s><emph type="italics"/>Qu&aelig;&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s></p><p type="main">
894 
895 <s><emph type="italics"/>Qu&aelig;&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s></p><pb pagenum="17"/><p type="main">
896 
897 <s><emph type="italics"/>Qu&aelig;&longs;t. 17. De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
898 
899 <s><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main">
900 
901 <s><emph type="italics"/>Qu&aelig;&longs;t. 19. De Securi. </s>
902 
903 <s>Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>eius mirabili.<emph.end type="italics"/></s></p><p type="main">
904 
905 <s><emph type="italics"/>Qu&aelig;&longs;t. 20. De Statera. <!-- KEEP S--></s>
906 
907 <s>Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s></p><p type="main">
908 
909 <s><emph type="italics"/>Qu&aelig;&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
910 
911 <s><emph type="italics"/>Qu&aelig;&longs;t. 22. De Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
912 
913 <s><emph type="italics"/>Qu&aelig;&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
914 
915 <s><emph type="italics"/>Qu&aelig;&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s></p><p type="main">
916 
917 <s><emph type="italics"/>Qu&aelig;&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s></p><p type="main">
918 
919 <s><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s></p><p type="main">
920 
921 <s><emph type="italics"/>Qu&aelig;&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s></p><p type="main">
922 
923 <s><emph type="italics"/>Qu&aelig;&longs;t. 28. De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
924 
925 <s><emph type="italics"/>Qu&aelig;&longs;t. 29. De onere &agrave; duobus phalanga ge&longs;iato.<emph.end type="italics"/></s></p><p type="main">
926 
927 <s><emph type="italics"/>Qu&aelig;&longs;t. 30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s></p><p type="head">
928 
929 <s>In libello De Mundo ad Alex.<!-- REMOVE S--><emph type="italics"/>Cap. 
930 
931 2. Ordo Planetarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
932 
933 <s><emph type="italics"/>Cap. 
934 
935 3. De Cometis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
936 
937 <s><emph type="italics"/>Cap. 
938 
939 5. De fluxu maris. </s>
940 
941 <s>noua de maris &aelig;&longs;tu &longs;ententia.<emph.end type="italics"/></s></p><p type="head">
942 
943 <s>In libro De Admirandis audit.</s></p><p type="main">
944 
945 <s><emph type="italics"/>Num. <!-- REMOVE S-->8. De nouo orbe.<emph.end type="italics"/></s>
946 
947 </p><p type="main">
948 
949 <s><emph type="italics"/>Nu. </s>
950 
951 <s>100. De I&longs;tro, error Ari&longs;t. &amp; veterum Geographorum.<emph.end type="italics"/></s></p><p type="head">
952 
953 <s>In libello De lineis in&longs;ecabilibus.</s></p><p type="main">
954 
955 <s><emph type="italics"/>Primus locus. </s>
956 
957 <s>De commen&longs;urabili, &amp; incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main">
958 
959 <s><emph type="italics"/>2. locus. </s>
960 
961 <s>De figuris incommen&longs;.<emph.end type="italics"/></s></p><p type="main">
962 
963 <s><emph type="italics"/>3. locus. </s>
964 
965 <s>Qu&aelig; linea rationalis, qu&aelig; irrationalis. </s>
966 
967 <s>Binomio, Apotome.<emph.end type="italics"/></s></p><p type="main">
968 
969 <s><emph type="italics"/>4. locus. </s>
970 
971 <s>De communi men&longs;ura.<emph.end type="italics"/></s></p><p type="main">
972 
973 <s><emph type="italics"/>5. locus. </s>
974 
975 <s>Line&aelig; rect&aelig; motus in &longs;emicirculum.<emph.end type="italics"/></s></p><p type="main">
976 
977 <s><emph type="italics"/>6. locus. </s>
978 
979 <s>Circulorum &aelig;qualium ab inuicem motus.<emph.end type="italics"/></s></p><p type="main">
980 
981 <s><emph type="italics"/>7. locus. </s>
982 
983 <s>Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
984 
985 <s><emph type="italics"/>8. locus. </s>
986 
987 <s>Si extarent indiuidua, omnes line&aelig; e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s></p><p type="main">
988 
989 <s><emph type="italics"/>9. locus. </s>
990 
991 <s>Idem probat alite&racute;.<emph.end type="italics"/></s></p><p type="main">
992 
993 <s><emph type="italics"/>10. locus. </s>
994 
995 <s>Idem ex triangulo.<emph.end type="italics"/></s></p><p type="main">
996 
997 <s><emph type="italics"/>11. locus. </s>
998 
999 <s>Idem ex quadrato.<emph.end type="italics"/></s></p><p type="main">
1000 
1001 <s><emph type="italics"/>12. Ex diui&longs;ione line&aelig; idem confirmatur.<emph.end type="italics"/></s></p><p type="main">
1002 
1003 <s><emph type="italics"/>13. Idem eodem fer&egrave; modo cum pr&aelig;cedenti.<emph.end type="italics"/></s></p><p type="main">
1004 
1005 <s><emph type="italics"/>14. A quadrato cuiu&longs;uis line&aelig;.<emph.end type="italics"/></s></p><p type="main">
1006 
1007 <s><emph type="italics"/>15. Idem probat ex &longs;uperficie, &amp; ex corpore.<emph.end type="italics"/></s></p><p type="main">
1008 
1009 <s><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s></p><p type="head">
1010 
1011 <s>Ex lib. 
1012 
1013 9. Hi&longs;tori&aelig; Animalium.</s></p><p type="main">
1014 
1015 <s><emph type="italics"/>Cap. 
1016 
1017 39. error Ari&longs;t. &amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head">
1018 
1019 <s>De Ince&longs;&longs;u Animal.<!-- KEEP S--></s></p><p type="main">
1020 
1021 <s><emph type="italics"/>Cap. 
1022 
1023 7. qua ratione in gre&longs;&longs;u &longs;iat bypotenu&longs;a. </s>
1024 
1025 <s>&amp; ea quid &longs;it.<emph.end type="italics"/></s></p><p type="head">
1026 
1027 <s>De Motu Animal.<!-- KEEP S--></s></p><p type="main">
1028 
1029 <s><emph type="italics"/>Cap. 
1030 
1031 1. in flexuris animalium e&longs;&longs;e centrum, &amp; circulum.<emph.end type="italics"/></s></p><p type="main">
1032 
1033 <s><emph type="italics"/>Cap. 
1034 
1035 3. Automata.<emph.end type="italics"/><!-- KEEP S--></s></p><pb pagenum="18"/><p type="head">
1036 
1037 <s>De Generatione Animal.<!-- KEEP S--></s></p><p type="main">
1038 
1039 <s><emph type="italics"/>Lib. 2. cap. 
1040 
1041 1. Automata.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1042 
1043 <s><emph type="italics"/>Lib. 2. cap. 
1044 
1045 4. Omnis triangulus habet tres, &amp;c. </s>
1046 
1047 <s>Ibidem Diametrum e&longs;&longs;e incommen&shy;<lb/>&longs;urabilem co&longs;t&aelig;, habet cau&longs;am, &amp; demon&longs;trationem.<emph.end type="italics"/></s></p><p type="head">
1048 
1049 <s>In Ethicis ad Nicom.</s></p><p type="main">
1050 
1051 <s><emph type="italics"/>Lib. 1. cap. 
1052 
1053 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main">
1054 
1055 <s><emph type="italics"/>Lib. 2. cap. 
1056 
1057 6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main">
1058 
1059 <s><emph type="italics"/>cap. 
1060 
1061 9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main">
1062 
1063 <s><emph type="italics"/>Lib. 3. cap. 3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>trica: Quid de&longs;ignatio.<emph.end type="italics"/></s></p><p type="main">
1064 
1065 <s><emph type="italics"/>Lib. 5. cap. 
1066 
1067 3. Vnitarius numerus. </s>
1068 
1069 <s>Quid Proportionalitas. <!-- KEEP S--></s>
1070 
1071 <s>Eam in 4. terminis con&shy;<lb/>&longs;i&longs;tere. </s>
1072 
1073 <s>Item quid Permutata proportio. </s>
1074 
1075 <s>Item quid Geometrica proportio. </s>
1076 
1077 <s>Propor&shy;<lb/>tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s></p><p type="main">
1078 
1079 <s><emph type="italics"/>cap. 
1080 
1081 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1082 
1083 <s><emph type="italics"/>Lib. 6. cap. 
1084 
1085 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main">
1086 
1087 <s><emph type="italics"/>cap. 
1088 
1089 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main">
1090 
1091 <s><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
1092 
1093 <s>Ex 1. Magnorum Moralium.</s></p><p type="main">
1094 
1095 <s><emph type="italics"/>Cap. 
1096 
1097 1. Numerus pariter par.<emph.end type="italics"/></s></p><p type="main">
1098 
1099 <s><emph type="italics"/>Cap. 
1100 
1101 2. Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s></p><p type="main">
1102 
1103 <s><emph type="italics"/>Cap. 
1104 
1105 10 Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s></p><p type="main">
1106 
1107 <s><emph type="italics"/>Cap. 
1108 
1109 16. Quadratum quatuor rectis &aelig;quales habere.<emph.end type="italics"/></s></p><p type="main">
1110 
1111 <s><emph type="italics"/>Cap. 
1112 
1113 30. Proportionale in quatuor terminis con&longs;i&longs;tit.<emph.end type="italics"/></s></p><p type="head">
1114 
1115 <s>Ex 1. lib. <!-- REMOVE S-->Moralium Eudemiorum.</s>
1116 
1117 </p><p type="main">
1118 
1119 <s><emph type="italics"/>Cap. 
1120 
1121 5. Duplum inter multiplices rationes primum tenet locum.<emph.end type="italics"/></s></p><p type="head">
1122 
1123 <s>Ex 1. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>
1124 
1125 
1126 
1127 </p><p type="main">
1128 
1129 <s><emph type="italics"/>Cap. 
11317 Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">
1132 
1133 <s><emph type="italics"/>Cap. 
1134 
1135 10. Diametrum commen&longs;. </s>
1136 
1137 <s>e&longs;&longs;e. </s>
1138 
1139 <s>Circuli quadratio.<emph.end type="italics"/></s></p><p type="main">
1140 
1141 <s><emph type="italics"/>Cap. 
1142 
1143 12. Triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="head">
1144 
1145 <s>Ex 7. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>
1146 
1147 
1148 
1149 </p><p type="main">
1150 
1151 <s><emph type="italics"/>Cap. 
1152 
1153 12. Diametralis oppo&longs;itio.<emph.end type="italics"/></s></p><p type="head">
1154 
1155 <s>Ex 3. lib. <!-- REMOVE S-->Politicorum.</s>
1156 
1157 </p><p type="main">
1158 
1159 <s><emph type="italics"/>Cap. 
1160 
1161 2. Modi Dorius, &amp; Phrygius apud Mu&longs;icos, qu&igrave;.<emph.end type="italics"/></s></p><p type="head">
1162 
1163 <s>Ex 4. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>
1164 
1165 </p><p type="main">
1166 
1167 <s><emph type="italics"/>Cap. 
1168 
1169 3. Modus Doricus, &amp; Phrygius.<emph.end type="italics"/></s></p><p type="head">
1170 
1171 <s>Ex 5. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>
1172 
1173 </p><p type="main">
1174 
1175 <s><emph type="italics"/>Cap. 
1176 
1177 1. Aequitas Arithmetica, &amp; qu&aelig; &longs;ecundum dignitatem.<emph.end type="italics"/></s></p><p type="head">
1178 
1179 <s>Ex 8. Polit.<!-- KEEP S--></s></p><p type="main">
1180 
1181 <s><emph type="italics"/>Cap. 
1182 
1183 5. Mu&longs;ica nuda, &amp; cum melodia. </s>
1184 
1185 <s>Rithmus quid.<emph.end type="italics"/></s></p><p type="main">
1186 
1187 <s><emph type="italics"/>Harmonia lydia. </s>
1188 
1189 <s>Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s></p><p type="main">
1190 
1191 <s><emph type="italics"/>Cap. 
1192 
1193 7. Harmoni&aelig;, &amp; Rithmi, vt in pr&aelig;cedenti.<emph.end type="italics"/></s></p><p type="head">
1194 
1195 <s>Ex Problematibus.</s></p><p type="main">
1196 
1197 <s><emph type="italics"/>Sectione 1. num. </s>
1198 
1199 <s>3. De ortu &longs;yderum innerrantium: Succul&aelig;, Hypades, Atlantides, <lb/>Virgili&aelig;, Pleiades. </s>
1200 
1201 <s>num. </s>
1202 
1203 <s>17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s></p><p type="main">
1204 
1205 <s><emph type="italics"/>Sectione 15. num. </s>
1206 
1207 <s>1. Diametri ethymon.<emph.end type="italics"/></s></p><p type="main">
1208 
1209 <s><emph type="italics"/>num. </s>
1210 
1211 <s>2. Iterum Diametri ethymologia.<emph.end type="italics"/></s></p><pb pagenum="19"/><p type="main">
1212 
1213 <s><emph type="italics"/>num. </s>
1214 
1215 <s>3. Denarius numerus cur perfectus. </s>
1216 
1217 <s>eius dignitates. </s>
1218 
1219 <s>Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s></p><p type="main">
1220 
1221 <s><emph type="italics"/>4. De in&aelig;quali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s></p><p type="main">
1222 
1223 <s><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotund&aelig;, quamuis per angulo&longs;a foramina ingre&shy;<lb/>diantur.<emph.end type="italics"/></s></p><p type="main">
1224 
1225 <s><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s>
1226 
1227 <s>vbi de illuminatione Lun&aelig;, <lb/>qu&aelig; experientia docetur.<emph.end type="italics"/></s></p><p type="main">
1228 
1229 <s><emph type="italics"/>7. Cur Sol, &amp; Luna videantur plana?<emph.end type="italics"/></s></p><p type="main">
1230 
1231 <s><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s></p><p type="main">
1232 
1233 <s><emph type="italics"/>9. Cur Lun&aelig;, qu&agrave;m Solis minores vmbr&aelig;?<emph.end type="italics"/></s></p><p type="main">
1234 
1235 <s><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiu&aelig; &longs;unt? </s>
1236 
1237 <s>modus commod&egrave; <lb/>videndi eclyp&longs;im Solis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1238 
1239 <s><emph type="italics"/>Sect. <!-- REMOVE S-->16. nu. </s>
1240 
1241 
1242 
1243 <s>1. Cur ba&longs;es bullarum in aquis &longs;unt alb&aelig;?<emph.end type="italics"/></s></p><p type="main">
1244 
1245 <s><emph type="italics"/>3. Opp lumbati tali.<emph.end type="italics"/></s></p><p type="main">
1246 
1247 <s><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s></p><p type="main">
1248 
1249 <s><emph type="italics"/>5. Cur conus, &amp; cylindrus diuers&egrave; moueantur.<emph.end type="italics"/></s></p><p type="main">
1250 
1251 <s><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s></p><p type="main">
1252 
1253 <s><emph type="italics"/>12. Idem cum pr&aelig;cedenti 3.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1254 
1255 <s><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>
1256 
1257 <s>reflexio radior&ubreve; pulchr&egrave; comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s></p><p type="head">
1258 
1259 <s>Ex &longs;ectione 19. De Mu&longs;ica.<!-- KEEP S--></s></p><p type="main">
1260 
1261 <s><emph type="italics"/>num. </s>
1262 
1263 <s>2. Line&aelig; dupl&aelig; quadratum quadruplum. </s>
1264 
1265 <s>Hoc loco &longs;equentium probl. </s>
1266 
1267 <s>cau&longs;a, <lb/>pr&aelig;mittitur totius Mu&longs;ic&aelig; ortus breuis tractatio.<emph.end type="italics"/></s></p><p type="main">
1268 
1269 <s><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s></p><p type="main">
1270 
1271 <s><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s></p><p type="main">
1272 
1273 <s><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s></p><p type="main">
1274 
1275 <s><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s></p><p type="main">
1276 
1277 <s><emph type="italics"/>8. Cur grauis &longs;onum potest acut&aelig;?<emph.end type="italics"/></s></p><p type="main">
1278 
1279 <s><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s></p><p type="main">
1280 
1281 <s><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s></p><p type="main">
1282 
1283 <s><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s></p><p type="main">
1284 
1285 <s><emph type="italics"/>12. Grauior &egrave; fidibus contilenam &longs;u&longs;cipit.<emph.end type="italics"/></s></p><p type="main">
1286 
1287 <s><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s></p><p type="main">
1288 
1289 <s><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s>
1290 
1291 <s>Punicum quid.<emph.end type="italics"/></s></p><p type="main">
1292 
1293 <s><emph type="italics"/>15. Leges Mu&longs;ic&aelig;, qu&aelig;. </s>
1294 
1295 <s>Genera, Diatonicum, Chromaticum, Encharmonium. <lb/></s>
1296 
1297 <s>Tetrachorda qu&aelig;.<emph.end type="italics"/></s></p><p type="main">
1298 
1299 <s><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s></p><p type="main">
1300 
1301 <s><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s>
1302 
1303 <s>Magadis quid. </s>
1304 
1305 <s>Magadare.<emph.end type="italics"/></s></p><p type="main">
1306 
1307 <s><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s></p><p type="main">
1308 
1309 <s><emph type="italics"/>19. Cur Diapente, &amp; Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s></p><p type="main">
1310 
1311 <s><emph type="italics"/>20. Me&longs;e &longs;ola di&longs;&longs;onante, totum de&longs;&longs;onat p&longs;alterium.<emph.end type="italics"/></s></p><p type="main">
1312 
1313 <s><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s></p><p type="main">
1314 
1315 <s><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s></p><p type="main">
1316 
1317 <s><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s></p><p type="main">
1318 
1319 <s><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s></p><p type="main">
1320 
1321 <s><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s>
1322 
1323 <s>Rithmus quid.<emph.end type="italics"/></s></p><p type="main">
1324 
1325 <s><emph type="italics"/>28. Cur cantilen&aelig; qu&aelig;dam leges de cebantur?<emph.end type="italics"/></s></p><p type="main">
1326 
1327 <s><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s></p><pb pagenum="20"/><p type="main">
1328 
1329 <s><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melop&aelig;os.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1330 
1331 <s><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s></p><p type="main">
1332 
1333 <s><emph type="italics"/>33. Cur apt&egrave; de acuto in graue, non &egrave; contra canitur?<emph.end type="italics"/></s></p><p type="main">
1334 
1335 <s><emph type="italics"/>34. Cur bi&longs;diapente, aut bi&longs;diate&longs;&longs;aron con&longs;onantia non e&longs;t.<emph.end type="italics"/></s></p><p type="main">
1336 
1337 <s><emph type="italics"/>35. Cur diapa&longs;on omnium pulcherrima e&longs;t con&longs;onantia?<emph.end type="italics"/></s></p><p type="main">
1338 
1339 <s><emph type="italics"/>36. Me&longs;e &longs;ola di&longs;&longs;onante, tota perit harmonia.<emph.end type="italics"/></s></p><p type="main">
1340 
1341 <s><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s></p><p type="main">
1342 
1343 <s><emph type="italics"/>38. Cur Rythmo, &amp; harmonij omnes gaudent?<emph.end type="italics"/></s></p><p type="main">
1344 
1345 <s><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s></p><p type="main">
1346 
1347 <s><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s></p><p type="main">
1348 
1349 <s><emph type="italics"/>41. Idem cum 5.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1350 
1351 <s><emph type="italics"/>42. Idem cum 34.<emph.end type="italics"/></s></p><p type="main">
1352 
1353 <s><emph type="italics"/>43. Idem cum 24. Iugum in lyra veteri quodnam fuerit, vna cum figura vete&shy;<lb/>ris lyr&aelig;.<emph.end type="italics"/></s></p><p type="main">
1354 
1355 <s><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s></p><p type="main">
1356 
1357 <s><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s></p><p type="main">
1358 
1359 <s><emph type="italics"/>46. Idem cum 22.<emph.end type="italics"/></s></p><p type="main">
1360 
1361 <s><emph type="italics"/>47. Idem cum 26.<emph.end type="italics"/></s></p><p type="main">
1362 
1363 <s><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s></p><p type="main">
1364 
1365 <s><emph type="italics"/>49. Idem cum 30. In choris trag&oelig;diarum, nec &longs;ubdorius, nec &longs;ubphrygius modus <lb/>erat in v&longs;u.<emph.end type="italics"/></s></p><p type="main">
1366 
1367 <s><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s></p><p type="main">
1368 
1369 <s><emph type="italics"/>51. Dolia duo &aelig;qualia, quorum alterum plenum &longs;it, alterum dimidium, Diapa&longs;on <lb/>re&longs;onant.<emph.end type="italics"/></s></p><p type="head">
1370 
1371 <s>Ex &longs;ectione 23.</s></p><p type="main">
1372 
1373 <s><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s></p><p type="head">
1374 
1375 <s>Ex &longs;ectione 30.</s></p><p type="main">
1376 
1377 <s><emph type="italics"/>6. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="head">
1378 
1379 <s>Ex &longs;ectione 31.</s></p><p type="main">
1380 
1381 <s><emph type="italics"/>7. Cur o culos, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla vi, ab inuicem di&longs;&longs;ociari nequimus?<emph.end type="italics"/></s></p><p type="main">
1382 
1383 <s><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s>
1384 
1385 <s>Cur aliquando rei vi&longs;&aelig; gemina&shy;<lb/>tio accidat.<emph.end type="italics"/></s></p><p type="main">
1386 
1387 <s><emph type="italics"/>11. Cur di&longs;tractis oculis res vna du&aelig; apparent?<emph.end type="italics"/></s></p><p type="main">
1388 
1389 <s><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s></p><p type="main">
1390 
1391 <s><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s></p><p type="head">
1392 
1393 <s>Auctarium De Oculi Pupilla.<!-- KEEP S--></s></p><p type="main">
1394 
1395 <s><emph type="italics"/>Oculi fabrica pr&aelig;mittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s></p><p type="main">
1396 
1397 <s><emph type="italics"/>Primo. </s>
1398 
1399 <s>De pupill&aelig; voce.<emph.end type="italics"/></s></p><p type="main">
1400 
1401 <s><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s></p><p type="main">
1402 
1403 <s><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s></p><p type="main">
1404 
1405 <s><emph type="italics"/>4. Pupill&aelig; definitio.<emph.end type="italics"/></s></p><p type="main">
1406 
1407 <s><emph type="italics"/>5. Cur mgra in omnibus hominibus.<emph.end type="italics"/></s></p><p type="main">
1408 
1409 <s><emph type="italics"/>6. Cur in Sole euane&longs; cat.<emph.end type="italics"/></s></p><p type="main">
1410 
1411 <s><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s></p><p type="main">
1412 
1413 <s><emph type="italics"/>8. Cur modo maior, modo minor videatur, &amp; cui&longs;dam lepida deceptio.<emph.end type="italics"/></s></p><pb pagenum="21"/><p type="main">
1414 
1415 <s>Additamentum de natura Mathematicarum di&longs;ciplinarum.</s></p><p type="main">
1416 
1417 <s><emph type="italics"/>Primo. </s>
1418 
1419 <s>De &longs;ubiecto Mathem. &longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio&shy;<lb/>nes Mathematic&aelig; e&longs;&longs;e perfecti&longs;&longs;im&aelig;.<emph.end type="italics"/></s></p><p type="main">
1420 
1421 <s>2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s></p><p type="main">
1422 
1423 <s>3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumni&aelig; diluuntur.<emph.end type="italics"/></s></p><p type="main">
1424 
1425 <s>4. <emph type="italics"/>De pr&aelig;stantia cognitionis, quam Geometria, &amp; Arithmetica gignunt.<emph.end type="italics"/></s></p><p type="main">
1426 
1427 <s>5. <emph type="italics"/>De 4. Mathematicis medijs: A&longs;tronomia, Per&longs;pectiua, Mu&longs;ica, Mechanica.<emph.end type="italics"/></s></p><p type="main">
1428 
1429 <s>6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1430 
1431 <s>7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s></p><p type="head">
1432 
1433 <s><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s></p></section><pb pagenum="22"/><section><p type="head">
1434 
1435 <s><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s></p><p type="main">
1436 
1437 <s><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s></p><p type="head">
1438 
1439 <s><emph type="italics"/>In Primo Elem. 
1440 
1441 Euclidis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1442 
1443 <s>Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. <!-- REMOVE S-->4. quinti <lb/>Methaph.<!-- KEEP S--></s>
1444 
1445 </p><p type="main">
1446 
1447 <s>Ad principia primi elementorum, vide infra tex. <!-- REMOVE S-->5. pri. <!-- REMOVE S-->Po&longs;ter.<!-- KEEP S--></s>
1448 
1449 
1450 
1451 </p><p type="main">
1452 
1453 <s>Ad definitionem 10. pri. <!-- REMOVE S-->pro angulo recto, vide 30. qu&aelig;&longs;t. </s>
1454 
1455 
1456 
1457 <s>Mecha&shy;<lb/>nic. <!-- REMOVE S-->&amp; cap. 
1458 
1459 7. lib. 
1460 
1461 1. Eth.<!-- KEEP S--></s>
1462 
1463 </p><p type="main">
1464 
1465 <s>Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>facile di&longs;&longs;olui. </s>
1466 
1467 <s>ea e&longs;t, vtrum marmor, aut adamas, aliudue quidpiam infle&shy;<lb/>xibile &longs;ucce&longs;&longs;iu&egrave; findi, &amp; aperiri po&longs;&longs;it. </s>
1468 
1469 <s>qui enim aiunt, &longs;ic refelluntur, quia <lb/>nimirum &longs;equeretur, duas rectas lineas habere &longs;egmentum commune: in&shy;<lb/>telligantur enim du&aelig; line&aelig;, vna in vna &longs;uperficie, altera vero in altera, qu&aelig; <lb/>antequam incipiat apertio, congruant; Quoniam igitur tota illa apertio <lb/>non fit in in&longs;tanti, &longs;ed &longs;ucce&longs;&longs;iu&egrave;, facta iam aliqua apertionis parte con&longs;i&shy;<lb/>derentur pr&aelig;dict&aelig; line&aelig;, erit igitur earum pars aliqua ab inuicem &longs;epara&shy;<lb/>ta, altera ver&ograve; adhuc alteri congruens, ergo &longs;equetur, duas lineas habere <lb/>&longs;egmentum commune, quod e&longs;t impo&longs;&longs;ibile, quia contra 10. axioma.</s></p><p type="main">
1470 
1471 <s>Ad Calcem axiomatum primi accommodetur tex. <!-- REMOVE S-->1. primi Po&longs;ter.<!-- KEEP S--></s>
1472 
1473 </p><p type="main">
1474 
1475 <s>Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>tiones, vide cap. 
1476 
1477 de Priori, &amp; cap. 
1478 
1479 24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>tex. <!-- REMOVE S-->4. quinti Methaph. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->&amp; cap. 
1480 
1481 3. lib. 
1482 
1483 3. Ethic. <lb/><!-- KEEP S--></s>
1484 
1485 
1486 
1487 
1488 
1489 
1490 
1491 
1492 
1493 <s>Item ad primam primi, vide tex. <!-- REMOVE S-->7. &longs;ecundi Po&longs;ter. loco 2.<!-- KEEP S--></s>
1494 
1495 </p><p type="main">
1496 
1497 <s>Ad 5. primi, vide cap. 
1498 
1499 24. &longs;ecti 1 lib. 
1500 
1501 1. Priorum.</s></p><p type="main">
1502 
1503 <s>Ad 21. primi, vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>
1504 
1505 
1506 
1507 </p><p type="main">
1508 
1509 <s>Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s></p><p type="main">
1510 
1511 <s>Ad 28. primi, vide cap. 
1512 
1513 21. &amp; cap. 
1514 
1515 22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->13. primi Po&longs;ter.<!-- KEEP S--></s>
1516 
1517 </p><p type="main">
1518 
1519 <s>Ad 32. primi, vide cap. 
1520 
1521 1. &longs;ecti 3. lib. 
1522 
1523 1. Prior. <!-- REMOVE S-->&amp; cap. 
1524 
1525 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->2. <lb/>primi Po&longs;ter. loco 4. &amp; tex. <!-- REMOVE S-->23. primi Po&longs;ter. <!-- REMOVE S-->vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam <lb/><expan abbr="dem&otilde;&longs;trationem">demon&longs;trationem</expan>. </s>
1526 
1527 
1528 
1529 
1530 
1531 
1532 
1533 
1534 
1535 <s>&amp; tex. <!-- REMOVE S-->37. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->39. primi Po&longs;ter. <!-- KEEP S--></s>
1536 
1537 
1538 
1539 
1540 
1541 <s>Ibidem <lb/>loco 4. &amp; tex. <!-- REMOVE S-->43. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->2. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->bis. </s>
1542 
1543 
1544 
1545 
1546 
1547 
1548 
1549 
1550 
1551 <s>&amp; tex. <!-- REMOVE S-->89. &longs;e&shy;<lb/>cundi Phy&longs;. &amp; tex. <!-- REMOVE S-->15. octaui Phy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>
1552 
1553 
1554 
1555 
1556 
1557 
1558 
1559 
1560 
1561 <s>&amp; tex. <!-- REMOVE S-->25. <lb/>&longs;ecundi de C&oelig;lo. <!-- KEEP S--></s>
1562 
1563 
1564 
1565 <s>tex 11. primi de Anima. <!-- REMOVE S-->&amp; cap. 
1566 
1567 1. de mem. </s>
1568 
1569 
1570 
1571 <s>&amp; remini&longs;c. <lb/></s>
1572 
1573 <s>&amp; tex. <!-- REMOVE S-->35. quinti Methaphy&longs;. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaphy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->22. &longs;exti <lb/>Methaphy&longs;. <!-- REMOVE S-->&amp; cap. 
1574 
1575 4. lib. 
1576 
1577 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>
1578 
1579 
1580 
1581 
1582 
1583 
1584 
1585 
1586 
1587 
1588 
1589 
1590 
1591 <s>&amp; cap. 
1592 
1593 5. lib. 
1594 
1595 6. Ethic. <!-- REMOVE S-->&amp; <lb/>cap. 
1596 
1597 2. Magnorum Moral. &amp; cap. 
1598 
1599 10. Mag. Moral. &amp; cap. 16. Mag. Moral. <lb/><!-- REMOVE S-->&amp; cap. <!-- REMOVE S-->7. &longs;ecundi Eudem. &amp; cap. <!-- REMOVE S-->12. &longs;ecundi Eudem. <!-- REMOVE S-->&amp; problema 6. &longs;ectio&shy;<pb pagenum="23"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica h&aelig;c Euclidis Demon&longs;tratio.</s>
1600 
1601 
1602 
1603 
1604 
1605 
1606 
1607 
1608 
1609 </p><p type="main">
1610 
1611 <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. <!-- REMOVE S-->39. primi Po&longs;ter. loco 3. Item <lb/>tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->loco vlt.</s>
1612 
1613 
1614 
1615 
1616 
1617 </p><p type="main">
1618 
1619 <s>Ad 45. primi, vide locum 9. de lineis in&longs;ecabilibus.</s></p><p type="main">
1620 
1621 <s>Ad 46. primi, vide locum 11. de lineis in&longs;ecabilibus.</s></p><p type="main">
1622 
1623 <s>Ad 47. primi, vide locum 11. de lineis in&longs;ecab. </s>
1624 
1625 <s>Item locum 14. de ij&longs;dem.</s></p><p type="head">
1626 
1627 <s><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1628 
1629 <s>Ad 2. definitionem 2. Gnomonis, vide cap. 
1630 
1631 de Motu in Po&longs;tpr&aelig;dicam. </s>
1632 
1633 <s>Qua&shy;<lb/>dratum augetur Gnomone circumpo&longs;ito.</s></p><p type="main">
1634 
1635 <s>Ad 14. propo&longs;. </s>
1636 
1637 <s>2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>vide igitur cap. 
1638 
1639 de relatione in pr&aelig;dicam. </s>
1640 
1641 <s>&amp; cap. 
1642 
1643 31. &longs;ecundi Priorum, &amp; <lb/>tex. <!-- REMOVE S-->23. primi Po&longs;ter. &amp; finem 1. cap. primi Elenchorum. </s>
1644 
1645 
1646 
1647 <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head">
1648 
1649 <s><emph type="italics"/>In tertio Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
1650 
1651 <s>Ad primam 3. vide cap. 
1652 
1653 9. lib. 
1654 
1655 2. Ethycorum.</s></p><p type="main">
1656 
1657 <s>Ad 2. tertij, vide tex. <!-- REMOVE S-->13. lib. 
1658 
1659 1. de Anima. <!-- REMOVE S-->&amp; locum 16. de lineis in&longs;ecab.</s>
1660 
1661 
1662 
1663 </p><p type="main">
1664 
1665 <s>Ad 31. tertij, vide tex. <!-- REMOVE S-->11. &longs;ecundi Po&longs;ter. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>
1666 
1667 
1668 
1669 
1670 
1671 </p><p type="head">
1672 
1673 <s><emph type="italics"/>In quarto.<emph.end type="italics"/></s></p><p type="main">
1674 
1675 <s>Ad commentarium P. <!-- REMOVE S-->Clauij extremum lib. 
1676 
1677 4. elementorum. </s>
1678 
1679 
1680 
1681 <s>lege tex. <!-- REMOVE S-->66. <lb/>tertij de C&oelig;lo.<!-- KEEP S--></s>
1682 
1683 </p><p type="head">
1684 
1685 <s><emph type="italics"/>In quinto.<emph.end type="italics"/></s></p><p type="main">
1686 
1687 <s>Ad 4. definitionem 5. vide cap. 
1688 
1689 3. lib. 
1690 
1691 2. Ethyc.<!-- KEEP S--></s></p><p type="main">
1692 
1693 <s>Ad 9. definitionem 5. vide cap. 
1694 
1695 3. lib. 
1696 
1697 5. Ethyc. <!-- REMOVE S-->loco 4. &amp; cap. 31. primi Ma&shy;<lb/>gnorum Moralium.</s>
1698 
1699 </p><p type="main">
1700 
1701 <s>Ad 10. definitionem 5. vide tex. <!-- REMOVE S-->29. primi Po&longs;ter. loco 2.<!-- KEEP S--></s>
1702 
1703 </p><p type="main">
1704 
1705 <s>Ad 12. definitionem 5. vide tex. <!-- REMOVE S-->13. primi Po&longs;ter. <!-- REMOVE S-->loco 3. &amp; tex. <!-- REMOVE S-->25. &longs;ecundi <lb/>Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->32. tertij de Anima. <!-- REMOVE S-->&amp; cap. 
1706 
1707 3. lib. 
1708 
1709 5. Ethyc. <!-- REMOVE S-->loco 4.<!-- KEEP S--></s>
1710 
1711 
1712 
1713 
1714 
1715 
1716 
1717 
1718 
1719 
1720 
1721 
1722 
1723 </p><p type="main">
1724 
1725 <s>Ad 16. propo&longs;. </s>
1726 
1727 <s>5. vide tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/><!-- REMOVE S-->comm. <!-- REMOVE S-->15. &longs;cilicet.</s>
1728 
1729 
1730 
1731 
1732 
1733 </p><p type="main">
1734 
1735 <s>Vt &longs;e habet voluntas antiqua ad antiquum effectum, <lb/>Ita &longs;e habet etiam voluntas noua ad effectum nouum: <lb/>Ergo permutando, ita &longs;e habebit voluntas antiqua ad effectum nouum. <lb/></s>
1736 
1737 <s>Quemadmodum voluntas noua ad effectum antiquum.</s></p><p type="main">
1738 
1739 <s>Non enim in permutando confert antecedentem ad antecedentem, &amp; con&shy;<lb/>&longs;equentem ad con&longs;equentem, vt par erat, &longs;ed confert antecedentem ad <lb/>con&longs;equentem, quod non licet.</s></p><p type="head">
1740 
1741 <s><emph type="italics"/>In &longs;exto.<emph.end type="italics"/></s></p><p type="main">
1742 
1743 <s>Ad 2. propo&longs;it. </s>
1744 
1745 <s>6. vide cap. 
1746 
1747 2. lib. 
1748 
1749 8. Topicorum loco 41.</s></p><p type="main">
1750 
1751 <s>Ad 13. &longs;exti, vide tex. <!-- REMOVE S-->12. &longs;ecundi de Anima, &amp; tex. <!-- REMOVE S-->3. tertij Methaphy&longs;.<!-- REMOVE S--><emph type="italics"/>In &longs;eptimo.<emph.end type="italics"/></s>
1752 
1753 
1754 
1755 </p><p type="main">
1756 
1757 <s>Ad primam definitionem 7. vide tex. <!-- REMOVE S-->5. primi Po&longs;ter.<!-- KEEP S--></s>
1758 
1759 </p><p type="main">
1760 
1761 <s>Ad 8. definitionem 7. vide cap. 
1762 
1763 1. lib. 
1764 
1765 1. Magnorum Moral.<!-- KEEP S--></s></p><p type="head">
1766 
1767 <s><emph type="italics"/>In octauo.<emph.end type="italics"/></s></p><p type="main">
1768 
1769 <s>Ad 4. propo&longs;. </s>
1770 
1771 <s>9. vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. loco 2.<!-- KEEP S--></s>
1772 
1773 </p><p type="main">
1774 
1775 <s>Ad 8. propo&longs;. </s>
1776 
1777 <s>9. vide problem. </s>
1778 
1779 <s>3. &longs;ectionis 15. loco 4.<!-- KEEP S--></s></p><pb pagenum="24"/><p type="head">
1780 
1781 <s><emph type="italics"/>In decimo.<emph.end type="italics"/></s></p><p type="main">
1782 
1783 <s>Ad primam definitionem 10. vide cap. 
1784 
1785 23. &longs;ecti 1. primi Priorum. </s>
1786 
1787 <s>&amp; tex. <!-- REMOVE S-->48. <lb/>primi de C&oelig;lo.<!-- KEEP S--></s>
1788 
1789 </p><p type="main">
1790 
1791 <s>Ad 118. decimi, vide cap. 
1792 
1793 23. &longs;ecti 1. libri 1. Priorum. </s>
1794 
1795 <s>&amp; &longs;ecto 2. cap. 
1796 
1797 23. li&shy;<lb/>bri 1. Priorum. </s>
1798 
1799 <s>&amp; cap. 22. lib. 
1800 
1801 2. Priorum. </s>
1802 
1803 <s>&amp; tex. <!-- REMOVE S-->5. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->44. <lb/>primi Po&longs;ter. <!-- REMOVE S-->&amp; cap. 
1804 
1805 15. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>
1806 
1807 
1808 
1809 
1810 
1811 
1812 
1813 
1814 
1815 
1816 
1817 <s>&amp; tex. <lb/><!-- REMOVE S-->120. quarti Phy&longs;. &amp; tex. <!-- REMOVE S-->21. tertij de Anima. <!-- REMOVE S-->&amp; cap. 
1818 
1819 1. primi Methaphy&longs;. <lb/><!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->28. quarti Met. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->34. quinti Met. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->8. &longs;exti Met. <!-- REMOVE S-->&amp; cap. 
1820 
1821 4. <lb/>lib. 
1822 
1823 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>
1824 
1825 
1826 
1827 
1828 
1829 
1830 
1831 
1832 
1833 
1834 
1835 
1836 
1837 
1838 
1839 
1840 
1841 
1842 
1843 
1844 
1845 
1846 
1847 <s>&amp; lib. 
1848 
1849 3. cap. 
1850 
1851 3. Ethyc. <!-- REMOVE S-->&amp; cap. 10. &longs;ecundi Eu&shy;<lb/>dem. <!-- KEEP S--></s>
1852 
1853 
1854 
1855 <s>tot Ari&longs;t. 
1856 
1857 loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s></p><p type="head">
1858 
1859 <s><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s></p><p type="main">
1860 
1861 <s>Ad primam propo&longs;. </s>
1862 
1863 <s>13. &longs;ecundum editionem Commandini, aut Zamberti. <lb/><!-- KEEP S--></s>
1864 
1865 <s>vide initio Priorum, in verbum (Re&longs;olutio)</s></p><p type="main">
1866 
1867 <s>Atqne h&aelig;c &longs;unt, qu&aelig; ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit, <lb/>qu&aelig;que nos infra explicabimus.</s></p><p type="head">
1868 
1869 <s><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s></p><p type="main">
1870 
1871 <s>Qu&aelig; ver&ograve; ad alias Mathematicas, Mu&longs;icam &longs;cilicet, Per&longs;pe&shy;<lb/>ctiuam, Mechanicam, &amp; A&longs;tronomiam pertinens, facil&egrave; <lb/>poterunt ex primo Indice ad vnamquamque earum &longs;eor&shy;<lb/>&longs;um cum libuerit, &longs;ecerni.</s></p></section><pb pagenum="25"/><section><p type="head">
1872 
1873 <s><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s></p><p type="head">
1874 
1875 <s><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/><lb/><arrow.to.target n="table2"/></s></p><table><table.target id="table2"/><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Abductio quid. eius inuentor. numero 16. marginali.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Acuti den&longs;um quid.<emph.end type="italics"/></cell><cell>399</cell></row><row><cell><emph type="italics"/>Aequalitas mathematica, qu&aelig;.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Ae&longs;tus maris natura.<emph.end type="italics"/></cell><cell>272</cell></row><row><cell><emph type="italics"/>Aequitas arithmetica, &amp; &aelig;quitas &longs;ecundum dignitatem.<emph.end type="italics"/></cell><cell>330</cell></row><row><cell><emph type="italics"/>Agathir&longs;i populi.<emph.end type="italics"/></cell><cell>382</cell></row><row><cell><emph type="italics"/>Angulus quid. vt nominari debeat 10. angulum in &longs;emicirculo e&longs;&longs;e rectum o&longs;tendi   per cau&longs;am materialem.<emph.end type="italics"/></cell><cell>71</cell></row><row><cell><emph type="italics"/>Angulus rectus vari&egrave; con&longs;ideratur &agrave; Geometra, &amp; &agrave; Fabro.<emph.end type="italics"/></cell><cell>301</cell></row><row><cell><emph type="italics"/>Antiphontis quadratura circuli.<emph.end type="italics"/></cell><cell>13</cell></row><row><cell><emph type="italics"/>Antenn&aelig; nauis problema.<emph.end type="italics"/></cell><cell>248</cell></row><row><cell><emph type="italics"/>Antipbon&aelig; voces.<emph.end type="italics"/> 358. 363. 370. 371.</cell><cell>373</cell></row><row><cell><emph type="italics"/>Apum mirabilis indu&longs;tria.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Apotome linea, qu&aelig;.<emph.end type="italics"/></cell><cell>279</cell></row><row><cell><emph type="italics"/>Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam ratione mathematica.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Arithmetica proportio.<emph.end type="italics"/></cell><cell>302</cell></row><row><cell><emph type="italics"/>Aranei industria patefacta, qua ad res inaca&longs;&longs; as tran&longs;eat.<emph.end type="italics"/></cell><cell>293</cell></row><row><cell><emph type="italics"/>filum emittit ex &longs;ece&longs;&longs;u contra Ari&longs;totelem pro Democrito.<emph.end type="italics"/></cell><cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Astronomi&aelig; principia duo, Apparentia, &amp; Ob&longs;eruatio.<emph.end type="italics"/></cell><cell>8</cell></row><row><cell><emph type="italics"/>Automata, qu&aelig;.<emph.end type="italics"/> 199. 298.</cell><cell><emph type="italics"/>a. b.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>B<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ba&longs;is ballarum in aqua, cur &longs;it alba, &amp; cur non faciat vmbram.<emph.end type="italics"/></cell><cell>351</cell></row><row><cell><emph type="italics"/>Binomium linea, qu&aelig;.<emph.end type="italics"/></cell><cell>279</cell></row><row><cell><emph type="italics"/>Bra&longs;ilien&longs;es, qua ratione numer are &longs;oliti.<emph.end type="italics"/></cell><cell>340</cell></row><row><cell><emph type="italics"/>Bry&longs;onis quadratura circuli.<emph.end type="italics"/></cell><cell>35</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Calippi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell><cell>236</cell></row><row><cell><emph type="italics"/>Cantilenam notam &longs;uauius, quam ignotam audimus.<emph.end type="italics"/></cell><cell>362</cell></row><row><cell><emph type="italics"/>Centrum circuli reperire. 303. Centrum mundi mathematic&egrave; o&longs;tenditur. 123. Cen-trum grauitatis, &amp; molis.<emph.end type="italics"/> 38.</cell><cell>112</cell></row><row><cell><emph type="italics"/>Chordarum veterum nomina.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Circuli quadratura quid. an po&longs;&longs;ibilis. num. 1. Circulorum concentricorum maiores   velocius moueri. 108. Circuli admiranda. 239. De circulorum concentricorum   volutatione.<emph.end type="italics"/></cell><cell>263</cell></row><row><cell><emph type="italics"/>Coaltern&aelig; line&aelig;, qu&aelig;.<emph.end type="italics"/> 12. 14.</cell><cell>44</cell></row><row><cell><emph type="italics"/>C&oelig;lorum ordinem petendum ex A&longs;tronomis 109. item numerum<emph.end type="italics"/></cell><cell>233</cell></row><row><cell><emph type="italics"/>Colores in mu&longs;ica 78. Colores oculorum vnde.<emph.end type="italics"/></cell><cell>408</cell></row><row><cell><emph type="italics"/>Cometarum tractatiuncula ex recentioribus, qui eas in C&oelig;lo collocant. 136. e&longs;&longs;e &longs;u-pra aerem longi&longs;&longs;imo &longs;altem interuallo o&longs;tenditur mathematic&egrave;. 129. in additione.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Con&longs;onantia, quid. 64. quibus numeris con&longs;onanti&aelig; con&longs;tent.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Conus, &amp; cylindrus, cur vari&egrave; mouentur.<emph.end type="italics"/></cell><cell>355</cell></row><pb pagenum="26"/><row><cell><emph type="italics"/>Cubus numerus. duo cubi cubus, quid &longs;ignificet.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell><emph type="italics"/>Curru problema.<emph.end type="italics"/></cell><cell>252</cell></row><row><cell><emph type="italics"/>Cunei problema.<emph.end type="italics"/></cell><cell>256</cell></row><row><cell><emph type="italics"/>Cylindri, &amp; coni motus comparatio problematica.<emph.end type="italics"/></cell><cell>335</cell></row><row><cell><emph type="italics"/>D<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Definitiones mathematic&aelig; e&longs;&longs;e e&longs;&longs;entiales, &amp; perfe&longs;&longs;imas. cap. 1. de nat. Math.   definitionum v&longs;us in Mathematicis.<emph.end type="italics"/></cell><cell>81</cell></row><row><cell><emph type="italics"/>De&longs;criptio, &amp; de&longs;cribere, quid.<emph.end type="italics"/> 2. 6. 7.</cell><cell>205</cell></row><row><cell><emph type="italics"/>De&longs;ignatio pro demon&longs;tratione mathematica.<emph.end type="italics"/></cell><cell>305</cell></row><row><cell><emph type="italics"/>Demon&longs;trationis perfect&aelig; exemplum. 36. demon&longs;trationum mathematicarum pr&aelig;-&longs;tantia. cap. 4. de nat. Mathem.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Dentiforcipis problema.<emph.end type="italics"/></cell><cell>260</cell></row><row><cell><emph type="italics"/>Denarij numeri perfectio. 339. cur <expan abbr="v&longs;q;">v&longs;que</expan> ad denari&ubreve; omnes <expan abbr="g&etilde;tes">gentes</expan> <expan abbr="numer&etilde;t">numerent</expan>.<emph.end type="italics"/></cell><cell>339. 8. <emph type="italics"/>&amp;c.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Diameter incommen&longs;urabilis cost&aelig;. 5. diametri etymon.<emph.end type="italics"/></cell><cell>337</cell></row><row><cell><emph type="italics"/>Diapa&longs;on quid. 90. 350. omnium con&longs;onantiarum pulcberrima.<emph.end type="italics"/></cell><cell>388</cell></row><row><cell><emph type="italics"/>Diapa&longs;on diapente.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Diapente con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Diate&longs;&longs;aron con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Di&longs;d apa&longs;on con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Die&longs;is, quid.<emph.end type="italics"/> 53.</cell><cell>226</cell></row><row><cell><emph type="italics"/>Dolia duo, quomodo aliquando Diapa&longs;on re&longs;onent.<emph.end type="italics"/></cell><cell>402</cell></row><row><cell><emph type="italics"/>Duplum inter multiplicia primum e&longs;t.<emph.end type="italics"/></cell><cell>322</cell></row><row><cell><emph type="italics"/>E<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Elementa mundi non componi ex figuris geometricis.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Elementa geometrica, qu&aelig;.<emph.end type="italics"/> 82.</cell><cell>213</cell></row><row><cell><emph type="italics"/>Eudoxi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell><cell>234</cell></row><row><cell><emph type="italics"/>Exempla mathematicorum, qualia. 11. non e&longs;&longs;e fal&longs;a.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>Exemplorum veritas, &amp; conformitas, quatenus requirantur.<emph.end type="italics"/></cell><cell>36</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Figuram omnem planam habere &longs;uos angulos externos <expan abbr="quotc&ubreve;q;">quotc&ubreve;que</expan> &aelig;quales quatuor   rectis angulis, qu&aelig; e&longs;t mira proprietas.<emph.end type="italics"/></cell><cell>59</cell></row><row><cell><emph type="italics"/>Figur&aelig; &longs;imiles, qu&aelig;.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell><emph type="italics"/>Figurarum planarum ordo 88. qu&aelig; nam totum locum repleant.<emph.end type="italics"/></cell><cell>96</cell></row><row><cell><emph type="italics"/>Figurarum &longs;olidarum, qu&aelig;nam totum locum repleant: vbi Ari&longs;t. &amp; omnium expo&longs;i-torum rratum aperitur.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Figuratio lucis.<emph.end type="italics"/></cell><cell>345</cell></row><row><cell><emph type="italics"/>Figurationes pro demonftrationibus Mathem.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Filum Araneorum, ex qua parte corporis exeat, &amp; ex qua materia.<emph.end type="italics"/></cell><cell>293</cell></row><row><cell><emph type="italics"/>Fluxus, ac refluxus maris.<emph.end type="italics"/></cell><cell>272</cell></row><row><cell><emph type="italics"/>Funium lectorum problema.<emph.end type="italics"/></cell><cell>264</cell></row><row><cell><emph type="italics"/>G<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Galaxia quid. 131. Ari&longs;toteles defen&longs;us.<emph.end type="italics"/> 132.</cell><cell>140</cell></row><row><cell><emph type="italics"/>Galibei recens ob&longs;eruatio.<emph.end type="italics"/></cell><cell>141</cell></row><row><cell><emph type="italics"/>Generatria Mu&longs;ic&aelig; veteris. 78. Fus&egrave; explicantur.<emph.end type="italics"/></cell><cell>371</cell></row><row><cell><emph type="italics"/>Geod&aelig;&longs;ia.<emph.end type="italics"/></cell><cell>207</cell></row><row><cell><emph type="italics"/>Geographi&aelig; veteris plura errata,<emph.end type="italics"/> 145. 146. 147. 148.</cell><cell>149</cell></row><pb pagenum="27"/><row><cell><emph type="italics"/>Gnomon, quid. 3. &amp;<emph.end type="italics"/></cell><cell>331</cell></row><row><cell><emph type="italics"/>Gnomones numeri.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Graue qua ratione ad centrum mundi de&longs;cenderet, eiqu&eacute; aptaretur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Grauiden&longs;um, quid.<emph.end type="italics"/></cell><cell>399</cell></row><row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Halonis demonfiratio.<emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>Hippocratis chij quadratura circuli. 17. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> quadratura lunul&aelig; optima.<emph.end type="italics"/></cell><cell>17</cell></row><row><cell><emph type="italics"/>Hyades, Atlantides, &amp; Succul&aelig;.<emph.end type="italics"/></cell><cell>335</cell></row><row><cell><emph type="italics"/>Hypate, quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Hypotenu&longs;a in ince&longs;&longs;u animalium.<emph.end type="italics"/></cell><cell>294</cell></row><row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Illuminationes Solis deficientis per foramina tran&longs;euntes, eur &longs;int defectiu&aelig;.<emph.end type="italics"/></cell><cell>350</cell></row><row><cell><emph type="italics"/>modus videndi eclyp&longs;im facilis, ac iucundus.<emph.end type="italics"/></cell><cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Ince&longs;&longs;us animalium lineis explicatur.<emph.end type="italics"/></cell><cell>294. <emph type="italics"/>&amp; <expan abbr="&longs;eqq.">&longs;eqque</expan><emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Incommen&longs;urabilia, qu&aelig;, &amp; eorum inuentores.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Indiui&longs;ibilia mathematica e&longs;&longs;e priuationes. 189. oriri ex diui&longs;ione. 231. eorum duo   genera.<emph.end type="italics"/></cell><cell>276</cell></row><row><cell><emph type="italics"/>Infinito, qua ratione vtantur Mathematici.<emph.end type="italics"/> 94.</cell><cell>96</cell></row><row><cell><emph type="italics"/>Iridis demon&longs;tratio &longs;ecundum Ari&longs;t. 163. &amp; &longs;equentibus. Item noua de Iride tra-ctatio. ibidem in additione.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Iugum in lyra quid, &amp; eius figura.<emph.end type="italics"/></cell><cell>396</cell></row><row><cell><emph type="italics"/>L<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Leges mu&longs;icales.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Libra maior, cur exactior. initio Mechanicarum qu&aelig;&longs;t.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Linea, qu&aelig; terminus est illuminationis in Luna, cur modo recta, modo curua vi-deatur.<emph.end type="italics"/></cell><cell>346</cell></row><row><cell><emph type="italics"/>Line&aelig; rationales, &amp; irrationales, &amp;c.<emph.end type="italics"/></cell><cell>279</cell></row><row><cell><emph type="italics"/>Lumen oculorum noctu videntium, in qua oculi parte manet. in addit. de Pupilla.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Lumen Solis, cur &longs;it circulare, quamuis per foramina angulo&longs;a ingrediatur.<emph.end type="italics"/></cell><cell>345</cell></row><row><cell><emph type="italics"/>Luna plana, cur appareat, cum &longs;it &longs;ph&aelig;rica. 347. cur in eadem altitudine cum Sole   &longs;upra horizontem, maiorem vmbram efficiat.<emph.end type="italics"/></cell><cell>349</cell></row><row><cell><emph type="italics"/>Lunam e&longs;&longs;e &longs;ph&aelig;ricam. 48. illuminari &longs;ph&aelig;ric&egrave; quid: ibidem &amp; de illuminatione Lu-n&aelig;. iterum e&longs;&longs;e &longs;ph&aelig;ricam ab eclyp&longs;ibus.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Luminarium Solis, &amp; Lun&aelig; ordo.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Lychanos, quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Lyr&aelig; veteris figura.<emph.end type="italics"/></cell><cell>396</cell></row><row><cell><emph type="italics"/>M<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Magalis, &longs;eu magas, &amp; magadi&longs;&longs;are.<emph.end type="italics"/> 373.</cell><cell>393</cell></row><row><cell><emph type="italics"/>Materia intelligibilis. fus&egrave; ver&ograve;. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Mathematic&aelig; medi&aelig;, &longs;eu &longs;ubalternat&aelig; habent propter quid &longs;uarum demon&longs;iratio-nem.<emph.end type="italics"/></cell><cell>50</cell></row><row><cell><emph type="italics"/>Mathematici negant reperiri quantitatem indiui&longs;ibilem, &longs;eu minimam.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>Mathematic&aelig; non &longs;unt contentio&longs;&aelig;. 83. ostendunt per cau&longs;am formalcm.<emph.end type="italics"/></cell><cell>91</cell></row><row><cell><emph type="italics"/>Mathematicas inuenerunt Aegyptij Sacerdotes.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Mathematic&aelig; o&longs;tendunt per cau&longs;am materialem, &amp; formalem. 205. earum vtilitas.   ibidem. De earum natura. in proprio tractatu.<emph.end type="italics"/></cell><cell/></row>
1876 <pb pagenum="28"/><row><cell><emph type="italics"/>Mathematic&aelig; maxim&egrave; tractant de Bono, &amp; Pulcro, qua ratione.<emph.end type="italics"/></cell><cell>237</cell></row><row><cell><emph type="italics"/>Mechanica facultas, qu&aelig;.<emph.end type="italics"/></cell><cell>238</cell></row><row><cell><emph type="italics"/>Melodia.<emph.end type="italics"/></cell><cell>331</cell></row><row><cell><emph type="italics"/>Melopeia quid.<emph.end type="italics"/></cell><cell>384</cell></row><row><cell><emph type="italics"/>Medium Demonstrationum Mathem. in earum tractatu.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Me&longs;e quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Mina in men&longs;uris quid.<emph.end type="italics"/></cell><cell>53</cell></row><row><cell><emph type="italics"/>Monochordium.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Motus nauigij, &amp; remi comparatio. 247. Pulchra P. Nonij in id annotatio con-tra Ari&longs;t.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Modi mu&longs;ici.<emph.end type="italics"/></cell><cell>383</cell></row><row><cell><emph type="italics"/>Modorum antiquorum ordo, numerus, &amp;c.<emph.end type="italics"/></cell><cell>383</cell></row><row><cell><emph type="italics"/>Motus primi mobilis, &longs;eu diurnus e&longs;t men&longs;ura c&oelig;lestium motuum.<emph.end type="italics"/></cell><cell>225</cell></row><row><cell><emph type="italics"/>Mu&longs;ici recentiores reprehen&longs;i. 331. &amp; in fine Chronologi&aelig;.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Mu&longs;ic&aelig; totius elementa.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Mu&longs;ica nuda, &amp; cum melodia.<emph.end type="italics"/></cell><cell>331</cell></row><row><cell><emph type="italics"/>N<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Nete quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Nucifragi in&longs;trumenti problema.<emph.end type="italics"/></cell><cell>261</cell></row><row><cell><emph type="italics"/>Numerus, par, impar, primus, &amp; compo&longs;itus, quadratus, &longs;eu &aelig;quilaterus, altera   parte longior. 24. Cubus num.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell><emph type="italics"/>Numeri capitales, qui.<emph.end type="italics"/></cell><cell>82</cell></row><row><cell><emph type="italics"/>Numerum parem e&longs;&longs;e cau&longs;am infiniti: imparem ver&ograve; finiti.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Numerorum parium alij &longs;unt primi, alij non.<emph.end type="italics"/></cell><cell>224</cell></row><row><cell><emph type="italics"/>Numerus vnitarius.<emph.end type="italics"/></cell><cell>307</cell></row><row><cell><emph type="italics"/>O<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Oculi cur moueantur con&longs;imiliter.<emph.end type="italics"/></cell><cell>405</cell></row><row><cell><emph type="italics"/>Oculi anathome.<emph.end type="italics"/></cell><cell>408. <emph type="italics"/>&amp;c.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Omophon&aelig; voces.<emph.end type="italics"/> 372.</cell><cell>392</cell></row><row><cell><emph type="italics"/>Oppo&longs;itio diametralis e&longs;t omnium maxima.<emph.end type="italics"/></cell><cell>327</cell></row><row><cell><emph type="italics"/>Ortus, &amp; occa&longs;us &longs;yderum, quid, &amp; quotuplex: vbide Orione, &amp; Canicula.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>P<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Paranete qu&aelig; voces, aut chord&aelig;.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Parame&longs;e<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Parhypate<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Parelia, cur appareant nondum &longs;atis explicari.<emph.end type="italics"/></cell><cell>182</cell></row><row><cell><emph type="italics"/>Parna&longs;&longs;us mons, vbinam &longs;it. Item paropame&longs;&longs;us.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Partes quantitatis &longs;unt materia illius.<emph.end type="italics"/></cell><cell>211</cell></row><row><cell><emph type="italics"/>Per&longs;pectiuus, quatenus con&longs;ideret lineam.<emph.end type="italics"/></cell><cell>89</cell></row><row><cell><emph type="italics"/>Pa&longs;&longs;iones Mathematicorum cum &longs;ubiecto conuertuntur.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Pila chri&longs;tallina, vel vitrea, qua ratione comburat.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Planet&aelig;, qua ratione moueantur duplici motu.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Plato &longs;olida ex planis componebat. 105. cur Elementis figuras Geometricas attri-bueret.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>Planetarum ordo.<emph.end type="italics"/></cell><cell>271</cell></row><row><cell><emph type="italics"/>Principia Mathematicorum.<emph.end type="italics"/> 2.</cell><cell>118</cell></row><pb pagenum="29"/><row><cell><emph type="italics"/>Principia &longs;cientiarum duplicia. Ex quibus, &amp; circa quod.<emph.end type="italics"/></cell><cell>61</cell></row><row><cell><emph type="italics"/>Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></cell><cell>315</cell></row><row><cell><emph type="italics"/>Proportio alterna. 28. multiplicata, &longs;eu multiplex &longs;ecundum C&aelig;neum.<emph.end type="italics"/></cell><cell>46</cell></row><row><cell><emph type="italics"/>P&longs;eudographia quid.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell><emph type="italics"/>Proportionalitas quid.<emph.end type="italics"/></cell><cell>308</cell></row><row><cell><emph type="italics"/>Proportio continuata, &amp; di&longs;iuncta quid. 310. alterna, &longs;eu permutata quid.<emph.end type="italics"/></cell><cell><emph type="italics"/>inibi.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Proportio Geometrica. 311. Arithmetica.<emph.end type="italics"/></cell><cell>302</cell></row><row><cell><emph type="italics"/>Proportio &longs;ecundum dignitatem, e&longs;t Geometrica.<emph.end type="italics"/></cell><cell>330</cell></row><row><cell><emph type="italics"/>Problemata mu&longs;icalia varia &agrave; 360. <expan abbr="v&longs;q;">v&longs;que</expan> ad finem &longs;ectionis 19. problematum.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Punicum, mu&longs;icum in&longs;trumentum.<emph.end type="italics"/></cell><cell>370</cell></row><row><cell><emph type="italics"/>Pupill&aelig; oculi etymon., &amp; natura. 408. cur in oculo no&longs;tro imago pupill&aelig; appareat.   problem.<emph.end type="italics"/> 2.</cell><cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Cur nigra in omnibus hominibus. probl.<emph.end type="italics"/> 5.</cell><cell/></row><row><cell><emph type="italics"/>Cur in Sole euane&longs;cat. probl.<emph.end type="italics"/> 6.</cell><cell/></row><row><cell><emph type="italics"/>Cur modo maior, modo minor appareat.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Pythagorici primi Mathematicis <expan abbr="oper&atilde;">operam</expan> dedere, eas&queacute; ceteris &longs;cientijs pr&aelig;poneb&abreve;t.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Qvadratura circuli. vide circulus. de quadratura figurarum rectangularum, &amp;   quadratur&aelig; duplex definitio cau&longs;alis, &amp; formalis.<emph.end type="italics"/></cell><cell>185</cell></row><row><cell><emph type="italics"/>Quantitas an conctet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis   mathematicis.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Remi problema.<emph.end type="italics"/></cell><cell>245</cell></row><row><cell><emph type="italics"/>Re&longs;olutio logica, &amp; mathematica, vt conueniant. 4. &amp;<emph.end type="italics"/></cell><cell>305</cell></row><row><cell><emph type="italics"/>Re&longs;ultus cadentium in terram, quibus angulis fiat.<emph.end type="italics"/></cell><cell>354</cell></row><row><cell><emph type="italics"/>Rythmus fus&egrave; explicatur.<emph.end type="italics"/></cell><cell>381</cell></row><row><cell><emph type="italics"/>Rubrum mare duplex.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>S<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Scythala quid, &amp; eius figura 250. &amp;<emph.end type="italics"/></cell><cell>252</cell></row><row><cell><emph type="italics"/>Securis problema, vbi de antiqu&aelig; &longs;euris figura, &amp; angulo pulchra demon&longs;tran-tur.<emph.end type="italics"/></cell><cell>258</cell></row><row><cell><emph type="italics"/>Semitonium, quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Solem e&longs;&longs;e terra multo maiorem: probatur.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Sph&aelig;ram planum tangit in puncto. demon&longs;tratur.<emph.end type="italics"/></cell><cell>184</cell></row><row><cell><emph type="italics"/>Statera antiqua, qu&aelig;: eius figura, &amp; problema.<emph.end type="italics"/></cell><cell>259</cell></row><row><cell><emph type="italics"/>Stereomatria, vt differat &agrave; Geometria.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell><emph type="italics"/>Succula.<emph.end type="italics"/></cell><cell>253</cell></row><row><cell><emph type="italics"/>Symphon&aelig; voces.<emph.end type="italics"/> 372.</cell><cell>392</cell></row><row><cell><emph type="italics"/>Symphonia.<emph.end type="italics"/></cell><cell>391</cell></row><row><cell><emph type="italics"/>T<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Temonis nauis problema.<emph.end type="italics"/></cell><cell>246</cell></row><row><cell><emph type="italics"/>Terram e&longs;&longs;e rotundam ex eclyp&longs;i. 114. Item aliter. 115. e&longs;&longs;e re&longs;pectu C&oelig;li   paruam valde. 115. e&longs;&longs;e cubum cur Plato voluerit.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>Terr&aelig; quantitas.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Terram paulatim reduci ad peff&eacute;ctam rotunditatem.<emph.end type="italics"/></cell><cell>151</cell></row><row><cell><emph type="italics"/>Tetragoni&longs;mus. vide Quadratura.<emph.end type="italics"/></cell><cell/></row><pb pagenum="30"/><row><cell><emph type="italics"/>Teretizare, quid.<emph.end type="italics"/></cell><cell>366</cell></row><row><cell><emph type="italics"/>Tetrachordon, quid.<emph.end type="italics"/></cell><cell>386</cell></row><row><cell><emph type="italics"/>Tollenonis problema.<emph.end type="italics"/></cell><cell>267</cell></row><row><cell><emph type="italics"/>Tonus mu&longs;icus, qui; vnde oriatur.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Trochle&aelig; problemata.<emph.end type="italics"/> 249. 250.</cell><cell>251</cell></row><row><cell><emph type="italics"/>Tunic&aelig; oculi. 408. in tractatu de Pupilla.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ventorum nomina, &amp; &longs;itus.<emph.end type="italics"/></cell><cell>160. <emph type="italics"/>a.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Vectis quotuplex, &amp; c.<emph.end type="italics"/></cell><cell>244</cell></row><row><cell><emph type="italics"/>Veteres canere &longs;olitos non &longs;olum in choris, &longs;ed etiam in &longs;cenis.<emph.end type="italics"/> 371. 384.</cell><cell>400</cell></row><row><cell><emph type="italics"/>Virgili&aelig;, Pleiades.<emph.end type="italics"/></cell><cell>335</cell></row><row><cell><emph type="italics"/>Vi&longs;&aelig; res gemmantur di&longs;tractis oculis.<emph.end type="italics"/></cell><cell>406</cell></row><row><cell><emph type="italics"/>Vi&longs;&aelig; rei geminatio non fit altero oculo in latera torto, cur.<emph.end type="italics"/></cell><cell>407</cell></row><row><cell><emph type="italics"/>Vi&longs;us res vi&longs;as, cur non duplicet, etiam &longs;i duos oculos habeamus.<emph.end type="italics"/></cell><cell>405</cell></row><row><cell><emph type="italics"/>Vmbelici litoralis problema.<emph.end type="italics"/></cell><cell>254</cell></row><row><cell><emph type="italics"/>Vmbram terr&aelig; parum &longs;upra Lunam tran&longs;cendere.<emph.end type="italics"/></cell><cell>137</cell></row><row><cell><emph type="italics"/>Vmbrarum incrementa, &amp; decrementa, cur in&aelig;qualia.<emph.end type="italics"/> 344.</cell><cell>348</cell></row><row><cell><emph type="italics"/>Vi&longs;us res geminat, &longs;i alter oculorum digito pellatur, cur.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Vocum mu&longs;icalium antiqu&aelig; appellationes.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Vox acuta velocior, grauis ver&ograve; tarda, cur.<emph.end type="italics"/></cell><cell>77</cell></row><row><cell><emph type="italics"/>Voluminum &longs;ectio modo rectam lineam, modo curuam refert, cur.<emph.end type="italics"/></cell><cell>356</cell></row><row><cell><emph type="italics"/>Vnitas, cur indiui&longs;ibilis.<emph.end type="italics"/></cell><cell>22</cell></row><row><cell><emph type="italics"/>Z<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Zonas terr&aelig;, vt Arist. de&longs;ignet: &amp; qu&aelig; &longs;ecundum ip&longs;um &longs;int habitabiles.<emph.end type="italics"/></cell><cell>156</cell></row><row><cell><emph type="italics"/>Zonam torridam quatuor reddunt habitabilem.<emph.end type="italics"/></cell><cell>159</cell></row></table><p type="head">
1877 
1878 <s>Finis Tertij Indicis.</s></p><pb pagenum="31"/>
1879       </section><section><p type="main">
1880 
1881 <s>Vi&longs;um e&longs;t etiam opportunum Lectori fore, ea &longs;imul in vnum <lb/>loca colligere, in quibus Ari&longs;toteles mihi vi&longs;us e&longs;t in Ma&shy;<lb/>thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&ecedil;&longs;ertim Peripa&shy;<lb/>tetici facilius ea inuenire, <expan abbr="atq;">atque</expan> de ij&longs;dem iudicium ferre <lb/>po&longs;&longs;int.<lb/><arrow.to.target n="table3"/></s></p><table><table.target id="table3"/><row><cell><emph type="italics"/>121<emph.end type="italics"/></cell><cell><emph type="italics"/>Nvmero marginali: vbi ait plura Octaedra, &longs;eu Pyramides re-plere locum: in quo omnes pariter expo&longs;itores lap&longs;i &longs;unt.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>124<emph.end type="italics"/></cell><cell><emph type="italics"/>Latitudinem figura, ait, cau&longs;am e&longs;&longs;e &longs;upernatationis. &amp; aquam   re&longs;i&longs;tere &longs;impliciter diui&longs;ioni.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>136<emph.end type="italics"/></cell><cell><emph type="italics"/>Cometas in &longs;uprema aeris regione collocat; cuius contrarium ibi   line ari demonctratione ostenditur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>147<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Tanaim, &amp; Indum oriri ex monte Paropami&longs;&longs;o. &amp; c.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>148<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait, tertia parte noctis Cauca&longs;i verticem illuminari &agrave; Sole.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>149<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Danubium ex Pyreneo monte defluere.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>150<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait fluuium quendam non minorem Rhodano in Liguria ab&longs;orberi,   &amp; iterum egredi.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>152<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Rubrum mare parum Atlantico Oceano commi&longs;ceri.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>159<emph.end type="italics"/></cell><cell><emph type="italics"/>Zonam torridam inhabit abilem exi&longs;timat.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>164<emph.end type="italics"/></cell><cell><emph type="italics"/>Putat Iridis angulos non po&longs;&longs;e vnum &longs;upra alterum collocari, &longs;ed   tantummodo in orbem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>182<emph.end type="italics"/></cell><cell><emph type="italics"/>Rationes, quas in Parelij dubitationibus affert, videntur inanes.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>236<emph.end type="italics"/></cell><cell><emph type="italics"/>In &longs;ubducendo c&oelig;le&longs;tium orbium numero, memoria labitur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>243<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait lineam O L, &longs;uperare lineam L R, quantitate P L, vt in figura.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>245<emph.end type="italics"/></cell><cell><emph type="italics"/>Remum ad vectem primi generis reducit.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>246<emph.end type="italics"/></cell><cell><emph type="italics"/>Temonem nauis reducit ad vectem primi generis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>247<emph.end type="italics"/></cell><cell><emph type="italics"/>In motu Remi collato cum motu Nauigij, &agrave; Nonio erroris manifest&egrave;   arguitur. eodem modo in motu Temonis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>250<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait maioribus trochleis, aut rotulis facilius onera &longs;ubleuari.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>256<emph.end type="italics"/></cell><cell><emph type="italics"/>Reducit cuneum ad vectem primi generis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>270<emph.end type="italics"/></cell><cell><emph type="italics"/>Cur res in vorticibus ad medium ferantur, veram cau&longs;am a&longs;signa-re non videtur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>275<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Danubium altero ramo in Mediterraneum, altero in Pontum   effluere.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>293<emph.end type="italics"/></cell><cell><emph type="italics"/>Negat Araneum filum ab intrin&longs;eco emittere, Democritum iniuria   refellens. quamuis hoc vltimum ad Phy&longs;icum pertineat.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>403<emph.end type="italics"/></cell><cell><emph type="italics"/>Problem. 2. &longs;ect. 2 3. non ben&egrave; videtur a&longs;signare cau&longs;am vari&aelig; im-mer&longs;ionis nauigij.<emph.end type="italics"/></cell></row></table></section><pb/><!--blank page --><pb pagenum="33"/>
1882 
1883 <section><p type="head"><s>LOCA<lb/>MATHEMATICA<lb/>EX LIBRO<lb/>PR&AElig;DICAMENTORVM<lb/>Per ordinem declarata.</s></p><p type="main">
1884 
1885 <s><arrow.to.target n="marg1"/></s></p><p type="margin">
1886 
1887 <s><margin.target id="marg1"/>1</s></p></section>
1888 </front><body><chap>
1889 <p type="main">
1890 <s>Ex c. <!-- REMOVE S-->3. De his, qu&aelig; ad aliquid. </s>
1891 
1892 
1893 <s>Porr&ograve; quemadmodum vnus angulus vni angulo &aelig;qualis e&longs;t, ita <lb/><expan abbr="aliqu&atilde;do">aliquando</expan> duo anguli &longs;unt vni angulo &aelig;quales, vt patet, &longs;i vnus angulus, v.g. <lb/><!-- REMOVE S-->angulus B A C, vbi ait <emph type="italics"/>(Scientia ver&ograve; &longs;i non &longs;it, <lb/>nihil probibet e&longs;&longs;e &longs;cibile, vt circuli quadratura, &longs;i e&longs;t &longs;cibilis, <lb/>&longs;cientia quidem eius nondum e&longs;t)<emph.end type="italics"/> Cum velit Ari&longs;t. 
1894 
1895 o&longs;tendere, <lb/>n&oacute; omnia correlatiua &longs;imul e&longs;&longs;e natura, id de &longs;cibili, &amp; &longs;cien&shy;<lb/>tia vari&egrave; probat, pr&aelig;&longs;ertim ver&ograve;, quia multa &longs;int &longs;cibilia, <lb/>qu&aelig; tamen nondum &longs;ciantur, vt patet, inquit, in Quadratu&shy;<lb/>ra circuli, &amp; &longs;cientia ip&longs;ius, quia quamuis ip&longs;a circuli quadratura &longs;it &longs;cibi&shy;<lb/>lis, nondum tamen &longs;imul cum ip&longs;a, &longs;cientia illius extat. </s>
1896 
1897 <s>Qu&aelig; vt perfect&egrave; <lb/>intelligantur, &longs;ciendum e&longs;t, quadraturam circuli, qu&aelig; &agrave; Gr&aelig;cis tetrago&shy;<lb/>ni&longs;mus dicitur, nihil aliud e&longs;&longs;e, qu&agrave;m propo&longs;ito cuilibet circulo exhibere <lb/>quadratum &aelig;quale. </s>
1898 
1899 <s>Qu&aelig; &aelig;qualitas debet intelligi de areis, &longs;eu &longs;patijs, ita <lb/>vt area circuli, &longs;eu &longs;patium illud, &longs;iue &longs;uperficies illa circularis, &longs;it &aelig;qualis <lb/>are&aelig;, &longs;eu &longs;uperficiei quadrat&aelig;. </s>
1900 
1901 <s>Qua in re plurimi decipiuntur exi&longs;timantes <lb/>per quadraturam cir culi inquiri &aelig;qualitatem linearum, ita vt circumferen&shy;<lb/>tia circuli debeat e&longs;&longs;e &aelig;qualis ambitui, &longs;eu quatuor lateribus quadrati: <lb/>quod omnino fal&longs;um e&longs;t.</s></p><p type="main">
1902 
1903 <s>Quadratio porr&ograve; circuli dupliciter proponi pote&longs;t, vel tanquam Theo&shy;<lb/>rema, vel tanquam Problema <emph type="italics"/>(theorema autem e&longs;t propo&longs;itio, in qua nihil fa&shy;<lb/>ciendum proponitur; problema ver&ograve; aliquid fieri expo&longs;cit)<emph.end type="italics"/> neutrum autem tem&shy;<lb/>pore Ari&longs;t. 
1904 
1905 erat adinuentum nam theorema inuentum e&longs;t po&longs;t ip&longs;um ducen&shy;<lb/>tis circiter annis ab Archimede: problema ver&ograve; nondum &agrave; quoquam per&shy;<lb/>fect&egrave; potuit reperiri. </s>
1906 
1907 <s>qua di&longs;tinctione &longs;aluari po&longs;&longs;unt nonnulli, vt Boetius <lb/>hocloco, qui aiunt, &longs;e vidi&longs;&longs;e Demon&longs;trationem quadratur&aelig; huius, &longs;i nimi&shy;<lb/>rum intelligant theorema. </s>
1908 
1909 <s>&amp; alij etiam verum a&longs;&longs;erunt, dum negant hacte&shy;<lb/>nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi&shy;<pb pagenum="34"/>medis e&longs;t propo&longs;itio prima acuti&longs;&longs;imi libelli de Dimen&longs;ione circuli; e&longs;t au&shy;<lb/>tem huiu&longs;modi. </s>
1910 
1911 <s>Quilibet circulus &aelig;qualis e&longs;t triangulo rectangulo, cuius <lb/>quidem &longs;emidiameter vni laterum, qu&aelig; circa rectum angulum &longs;unt, ambi&shy;<lb/>tus ver&ograve; ba&longs;i eius e&longs;t &aelig;qualis.</s></p><figure place="text" xlink:href="figures-la/009.01.034.1.tif"/><p type="main">
1912 
1913 <s>Sit, v.g. <!-- REMOVE S-->datus circulus, cuius &longs;emidiameter A B; &amp; fit trian gulum rectangu&shy;<lb/>lum A B C, cuius angulus B, &longs;it rectus, &amp; latus B A, <expan abbr="con&longs;titu&etilde;s">con&longs;tituens</expan> angulum re&shy;<lb/>ctum B, cum ba&longs;i B C, &longs;it &aelig;quale &longs;emidiametro A B; ba&longs;is ver&ograve; B C, &longs;it &aelig;qua&shy;<lb/>lis peripheri&aelig; eiu&longs;dem circuli dati. </s>
1914 
1915 
1916 
1917 <s>demon&longs;trat iam ibi Archimedes acuta <lb/>&aelig;qu&egrave;, ac euidenti demon&longs;tratione triangulum i&longs;tud &aelig;quale e&longs;&longs;e circulo illi. <lb/></s>
1918 
1919 <s>quod perinde e&longs;t, ac &longs;i o&longs;tendi&longs;&longs;et cuinam quadrato &longs;it &aelig;qualis, cum per vl&shy;<lb/>timam 2. Eucl. <!-- REMOVE S-->po&longs;&longs;imus triangulo huic quadratum &aelig;quale con&longs;truere, quod <lb/>con&longs;equenter dato circulo &aelig;quale erit. </s>
1920 
1921 
1922 
1923 <s>Quod &longs;i in modum Problematis ita <lb/>proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta <lb/>e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc <lb/>e&longs;t ad &aelig;qualitatem mathematicam, &longs;eu exacti&longs;&longs;imam effici po&longs;&longs;it, <expan abbr="tota&qacute;">totaque</expan>; dif&shy;<lb/>ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;<lb/>neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s>
1924 
1925 <s>quam nullus hactenus <lb/>geometric&egrave; illi &aelig;qualem potuit exhibere, <expan abbr="atq;">atque</expan> exhibita <expan abbr="euid&etilde;ti">euidenti</expan> demon&longs;tra&shy;<lb/>tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib. 
1926 
1927 de <lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;<lb/>&longs;tigauit. </s>
1928 
1929 <s>nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam <lb/>&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;<lb/>rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s>
1930 
1931 <s>tu ip&longs;um con&longs;ule, <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s>
1932 
1933 <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib. 
1934 
1935 4. Math. coll. </s>
1936 
1937 <s>&amp; Ioannes Buteo vnico volumine om&shy;<lb/>nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s>
1938 
1939 <s>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. &amp; alij. </s>
1940 
1941 <s>&longs;olet autem &agrave; non&shy;<lb/>nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/>cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy;<lb/>nus adinuentam e&longs;&longs;e. </s>
1942 
1943 <s>ego quidem e&longs;&longs;e po&longs;&longs;ibilem exi&longs;timo, quis enim dubi&shy;<lb/>tare pote&longs;t, po&longs;&longs;e exi&longs;tere quadratum &aelig;quale circulo propo&longs;ito? </s>
1944 
1945 <s>Quod &longs;i po&shy;<lb/>te&longs;t fieri, quare non etiam demon&longs;trari? </s>
1946 
1947 <s>pr&ecedil;fertim cum videamus ab Archi&shy;<lb/>mede iam inuentam e&longs;&longs;e, quatenus Theorema e&longs;t. </s>
1948 
1949 <s>&amp; pr&aelig;terea con&longs;tet, Hip&shy;<lb/>pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, &amp; Archimedem in libel&shy;<pb pagenum="35"/>lo de quadratura Paraboles, quadra&longs;&longs;e ip&longs;am Parabolem, qu&aelig; tamen du&aelig; fi&shy;<lb/>gur&aelig;, lunula &longs;cilicet, &amp; parabola &longs;unt curuiline&aelig;.</s></p><p type="main">
1950 
1951 <s><arrow.to.target n="marg2"/></s></p><p type="margin">
1952 
1953 <s><margin.target id="marg2"/>2</s></p><p type="main">
1954 
1955 <s>Ex cap. 
1956 
1957 de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine, <lb/>elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy;<lb/>matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s>
1958 
1959 <s>qu&aelig; non &longs;unt in antiqua tran&shy;<lb/>&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo gr&aelig;co codice editionis Francfor&shy;<lb/>dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta, <lb/><foreign lang="greek">ai/gar arxai/ pro/terai tw_n qewrhma/twn th ta/xei.</foreign> per &longs;cientias autem demon&longs;tra&shy;<lb/>tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis <lb/>a&longs;&longs;ignet Ari&longs;t. De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy;<lb/>nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy;<lb/>rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy;<lb/>ba illa &agrave; nobis addita ex gr&aelig;co, optim &egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy;<lb/>menta intelligantur principia, qualia &longs;unt initio Euclidis, &amp; per de&longs;criptio&shy;<lb/>nes exponant theoremata. </s>
1960 
1961 <s>quod autem principia illa ordine priora &longs;int de&shy;<lb/>mon&longs;trationibus, &longs;iue ip&longs;as pr&aelig;cedant, ex ip&longs;a primi Euclidis in&longs;pectione <lb/>patere pote&longs;t.</s></p><p type="main">
1962 
1963 <s><arrow.to.target n="marg3"/></s></p><p type="margin">
1964 
1965 <s><margin.target id="marg3"/>3</s></p><p type="main">
1966 
1967 <s>Ex cap. 
1968 
1969 de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox <lb/>gr&aelig;ca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/><figure place="text" xlink:href="figures-la/009.01.035.1.tif"/><lb/>tum normam appellant, Itali ver&ograve;, Squadra, ad <lb/>cuius &longs;imilitudinem Geometr&aelig; denominarunt fi&shy;<lb/>guram quandam, &longs;eu portionem cuiu&longs;uis paralle&shy;<lb/>logrammi, vt videre e&longs;t in definitione &longs;ecunda <lb/>2. elem. </s>
1970 
1971 <s>&amp; in pr&aelig;&longs;enti figura, in qua quadratum <lb/>A B C D, circumpo&longs;ito gnomone E F G, augetur, <lb/>&amp; fit maius quadratum H B I L.<!-- KEEP S--></s></p><p type="main">
1972 
1973 <s>Idem etiam verum e&longs;t in quadrato arithmeti&shy;<lb/>co, &longs;iue in numero quadrato: is enim pariter ad&shy;<lb/>dito Gnomone augetur. </s>
1974 
1975 <s>i. </s>
1976 
1977 <s>addito numero impari. <lb/></s>
1978 
1979 <s>quemadmodum infra 3. Phy&longs;. tex. <!-- REMOVE S-->26. fus&egrave; explicabimus.</s>
1980 
1981 </p><p type="head">
1982 
1983 <s><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s></p>
1984 </chap><chap>
1985 <p type="main">
1986 <s><arrow.to.target n="marg4"/></s></p><p type="margin">
1987 
1988 <s><margin.target id="marg4"/>4</s></p><p type="main">
1989 
1990 <s>Aliquorum opinio e&longs;t, Ari&longs;totelem ho&longs;ce libros appella&longs;&longs;e re&longs;olu&shy;<lb/>torios, quod per illos doceat &longs;yllogi&longs;mum, ac demon&longs;trationem <lb/>iam factam in &longs;ua immediata principia re&longs;oluere, quam opinio&shy;<lb/>nem meum non e&longs;t, nunc refellere. </s>
1991 
1992 <s>per&longs;ua&longs;um tamen mihi e&longs;t, rem <lb/>multo aliter &longs;e habere, veram rationem huius tituli petendam e&longs;&longs;e ex peni&shy;<lb/>tiori Mathematicorum eruditione. </s>
1993 
1994 <s>Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>Alex. initio &longs;eptimi Mathem. collect. </s>
1995 
1996 <s>antiqui&longs;&longs;imos videlicet Geometras, <lb/>Euclidem, Apollonium Perg&aelig;um, &amp; Ari&longs;t&ecedil;um &longs;crip&longs;i&longs;&longs;e libros de re&longs;olutio&shy;<lb/>ne, in quibus ars tradebatur, qua propo&longs;ito quouis theoremate, aut proble&shy;<lb/>mate po&longs;&longs;ent facile ex eo, tanquam vero accepto inue&longs;tigare aliquam veri&shy;<lb/>tatem, per quam deinde componerent illius, quod qu&aelig;rebatur, Demon&longs;tra&shy;<lb/>tionem; inue&longs;tigationem illam appellabant re&longs;olutionem: compo&longs;itionem <lb/>ver&ograve; nominabant di&longs;cur&longs;um <expan abbr="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s>
1997 
1998 <s>Porr&ograve; Diogenes Laert. <!-- REMOVE S-->huius re&longs;olutionis in&shy;<lb/>uentorem facit Platonem: &agrave; quo eam Leodamas Tha&longs;ius didicit, cuius be&shy;<lb/>neficio, pluries deinde Geometricas demon&longs;trationes adinuenit. </s>
1999 
2000 
2001 
2002 <s>definitio <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s>
2003 
2004 <s>13. Elem. iuxta tran&longs;latio&shy;<lb/>nem Zamberti, &amp; Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri&shy;<lb/>m&ograve; per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, qu&aelig; tan&shy;<lb/>quam per&longs;picua exempla rei propo&longs;it&aelig; in&longs;eruire po&longs;&longs;unt. </s>
2005 
2006 <s>&longs;unt pr&aelig;terea fre&shy;<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy;<lb/>pi. </s>
2007 
2008 <s>extat adhuc liber Datorum Euclidis, qui geometricis re&longs;olutionibus in&shy;<lb/>&longs;eruiebat. </s>
2009 
2010 <s>vtinam extarent etiam alij de re&longs;olutione, quorum auxilio non <lb/>tantopere recentiores Mathematici in inueniendis Demo&longs;trationibus la&shy;<lb/>borarent; hanc re&longs;olutionem, &longs;ic Pappus fu&longs;ius, quam Euclides explicat; <lb/>re&longs;olutio e&longs;t via &agrave; qu&aelig;&longs;ito tanquam conce&longs;&longs;o per ea, qu&aelig; exip&longs;o con&longs;equun&shy;<lb/>tur ad aliquod certum, &amp; conce&longs;&longs;um: in re&longs;olutione enim id, quod qu&aelig;ritur <lb/>tanquam factum, &amp; verum &longs;upponentes, quid ex hoc &longs;equatur, con&longs;idera&shy;<lb/>mus, quou&longs;que incidamus in aliquod iam cognitum, vel quod &longs;it &egrave; numero <lb/>principiorum. </s>
2011 
2012 <s>Quod quidem erat fignum euidens, qu&aelig;&longs;itum quoque verum <lb/>e&longs;&longs;e. </s>
2013 
2014 <s>eadem omnino habet Proclus in comm. <!-- REMOVE S-->ad &longs;extam primi elem. </s>
2015 
2016 
2017 
2018 <s>Quod <lb/>porr&ograve; Ari&longs;t. ip&longs;e hanc re&longs;olutionem Mathematicam cognouerit e&longs;&longs;e medij <lb/>inqui&longs;itionem manife&longs;tum e&longs;t ex cap. 3. lib.  3. Ethyc. <!-- REMOVE S-->vbi &longs;ic ait <emph type="italics"/>(Qui enim <lb/>con&longs;ultat, qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, quemadmodum de&longs;igna&shy;<lb/>tiones)<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt <lb/>&longs;upra innuimus, &amp; infra probabimus; cum ergo con&longs;ultatio nihil aliud &longs;it, <lb/>quam medij idonei ad finem in rebus agendis inqui&longs;itio, eamque dicat e&longs;&longs;e <lb/>&longs;imilem re&longs;olutioni Geometric&aelig;, manife&longs;tum e&longs;t, ip&longs;am <expan abbr="quoq;">quoque</expan> re&longs;olutionem <lb/>e&longs;&longs;e medij in rebus &longs;peculatiuis idonei perue&longs;tigationem. </s>
2019 
2020 
2021 
2022 <s>Exi&longs;timo igitur <lb/>cum docti&longs;&longs;imis Zabarella, Burana, Toleto, &amp; alijs, Ari&longs;totilem non &longs;olum <lb/>hanc &longs;uam logicam ad mathematicarum &longs;cientiarum typum compegi&longs;&longs;e, <lb/>verum potius imitatum e&longs;&longs;e opus illud Euclidis de re&longs;olutione, atque ex eo <lb/>non &longs;olum plurima exempla Geometrica, verum etiam titulum de&longs;ump&longs;i&longs;&longs;e, <lb/>pr&aelig;&longs;ertim cum argumentum e&longs;&longs;et fer&egrave; idem vtrobique, &longs;ed Ari&longs;t. 
2023 
2024 intentio <lb/>fuerit accommodare re&longs;olutionem omnibus <expan abbr="&longs;ci&etilde;tijs">&longs;cientijs</expan>; Euclidis ver&ograve;, &amp; alio&shy;<lb/>rum Geometri&aelig; &longs;oli. </s>
2025 
2026 <s>hinc patere pote&longs;t, cur hi libri re&longs;olutorij in&longs;cribantur, <lb/>quod &longs;cilicet tradunt methodum, qua valeamus qu&aelig;&longs;itum quoduis re&longs;olue&shy;<lb/>re, ide&longs;t, ex qu&aelig;&longs;ito tanquam vero inue&longs;tare aliquam veritatem, per quam <lb/>deinde propo&longs;it&aelig; qu&aelig;&longs;tionis rationem methodo compo&longs;itiua reddamus. </s>
2027 
2028 <s>Et <lb/>ver&ograve; cum reliquas appellationes Problematis, Theorematis, Propo&longs;itionis, <lb/>definitionum, po&longs;tulatorum, axiomatum, &amp; alia huiu&longs;modi ex Geometri&shy;<lb/>cis ad omnes &longs;cientias tran&longs;tulerit, quid ni etiam re&longs;olutionem? </s>
2029 
2030 <s>maxim&egrave; <lb/>ver&ograve;, quia &longs;i horum lib. 
2031 
2032 intentio e&longs;&longs;et docere iam factum &longs;yllogi&longs;mum in &longs;ua <lb/>principia re&longs;oluere, parum e&longs;&longs;et vtilis; im&ograve; nec vtilis, &longs;ed &longs;uperfluum quid. <lb/></s>
2033 
2034 <s>at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s>
2035 
2036 <s>profecto nullibi. </s>
2037 
2038 <s>quid opus e&longs;t <lb/>iam factum &longs;yllogi&longs;mum re&longs;oluere? </s>
2039 
2040 <s>at ver&ograve; propo&longs;itam qu&aelig;&longs;tionem re&longs;ol&shy;<lb/>uere veterum mathematicorum more, hoc opus, hic labor e&longs;t.</s></p><p type="main">
2041 
2042 <s>Hanc porr&ograve; re&longs;olutionem attendendam e&longs;&longs;e prim&ograve; penes formam, quam <lb/>docet primis duobus analyticis; &longs;ecund&ograve; penes materiam, quam tradit duo&shy;<pb pagenum="37"/>bus vltimis, non pr&aelig;tereundum. </s>
2043 
2044 <s>reliquas duas logic&aelig; partes, Topicam &longs;ci&shy;<lb/>licet, &amp; Elenchos, qu&aelig; &longs;yllogi&longs;mos probabilem, &amp; apparentem docent, no&shy;<lb/>luit appellare re&longs;olutorios, quamuis inuentionem mediorum doceant, quia <lb/>iam mos i&longs;te inoleuerat apud Philo&longs;ophos, &amp; Mathematicos, vt illa &longs;ola <lb/>pars, qu&aelig; ex materia nece&longs;&longs;aria doceret &longs;yllogi&longs;mum demon&longs;tratiuum con&shy;<lb/>&longs;truere, diceretur re&longs;olutio: cum Mathematici, qui primi de re&longs;olutione <lb/>&longs;crip&longs;erunt, talem materiam &longs;olum con&longs;iderent.</s></p><p type="main">
2045 
2046 <s><arrow.to.target n="marg5"/></s></p><p type="margin">
2047 
2048 <s><margin.target id="marg5"/>5</s></p><p type="main">
2049 
2050 <s>Ex cap. 
2051 
2052 23. &longs;ecti primi lib. 
2053 
2054 1. <emph type="italics"/>(Vt quod diameter incommen&longs;urabilis eo, quod <lb/>imparia &aelig;qualia paribus fiant, &longs;i fuerit po&longs;ita commen&longs;ur abilis. </s>
2055 
2056 <s>&aelig;qualia igitur fieri <lb/>imparia paribus ratiocinantur, diametrum vtr&ograve; incommen&longs;urabilem e&longs;&longs;e ex &longs;uppo&shy;<lb/>&longs;itione <expan abbr="mon&longs;tr&atilde;t">mon&longs;trant</expan>, quoniam fal&longs;um accidit propter contradictionem)<emph.end type="italics"/> Euclides pri&shy;<lb/>mis duabus definitionibus 10. elem. </s>
2057 
2058 <s>definit, qu&aelig; nam &longs;int magnitudines <lb/>commen&longs;. </s>
2059 
2060 <s>&amp; qu&aelig; incommen&longs;. </s>
2061 
2062 <s>&longs;ic; commen&longs;. </s>
2063 
2064 <s>magnitudines dicuntur, quas <lb/><figure place="text" xlink:href="figures-la/009.01.037.1.tif"/><lb/>eadem men&longs;ura metitur, vt &longs;i fuerint du&aelig; magnitu&shy;<lb/>dines, A, &amp; B, quas eadem men&longs;ura C, ide&longs;t quan&shy;<lb/>titas C, metiatur, ide&longs;t <expan abbr="qu&atilde;titas">quantitas</expan> C, applicata quan&shy;<lb/>titati A, &amp; per ip&longs;am aliquoties replicata ip&longs;am ad&shy;<lb/>&aelig;quat&egrave; ab&longs;umat, vt &longs;i linea C, quinquies &longs;uper li&shy;<lb/>neam A, replicata eam pr&aelig;cis&egrave;, &amp; perfect&egrave; omnin&ograve; <lb/>ad&aelig;quaret: &amp; eadem linea C, applicata line&aelig; B, &amp; &longs;uper illam ter, v.g. <!-- REMOVE S-->re&shy;<lb/>petita ip&longs;am con&longs;umeret, diceretur <expan abbr="vtranq;">vtranque</expan> metiri, &amp; proinde duas lineas <lb/>A, &amp; B, e&longs;&longs;e comm. <!-- REMOVE S-->definit po&longs;tea <expan abbr="incomm&etilde;&longs;">incommen&longs;</expan> hoc modo, incomm, autem, qua&shy;<lb/>rum nullam contingit communem men&longs;uram reperiri; vt &longs;i duarum linea&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.037.2.tif"/><lb/>rum, A, B, nunquam po&longs;&longs;et reperiri aliqua men&longs;u&shy;<lb/>ra, qu&aelig; <expan abbr="vtranq;">vtranque</expan> ad&aelig;quat&egrave; metiretur, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i linea <lb/>C, men&longs;uraret A, quater &longs;umpta, ter autem &longs;umpta <lb/>non ad&aelig;quaret omnino <expan abbr="line&atilde;">lineam</expan> B, &longs;ed deficeret, vel ex&shy;<lb/>cederet aliquantulum, <expan abbr="atq;">atque</expan> hoc fieret in quauis alia <lb/>men&longs;ura, loco ip&longs;ius C, a&longs;&longs;umpta, &longs;iue maior, &longs;iue <lb/>minor ip&longs;a C, vt <expan abbr="vtranq;">vtranque</expan> nunquam perfect&egrave; metiretur, e&longs;&longs;ent du&aelig; ill&aelig; line&aelig; <lb/>incommen&longs;. </s>
2065 
2066 
2067 
2068 
2069 
2070 
2071 
2072 
2073 
2074 <s>Extare porr&ograve; tales lineas, &amp; &longs;uperficies, &amp; corpora, <expan abbr="ea&qacute;">eaque</expan>; quam&shy;<lb/>plurima, ac pen&egrave; infinita ex 10. Elem. manife&longs;tum e&longs;t. </s>
2075 
2076 <s>inuentum autem hu&shy;<lb/>ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um <lb/>e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy;<lb/>&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s>
2077 
2078 <s>Quapropter <lb/>non immerit&ograve; diuinus ille Plato lib. 
2079 
2080 7. de legib. </s>
2081 
2082 <s>huius a&longs;ymmetri&aelig; ignora&shy;<lb/>tionem, adeo dete&longs;tatus e&longs;t, vt eam non hominum, &longs;ed &longs;uum, pecorumque <lb/>ignorantiam cen&longs;uerit. </s>
2083 
2084 <s>inter lineas incommen&longs;. </s>
2085 
2086 <s>&longs;unt diameter, &amp; latus eiu&longs;&shy;<lb/>dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti <lb/><figure place="text" xlink:href="figures-la/009.01.037.3.tif"/><lb/>e&longs;t lineola E, in pr&aelig;&longs;enti quadrato, etiam&longs;i illam in <lb/>infinitum &longs;ubdiuidas, qu&aelig; <expan abbr="vtranq;">vtranque</expan> lineam, diame&shy;<lb/>trum &longs;cilicet A C, &amp; latus quoduis ex quatuor, v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->latus B C, pr&aelig;cis&egrave; omnino metiatur. </s>
2087 
2088 
2089 
2090 
2091 
2092 <s>theorema <lb/>i&longs;tud demon&longs;tratur in vltima 10. Elem. eodem me&shy;<lb/>dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb pagenum="38"/>propo&longs;itionis, qu&aelig;fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito pr&aelig;dictas lineas e&longs;&longs;e comm. <lb/><!-- REMOVE S-->deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t. 
2093 
2094 fal&longs;um ratiocinatur, quod &longs;ci&shy;<lb/>licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. &longs;ignificat, quando ait, <lb/>imparia &aelig;qualia paribus fiunt. </s>
2095 
2096 
2097 
2098 <s>ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy;<lb/>ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. <!-- REMOVE S-->&amp; proinde altera pars con&shy;<lb/>tradictionis, qu&aelig; e&longs;t, e&longs;&longs;e incomm. <!-- REMOVE S-->vera a&longs;truitur. </s>
2099 
2100 
2101 
2102 
2103 
2104 <s>ex quibus &longs;atis videtur ex&shy;<lb/>plicari hic locus. </s>
2105 
2106 <s>videas igitur, qu&agrave;m leuiter nonnulli no&longs;tr&aelig; tempe&longs;tatis <lb/>ageometreti i&longs;tud exponant, dicentes diametrum e&longs;&longs;e incomm. <!-- REMOVE S-->co&longs;t&aelig;, nihil <lb/>aliud &longs;igni&longs;icare, quam diametrum e&longs;&longs;e longiorem co&longs;ta, qua expo&longs;itione <lb/>nihil ineptius. </s>
2107 
2108 
2109 
2110 <s>Aduerte tandem figuram vulgat&aelig; editionis e&longs;&longs;e ineptam, <lb/>cum habeat duo quadrata alterum &longs;uper diametro alterius, quorum maius <lb/>&longs;uperuacaneum e&longs;t.</s></p><p type="main">
2111 
2112 <s><arrow.to.target n="marg6"/></s></p><p type="margin">
2113 
2114 <s><margin.target id="marg6"/>6</s></p><p type="main">
2115 
2116 <s>Et cap. 
2117 
2118 24. &longs;ecti primi libri primi <emph type="italics"/>(Sed magis efficitur manife&longs;tum in de&longs;cri&shy;<lb/>ptionibus, vt quod &aelig;quicruris, qui ad ba&longs;im &aelig;quales &longs;int, ad centrum duct&aelig; A B, <lb/>A C, &longs;i igitur &aelig;qualem accipiat A G, angulum ip&longs;i A B D, non omnino ex. </s>
2119 
2120 <s>&longs;timans <lb/>&aelig;quales, qui &longs;emicirculorum, &amp; rur&longs;us G, ip&longs;i D, non omnem a&longs;&longs;umens eum, qui &longs;e&shy;<lb/>cti. </s>
2121 
2122 <s>amplius ab &aelig;qualibus existentibus totis angulis, &amp; ablatorum &aelig;quales e&longs;&longs;e re&shy;<lb/>tiquos E, F, quod ex principio petet, ni&longs;i acceperit ab &aelig;qualibus demptis &aelig;qualia <lb/>derelinqui.)<emph.end type="italics"/> Primum &longs;cias characteres vulgat&aelig; editionis, vna cum figura ip&shy;<lb/>&longs;is re&longs;pondente, e&longs;&longs;e mendo&longs;os; propterea ex textu gr&aelig;co vtrunque corri&shy;<lb/>gendum putaui in hunc, quem vidi&longs;ti modum. </s>
2123 
2124 <s>Secundo, per de&longs;criptiones <lb/>Ari&longs;t. 
2125 
2126 intelligere <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> Geometricas &longs;upra diximus, quod ex hoc <lb/>loco euidenter confirmatur, vbi manife&longs;t&egrave; loco de&longs;criptionis &longs;upponit li&shy;<lb/>nearem demon&longs;trationem. </s>
2127 
2128 <s>In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t. 
2129 
2130 illud demon&shy;<lb/>&longs;trare, quod Euclides in 5. primi o&longs;tendit, alio tamen modo, &longs;cilicet I&longs;o&longs;ce&shy;<lb/>lium triangulorum, qui ad ba&longs;im &longs;unt anguli, inter &longs;e &longs;unt &aelig;quales. </s>
2131 
2132 <s>e&longs;t au&shy;<lb/>tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="r&egrave;&longs;t&imacr;tuendam">r&egrave;&longs;tintuendam</expan> e&longs;&longs;e <lb/>ex quodam gr&aelig;co codice, qui characteres hoc modo appo&longs;uerat. </s>
2133 
2134 <s>&longs;it I&longs;o&longs;ce&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.038.1.tif"/><lb/>les C A B, cuius ba&longs;is C B, Dico angulos &longs;upra ba&longs;im, <lb/>in quibus liter&aelig; E F, e&longs;&longs;e inuicem &aelig;quales. </s>
2135 
2136 <s>facto centro <lb/>in A, de&longs;cribatur circulus A B C, tran&longs;iens per puncta <lb/>C B, iam &longs;ic. </s>
2137 
2138 <s>omnes anguli &longs;emicirculi &longs;unt &aelig;quales in&shy;<lb/>ter &longs;e, ergo anguli A C G, A B D, &longs;unt &aelig;quales. </s>
2139 
2140 <s>Pr&aelig;te&shy;<lb/>rea c&ugrave;m anguli ciu&longs;dem &longs;ectionis &longs;int &aelig;quales ad inui&shy;<lb/>cem, erunt anguli &longs;ectionis C B D G, nimirum anguli, <lb/>in quibus &longs;unt G, &amp; D, inter &longs;e &aelig;quales: <expan abbr="cum&qacute;">cumque</expan>; hi duo <lb/>anguli &longs;ectionis &longs;int partes <expan abbr="angulor&utilde;">angulorum</expan> &longs;emicirculi A C G, <lb/>A B D, &longs;i illi ab his auferantur, auferuntur &aelig;quales anguli ab &aelig;qualibus an&shy;<lb/>gulis, ergo anguli, qui remanent, &longs;cilicet E, &amp; F, erunt &aelig;quales, quod erat <lb/>demon&longs;trandum. </s>
2141 
2142 <s>hinc Ari&longs;t. 
2143 
2144 infert manife&longs;tum e&longs;&longs;e oportere in omni &longs;yllo&shy;<lb/>gi&longs;mo, reperiri vniuer&longs;ales, &amp; affirmatiuas propo&longs;itiones, vt Factum e&longs;t in <lb/>pr&aelig;cedenti aliter e&longs;&longs;et petitio principij. </s>
2145 
2146 <s>Qu&aelig;nam vero &longs;it &aelig;qualitas, quam <lb/>Geometr&aelig; con&longs;iderant, infra cap. 1. &longs;ecti 3. explicabicur.</s></p><p type="main">
2147 
2148 <s><arrow.to.target n="marg7"/></s></p><p type="margin">
2149 
2150 <s><margin.target id="marg7"/>7</s></p><p type="main">
2151 
2152 <s>Ex cap. 
2153 
2154 2. &longs;ecti 2. lib. 
2155 
2156 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum <lb/>veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;t&egrave; vtitur <lb/>verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. &longs;ignificari <lb/>Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e&shy;<lb/>quentibus verbis, cum dixit (ad diale cticos autem &longs;yllogi&longs;mos ex propo&longs;i&shy;<lb/>tionibus &longs;ecundum opinionem) hac adhibita con&longs;ideratione, quam inter&shy;<lb/>pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s></p><p type="main">
2157 
2158 <s><arrow.to.target n="marg8"/></s></p><p type="margin">
2159 
2160 <s><margin.target id="marg8"/>8</s></p><p type="main">
2161 
2162 <s>Ex eodem loco paulo po&longs;t <emph type="italics"/>(Quare principia quidem, qu&aelig; &longs;ecundum <expan abbr="vnum-quodq;">vnum&shy;<lb/>quodque</expan> &longs;unt experimenti est tradere: dico autem, vt a&longs;trologicam experientiam <lb/>a&longs;trologic&aelig; &longs;cienti&aelig;: acceptis enim apparentibus <expan abbr="&longs;uffici&etilde;ter">&longs;ufficienter</expan>, ita inuent&aelig; &longs;unt a&longs;tro&shy;<lb/>logic&aelig; demonstrationes)<emph.end type="italics"/> Cum rationem tradat inueniendorum mediorum ad <lb/>quodlibet problema demon&longs;trandum; nunc docet, non omnia in &longs;eientijs <lb/>po&longs;&longs;e probari, aut demou&longs;trari: principia enim &longs;cientiarum <expan abbr="n&otilde;">non</expan> demon&longs;tran&shy;<lb/>tur, &longs;ed &longs;ola experientia manife&longs;ta &longs;unt; vt patet in A&longs;tronomia, qu&aelig; ab ex&shy;<lb/>perientia &longs;ua &longs;olet &longs;tabilire principia: principijs autem <expan abbr="experim&etilde;to">experimento</expan> con&longs;ti&shy;<lb/>tutis ex ip&longs;is reliqua problemata <expan abbr="demon&longs;tr&atilde;tur">demon&longs;trantur</expan>. </s>
2163 
2164 <s>duo autem &longs;unt apud a&longs;tro&shy;<lb/>nomos genera experimenti, primum dicitur Ph&aelig;nomena, ide&longs;t, <expan abbr="appar&etilde;ti&aelig;">apparenti&aelig;</expan>; <lb/>&amp; &longs;unt ea, qu&aelig; vulgo omnibus patent, vt Solem oriri, &amp; occidere; a&longs;tra fer&shy;<lb/>ri circulariter, diem augeri modo, modo minui: &amp; his &longs;imilia. </s>
2165 
2166 <s>alterum ge&shy;<lb/>nus dicitur ob&longs;eruationes, qu&aelig; tantummodo a&longs;tronomi&aelig; peritis per ob&longs;er&shy;<lb/>uationem innote&longs;cunt, vt Solem in&aelig;qualiter ferri proprio motu per Zodia&shy;<lb/>cum; aliquando maiorem, aliquando minorem videri; plures dies immo&shy;<lb/>rari citra &aelig;quatiorem in parte Zodiaci boreali, quam in altera vltra &aelig;qua&shy;<lb/>torem au&longs;trali. </s>
2167 
2168 <s>dies naturales e&longs;&longs;e inuicem in&aelig;quales, &amp;c. </s>
2169 
2170 <s>ex quibus deinde <lb/>ponunt eccentricos, &amp; augem, ad &longs;aluandas tum apparentias, tum ob&longs;erua&shy;<lb/>tiones; &amp; hac ratione a&longs;trologica &longs;cientia paulatim reperta e&longs;t, ac in dies <lb/>reperitur.</s></p><p type="main">
2171 
2172 <s><arrow.to.target n="marg9"/></s></p><p type="margin">
2173 
2174 <s><margin.target id="marg9"/>9</s></p><p type="main">
2175 
2176 <s>Ex cap. 
2177 
2178 3. &longs;ecti 2. lib. 
2179 
2180 1. <emph type="italics"/>(Vt an ne diameter incomm.)<emph.end type="italics"/> loquitur de a&longs;ymme&shy;<lb/>tria diametri, &amp; co&longs;t&aelig; eiu&longs;dem quadrati, de qua fus&egrave; egimus &longs;uperius in <lb/>cap. 
2181 
2182 23. &longs;ecti 1. huius libri; qu&aelig; &longs;i repetantur, optim&egrave; hunc <expan abbr="loc&utilde;">locum</expan> declarant.</s></p><p type="main">
2183 
2184 <s><arrow.to.target n="marg10"/></s></p><p type="margin">
2185 
2186 <s><margin.target id="marg10"/>10</s></p><p type="main">
2187 
2188 <s>Ex cap. 
2189 
2190 1. &longs;ecti 3. lib. 
2191 
2192 1. <emph type="italics"/>(Sit A, duo recti, in quo B, triangulus, in quo C, <lb/>&aelig;quicrus, ip&longs;i <expan abbr="itaq;">itaque</expan> C, ine&longs;t A. per B; ip&longs;i vero B, non amplius per aliud, per &longs;e <lb/>namque triangulus habet duos rectos)<emph.end type="italics"/> nullum aliud exemplum tam frequenter <lb/>v&longs;urpat Philo&longs;ophus, quam i&longs;tud ex Mathematicis de&longs;umptum de triangu&shy;<lb/>lo, &longs;cilicet, omnis triangulus habet tres angulos &aelig;quales duobus rectis an&shy;<lb/>gulis, cuius Demon&longs;tratio e&longs;t in 32. primi Elem. 
2193 
2194 quod, vt prob&egrave; intelliga&shy;<lb/>tur, explicandum e&longs;t penes quid attendenda &longs;it &aelig;qualitas inter angulum, &amp; <lb/>angulum, quod facile a&longs;&longs;equemur, &longs;i meminerimus angulum e&longs;&longs;e in clinatio&shy;<lb/>nem illam, quam du&aelig; line&aelig; non in directum po&longs;it&aelig; faciunt: &longs;iue etiam (vt <lb/>melius percipiamus) angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="ill&utilde;">illum</expan>, quem <lb/>du&aelig; line&aelig; non in directum con&longs;titut&aelig; faciunt, vt duarum linearum A B, A C, <lb/><figure place="text" xlink:href="figures-la/009.01.039.1.tif"/><lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>e&longs;t ratio anguli. </s>
2195 
2196 <s>&longs;olum igitur duo anguli erunt &aelig;qua&shy;<lb/>les, <expan abbr="qu&atilde;do">quando</expan> vnius acumen &aelig;quale erit acumini alterius; <lb/>etiam &longs;i line&aelig; con&longs;tituentes vnum angulum &longs;int lon&shy;<lb/>giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb pagenum="40"/><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, &amp; mucronem, quem faciunt: vnde etiam&longs;i <lb/>du&aelig; line&aelig; pr&aelig;dict&aelig; A B, A C, product&aelig;, &longs;iue etiam decurtat&aelig; fuerint, dum&shy;<lb/>modo &longs;itus, &longs;iue po&longs;itio ip&longs;arum, quam ad inuicem habent, non varietur, <lb/>erit &longs;emper eadem quantitas anguli A. <!-- KEEP S--></s>
2197 
2198 <s>Aduertendum pr&aelig;terea rationem <lb/>anguli non po&longs;&longs;e &longs;aluari in &longs;olo puncto A, in quo line&aelig; concurrunt, &longs;ed ne&shy;<lb/>ce&longs;&longs;ariam e&longs;&longs;e aliquam quantitatem, quamuis exiguam, linearum A B, A C. <lb/><!-- KEEP S--></s>
2199 
2200 <s>Notandum etiam, quod in nominatione angulorum, qu&aelig; fit per tres lite&shy;<lb/>ras, &longs;emper literam illam e&longs;&longs;e medio loco proferendam, qu&aelig; ad acumen ip&shy;<lb/>&longs;um po&longs;ita e&longs;t, vt in &longs;uperiori, litera A, debet &longs;emper media proferri, dicen&shy;<lb/>do angulum B A C, &longs;iue C A B, <expan abbr="n&utilde;quam">nunquam</expan> tamen licet dicere angulum A C B, <lb/>vel C B A. <!-- KEEP S--></s>
2201 
2202 <s>Porr&ograve; quemadmodum vnus angulus vni angulo &aelig;qualis e&longs;t, ita <lb/><expan abbr="aliqu&atilde;do">aliquando</expan> duo anguli &longs;unt vni angulo &aelig;quales, vt patet, &longs;i vnus angulus, v.g. <lb/><!-- REMOVE S-->angulus B A C, diuidatur in duos angulos &agrave; linea A D. tunc enim duo angu&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.040.1.tif"/><lb/>li partiales B A D, D A C, erunt &aelig;quales totali angulo <lb/>B A C, cum partes omnes &longs;imul &longs;umpt&aelig; &longs;int &longs;uo toti &aelig;qua&shy;<lb/>les. </s>
2203 
2204 
2205 
2206 <s>pariter tres anguli po&longs;&longs;unt &aelig;quari &amp; vni, &amp; duobus <lb/>alijs angulis, quando nimirum a cumina, &longs;iue mucrones il&shy;<lb/>li &longs;imul ad vnum punctum con&longs;tituti <expan abbr="ad&aelig;quar&etilde;tur">ad&aelig;quarentur</expan> mucro&shy;<lb/>niilli, quem con&longs;tituerent alij duo anguli, quibus illi tres <lb/>&longs;unt pares, v.g. <!-- REMOVE S-->&longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti, <lb/><figure place="text" xlink:href="figures-la/009.01.040.2.tif"/><lb/>quos linea perpendicularis D E, facit cum li&shy;<lb/>nea F G; &longs;it <expan abbr="inqu&atilde;">inquam</expan> anguli recti D E F, D E G, <lb/>tunc tres anguli illius <expan abbr="tri&atilde;guli">trianguli</expan> <expan abbr="dic&etilde;tur">dicentur</expan> &aelig;qua&shy;<lb/>les duobus hi&longs;ce rectis, &longs;i tres illi mucrones <lb/>trianguli fimul &longs;umpti, &amp; vniti ad punctum <lb/>E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum <lb/><figure place="text" xlink:href="figures-la/009.01.040.3.tif"/><lb/>rectorum coeunt, congruent omnino duobus <lb/>pr&aelig;dictis angulis rectis, &longs;iue duobus illis mu&shy;<lb/>cronibus angulorum rectorum, &longs;iue con&longs;ti&shy;<lb/>tuent lineam rectam F E G, &longs;icuti faciunt <lb/>etiam duo illi anguli recti; &longs;iue etiam dica&shy;<lb/>mus, occupabunt idem &longs;patium omnin&ograve;, &amp; <lb/>pr&aelig;cis&egrave;, quod occupant duo recti: v.g. <!-- REMOVE S-->&longs;i mucro B, ibi poneretur, faceret <lb/>angulum F E H, &amp; &longs;i ibi iuxta ip&longs;um apponeretur mucro A, faceret angulum <lb/>H E I. quem &longs;i deinceps &longs;ub&longs;equetur reliquus angulus C, con&longs;titueret <expan abbr="reli-qu&utilde;">reli&shy;<lb/>quum</expan> angulum I E G. iam, vt vides, illi tres anguli ad E, tran&longs;lati, &longs;unt &aelig;qua&shy;<lb/>les duobus rectis ad E, pariter con&longs;titutis, cum illi tres fiant partes duorum <lb/>rector&uacute;, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G, <lb/>con&longs;tituant. </s>
2207 
2208 
2209 
2210 
2211 
2212 <s>habet igitur omne triangulum &longs;iue &ecedil;quilaterum, &longs;iue &longs;calenum, <lb/>&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian&shy;<lb/>guli &longs;int &aelig;quales duobus rectis angulis. </s>
2213 
2214 <s>Quam demon&longs;trationem primi om&shy;<lb/>nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli&shy;<lb/>des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s>
2215 
2216 <s>Quod &longs;i <lb/>quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam (cum &aelig;qua&shy;<lb/>litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe qu&aelig; in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, &amp; cuius <pb pagenum="41"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>vitare ob &longs;ui imperfectionem non licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave; <lb/>&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reperire differentiam) &longs;umat <lb/>inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po&shy;<lb/>ce&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/>qu&aelig; &longs;cilicet faciat, cum illa duos angulos rectos. </s>
2217 
2218 <s>po&longs;tea ab&longs;cindat tres an&shy;<lb/>gulos trianguli materialis, <expan abbr="eos&qacute;">eosque</expan>; ita &longs;imul componat, vt mucrones illorum <lb/>&longs;int vniti, &amp; contigui ad punctum line&aelig; perpendicularis cum altera, vti e&longs;t <lb/>in &longs;uperiori figura punctnm E; &amp; illic&ograve; apparebit tres illos angulos mate&shy;<lb/>riales obtegere ad&aelig;quat&egrave; totum illud &longs;patium duorum rectorum, quos per&shy;<lb/>pendicularis con&longs;tituit. </s>
2219 
2220 <s>Hoc autem experiri poteris in diuer&longs;is admodum <lb/>triangulis Scalenis, Rectangulis, I&longs;o&longs;celibus, Aequilateris, &amp;c. </s>
2221 
2222 <s>non &longs;ine de&shy;<lb/>lectatione, atque hic e&longs;t &longs;en&longs;us illorum verborum, omnis triangulus habet <lb/>tres &ecedil;quales duobus rectis. </s>
2223 
2224 <s>Ab&longs;tineo &agrave; demon&longs;trationibus geometricis, quo&shy;<lb/>niam ij, qui Mathematicis &longs;unt imbuti, no&longs;tra hac opera parum indigent. <lb/></s>
2225 
2226 <s>&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. <!-- KEEP S--></s>
2227 
2228 <s>Ex hac igitur declaratione <lb/>licet cogno&longs;cere nonnullos ageometretos locum hunc, &amp; &longs;imiles &longs;ub&longs;equen&shy;<lb/>tes non &longs;atis intelligere, dicentes, nihil aliud verba illa Ari&longs;t. 
2229 
2230 velle &longs;ignifi&shy;<lb/>care, qu&agrave;m omnem triangulum habere tres angulos, quod inquiunt, noti&longs;&shy;<lb/>&longs;imum e&longs;t. </s>
2231 
2232 <s>Sed &longs;i incidant in &longs;equentia; &aelig;quales duobus rectis, tunc, cum <lb/>h&aelig;c non intelligant, ab&longs;tinent etiam &agrave; priorum declaratione, quibus pr&aelig;&shy;<lb/>mi&longs;&longs;is facile e&longs;t Ari&longs;t. 
2233 
2234 textum percipere. </s>
2235 
2236 <s>&longs;it A, duo recti, ide&longs;t, duo anguli <lb/>recti &longs;int pa&longs;&longs;io demon&longs;tranda, in quo B, triangulus, in quo C, &aelig;quicrus. </s>
2237 
2238 <s>ip&longs;i <lb/>itaque C, ide&longs;t triangulo &aelig;quicru&longs;i, ine&longs;t A, &longs;cilicet duo recti, hoc e&longs;t, ine&longs;t <lb/>&aelig;quicru&longs;i h&aelig;c, pa&longs;&longs;io habere tres angulos &aelig;quales duobus rectis per B, ide&longs;t <lb/>per <expan abbr="triangul&utilde;">triangulum</expan> vniuer&longs;ale, quia h&aelig;c proprietas e&longs;t trianguli propria, &amp; <expan abbr="c&otilde;pe-tit">compe&shy;<lb/>tit</expan> &aelig;quicru&longs;i, non vt &aelig;quicrus e&longs;t, &longs;ed, vt triangulum e&longs;t; quare B, non crit <lb/>medium ip&longs;ius A, quia pr&aelig;dicta pa&longs;&longs;io. </s>
2239 
2240 <s>A, non competit triangulo B, per <lb/>aliud, &longs;ed per &longs;e, de eo enim primo, &amp; per &longs;e demon&longs;tratur in 32. primi Elem. <lb/>optim&egrave; Aegydius, &amp; Niphus in hunc locum.</s></p><p type="main">
2241 
2242 <s><arrow.to.target n="marg11"/></s></p><p type="margin">
2243 
2244 <s><margin.target id="marg11"/>11</s></p><p type="main">
2245 
2246 <s>Ex eodem cap. <emph type="italics"/>(Non oportet autem exi&longs;timare penes id, quod exponimus, ali&shy;<lb/>quid accidere ab&longs;urdum, nihil enim vtimur eo, quod e&longs;t hoc aliquid e&longs;&longs;e. </s>
2247 
2248 <s>&longs;ed &longs;icut <lb/>Geometra pedalem, &amp; rectam hanc, &amp; &longs;ine latitudine dicit, qu&aelig; non &longs;unt. </s>
2249 
2250 <s>verum <lb/>non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t. 
2251 
2252 in exemplis affert <lb/>pro rebus characteres, A, B, C, po&longs;&longs;et qui&longs;piam &longs;u&longs;picari aliquod propterea <lb/>ab&longs;urdum accidere: cui &longs;u&longs;picioni Ari&longs;t. 
2253 
2254 re&longs;pondet, dicens, nihil inde ab&longs;ur&shy;<lb/>di accidere po&longs;&longs;e, quoniam ip&longs;e vtitur hi&longs;ce literis, <expan abbr="n&otilde;">non</expan> quatenus liter&aelig; &longs;unt, <lb/>&longs;ed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum <lb/>etiam Geometr&aelig; faciunt, qui lineam, qu&aelig; pedalis non e&longs;t, pedalem, &amp; qu&aelig; <lb/>non e&longs;t recta, rectam; &amp; qu&aelig; lata e&longs;t, non latam, &longs;upponunt, &amp; tamen nihil <lb/>inde ab&longs;urdi contingit. </s>
2255 
2256 <s>Ex quibus intelligimus per lineas illas &longs;en&longs;ibiles, &amp; <lb/>phy&longs;icas, quas Geometr&aelig; in &longs;uis figuris ducunt, intelligendas e&longs;&longs;e lineas ve&shy;<lb/>r&egrave; Mathematicas omni latitudine carentes; vtitur enim inquit Ari&longs;t. <!-- REMOVE S-->Geo&shy;<lb/>metra lineis phy&longs;icis, non tanquam phy&longs;icis, nec de eis tanquam de phy&longs;icis <lb/>lineis ratiocinatur, &longs;ed ijs vtitur tanquam ver&egrave; mathematicis. </s>
2257 
2258 
2259 
2260 <s>idem dicen&shy;<lb/>dum e&longs;t de &longs;uperficiebus, necnon de corporibus, qu&aelig; ijdem Goometr&aelig; de&shy;<lb/>&longs;cribunt, vt per ea, de ver&egrave; mathematicis di&longs;currant.</s></p></chap><pb pagenum="42"/>
2261 <chap><p type="head">
2262 <s><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s></p><p type="main">
2263 
2264 <s><arrow.to.target n="marg12"/></s></p><p type="margin">
2265 
2266 <s><margin.target id="marg12"/>12</s></p><p type="main">
2267 
2268 <s>Ex cap. 
2269 
2270 21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;i<lb/>&longs;e ip&longs;os talia accip entes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exi&longs;tentibus
<lb/>coalternis)<emph.end type="italics"/> Vult Ari&longs;t. 
2271 
2272 exemplo mathematico explicare, quid &longs;it pe&shy;<lb/>titio principij. </s>
2273 
2274 <s>vbi per coalternas intelligit parallelas lineas, vox <lb/>enim gr&aelig;ca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, &amp; coalternus. </s>
2275 
2276 <s>quoad <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens. <lb/><figure place="text" xlink:href="figures-la/009.01.042.1.tif"/><lb/>probat Euclides in 28. primi Elem. 
2277 
2278 quod &longs;i <lb/>linea recta qu&aelig;dam, vti E F, cadens &longs;uper <lb/>duas rectas, vti &longs;unt A B, C D, fe cerit angu&shy;<lb/>los alternos &ecedil;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H, <lb/>G H D, ij enim dicuntur alterni; &longs;iue alios <lb/>dnos, nimirum B G H, G H C, hi enim &longs;unt <lb/><expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li&shy;<lb/>neas A B, C D, e&longs;&longs;e inuicem parallelas. </s>
2279 
2280 <s>Iam &longs;i quis vellet probare, &longs;e duas <lb/>parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet fa ciunt pr&aelig;dictos angulos al&shy;<lb/>ternos &aelig;quales; &amp; probaret facere angulos alternos &aelig;quales, quia &longs;unt pa&shy;<lb/>rallel&aelig;, hic peteret principium, ide&longs;t, illud, quod principio <expan abbr="proband&utilde;">probandum</expan> erat, <lb/>afferret pro ratione, &amp; cau&longs;a, quod dicitur peti principium, quia tunc pe&shy;<lb/>timus, vt concedatur nobis, id, quod principio, &amp; primo omnium demon&shy;<lb/>&longs;trare propo&longs;ueramus. </s>
2281 
2282 <s>aduerte, quod characteres, qui &longs;unt in &longs;equentibus <lb/>verbis huius loci, non appellant characteres figur&aelig; appo&longs;it&aelig;; in quo quidam <lb/>decepti, nullo pacto poterant locum hunc intelligere.</s></p><p type="main">
2283 
2284 <s><arrow.to.target n="marg13"/></s></p><p type="margin">
2285 
2286 <s><margin.target id="marg13"/>13</s></p><p type="main">
2287 
2288 <s>Ex cap. 
2289 
2290 22. lib. 
2291 
2292 2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy;<lb/>men&longs;. argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. 
2293 
2294 1. <lb/>fus&egrave; explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea&shy;<lb/>dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com&shy;<lb/>munis, qu&aelig; debet vtramq, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, uimirum medietates medietatum in in&longs;initum, <lb/>e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, &amp; propterea <lb/>non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="qu&atilde;titatibus">quantitatibus</expan>, qu&aelig; putaban&shy;<lb/>tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t. 
2295 
2296 non cau&longs;am pro cau&longs;a.</s></p><p type="main">
2297 
2298 <s><arrow.to.target n="marg14"/></s></p><p type="margin">
2299 
2300 <s><margin.target id="marg14"/>14</s></p><p type="main">
2301 
2302 <s>Ex eodem cap. <emph type="italics"/>(Quoniam idem <expan abbr="vtiq;">vtique</expan> fal&longs;um per plures petitiones accidere <lb/>nihil forta&longs;&longs;e inconueniens, veluti coalternas coincidere; &amp; &longs;i maior e&longs;t extrin&longs;ecus <lb/>angulus intrin&longs;eco; &amp; &longs;i triangulus habet plures rectos duobus)<emph.end type="italics"/> per plures po&longs;i&shy;<lb/>tiones &longs;ubaudi fal&longs;as. </s>
2303 
2304 <s>per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy;<lb/>rallelas, vt in &longs;uperiori cap. 
2305 
2306 monuimus. </s>
2307 
2308 <s>C&aelig;terum Euclides propo&longs;. </s>
2309 
2310 <s>28. pri&shy;<lb/>mi Elem. 
2311 
2312 o&longs;tendit, quod &longs;i fuerint du&aelig; parallel&aelig; veluti in pr&aelig;cedenti figura, <lb/>A B, C D, &longs;uper quas alia recta E F, incidat, nece&longs;&longs;ario faciet angulum ex&shy;<lb/>trin&longs;ecum E G B, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&aelig;qualem interno, &amp; oppo&longs;ito, &amp; ad ea&longs;dem partes, <lb/>angulo videlicet G H D. &longs;i ergo inquit Ari&longs;t &longs;upponamus i&longs;tud fal&longs;um, an&shy;<lb/>gulum &longs;cilicet E G B, externum e&longs;&longs;e maiorem angulo interno G H D, &longs;equi&shy;<lb/>tur etiam fal&longs;um, videlicet lineas <expan abbr="&aelig;quidi&longs;t&atilde;tes">&aelig;quidi&longs;tantes</expan> A B, C D, concurrere. </s>
2313 
2314 
2315 
2316 
2317 
2318 <s>&amp; pro&shy;<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb pagenum="43"/>G H D, appo&longs;ito <expan abbr="vtiq;">vtique</expan> communi angulo B G H, erant primum, duo anguli <lb/>E G B, B G H, maiores, quam &longs;int duo B G H, G H D, quia &longs;i in&aelig;qualibus <lb/>&aelig;qualia addantur, tota erunt in&aelig;qualia, vt prius per 4, axioma: hoc loco <lb/>communis angulus additur &longs;emel maiori angulo, &amp; &longs;emel minori; &amp; ideo <lb/>totum illud, in quo e&longs;t maior angulus, adhuc maius e&longs;t altero toto, in quo <lb/>minor angulus continetur. </s>
2319 
2320 <s>at illi duo E G B, B G H, per 13. primi, &longs;unt <lb/>&aelig;quales duobus rectis angulis, ergo duo <expan abbr="quoq;">quoque</expan> recti erunt maiores duobus <lb/>internis B G H, D H G, &longs;iue hi duo interni erunt minores duobus rectis. <lb/></s>
2321 
2322 <s>At quando hi duo interni &longs;unt minores duobus rectis, tunc line&aelig; A B, C D, <lb/>&longs;unt concurrentes, &longs;i protrahantur ad partes pr&aelig;dictorum <expan abbr="angulor&utilde;">angulorum</expan>. </s>
2323 
2324 <s>quod <lb/>P. <!-- REMOVE S-->Clauius luculenti, &amp; hactenus de&longs;iderata demon&longs;tratione ad 28. primi <lb/>demon&longs;trauit. </s>
2325 
2326 
2327 
2328 <s><expan abbr="Atq;">Atque</expan> hoc pacto ex prima fal&longs;a &longs;uppo&longs;itione, nimirum angu&shy;<lb/>lum illum externum e&longs;&longs;e maiorem interno, &amp; oppo&longs;ito; &longs;equitur fal&longs;um, ni&shy;<lb/>mirum lineas parallelas concurrere.</s></p><p type="main">
2329 
2330 <s>Pr&aelig;terea &longs;i &longs;upponamus aliam fal&longs;itatem, &longs;cilicet triangulum habere tres <lb/>angulos maiores duobus rectis, &longs;equetur eadem iterum fal&longs;itas, &longs;cilicet pa&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.043.1.tif"/><lb/>rallelas coincidere, &amp; probatur &longs;ic; &longs;int enim <lb/><expan abbr="tri&atilde;guli">trianguli</expan> A B C, tres anguli maiores, quam duo <lb/>recti anguli, &amp; per punctum C, ducta &longs;it recta <lb/>C D, parallela lateri B A. quia ergo angulus <lb/>A, &aelig;qualis e&longs;t angulo &longs;ibi alterno A C D, per <lb/>29. primi, &amp; quia totalis angulus B C D, &aelig;qua&shy;<lb/>lis e&longs;t duobus angulis B C A, A C D, quos tanquam &longs;uas partes ad&aelig;quatas <lb/>continet, quorum alter, &longs;cilicet A C D, e&longs;t &aelig;qualis angulo A. erit idem to&shy;<lb/>talis angulus B C D, &aelig;qualis duobus angulis A, &amp; A C B, trianguli propo&longs;i&shy;<lb/>ti. </s>
2331 
2332 <s>ergo totus i&longs;te angulus B C D, &longs;imul cum reliquo <expan abbr="tri&atilde;guli">trianguli</expan> angulo B. con&shy;<lb/>flabit compo&longs;itionem ex tribus angulis trianguli dati: &amp; con&longs;equenter ta&shy;<lb/>lis compo&longs;itio trium angulorum erit maior, quam &longs;int duo anguli recti. </s>
2333 
2334 <s>ex <lb/>quo &longs;equitur duas rectas B A, C D, &longs;uper quas cadit linea B C, faciens duos <lb/>angulos internos, &amp; ad ea&longs;dem partes, &longs;cilicet A B D, maiores duobus re&shy;<lb/>ctis non e&longs;&longs;e parallelas, &longs;ed concurrentes (vt patet ex nuper citata demon&shy;<lb/>&longs;tratione P. Clauij) quod fal&longs;um e&longs;t. </s>
2335 
2336 <s>&amp; &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio&shy;<lb/>ne. </s>
2337 
2338 <s>ex quibus textus Ari&longs;t. 
2339 
2340 videtur &longs;atis clarus.</s></p><p type="main">
2341 
2342 <s><arrow.to.target n="marg15"/></s></p><p type="margin">
2343 
2344 <s><margin.target id="marg15"/>15</s></p><p type="main">
2345 
2346 <s>Ex cap. 
2347 
2348 26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C, <lb/>&longs;en&longs;ibuis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis <lb/>triangulus habet duos rectos: quare &longs;imul no&longs;cet, &amp; ignorabit idem. </s>
2349 
2350 <s>no&longs;ce enim <lb/>omnem triangulum, quod duobus rectis, non &longs;implex e&longs;t: &longs;ed hoc quidem eo, quod <lb/>vniuer&longs;alem habet &longs;cientiam: illud autem eo, quod &longs;ingularem. </s>
2351 
2352 <s>&longs;ic igitur, vt vni&shy;<lb/>uer&longs;ale nouit C, quod duo recti; vt autem &longs;ingulare non nouit, quare non habebit <lb/>contrarias)<emph.end type="italics"/> vide, qu&aelig; diximus lib. 
2353 
2354 1. &longs;ecto 3. cap. 
2355 
2356 1. ex quibus quidquid Ma&shy;<lb/>thematicum e&longs;t hic, clarum redditur. </s>
2357 
2358 <s>reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy;<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s></p><p type="main">
2359 
2360 <s>In cap. 
2361 
2362 31. de Abductione.<!-- KEEP S--></s></p><p type="main">
2363 
2364 <s><arrow.to.target n="marg16"/></s></p><p type="margin">
2365 
2366 <s><margin.target id="marg16"/>16</s></p><p type="main">
2367 
2368 <s>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap. 
2369 
2370 agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t. 
2371 
2372 quemadmodum multa <lb/>alia &agrave; Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s>
2373 
2374 <s>e&longs;&longs;e <pb pagenum="44"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib. 
2375 
2376 3. <lb/>in comm. <!-- REMOVE S-->Elem. 
2377 
2378 Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s>
2379 
2380 
2381 
2382 <s>121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy;<lb/>remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy;<lb/>cuum e&longs;t. </s>
2383 
2384 <s>Exempli cau&longs;a, cum cubi duplicatio propo&longs;ita e&longs;&longs;et ad inue&longs;ti&shy;<lb/>gandam qu&aelig;&longs;tionem in aliud tran&longs;tulere, quod illud propo&longs;itum con&longs;equi&shy;<lb/>tur, ad duarum nempe mediarum linearum inuentionem tran&longs;lata e&longs;t qu&aelig;&shy;<lb/>&longs;tio, &amp; &longs;ic qu&aelig;rebant deinceps, quonam modo datis duabus rectis lineis, <lb/>du&aelig; medi&aelig; proportionales reperirentur. </s>
2385 
2386 <s>Primum autem dicunt Hippocra&shy;<lb/>tem Chium pr&ecedil;dictorum titulorum, Abductionem feci&longs;&longs;e, qui &amp; lunul&aelig; qua&shy;<lb/>dratum fecit &aelig;quale, &amp; alia multa in Geometria inuenit. </s>
2387 
2388 <s>h&aelig;c Proclus. <!-- KEEP S--></s>
2389 
2390 <s>vbi <lb/>non di&longs;&longs;imulandum nos re&longs;titui&longs;&longs;e verbum, Abductionem, cuius loco inter&shy;<lb/>pres Procli vtitur inductionis voce, &longs;equuti &amp; rationem, &amp; gr&aelig;cum textum, <lb/>qui no&longs;tram hanc expo&longs;itionem euidenter po&longs;tulat, <foreign lang="greek">apagwgh\</foreign> enim valet &amp; <lb/>inductionem, &amp; abductionem, &longs;ed abductio omnino rei propo&longs;it&aelig; quadrat.</s></p><p type="main">
2391 
2392 <s>Notandum pr&aelig;terea Hippoetatem Chium fui&longs;&longs;e auctorem huius Abdu&shy;<lb/>ctionis, <expan abbr="eum&qacute;">eumque</expan>; feci&longs;&longs;e Abductionem &agrave; propo&longs;ito Problemate quadrandi cir&shy;<lb/>culi, vnde manife&longs;t&egrave; apparet, Ari&longs;totelem ex Mathematicis hunc terminum <lb/>mutu&ograve; accepi&longs;&longs;e, quandoquidem ex ij&longs;dem accepit etiam exemplum Abdu&shy;<lb/>ctionis Mathematic&aelig;, im&ograve; etiam exemplum ip&longs;ius authoris Abductionis<lb/>Mathematic&aelig;. </s>
2393 
2394 <s>&longs;yllogi&longs;mus autem Hippocratis, quo o&longs;tendebat circuli qua&shy;<lb/>draturam reducebatur ad has propo&longs;itiones, omnis rectilinea figura qua&shy;<lb/>dratur, &longs;ed circulus reducitur ad figuram rectilineam, ergo circulus qua&shy;<lb/>dratur. </s>
2395 
2396 <s>in probatione minoris facta e&longs;t Abductio, cum enim ip&longs;e vellet re&shy;<lb/>ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam, <lb/>quandam quadratricem, vt e&longs;t apud Pappum <expan abbr="Alexandrin&utilde;">Alexandrinum</expan>, &amp; apud P. <!-- REMOVE S-->Cla&shy;<lb/>uium in fine &longs;exti Elem. 
2397 
2398 &amp; alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio <lb/>circa probationem minoris, in qua adhuc Mathematici verfantur; qu&aelig; pro&shy;<lb/>batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro&shy;<lb/>blema, nimirum circulus quadraretur; vide qu&aelig; &longs;crip&longs;imus in cap. 
2399 
2400 3. Pr&aelig;&shy;<lb/>dicam. <!-- REMOVE S-->de hac re, quia plurimum hunc conferunt. </s>
2401 
2402 
2403 
2404 
2405 
2406 <s>&longs;ed iam ad textus expli&shy;<lb/>cationem veniamus.</s></p><p type="main">
2407 
2408 <s><arrow.to.target n="marg17"/></s></p><p type="margin">
2409 
2410 <s><margin.target id="marg17"/>17</s></p><p type="main">
2411 
2412 <s>Ex eodem cap. <emph type="italics"/>(Veluti &longs;i K, e&longs;&longs;et quadrari, in quo autem E, rectilineum, in <lb/>quo ver&ograve; F, circulus, &longs;i ip&longs;ius E F, vnum &longs;olum e&longs;&longs;et medium, hoc, quod e&longs;t, cum <lb/>lunulis &aelig;qualem fieri circulum rectilineo, e&longs;&longs;e po&longs;&longs;et prop&egrave; ip&longs;um cogno&longs;cere, cum <lb/>vero B C, neque credibilius &longs;it, quam A C, <expan abbr="neq;">neque</expan> pauca media, non dico Abductio&shy;<lb/>nem: <expan abbr="neq;">neque</expan> quando B C, &longs;it immediatum, tale enim &longs;cientia est)<emph.end type="italics"/> Aduerte figuram <lb/>vulgat&aelig; editionis e&longs;&longs;e mendo&longs;am, &amp; propterea re&longs;tituendam e&longs;&longs;e, qualis pri&shy;<lb/>ma &longs;equens ex Simplicio ad tex. <!-- REMOVE S-->11. primi Phy&longs;ic. <!-- REMOVE S-->hoc modo Hippocrates <lb/>Chius conabatur circulum ad quadrum redigere; fit circulus A B G C, qua&shy;<lb/>drandus; con&longs;tituatur <expan abbr="itaq;">itaque</expan> &longs;uper diametro cius B C, quadratum B C D F, <lb/>cuius diameter B D, &longs;ecatur bifariam in G, &agrave; circumferentia circuli dati, <lb/>quod patet ducta &longs;emidiametro H G, perpendiculari ex B C, qu&aelig; &longs;uo extre&shy;<lb/>mo puncto G, &longs;ecat bifariam, &amp; <expan abbr="diametr&utilde;">diametrum</expan> B D, &amp; circumferentiam B G C. <lb/>facto ergo centro G, de&longs;cribatur alter circulus per puncta B C D F, <expan abbr="conne-ctatur&qacute;">conne&shy;<lb/>ctaturque</expan>; recta G C. in triangulo orthogonio B C D, latus B D, &longs;ubtenditur <pb pagenum="45"/><figure place="text" xlink:href="figures-la/009.01.045.1.tif"/><lb/>angulo recto C, ergo quadratum eius ex eorol&shy;<lb/>lario 47. primi, duplum erit quadrati B C, quare <lb/>etiam circulus B C D F, duplus erit circuli A B&shy;<lb/>G C, per 2. duodecimi, &amp; &longs;emicirculus B C D, <lb/>duplus erit &longs;emicirculi B A C: &amp; quadrans B E&shy;<lb/>C G, &aelig;qualis erit &longs;emicirculo B A C: ablato igi&shy;<lb/>tur communi &longs;egmento B E C H, remanet lunu&shy;<lb/>la B A C E, &aelig;qualis triangulo B C G, quod trian&shy;<lb/>gulum &longs;i per vltimam &longs;ecundi quadretur, erit lu&shy;<lb/>nula B A C, con&longs;equenter quadrata. </s>
2413 
2414 
2415 
2416 
2417 
2418 <s><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be&shy;<lb/>n&egrave; procedit Hippocrates. <!-- KEEP S--></s>
2419 
2420 <s>&longs;ed vt reliquum circu&shy;<lb/>li quadret, &longs;ic pergit, ponatur recta L M, dupla <lb/>ip&longs;ius B C, &longs;upra quam &longs;emicirculus de&longs;cribatur <lb/><figure place="text" xlink:href="figures-la/009.01.045.2.tif"/><lb/>L O M, cui in&longs;cribatur hexagoni <lb/>&aelig;quilateri dimidium L Q S M, &amp; &longs;u&shy;<lb/>per tribus hexagoni lateribus, &longs;int <lb/>tres &longs;emicirculi, vt in figura. </s>
2421 
2422 <s>&amp; <expan abbr="quo-ni&atilde;">quo&shy;<lb/>niam</expan> diameter L M, dupla e&longs;t <expan abbr="vniu&longs;-cuiu&longs;q;">vniu&longs;&shy;<lb/>cuiu&longs;que</expan> <expan abbr="diametror&utilde;">diametrorum</expan> B C, L Q, Q S, <lb/>S M, erit &longs;emicirculus L O M, &ecedil;qua&shy;<lb/>lis quatuor &longs;emicirculis pr&aelig;dictis <lb/>per 2. duodecimi, &amp; per 4. &longs;ecundi <lb/>ablatis igitur tribus <expan abbr="&longs;egm&etilde;tis">&longs;egmentis</expan> com&shy;<lb/>munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, &aelig;quale &longs;e&shy;<lb/>micirculo B A C, &amp; tribus lunulis L H Q N, Q R S O, S X M P, ab&longs;cindan&shy;<lb/>tur <expan abbr="itaq;">itaque</expan> detrapezio tria triangula &aelig;qualia tribus lunulis, eo modo, quo &longs;u&shy;<lb/>pra in prima figura factum e&longs;t, &amp; quod relinquetur &aelig;quale erit &longs;emicirculo <lb/>B A C. quod deinde quadretur per vlt. </s>
2423 
2424 <s>&longs;ecundi, &longs;ed aduerte, quod quando <lb/>ait, ab&longs;cindantur de trapezio tria triangula &aelig;qualia lunulis, eo modo, quo <lb/>&longs;upra, committit deceptionem, quia eodem modo, quo &longs;upra minim&egrave; id fa&shy;<lb/>cere po&longs;&longs;umus, quia in &longs;uperiori figura triangula erant con&longs;tituta &longs;uper la&shy;<lb/>tus B C, quadrati B C D F, intra circulum de&longs;cripti, qui circulus facit cum <lb/>B C, maius <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan>, quam faciat &longs;emicirculus L O M, cum lateribus L Q, <lb/>Q S, S M. &amp; propterea &longs;emicirculus i&longs;te non habet eandem proportionem <lb/>ad vnamquamque lunularum &longs;uarum, quam habet &longs;emicirculus &longs;uperior <lb/>B C D, ad lunulam B A C E. <expan abbr="atq;">atque</expan> h&aelig;c e&longs;t fallacia, quam authorem &longs;uum mi&shy;<lb/>nim&egrave; latui&longs;&longs;e putandum, cuius Ari&longs;t. &longs;&aelig;pius mentionem in &longs;equentibus fa&shy;<lb/>ciet : qu&igrave; enim fieri pote&longs;t, vt tam acutus inuentor, adeo manife&longs;tum erro&shy;<lb/>rem non vidi&longs;&longs;et, verum propter adinuenti excellentiam, authori &longs;uo pla&shy;<lb/>cuit paralogy&longs;mus. </s>
2425 
2426 <s>mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig; <lb/>quadratio. </s>
2427 
2428 <s>Ex quibus &longs;atis clara e&longs;&longs;e po&longs;&longs;unt ea, qu&aelig; ad <expan abbr="Mathematic&utilde;">Mathematicum</expan> per&shy;<lb/>tinent, ad locum hunc de Abductione declarandum. </s>
2429 
2430 <s>facta e&longs;t igitur abdu&shy;<lb/>ctio ab Hippocrate in quadratione trium po&longs;teriorum lunularum, in qua&shy;<lb/>rum quadratione diu immoratus, nunquam ni&longs;i cum paralogy&longs;mo quadra&shy;<lb/>re valuit. </s>
2431 
2432 <s>H&aelig;c pluribus, vt &longs;equentibus etiam textibus, in quibus huius te&shy;<lb/>tragoni&longs;mi fit mentio &longs;atisfacere po&longs;&longs;imus. </s>
2433 
2434 <s>Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>Aphrod. <!-- REMOVE S-->in Primum Meteororum de Cometis.<!-- KEEP S--></s>
2435 
2436 </p></chap><chap><p type="head">
2437 
2438 <s><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s></p><p type="main">
2439 
2440 <s><arrow.to.target n="marg18"/></s></p><p type="margin">
2441 
2442 <s><margin.target id="marg18"/>18</s></p><p type="main">
2443 
2444 <s>Textu primo <emph type="italics"/>(Omnis doctrina, &amp; omnis di&longs;ciplina di&longs;cur&longs;iua ex pr&aelig;exi&shy;<lb/>&longs;tenti fit cognitione. </s>
2445 
2446 <s>manife&longs;tum autem hoc &longs;peculantibus in omnibus, <lb/>Mathematic&aelig; <expan abbr="namq;">namque</expan> &longs;cientiarum per hunc modum accedunt)<emph.end type="italics"/> quo mo&shy;<lb/>do Mathematic&aelig; fiant ex pr&aelig;cedenti cognitione, &longs;cilicet Princi&shy;<lb/>piorum per&longs;picu&egrave; quilibet videbit, qui &longs;altem primum <expan abbr="Elem&etilde;torum">Elementorum</expan> Eucli&shy;<lb/>dis, vel &egrave; ianuis in&longs;pexerit; pr&ecedil;cedunt enim primo principiorum tria gene&shy;<lb/>ra, quorum primum continet definitiones &longs;ubiecti Geometri&aelig;, vt definitio&shy;<lb/>nes line&aelig;, &longs;uperficiei, trianguli, &amp;c: Secundum continet Po&longs;tulata. </s>
2447 
2448 <s>Tertium <lb/>Axiomata, &longs;eu communes omnium conceptiones, &amp; &longs;ententias, ex quibus <lb/>tanquam ex vberrimis, &amp; chri&longs;taltinis fontibus Demon&longs;trationes Geome&shy;<lb/>tric&aelig; deriuantur. </s>
2449 
2450 <s>Idem v&igrave;dere licet in operibus aliorum Geometrarum, <lb/>Archimedis, Apollonij, Pappi, &amp; c&aelig;terorum. </s>
2451 
2452 <s>Ali&aelig; &longs;iniliter mathematic&aelig;, <lb/>vt Arithmetica, Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia, non ni&longs;t ex <lb/>pr&aelig;mi&longs;&longs;is, ac manife&longs;ti&longs;simis principijs &longs;uas demon&longs;trationes deducunt. <lb/></s>
2453 
2454 <s>Nulla porr&ograve; alia &longs;cientia tam di&longs;tinct&egrave; &longs;ua pr&aelig;mittit principia, <expan abbr="tam&qacute;">tamque</expan>; per&shy;<lb/>&longs;picua, &longs;icuti Mathematic&aelig;, vt non immerit&ograve; Philo&longs;ophus eas, tamquam <lb/>ver&aelig; &longs;cienti&aelig; <expan abbr="typ&utilde;">typum</expan>, <expan abbr="eum&qacute;">eumque</expan>; omnibus numeris ab&longs;olutum &longs;ibi ob oculos pro&shy;<lb/>po&longs;uerit, ex quo ver&aelig; &longs;cienti&aelig; de&longs;criptionem hi&longs;ce libris complecteretur.</s></p><p type="main">
2455 
2456 <s><arrow.to.target n="marg19"/></s></p><p type="margin">
2457 
2458 <s><margin.target id="marg19"/>19</s></p><p type="main">
2459 
2460 <s>Tex. 2. <emph type="italics"/>(Quod enim omne triangulum habet duobus rectis &aelig;quales, pr&aelig;&longs;ciuit: <lb/>quod autem hoc, quod e&longs;t in &longs;emicirculo triangulum e&longs;t, &longs;imul inducens cognouit)<emph.end type="italics"/><lb/>vide primo, qu&aelig; &longs;upra libro 1. Prior. <!-- REMOVE S-->&longs;ecto 3. cap. 
2461 
2462 1. explicaui de angulis <lb/>trianguli. </s>
2463 
2464 
2465 
2466 <s>deinde &longs;cias, quod quando Ari&longs;t. 
2467 
2468 ait, hoc, quod e&longs;t in &longs;emicir cu&shy;<lb/>lo triangulum, &amp;c. </s>
2469 
2470 <s>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem. 
2471 
2472 Euclidis 31. in qua talis fi&shy;<lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.046.1.tif"/><lb/>micirculo. </s>
2473 
2474 <s>tunc autem dicitur triangulum in <lb/>&longs;emicirculo, quando ba&longs;is ip&longs;ius e&longs;t diameter <lb/>&longs;emicirculi, &amp; reliqua duo latera ita concur&shy;<lb/>runt &longs;imul in angulum B, vt ip&longs;um paricer in <lb/>circumferentia con&longs;tituant, quibus pr&ecedil;mi&longs;sis <lb/>&longs;ic textum explicaueris: quod enim omne <lb/>triangulum habet tres angulos &aelig;quales duo&shy;<lb/>bus rectis angulis pr&aelig;&longs;ciuit vniuer&longs;aliter per <lb/>32. primi; quod autem hoc particulare triangulum A B C, quod e&longs;t in &longs;e&shy;<lb/>micirculo habeat eandem proprietatem, &longs;imul, ac qui&longs;piam animaduertit <lb/>illud e&longs;&longs;e triangulum cogno&longs;cit, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla demon&longs;tratione, &longs;ed &longs;olum virtu&shy;<lb/>te illius maioris propo&longs;itionis; omne triangulum habet tres, &amp;c.</s></p><p type="main">
2475 
2476 <s><arrow.to.target n="marg20"/></s></p><p type="margin">
2477 
2478 <s><margin.target id="marg20"/>20</s></p><p type="main">
2479 
2480 <s>Tex. 5. <emph type="italics"/>(Vera quidem igitur oporter e&longs;&longs;e, quoniam non e&longs;t non ens &longs;cire, vt quod <lb/>diameter &longs;it commen&longs;urabi is)<emph.end type="italics"/> con&longs;ule ea, qu&aelig; &longs;crip&longs;imus ad cap. 
2481 
2482 23. primi <lb/>Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per&shy;<lb/>ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom&shy;<pb pagenum="47"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com&shy;<lb/>men&longs;urabilem pr&aelig;dicto lateri, quod autem fal&longs;um e&longs;t, illud non e&longs;t; igitur <lb/>impo&longs;sibile e&longs;t &longs;cire diametrum e&longs;&longs;e commen&longs;urabile.</s></p><p type="main">
2483 
2484 <s><arrow.to.target n="marg21"/></s></p><p type="margin">
2485 
2486 <s><margin.target id="marg21"/>21</s></p><p type="main">
2487 
2488 <s>Hoc eodem cap. 
2489 
2490 plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy;<lb/>ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo <lb/>&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy;<lb/>templatione primi libri Elem. 
2491 
2492 Euclidis percipi pote&longs;t. </s>
2493 
2494 <s>vt propterea ben&egrave; ij <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main">
2495 
2496 <s><arrow.to.target n="marg22"/></s></p><p type="margin">
2497 
2498 <s><margin.target id="marg22"/>22</s></p><p type="main">
2499 
2500 <s>Eodem tex. <!-- REMOVE S-->5. <emph type="italics"/>(Ponit enim Arithmeticus vnitatem indiui&longs;ibilem e&longs;&longs;e &longs;ecun&shy;<lb/>dum quantum)<emph.end type="italics"/> hoc quamquam non ponatur ab Arithmeticis expre&longs;s&egrave;, pr&aelig;&shy;<lb/>&longs;upponitur tamen ab eis: nu&longs;quam enim Euclides in totis tribus Arithme&shy;<lb/>ticis libris, infra vnitatem de&longs;cendit, vt propterea appareat, ip&longs;am in quan&shy;<lb/>titate di&longs;creta e&longs;&longs;e minimum, &amp; indiui&longs;ibile. </s>
2501 
2502 
2503 
2504 <s>Verum dubitabit forr&egrave; qui&longs;&shy;<lb/>piam hoc modo, &longs;i vnitas minimum, <expan abbr="atq;">atque</expan> indiui&longs;ibile e&longs;t in quanto di&longs;creto, <lb/>qua igitur ratione Arithmetici practici eam diuidunt in dimidium, in trien&shy;<lb/>tem, in quadrantem, &amp; alijs &longs;imiliter modis, vnde numeri illi, qui fractio&shy;<lb/>nes appellantur, exurgunt? </s>
2505 
2506 <s>Re&longs;pondemus, <expan abbr="quotie&longs;eunq;">quotie&longs;eunque</expan> vnitas diuiditur ab <lb/>Arithmeticis, tunc ip&longs;i eam accipiunt tanquam totum quoddam <expan abbr="c&otilde;tinuum">continuum</expan> <lb/>in plures partes diui&longs;ibile: &longs;iue tanquam aggregatum quoddam vnitatum, <lb/>qu&aelig; vnitates &longs;unt partes illius, vt quando dicunt, vnum hor&aelig; quadrantem, <lb/>vel duos hor&aelig; quadrantes, vel tres hor&aelig; quadrantes, accipiunt horam tan&shy;<lb/>quam aggregatum quatuor quadrantum, &amp; propterea numeri illi 1/4. 2/4. 3/4. <lb/>&amp; &longs;imiles fractiones, nihil aliud &longs;unt, quam numeri partium vnius hor&aelig;: ex <lb/>quo patet huiu&longs;modi fractiones omnes reduci ad numeros integros, qui <lb/>enim dicit tres quadrantes 3/4. dicit tres partes alicuius totius, quod intel&shy;<lb/>ligitur diui&longs;um e&longs;&longs;e in 4. &aelig;quales partes, ex quibus ill&aelig; tres tantummodo <lb/>numerat.</s></p><p type="main">
2507 
2508 <s><arrow.to.target n="marg23"/></s></p><p type="margin">
2509 
2510 <s><margin.target id="marg23"/>23</s></p><p type="main">
2511 
2512 <s>Tex. 9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy;<lb/>nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy;<lb/>te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy;<lb/>tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s>
2513 
2514 <s>quorum primus e&longs;t, ea &longs;cilicet, <lb/>per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy;<lb/>iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo, <lb/>i&longs;tud de linea; in de&longs;initione enim trianguli ponitur linea recta, quia linea <lb/>recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli <lb/>naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/>tribus lineis rectis terminata. </s>
2515 
2516 <s>&longs;imiliter in definitione line&aelig;, non in&longs;init&aelig;, <lb/>&longs;ed finit&aelig;, &amp; terminat&aelig; ponitur punctum, quia duo puncta, qu&aelig; &longs;unt extre&shy;<lb/>ma illius, faciunt, vt ea &longs;it line a finita, &amp; definitur &longs;ic, linea finita e&longs;t lon&shy;<lb/>gitudo, caius extrema &longs;unt puncta. </s>
2517 
2518 <s>quamuis autem h&aelig;c definitio apud Eu&shy;<lb/>clidem expre&longs;&longs;a non habeatur, tamen ex definitionibus ip&longs;ius pr&aelig;&longs;ertim &longs;e&shy;<lb/>cunda, tertia, &amp; quarta elici pote&longs;t.</s></p><p type="main">
2519 
2520 <s><arrow.to.target n="marg24"/></s></p><p type="margin">
2521 
2522 <s><margin.target id="marg24"/>24</s></p><p type="main">
2523 
2524 <s>Eodem tex. <!-- REMOVE S-->9. <emph type="italics"/>(Et <expan abbr="quibu&longs;cunq;">quibu&longs;cunque</expan> iuexi&longs;tentium ip&longs;is, ip&longs;&aelig; &longs;unt in oratione, quid<emph.end type="italics"/><pb pagenum="48"/><emph type="italics"/>est declarante, quemadmodum rectum ine&longs;t line&aelig;, &amp; circulare: &amp; impar, &amp; par<lb/>numero, &amp; primum, &amp; compo&longs;itum, &amp; &aelig;quilaterum, &amp; altera parte longius. </s>
2525 
2526 
2527 
2528 <s>&amp; <lb/><expan abbr="o&itilde;bus">oimbus</expan> bis in&longs;unt in oratione, quid e&longs;t <expan abbr="declar&atilde;te">declarante</expan>, ibi quidem linea, hic vero numerus)<emph.end type="italics"/><lb/>quia locus hic ben&egrave; exponitur &agrave; Toleto, &amp; melius etiam &agrave; Conymbr. </s>
2529 
2530 <s>addam <lb/>tantummodo qu&aelig;dam, qu&aelig; ad perfectam eius intelligentiam de&longs;iderantur. <lb/></s>
2531 
2532 <s>Sciendum igitur prim&ograve;, nu&longs;quam ab Euclide definiri rectum, circulare, <lb/>impar, par, primum, compo&longs;itum, &aelig;quilaterum, nec altera parte longius: <lb/><expan abbr="ver&utilde;">verum</expan> ab ip&longs;o in definitionibus primi definiri lineam rectam, non tamen cir&shy;<lb/>cularem expre&longs;s&egrave;. </s>
2533 
2534 <s>in definitionibus deinde &longs;eptimi definiri <expan abbr="numer&utilde;">numerum</expan> parem, <lb/>&amp; imparem, item numerum primum, &amp; compofitum, &amp; &aelig;quilaterum, &amp; al&shy;<lb/>tera parte longiorem. </s>
2535 
2536 <s>ex quibus definitionibus po&longs;&longs;unt erui definitiones re&shy;<lb/>cti, circularis, imparis, &amp; c&aelig;terorum, quorum hic Ari&longs;toteles meminit. <lb/></s>
2537 
2538 <s>C&aelig;terum Euclides definitione 11. &longs;eptimi, &longs;ic definit numerum primum: <lb/>primus numerus e&longs;t, quem vnitas &longs;ola metitur. </s>
2539 
2540 <s>numerus autem, vel vnitas <lb/>metiri dicitur alium numerum, quando &longs;&aelig;pius repetita ip&longs;um omnino ad&shy;<lb/>&aelig;quat, vt ternarius metitur nouenarium, quia ter repetitus ip&longs;um ad vn&shy;<lb/>guem explet. </s>
2541 
2542 <s>illi igitur numeri dicuntur ab Arithmeticis primi, qui &agrave; nullo <lb/>alio, pr&aelig;terquam ab vnitate men&longs;urantur, quales &longs;unt, 2. 3. 5. 7. &amp;c. </s>
2543 
2544 <s>Defi&shy;<lb/>nitione ver&ograve; 13. definit numerum compo&longs;itum &longs;ic; compo&longs;itus numerus e&longs;t, <lb/>quem numerus qui&longs;piam metitur, vt &longs;enarius erit compo&longs;itus, quia ip&longs;um <lb/>binarius metitur, nam ter repetitus, ip&longs;i perfect&egrave; ad&aelig;quatur.</s></p><p type="main">
2545 
2546 <s>Per &aelig;quilaterum, intelligit quadratum, quadratus autem numerus defi&shy;<lb/>nitione 18. &longs;eptimi &longs;ic explicatur: Quadratus numerus e&longs;t, qui &longs;ub duobus <lb/>&aelig;qualibus numeris continetur, ide&longs;t, qui fit ex ductu vnius numeri in &longs;e ip&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.048.1.tif"/><lb/>&longs;um, vt &longs;i ducantur 3. in 3. fient 9. qui continetur &longs;ub duobus <lb/>ternarijs; omnes autem ternarij &longs;unt &aelig;quales. </s>
2547 
2548 <s>is autem nu&shy;<lb/>merus dicetur quadratus, quia, vt apparet in figura, nouem <lb/>ip&longs;ius vnitates po&longs;&longs;unt in plano ita ad inuicem collocari, vt <lb/>referant quadratum; &amp; &longs;icuti quadratum geometricum ha&shy;<lb/>bet latera &aelig;qualia, ita etiam quadratum arithmeticum: &longs;i&shy;<lb/>ue numerus quadratus, habet &longs;ua latera &aelig;qualia, quot enim vnitates &longs;unt <lb/>in vno, tot etiam &longs;unt in reliquis, vt in pr&aelig;&longs;enti &longs;unt tres vnitates in &longs;ingulis <lb/>lateribus. </s>
2549 
2550 <s>pr&ecedil;terea quemadmodum quadratum geometricum re&longs;olni pote&longs;t <lb/>in plura quadrata, ita etiam arithmeticum, vt pr&aelig;&longs;ens, qui re&longs;oluitur in <lb/>quatuor quadrata arithmetica. </s>
2551 
2552 <s><expan abbr="Neq;">Neque</expan> enim pote&longs;t quilibet numerus, vt opi&shy;<lb/>nantur ageometreti, in hunc modum di&longs;poni, &longs;ed &longs;olum ij, qui producuntur <lb/>ex multiplicatione numeri alicuius in &longs;e ip&longs;um.</s></p><p type="main">
2553 
2554 <s>Per altera parte longius, intelligit numerum, qui producitur &agrave; duobus <lb/><figure place="text" xlink:href="figures-la/009.01.048.2.tif"/><lb/>numeris in&aelig;qualibus inuicem multiplicatis, qualis e&longs;t <lb/>duodenarius, qui ex ductu trium in quatuor produci&shy;<lb/>tur, &amp; refert figuram altera parte longiorem, &longs;iue, vt <lb/>ait Boetius longilateram, cuius vnum latus e&longs;t maius <lb/>altero, vt in appo&longs;ita figura videre licet. </s>
2555 
2556 <s>atque h&aelig;c <lb/>&longs;unt, qu&aelig; ex Mathematicis petenda erant, ad huius <lb/>loci intelligentiam.</s></p><p type="main">
2557 
2558 <s><arrow.to.target n="marg25"/></s></p><p type="margin">
2559 
2560 <s><margin.target id="marg25"/>25</s></p><p type="main">
2561 
2562 <s>Tex. 11. <emph type="italics"/>(Per &longs;e autem, &amp; &longs;ecundum quod ip&longs;um, idem, vt per &longs;e line&aelig; inest<emph.end type="italics"/><pb pagenum="49"/><emph type="italics"/>punctum, &amp; rectum; etenim &longs;ecundum quod linea, &amp; triangulo, &longs;ecundum quod <lb/>triangulum duo recti: etenim per &longs;e triangulum duobus rectis &aelig;quale. </s>
2563 
2564 <s>Vniuer&longs;ale <lb/>autem e&longs;t tunc, quando in quolibet, &amp; primo mon&longs;tratur, vt duos rectos habere, <lb/><expan abbr="neq;">neque</expan> figur&aelig; e&longs;t vniuer&longs;ale, quamuis e&longs;t mon&longs;irare de figura, quod duos rectos habet, <lb/>&longs;ed non de qualibet figura, <expan abbr="neq;">neque</expan> vtitur qualibet figura monstrans, quadrangulum <lb/>enim figura a quidem est, non habet autem duobus rectis &aelig;quales. </s>
2565 
2566 <s>Aequicrus ver&ograve; <lb/>babet quidem <expan abbr="quodcunq;">quodcunque</expan> duobus rectis &aelig;quales, &longs;ed non prim&ograve;, &longs;ed triangulum <lb/>prius. </s>
2567 
2568 <s>quod igitur quoduis primum mon&longs;tratur duos rectos habens, aut <expan abbr="quodcunq;">quodcunque</expan> <lb/>aliud, huic primo ine&longs;t vniuer&longs;ale, &amp; demonstratio de hoc vniuer&longs;aliter e&longs;t, de alijs <lb/>ver&ograve; quodammodo, non per &longs;e, <expan abbr="neq;">neque</expan> de &aelig;quicrure e&longs;t vniuer&longs;aliter, &longs;ed in plus)<emph.end type="italics"/> pro <lb/>quorum intelligentia nece&longs;&longs;aria &longs;unt ea, qu&aelig; primo Priorum &longs;ecto 3. cap. 
2569 
2570 1. <lb/>&longs;crip&longs;imus. </s>
2571 
2572 <s>deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy;<lb/>angulum vniuer&longs;alius &aelig;quicrure. </s>
2573 
2574 <s>quando ait (vt duos rectos habere) vult <lb/>dicere, habere duos angulos rectos non actu, &longs;ed potentia; qu&aelig; affectio e&longs;t <lb/>trianguli, quia, vt &longs;uperius diximus, habet tres angulos &aelig;quales duobus <lb/>rectis angulis: qu&aelig; proprietas vniuer&longs;aliter, &amp; prim&ograve; competit triangulo. <lb/></s>
2575 
2576 <s>non autem figur&aelig;, quia figura e&longs;t vniuer&longs;alior. </s>
2577 
2578 <s><expan abbr="neq;">neque</expan> i&longs;o&longs;celi, quia i&longs;o&longs;celes e&longs;t <lb/>re&longs;trictius triangulo. </s>
2579 
2580 <s>omittimus reliqua &longs;ingillatim exponere, tum quia &longs;a&shy;<lb/>tis clara &longs;unt, tum quia ab interpretibus ben&egrave; explicantur.</s></p><p type="main">
2581 
2582 <s><arrow.to.target n="marg26"/></s></p><p type="margin">
2583 
2584 <s><margin.target id="marg26"/>26</s></p><p type="main">
2585 
2586 <s>Tex. 13. <emph type="italics"/>(Si quis igitur mon&longs;trauerit, quod rect&aelig; <expan abbr="n&otilde;">non</expan> coincidunt, videbitur <expan abbr="vtiq;">vtique</expan> <lb/>buius e&longs;&longs;e demonstratio, eo quod in omnibus e&longs;t rectis; non e&longs;t autem: &longs;i quidem <lb/>non quoniam &longs;ic &aelig;quales, fit hoc, &longs;ed &longs;ecundum quod <expan abbr="quomodocunq;">quomodocunque</expan> &aelig;quales)<emph.end type="italics"/> pro&shy;<lb/>ponit tres errores, qui circa demon&longs;trationem de vniuer&longs;ali contingunt, <lb/>quos omnes Geometricis exemplis illu&longs;trat; affert autem primo pro tertio <lb/>errore duo exempla, quorum primum in pr&aelig;mi&longs;&longs;is verbis continetur, <expan abbr="atq;">atque</expan> <lb/>ex 28. primi Elem. 
2587 
2588 de&longs;umitur, quam propterea primo loco exponendam <lb/><figure place="text" xlink:href="figures-la/009.01.049.1.tif"/><lb/>cen&longs;ui. </s>
2589 
2590 <s>Quando igitur du&aelig; rect&aelig; con&longs;titu&shy;<lb/>t&aelig; fuerint, vt A B, C D, in quas alia recta, <lb/>vt G F, incidens, faciat duos angulos in&shy;<lb/>ternos, re&longs;pectu rectarum A B, C D, &amp; ad <lb/>ea&longs;dem partes rect&aelig; E F, vt &longs;unt ex parte <lb/>&longs;ini&longs;tra anguli A G H, C H G; exparte ve&shy;<lb/>r&ograve; dextra B G H, D H G; &longs;i <expan abbr="inqu&atilde;">inquam</expan> linea E F, <lb/>fecerit duos illos angulos ex parte &longs;ini&longs;tra &longs;imul &longs;umptos, &aelig;quales duobus <lb/>rectis angulis, vel duos ex parte dextra pariter &aelig;quales duobus rectis, pro&shy;<lb/>bat Euclides rectas A B, C D, non concurrere, &longs;iue parallelas e&longs;&longs;e. </s>
2591 
2592 <s>Verum, <lb/>quia linea E F, pote&longs;t facere aliquando pr&aelig;dictos angulos non <expan abbr="tant&utilde;">tantum</expan> &aelig;qua&shy;<lb/>les duobus rectis, verum etiam rectos, quo etiam modo <expan abbr="probar&etilde;tur">probarentur</expan> c&aelig;dem <lb/>line&aelig; e&longs;&longs;e parallel&aelig;, vt in &longs;equenti figura, cum &longs;int anguli A G I, C I G, re&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.049.2.tif"/><lb/>cti, probabitur de rectis A B, C D, &aelig;quidi&longs;tan&shy;<lb/>tia. </s>
2593 
2594 <s>Ex his facile textum in hunc modum expo&shy;<lb/>nemus; &longs;i quis igitur mon&longs;trauerit, quod rect&aelig; <lb/>A B, C D, nunquam coincidunt, etiam&longs;i in in&longs;i&shy;<lb/>nitum producantur, &longs;eu quod &longs;unt &aelig;quidi&longs;tantes, <lb/>quando anguli pr&aelig;dicti interni &longs;unt duo recti, <lb/>videbitur <expan abbr="vtiq;">vtique</expan> huius e&longs;&longs;e demon&longs;tratio de vniuer&longs;ali per &longs;e, &amp; de primo &longs;u&shy;<pb pagenum="50"/>biecto, vel &longs;ecundum quod ip&longs;um, e&ograve; quod probatur vniuer&longs;aliter de lineis <lb/>omnibus habentibus pr&aelig;dictos angulos rectos. </s>
2595 
2596 <s>non autem de omni, &longs;ecun&shy;<lb/>dum quod ip&longs;um, &longs;i quidem non competit affectio h&aelig;c, e&longs;&longs;e parallelas, li&shy;<lb/>neis habentibus illos angulos rectos actu; &longs;ed prim&ograve;, &amp; vniuer&longs;aliter, &amp; &longs;e&shy;<lb/>cundum quod ip&longs;um competit lineis habentibus illos angulos &aelig;quales duo&shy;<lb/>bus rectis, <expan abbr="quomodocunq;">quomodocunque</expan> &aelig;quales &longs;int duobus rectis, &longs;iue ambo &longs;int recti, <lb/>&longs;iue vnus acutus, alter obtu&longs;us, &longs;ed tamen ambo &longs;imul &aelig;quentur duobus re&shy;<lb/>ctis, quales &longs;unt line&aelig; prim&aelig; figur&aelig;. </s>
2597 
2598 <s>In tertio igitur errore, vniuer&longs;ale exi&shy;<lb/>&longs;tit quidem, &amp; habet nomen, &longs;ed tamen pr&aelig;termittetur, &longs;eu &longs;trictius &longs;ume&shy;<lb/>tur, quam oportet. </s>
2599 
2600 <s>alij latini, quos quidem viderim, pr&aelig;ter Zabarellana <lb/>perperam omnino ob mathematicarum ignorantiam, exemplum i&longs;tud in&shy;<lb/>terpretantur.</s></p><p type="main">
2601 
2602 <s><arrow.to.target n="marg27"/></s></p><p type="margin">
2603 
2604 <s><margin.target id="marg27"/>27</s></p><p type="main">
2605 
2606 <s>Ibidem <emph type="italics"/>(Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, &longs;ecundum quod I&longs;o&shy;<lb/>&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e)<emph.end type="italics"/> i&longs;tud e&longs;t &longs;ecundum exemplum tertij erroris. </s>
2607 
2608 <s>Por&shy;<lb/>r&ograve; cum tres &longs;int &longs;pecies triangulorum, &aelig;quilaterum, I&longs;o&longs;celes, Scalenum, &longs;i <lb/>accideret, vt ex illis tribus vna tantum &longs;pecies, v. <!-- REMOVE S-->g. <!-- REMOVE S-->I&longs;o&longs;celes in mundo re&shy;<lb/>periretur; <expan abbr="tunc&qacute;">tuncque</expan>; qui&longs;piam de I&longs;o&longs;cele o&longs;tenderet affectionem quampiam, <lb/>putans &longs;e <expan abbr="o&longs;t&etilde;di&longs;&longs;e">o&longs;tendi&longs;&longs;e</expan> pa&longs;&longs;ionem de proprio &longs;ubiecto, &amp; primo, falleretur, quia <lb/>aifectio illa competeret I&longs;o&longs;celi, non vt huic &longs;peciei I&longs;o&longs;celis, &longs;ed quatenus <lb/>e&longs;t triangulum, cui primo, &amp; per &longs;e, &amp; &longs;ecundum quod ip&longs;um conuenit. </s>
2609 
2610 
2611 
2612 
2613 
2614 <s>hoc <lb/>loco di&longs;ce&longs;&longs;imus &agrave; Zabarella, qui putat i&longs;tud e&longs;&longs;e exemplum primi erroris, <lb/>cum verba textus adeo clara &longs;int, vt expo&longs;itionem illius nullo modo admit&shy;<lb/>tant. </s>
2615 
2616 <s>&longs;unt autem h&aelig;c textus verba <emph type="italics"/>(Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o&shy;<lb/>&longs;celes, &longs;ecundum quod I&longs;o&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e)<emph.end type="italics"/> quibus verbis manife&longs;t&egrave; <lb/>apparet Ari&longs;t. 
2617 
2618 accipere pro &longs;ubiecto vniuer&longs;ali non indiuiduum vnum, vt in <lb/>primo errore contingit, &longs;ed &longs;peciem loco generis, &longs;cilicet I&longs;o&longs;celes, quod <lb/>e&longs;t &longs;pecies trianguli pro genere ip&longs;o, nimirum pro Triangulo. </s>
2619 
2620 <s>ait enim, &longs;i <lb/>non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quod I&longs;o&longs;celes: quibus verbis cla&shy;<lb/>r&egrave; &longs;peciem, non indiuiduum, &longs;igni&longs;icat, ex his duobus exemplis manife&longs;tus <lb/>e&longs;t tertius error, qui erat, quando erat <emph type="italics"/>(vt in parte totum)<emph.end type="italics"/> <expan abbr="quod&qacute;">quodque</expan>; illis verbis <lb/>expo&longs;uerat <emph type="italics"/>(vei contingit etiam, vt in parte totum, in quo mon&longs;tratur: ijs emm, <lb/>qu&aelig; &longs;unt in parte inerit quidem demon&longs;tratio, &amp; erit de omni, &longs;ed tamen non erit <lb/>buius primi vniuer&longs;aliter demon&longs;tratio. </s>
2621 
2622 <s>dico auttm huius primi, &longs;ecundum quod <lb/>buius demonstrationem, quando &longs;it primi vniuer&longs;aliter)<emph.end type="italics"/> ide&longs;t, quando vniuer&longs;ale <lb/>&longs;ubiectum exi&longs;tit quidem, &longs;ed tamen non de ip&longs;o &longs;it demon&longs;tratio, &longs;ed de ali&shy;<lb/>qua parte ip&longs;ius, v. <!-- REMOVE S-->g. <!-- REMOVE S-->de &longs;pecie aliqua demon&longs;tratur aliquid, quod deberet <lb/>o&longs;tendi prim&ograve; de ip&longs;o vniuer&longs;ali, cum illi prim&ograve; competat.</s>
2623 
2624 
2625 
2626 </p><p type="main">
2627 
2628 <s><arrow.to.target n="marg28"/></s></p><p type="margin">
2629 
2630 <s><margin.target id="marg28"/>28</s></p><p type="main">
2631 
2632 <s>Ibidem <emph type="italics"/>(Et proportionale, quod alternatim, &longs;ecundum quod numeri, &amp; &longs;ecun&shy;<lb/>dum quod line&aelig;, &amp; &longs;ecundum quod &longs;olida, &amp; &longs;ecundum quod tempora: quemad&shy;<lb/>modum &amp; mon&longs;trabatur aliquando &longs;eor&longs;um, contingens <expan abbr="vtiq;">vtique</expan> de omnibus vnica <lb/>demon&longs;tratione mon&longs;irari; &longs;ed quia non &longs;unt nominatum quidam omnia h&aelig;c vnum, <lb/>numeri, longitudines, tempora &longs;olida, &amp; &longs;pecie differunt &agrave; &longs;einuicem &longs;cor&longs;um <expan abbr="ac-cipieb&atilde;tur">ac&shy;<lb/>cipiebantur</expan>. </s>
2633 
2634 <s>nunc autem vniuer &longs;aliter mon&longs;tratur, <expan abbr="neq;">neque</expan> enim &longs;ecundum quod line&aelig;, <lb/>aut &longs;ecundum quod numeri, inerat; &longs;ed &longs;ecundum quod boc, quod vniuer &longs;ale &longs;up&shy;<lb/>ponunt e&longs;&longs;e)<emph.end type="italics"/> affert exemplum &longs;ecundi erroris, quiaccidit, quando vniuer&longs;a&shy;<lb/>le exi&longs;tit quidem, &longs;ed tamen e&longs;t innominatum, pro cuius explicatione &longs;cien&shy;<pb pagenum="51"/>dum quid &longs;it alterna proportio. </s>
2635 
2636 <s>Alternam igitur proportionem definit Eu&shy;<lb/>clides definitione 12. quinti, &longs;ic, e&longs;t &longs;umptio antecedentis ad <expan abbr="anteced&etilde;tem">antecedentem</expan>, <lb/><figure place="text" xlink:href="figures-la/009.01.051.1.tif"/><lb/>&amp; con&longs;equentis ad con&longs;equentem. </s>
2637 
2638 <s>Explico, exponantur qua&shy;<lb/>tuor quantitates proportionales, v.g. <!-- REMOVE S-->vt 6. ad 3. ita &longs;int 4. ad <lb/>2. &longs;i igitur argumentemur &longs;ic, vt 6. ad 3. ita 4. ad 2. ergo al&shy;<lb/>ternatim erit, vt 6. ad 4. ita 3. ad 2. &longs;iue dixerimus, vt pri&shy;<lb/>mum ad &longs;ecundum, ita tertium ad quartum, igitur alterna&shy;<lb/>tim erit, vt primum ad tertium, ita &longs;ecundum ad quartum: valebit con&longs;e&shy;<lb/>quentia; qu&aelig; quidem probatur deinde propo&longs;itione 16. quinti de magnitu&shy;<lb/>dinibus, hoc e&longs;t in vniuer&longs;um de lineis, &longs;uperficiebus, &amp; &longs;olidis. </s>
2639 
2640 
2641 
2642 <s>quando igi&shy;<lb/>tur Ari&longs;t. 
2643 
2644 ait, mon&longs;tramus proportionale, ide&longs;t, qua&longs;uis quatuor quantita&shy;<lb/>tes proportionales, habere hanc proprietatem, vt &longs;int etiam alternatim <lb/>proportionales, &amp; non mon&longs;tramus vnica demon&longs;tratione de omni quouis <lb/>proportionali, &longs;ed &longs;eparatim de magnitudinibus in 16. quinti, de numeris <lb/>in 13. &longs;eptimi, &amp; &longs;eor&longs;um de temporibus in a&longs;tronomia, vel phy&longs;ica; hoc <lb/>modo non o&longs;tendimus vniuer&longs;aliter de primo &longs;ubiecto, quia talis affectio <lb/>conuenit &longs;ingulis, non vt numeri, aut ma gnitudines, aut tempora &longs;unt, &longs;ed <lb/>&longs;ecundum quandam naturam illis omnibus communem, cui prim&ograve; illa pa&longs;&shy;<lb/>&longs;io debetur; qu&aelig; quidem natura communis nomine caret, &amp; propterea e&longs;t <lb/>cau&longs;a erroris.</s></p><p type="main">
2645 
2646 <s><arrow.to.target n="marg29"/></s></p><p type="margin">
2647 
2648 <s><margin.target id="marg29"/>29</s></p><p type="main">
2649 
2650 <s><emph type="italics"/>Nunc autem vniuer&longs;aliter demon&longs;tratur)<emph.end type="italics"/> nu&longs;quam apud Mathematicos in&shy;<lb/>uenio hanc demon&longs;trationem vniuer&longs;alem de illo communi omnibus pr&aelig;&shy;<lb/>dictis, quare dicendum cum Zabarella, illud, nunc, e&longs;&longs;e intelligendum &longs;ic, <lb/>nunc autem, ide&longs;t, in pr&aelig;&longs;entia autem deberet vniuer&longs;aliter demon&longs;trari, <lb/>quod tamen cum non &longs;iat, contingit nos decipi putantes vniuer&longs;aliter de&shy;<lb/>mon&longs;tra&longs;&longs;e. </s>
2651 
2652 <s>vel dicendum i&longs;tud verificari tantum de lineis, &longs;uperficiebus, &amp; <lb/>&longs;olidis, de quibus &longs;imul in vnica natura communi, qu&aelig; e&longs;t magnitudo, de&shy;<lb/>mon&longs;tratur in 16. quinti vniuer&longs;aliter. </s>
2653 
2654 <s><expan abbr="atq;">atque</expan> hoc modo explicatum e&longs;t exem&shy;<lb/>plum &longs;ecundi erroris, qui verbis illis <emph type="italics"/>(Vel &longs;it quidem, &longs;ed innominatum &longs;it in <lb/>rebus &longs;pecie differentibus)<emph.end type="italics"/> continebatur.</s></p><p type="main">
2655 
2656 <s><arrow.to.target n="marg30"/></s></p><p type="margin">
2657 
2658 <s><margin.target id="marg30"/>30</s></p><p type="main">
2659 
2660 <s>Ibidem <emph type="italics"/>(Propter hoc &longs;i quis mon&longs;trauerit &longs;ingulum triangulum. </s>
2661 
2662 <s>demon&longs;tratio&shy;<lb/>ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="&aelig;quilatei&utilde;">&aelig;quilateium</expan> &longs;eor&longs;um, <lb/>&amp; &longs;calenum, &amp; &aelig;quicrus: nondum nouit triangulum, quod duobus rectis, ni&longs;i &longs;o&shy;<lb/>phi&longs;tico modo, <expan abbr="neq;">neque</expan> vniuer&longs; aliter triangulum, <expan abbr="neq;">neque</expan> &longs;i vllum e&longs;t pr&aelig;ter pr&aelig;dicta <lb/>triangulum alterum. </s>
2663 
2664 <s>non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omnetriangulum, <lb/>ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; &amp; &longs;i nullum e&longs;t, quod <lb/>non nouit)<emph.end type="italics"/> vltimo loco ponit exemplum primi erroris, quem &longs;upra verbis il&shy;<lb/>lis <emph type="italics"/>(Quando vel nibil &longs;it accipere &longs;uperius, pr&aelig;ter &longs;ingulare)<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/>vt ben&egrave; intelligamus, opus e&longs;t ea, legere, qu&aelig; libro primo Priorum &longs;ecto 3. <lb/>cap. 
2665 
2666 1. &longs;crip&longs;imus de proprietate illa trianguli, quod &longs;cilicet habet tres an&shy;<lb/>gulos &aelig;quales duobus rectis angulis, quibus pr&aelig;mi&longs;&longs;is, &longs;ic deinde locum <lb/>hunc interpretaberis; Propter hoc, quod pr&aelig;cedenti textu dictum e&longs;t; no&shy;<lb/>tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten&shy;<lb/>ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian&shy;<lb/>gulo in &longs;ingulari, &longs;cilicet de vno &aelig;quilatero, tantum, &amp; de vno Scaleno, &amp; <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens auteadem demon&longs;trationc dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52"/>&longs;epatatim o&longs;tendit, aut vtens diuerfis demon&longs;trationibus, vna pro &aelig;quila&shy;<lb/>tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>illorum habet tres angules &aelig;quales duobus rectis angulis; i&longs;te nondum no&shy;<lb/>uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>non cogno&longs;cit hanc affectionem illis <expan abbr="c&otilde;petere">competere</expan> propter naturam illam com&shy;<lb/>munem trianguli, cui primo, &amp; per &longs;e competit; &amp; neque vniuer&longs;aliter co&shy;<lb/>gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian&shy;<lb/>gulum, pr&aelig;ter illud &aelig;quilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/>quibus &longs;eparatim <expan abbr="dem&otilde;&longs;trauit">demon&longs;trauit</expan>, &amp; &longs;ecundum numernm, ide&longs;t de vnoquoque, <lb/>quatenus e&longs;t vnum numero. </s>
2667 
2668 <s>non nouit autem &longs;ecundum &longs;peciem, ideft fecun&shy;<lb/>dum naturam, &amp; formam communem illis tribus indiuiduis, qu&aelig; e&longs;t natu&shy;<lb/>ra trianguli. </s>
2669 
2670 <s>hoc autem e&longs;&longs;e exemplum primi erroris manife&longs;t&egrave; conuincitnr, <lb/>tum ex verbis illis, quando nihil &longs;it &longs;uperius, pr&aelig;ter &longs;ingulare, tum ex hu&shy;<lb/>ius textus verbis illis <emph type="italics"/>(Singulum triangulum)<emph.end type="italics"/> &amp; ex illis <emph type="italics"/>(Ni&longs;i &longs;ecundum nume&shy;<lb/>rum)<emph.end type="italics"/> ide&longs;t, ni&longs;i de vno, quod &longs;it vnum numero. </s>
2671 
2672 <s>propterea nos de &longs;in gulari <lb/>triangulo omi&longs;&longs;a Zabarell&aelig; &longs;ententia explicauimus tandem in confirma&shy;<lb/>tionem no&longs;tr&aelig; expo&longs;itionis in h&aelig;c tria errata illud non omittendum, &longs;atius<lb/>e&longs;&longs;e dicere, Ari&longs;t. 
2673 
2674 attuli&longs;&longs;e pro tribus erratis tria exempla ordine retrogra&shy;<lb/>do, qu&agrave;m, quod facit Zabarella, primum e&longs;&longs;e pro tertio, &longs;ecundum pro pri&shy;<lb/>mo, tertium ver&ograve; pro &longs;ecundo; eo enim modo, Ari&longs;t. 
2675 
2676 confu&longs;ionem nulla ra&shy;<lb/>tione, im&ograve; contra omnem rationem imponimus.</s></p><p type="main">
2677 
2678 <s><arrow.to.target n="marg31"/></s></p><p type="margin">
2679 
2680 <s><margin.target id="marg31"/>31</s></p><p type="main">
2681 
2682 <s>Textu 14. continet quidem qu&aelig;dam mathematica, &longs;ed fer&egrave; eadem cum <lb/>&longs;uperioribus, qu&aelig; quia tum ex pr&aelig;dictis facile intelligi po&longs;&longs;unt, tum quia <lb/>ben&egrave; ab expo&longs;itoribus explicantur, ne actum agamus, pr&aelig;termittimus.</s></p><p type="main">
2683 
2684 <s><arrow.to.target n="marg32"/></s></p><p type="margin">
2685 
2686 <s><margin.target id="marg32"/>32</s></p><p type="main">
2687 
2688 <s>Tex. 20. <emph type="italics"/>(Ni&longs;i magnitudines numeri &longs;int)<emph.end type="italics"/> hoc e&longs;t, ni&longs;i magnitudines &longs;int di&shy;<lb/>fcret&aelig;, ita vt cadant &longs;ub numernm, vt &longs;i linea qu&aelig;piam diuidatur in partes <lb/>decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s>
2689 
2690 <s>&amp; tunc <lb/>linca numerus e&longs;t. </s>
2691 
2692 <s>idem de &longs;uperficie, ac &longs;olido intelligendum.</s></p><p type="main">
2693 
2694 <s><arrow.to.target n="marg33"/></s></p><p type="margin">
2695 
2696 <s><margin.target id="marg33"/>33</s></p><p type="main">
2697 
2698 <s>Ibidem <emph type="italics"/>(Propter hoc Geometri&aelig; non licet mon&longs;trare, quod contrariorum vna <lb/>e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus)<emph.end type="italics"/> quo ad verba illa, duo cubi cubus, <lb/>qu&aelig; ad nos pertinent, vult Ari&longs;t. 
2699 
2700 docere, quod non debet Geometra o&longs;ten&shy;<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometric&egrave; o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem. 
2701 
2702 &longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>multiplicauerit, productus numerus erit pariter cubus. </s>
2703 
2704 <s>nonnulli latinorum <lb/>perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/>geometricos, at Euclides definit. </s>
2705 
2706 <s>19. &longs;eptimi, &longs;ic arithmeticum cubum de&shy;<lb/>finit, cubus numerus e&longs;t, qui &longs;ub tribus numeris &aelig;qualibus continetur, qua&shy;<lb/>lis e&longs;t. </s>
2707 
2708 <s>8. qui e&longs;t ad in&longs;tar cubi geometrici, &amp; continetur&longs;ub tribus binarijs <lb/>multiplicatis inuicem, qu&aelig; multiplicatio &longs;ic in&longs;tituitur, exponuntur tres bi&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.052.1.tif"/><lb/>narij, 2, 2, 2, primus ducitur in &longs;ecundum, &amp; producitur. <lb/></s>
2709 
2710 <s>4. qui e&longs;t numerus quadratus huius figur&aelig;, <figure place="text" xlink:href="figures-la/009.01.052.2.tif"/>, deinde <lb/>tertius binarius ducitur in pr&aelig;dictum quadratum 4. &amp; pro&shy;<lb/>ducitur 8. qui dicitur cubus, quia &longs;i intelligantur duo qua&shy;<lb/>ternarij, vnus &longs;upra alterum, vt in pr&aelig;&longs;enti figura refe&shy;<lb/>runt cubicam figuram, cuius tam longitudo, quam latitudo, <pb pagenum="53"/>&amp; altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna&shy;<lb/>rijs inuicem modo pr&aelig;dicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis &longs;it 9. <lb/><figure place="text" xlink:href="figures-la/009.01.053.1.tif"/><lb/>qui e&longs;t quadratus. </s>
2711 
2712 <s>quo deinde ducto in tertium ter&shy;<lb/>narium, producitur 27. qui e&longs;t cubus, &amp; refert &longs;igu&shy;<lb/>ram cubicam hanc. </s>
2713 
2714 <s>Iam ver&ograve; &longs;i cubus 8. multipli&shy;<lb/>cet cubum 27. procreabitur 216. qui pariter cubus <lb/>e&longs;t. </s>
2715 
2716 <s><expan abbr="atq;">atque</expan> hoc &longs;ibi volunt verba illa, &longs;i duo cubi cubus, <lb/>ide&longs;t, &longs;i duo numeri cubi multiplicentur mutu&ograve;, cu&shy;<lb/>bus alter producetur; ex quibus videas, quam in&shy;<lb/>ept&egrave; illi <expan abbr="interpret&etilde;tur">interpretentur</expan> hunc locum, qui dicunt, Ari&shy;<lb/>&longs;totilem velle dicere non pertinere ad Geometram <lb/>probare duos cubos geometricos &longs;ibi additos face&shy;<lb/>re alium cubum, quod erat problema Delphicum de <lb/>duplatione cubi, nondum inuentum; bis enim i&longs;ti peccant, primo in Logi&shy;<lb/>cam, quia &longs;ic non tran&longs;iret Geometra de genere in genus, ip&longs;ius enim e&longs;t <lb/>agere de duplatione cubi; &longs;ecund&ograve; in Mathematicas, cum nondum noue&shy;<lb/>rint arithmeticos cubos; &amp; pr&aelig;terca ignorent duos cubos &longs;ibi additos, non <lb/>facere alium cubum. </s>
2717 
2718 <s>Quod pr&aelig;terea hoc loco intelligendi &longs;int cubi arith&shy;<lb/>metici cert&ograve; certius con&longs;tat, ex &longs;equenti 24. textu, vbi &longs;ic dicitur <emph type="italics"/>(Veluti <lb/>Arithmetica quidem, quid impar, aut par, aut quadrangulum, aut cubus.)<emph.end type="italics"/></s></p><p type="main">
2719 
2720 <s><arrow.to.target n="marg34"/></s></p><p type="margin">
2721 
2722 <s><margin.target id="marg34"/>34</s></p><p type="main">
2723 
2724 <s>Ibidem <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> alij &longs;cienti&aelig; quod alterius, ni&longs;i <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ita &longs;e habent inter &longs;e, <lb/>vt &longs;it alterum &longs;ub altero, vt per&longs;pectiua ad Geometriam, &amp; harmonica ad Arith&shy;<lb/>meticam)<emph.end type="italics"/> excipit ab illa regula (qua prohibetur, quamuis &longs;cientiam in alie&shy;<lb/>nam falcem immittere) &longs;cientias &longs;ubalternatas, qu&aelig; propri&egrave; in Mathemati&shy;<lb/>cis reperiuntur, Per&longs;pectiua enim propri&egrave; &longs;ubalternatur Geometri&aelig;, quia <lb/>vtitur Demon&longs;trationibus linearibus, quas applicat lineis vi&longs;ualibus, &amp; Mu&shy;<lb/>&longs;ica &longs;ubalternatur Arithmetic&aelig;, quia ab ip&longs;a mutuatur <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> nu&shy;<lb/>merorum, quas applicat numeris &longs;onoris. </s>
2725 
2726 <s>v.g. <!-- REMOVE S-->Per&longs;pectiua dicit, ea, qu&aelig; vi&shy;<lb/>dentur eminus videri minora, quam qu&aelig; videntur cominus, quia illa viden&shy;<lb/>tur &longs;ub angulo minori, h&aelig;c ver&ograve; &longs;ub angulo maiori, quod ver&ograve; remotiora <lb/>videantur &longs;ub angulo minori, quam propinquiora c&aelig;teris paribus probat <lb/><figure place="text" xlink:href="figures-la/009.01.053.2.tif"/><lb/>per 21. primi Elem. 
2727 
2728 &longs;it enim ma&shy;<lb/>gnitudo vi&longs;a A B, remotior ab o&shy;<lb/>culo in C, po&longs;ito, &amp; vi&longs;a propin&shy;<lb/>quior ab oculo in D. ductis lineis <lb/>vi&longs;ualibus C A, C B: D A, D B; ab <lb/>oculis C, &amp; D, ad extremitates <lb/>&longs;pectat&aelig; magnitudinis, erit remo&shy;<lb/>tioris vi&longs;ionis angulus C, minor <lb/>angulo D, propinquioris, vt ex pr&aelig;allegata Demon&longs;tratione pater. </s>
2729 
2730 
2731 
2732 <s>Hine <lb/>per&longs;picu&egrave; vides, qua ratione Per&longs;pectiua Geometri&aelig; &longs;ubalternetur, &longs;iue <lb/>quid &longs;it ip&longs;a &longs;ubalternatio, vbi medium e&longs;t Geometricum, conclu&longs;io autem <lb/>optica. </s>
2733 
2734 <s>Exemplum &longs;ubalternationis Mufic&aelig; &longs;it, <expan abbr="con&longs;on&atilde;tia">con&longs;onantia</expan> Diapa&longs;on, quam <lb/>vulg&ograve; octauam appellant in data chorda collocare, hoc e&longs;t, vocem grauio&shy;<lb/>rem facere duplam vocis acutioris &longs;umatur chorda A B, &amp; diuidatur bifa&shy;<lb/>riam, &longs;ine in &aelig;qualia in C; tota igitur chorda A B, ad dimidium A C, haber <pb pagenum="54"/><figure place="text" xlink:href="figures-la/009.01.054.1.tif"/><lb/>proportionem, quam 2. ad 1. <lb/>&longs;iue duplam, ergo etiam &longs;o&shy;<lb/>nus totius chord&aelig; A B, ad <expan abbr="&longs;o-n&utilde;">&longs;o&shy;<lb/>num</expan> chord&aelig; dimidi&aelig; A C, ha&shy;<lb/>bebit eandem rationem, <expan abbr="nimir&utilde;">nimirum</expan> quam 2. ad 1. &longs;iue duplam. </s>
2735 
2736 <s>&longs;ed &longs;onus chor&shy;<lb/>d&aelig; A B, ad &longs;onum chord&aelig; A C, con&longs;onat diapa&longs;on, &longs;eu octauam, ergo in <lb/>data chorda collocata e&longs;t con&longs;onantia diapa&longs;on, quod oportebat. </s>
2737 
2738 <s>vides me&shy;<lb/>dium e&longs;&longs;e arithmeticam, conclu&longs;ionem ver&ograve; harmonicam. </s>
2739 
2740 <s>Aliud exemplum <lb/>Tonus, quod e&longs;t <expan abbr="interuall&utilde;">interuallum</expan> prim&aelig; vocis, Vt, ad &longs;ecundam, R&egrave;, in duo &aelig;qua&shy;<lb/>lia &longs;emitonia diuidi nequit, ratio e&longs;t Arithmetica, quia proportio &longs;uper&shy;<lb/>particularis in duo &aelig;qualia arithmetic&egrave; &longs;ecari nequit; at Tonus con&longs;i&longs;tit in <lb/>ratione &longs;uperparticulari, nemp&egrave; in &longs;e&longs;quioctaua, ergo Tonus bifariam diui&shy;<lb/>di nequit. </s>
2741 
2742 <s>de&longs;umptum e&longs;t ex Boetio.</s></p><p type="main">
2743 
2744 <s><arrow.to.target n="marg35"/></s></p><p type="margin">
2745 
2746 <s><margin.target id="marg35"/>35</s></p><p type="main">
2747 
2748 <s>Tex. 23. <emph type="italics"/>(Est autem &longs;ic mon&longs;trare, quemadmodum Bry&longs;o quadraturam, &longs;ecun&shy;<lb/>dum enim commune mon&longs;trant tales rationes)<emph.end type="italics"/> cum velit e&longs;tendere veram de&shy;<lb/>mon&longs;trationem con&longs;tare debere ex proprijs, non autem ex communibus; <lb/>primum affert exemplum demon&longs;trationis cuiu&longs;dam Bry&longs;onis, qu&aelig; ex com&shy;<lb/>munibus procedat, vt autem ben&egrave; intelligamus, quale&longs;nam &longs;int huin&longs;modi <lb/>demon&longs;trationes, qu&aelig; per communia o&longs;tendunt, legenda prius ea &longs;unt, qu&aelig; <lb/>&longs;crip&longs;imus de quadratura circuli in pr&ecedil;dicamento relationis. </s>
2749 
2750 <s>Bry&longs;o itaque, <lb/>vt tradit Alexander, in hunc modum conabatur quadrare <expan abbr="circul&utilde;">circulum</expan>. </s>
2751 
2752 <s>&longs;it qua&shy;<lb/>drandus circulus A B C D, cui circum&longs;eribatur quadratum E F G H. per <lb/>7 quarti, &amp; alterum quadratum I L M N, eidem in&longs;cribatur per 6. quarti, <lb/>quid autem &longs;it circum&longs;cribere, &amp; in&longs;cribere figuram circulo, ex definitione <lb/><figure place="text" xlink:href="figures-la/009.01.054.2.tif"/><lb/>3. &amp; 4. eiu&longs;dem libri petatur, quamuis <lb/>ex in&longs;pectione figur&aelig; <expan abbr="pr&ecedil;s&etilde;tis">pr&ecedil;sentis</expan> &longs;atis per&shy;<lb/>cipi po&longs;&longs;it; deinde aliud <expan abbr="quadrat&utilde;">quadratum</expan> me&shy;<lb/>dium inter pr&aelig;dicta duo con&longs;tituatur, <lb/><expan abbr="&longs;it&qacute;">&longs;itque</expan>; O P Q R. </s>
2753 
2754 <s>Iam &longs;ic o&longs;tendebat i&longs;tud <lb/>medium quadratum e&longs;&longs;e &aelig;quale circu&shy;<lb/>lo propo&longs;ito. </s>
2755 
2756 <s><expan abbr="Qu&aelig;cunq;">Qu&aelig;cunque</expan> &longs;unt, &longs;imul ma&shy;<lb/>iora eodem, &amp; minora eodem, &longs;unt in&shy;<lb/>uicem &aelig;qualia, &longs;ed circulus, &amp; quadra&shy;<lb/>tum medium, &longs;unt ambo maiora qua&shy;<lb/>drato in&longs;cripto, &amp; ambo minora qua&shy;<lb/>drato circum&longs;cripto, ergo circulus, &amp; <lb/>quadratum medium, &longs;unt &aelig;qualia. </s>
2757 
2758 <s>vte&shy;<lb/>batur, inquit Ari&longs;t pr&ecedil;dicto principio, <lb/>etiam numeris, lineis, temporibus, &amp; <lb/>qualitatibus communi, <expan abbr="neq;">neque</expan> deducto ex natura circuli, aut quadrati, de qui&shy;<lb/>bus erat demon&longs;tratio. </s>
2759 
2760 <s>pr&aelig;terea aduertendum e&longs;t, illud e&longs;&longs;e fal&longs;um, nam &longs;ex, <lb/>&amp; quinque, ambo &longs;unt maiores, quam quatuor, &amp; minores, quam &longs;eptem, <lb/>&amp; tamen non &longs;unt &aelig;quales.</s></p><p type="main">
2761 
2762 <s><arrow.to.target n="marg36"/></s></p><p type="margin">
2763 
2764 <s><margin.target id="marg36"/>36</s></p><p type="main">
2765 
2766 <s>In codem textu <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus, non &longs;ecundum accidens, quando <lb/>&longs;ecundum illud cogno&longs;camus, &longs;ecundum quod ine&longs;t ex principijs illius, &longs;ecundam <lb/>quod illud; vt duobus rectis &aelig;quales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/><pb pagenum="55"/><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, qu&aelig; non <lb/>ex communibus, vt pr&aelig;cedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>affectionem de &longs;ubiecto proprio. </s>
2767 
2768 <s>E&longs;t autem illud exemplum toties decan&shy;<lb/>tatum de triangulo habente tres angulos &aelig;quales duobus rectis angulis; id&shy;<lb/>circo oper&aelig;pretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli&shy;<lb/>dis, qu&aelig; i&longs;tud ex proprijs principijs demon&longs;trat, &amp; quam hoc loco Ari&longs;to&shy;<lb/>teles innuit, hoc enim modo ip&longs;ius Ari&longs;t. 
2769 
2770 mentem prob&egrave; penetrare poteri&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.055.1.tif"/><lb/>mus. </s>
2771 
2772 <s>&longs;it ergo <expan abbr="tri&atilde;gulum">triangulum</expan> A B C. <!-- KEEP S--></s>
2773 
2774 <s>Dico ag&shy;<lb/>gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>e&longs;&longs;e &aelig;quale aggregato ex duobus angu&shy;<lb/>lis rectis (vt autem melius intelligas, qu&aelig; <lb/>&longs;equuntur, lege prius ea, qu&aelig; dicta &longs;unt <lb/>in lib. 
2775 
2776 1. Priorum &longs;ecto 3. cap. 
2777 
2778 1.) produ&shy;<lb/>catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro&shy;<lb/>batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>duobus rectis: &amp; quia pariter in prima parte huins propo&longs;. </s>
2779 
2780 <s>32. probatum <lb/>e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e &aelig;quales externo angulo A C D: &longs;i ter&shy;<lb/>tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>&amp; &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> &aelig;qualia &aelig;qualibus, &amp; propterea tres <lb/>anguli A, B, A C B, &longs;imul &longs;umpti, erunt &aelig;quales duobus A C D, A C B, &longs;imul <lb/>&longs;umptis; &longs;ed his duobus &longs;unt &aelig;quales duo recti, ergo cum qu&aelig; &longs;unt &aelig;qualia <lb/>vni tertio, &longs;int etiam &aelig;qualia inuicem, erit aggregatum trium angulorum <lb/>A, B, A C B, &aelig;quale aggregato duorum rectorum; quod erat demon&longs;tran&shy;<lb/>dum. </s>
2781 
2782 <s>Medium <expan abbr="itaq;">itaque</expan> huius demon&longs;trationis, &longs;i res ad trutinam Logicam ex&shy;<lb/>pendatur, e&longs;t, quod partes aggregati <expan abbr="tri&utilde;">trium</expan> <expan abbr="angulor&utilde;">angulorum</expan> A, B, A C B, &longs;unt &aelig;qua&shy;<lb/>les partibus aggregati <expan abbr="duor&utilde;">duorum</expan>, &amp; ideo <expan abbr="aggregat&utilde;">aggregatum</expan>, aggrega to &aelig;qua&shy;<lb/>le e&longs;t. </s>
2783 
2784 <s>quod medium e&longs;t in genere cau&longs;&aelig; materialis. </s>
2785 
2786 <s>quod ver&ograve; partes illius <lb/>&longs;int &aelig;quales partibus huius, probatur, per dignitatem <expan abbr="ill&atilde;">illam</expan>, qu&aelig; &longs;unt &aelig;qualia <lb/>vni tertio, &longs;unt etiam inter &longs;e. </s>
2787 
2788 <s>partes porr&ograve; aggregati trium angulorum <lb/>erant h&aelig;, anguli A, B, vna; altera ver&ograve; angulus A C B; partes ver&ograve; aggre&shy;<lb/>gati duorum rectorum erant A C B, A C D, quibus partibus, ill&aelig; &longs;unt &aelig;qua&shy;<lb/>les, &amp; ideo totum toti &aelig;quale. </s>
2789 
2790 <s>quod medium e&longs;t omnino intrin&longs;ecum, &amp; ex <lb/>proprijs ip&longs;ius trianguli, &longs;iue ex proprijs angulorum ip&longs;ius, cum &longs;int ip&longs;ius <lb/>partes. </s>
2791 
2792 <s>quod pariter medium ex parte pa&longs;&longs;ionis, qu&aelig; demon&longs;tratur, e&longs;t ex <lb/>proprijs, cum &longs;int partes illius materiales. </s>
2793 
2794 <s>per materiam autem oportet <lb/>hoc loco intelligere materiam intelligibilem, ide&longs;t quantitatem &agrave; qualita&shy;<lb/>tibas ab&longs;tractam, &amp; terminatam, de qua pluribus agemus infra in tractatu <lb/>de natura mathematicarum. </s>
2795 
2796 <s>Hinc videas eos magnopere decipi, qui pu&shy;<lb/>tant, hanc demon&longs;trationem e&longs;&longs;e per extrin&longs;eca, e&ograve; quod ad demon&longs;tran&shy;<lb/>dum producatur linea B C, in D, putantes lineam illam productam C D, <lb/>e&longs;&longs;e demon&longs;trationis medium; line&aelig; <expan abbr="namq;">namque</expan> huiu&longs;modi, qu&aelig; in demon&longs;tra&shy;<lb/>tionibus geometricis con&longs;truuntur, nunquam &longs;unt media propria demon&shy;<lb/>&longs;trationum, &longs;ed tantummodo a&longs;&longs;umuntur ad probandum medium iam ex&shy;<lb/>cogitatum e&longs;&longs;e veram cau&longs;am conclu&longs;ionis. </s>
2797 
2798 <s>Hinc etiam manife&longs;t&egrave; colligas <pb pagenum="56"/>Mathematicas facultates habere demon&longs;trationes perfecti&longs;&longs;imas, quod <lb/>ageometreti negare &longs;olent, &longs;ed audacter aiunt exempla Ari&longs;t. 
2799 
2800 non e&longs;&longs;e vera: <lb/><expan abbr="neq;">neque</expan> requiri veritatem exemplorum; in <expan abbr="quor&utilde;">quorum</expan> <expan abbr="vtroq;">vtroque</expan> peccant, nam dictum <lb/>illud v&longs;urpari &longs;olet, &amp; debet de exemplis moralibus. </s>
2801 
2802 <s>at vero requiri confor&shy;<lb/>mitatem exemplorum cum regulis traditis, nemo &longs;an&aelig; mentis dubitabit. <lb/></s>
2803 
2804 <s>Vernm i&longs;ti confundunt conformitatem cum veritate. </s>
2805 
2806 <s>Veritas exemplo tunc <lb/>ine&longs;t, quando illud, quod in exemplo narratur, ver&egrave; extitit, vt &longs;i quis in <lb/>exemplum pudiciti&aelig; afferret hi&longs;toriam Io&longs;ephi, <expan abbr="ver&utilde;">verum</expan> i&longs;tu&agrave; e&longs;&longs;et exemplum. <lb/></s>
2807 
2808 <s>qu&aelig; veritas in exemplis moralibus non &longs;emper e&longs;t nece&longs;&longs;aria, talia exempla <lb/>&longs;unt &longs;&aelig;p&egrave; parabol&aelig;, &amp; fabul&aelig;, qu&aelig; nunquam extiterunt, v. <!-- REMOVE S-->g. <!-- REMOVE S-->narratur ab <lb/>Ari&longs;t. 
2809 
2810 de quodam filio, qui patrem crudeliter traxerat, qui po&longs;tea grandior <lb/>factus, cum filium procrea&longs;&longs;et, ab eodem pariter raptatus e&longs;t ip&longs;e, v&longs;que ad <lb/>eundem locum, quo ip&longs;e patrem &longs;uum impi&egrave; raptauerat. </s>
2811 
2812 
2813 
2814 
2815 
2816 <s>non e&longs;t nece&longs;&longs;e, ta&shy;<lb/>lem extiti&longs;&longs;e filium, <expan abbr="neq;">neque</expan> patrem. </s>
2817 
2818 <s>Verumtamen &longs;emper conformitas exem&shy;<lb/>pli cum regulis, &amp; pr&aelig;ceptis, qu&aelig; traduntur nece&longs;&longs;aria e&longs;t, alioquin exem&shy;<lb/>pla de&longs;truerent id, quod pr&aelig;ceptio con&longs;truit, <expan abbr="illi&qacute;">illique</expan> contraria e&longs;&longs;et, quod om&shy;<lb/>nino ab&longs;urdum foret. </s>
2819 
2820 <s>non &longs;ecus, ac &longs;i quis vellet alium docere characteres <lb/>latinos, <expan abbr="illi&qacute;">illique</expan>; barbaros, quos Gothicos vocant in exemplum proponeret. </s>
2821 
2822 <s>re&shy;<lb/>quiritur igitur &longs;emper in omni exemplo conformitas cum eo, quod doce&shy;<lb/>tur; in moralibus tamen non &longs;emper requiritur veritas, vti diximus; Alij <lb/>ver&ograve; dicunt non requiri in exemplis determinatam veritatem, &longs;ed &longs;atis e&longs;&longs;e, <lb/>&longs;i exemplum verum &longs;it &longs;ecundum opinionem aliquorum: <expan abbr="quor&utilde;">quorum</expan> &longs;ententiam <lb/>non improbamus. </s>
2823 
2824 <s>Exempla igitur ab Ari&longs;t. 
2825 
2826 pa&longs;&longs;im ex mathem aticis allata, <lb/>congrua, <expan abbr="conformia&qacute;">conformiaque</expan>; omnin&ograve; &longs;unt ip&longs;ius doctrin&aelig;, aliter ip&longs;um perpetu&ograve; <lb/>mentientem facimus. </s>
2827 
2828 <s>Po&longs;trem&ograve; illud etiam e&longs;t aduertendum, fort&egrave; Ari&longs;t. 
2829 
2830 in <lb/>pr&aelig;&longs;enti textu &longs;pecta&longs;&longs;e <expan abbr="n&otilde;">non</expan> ad hanc Euclidianam demon&longs;trationem, &longs;ed po&shy;<lb/>tius ad Pithagoricam. </s>
2831 
2832 <s>Pithagorei enim eam aliter, quamuis per idem me&shy;<lb/>dium, &longs;cilicet &agrave; cau&longs;a materiali, demon&longs;trabant; con&longs;truebant enim aliter, <lb/><expan abbr="neq;">neque</expan> vlla vtebantur diui&longs;ione. </s>
2833 
2834 <s>quod dictum velim propter nonnullos, qui ab <lb/>huiu&longs;modi diui&longs;ionibus abhorrent, <expan abbr="timent&qacute;">timentque</expan>; ne demon&longs;trationis perfectio&shy;<lb/>ni per eas plurimum derogetur. </s>
2835 
2836 <s>Pithagoreorum demon&longs;trationem vide <lb/>apud Clauium in &longs;cholio 32. primi Euclidis, quam ex Eudemo etiam Pro&shy;<lb/>clus in comm. <!-- REMOVE S-->eiu&longs;dem recitat.</s>
2837 
2838 </p><p type="main">
2839 
2840 <s><arrow.to.target n="marg37"/></s></p><p type="margin">
2841 
2842 <s><margin.target id="marg37"/>37</s></p><p type="main">
2843 
2844 <s>Ibidem <emph type="italics"/>(Sed quemadmod&ubreve; harmonica per Arithmeticam)<emph.end type="italics"/> vide &longs;upra tex. <!-- REMOVE S-->20.</s>
2845 
2846 </p><p type="main">
2847 
2848 <s><arrow.to.target n="marg38"/></s></p><p type="margin">
2849 
2850 <s><margin.target id="marg38"/>38</s></p><p type="main">
2851 
2852 <s>Ibidem <emph type="italics"/>(Demon&longs;tratio autem non computatur in aliud genus; m&longs;i, vt dictum <lb/>e&longs;t geometric&aelig; demon&longs;trationes in Per&longs;pectiuas, aut Mcchamcas, &amp; arithmetic&aelig; in <lb/>harmonicas)<emph.end type="italics"/> exempla &longs;ubalternationis Per&longs;pectiu&aelig;, &amp; Mu&longs;ic&aelig; in tex. <!-- REMOVE S-->20. at&shy;<lb/>tulimus; nunc Mechanic&aelig; &longs;ubalternationis, quam hic Ari&longs;t. 
2853 
2854 in&longs;inuat, exem&shy;<lb/>plum &longs;it illud, quod Archimedes prop. 
2855 
2856 14. primi Aequep. <!-- REMOVE S-->demon&longs;trat, ni&shy;<lb/>mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rect&aelig; <lb/>line&aelig; ab angulis trianguli ad dimidia latera oppo&longs;ita duct&aelig; concurrunt. </s>
2857 
2858 
2859 
2860 
2861 
2862 <s>&longs;it <lb/>triangulum A B C, &agrave; cuius angulis A, &amp; B, ducantur du&aelig; rect&aelig; A D, B E, ita <lb/>vt bifariam &longs;ecent latera A C, B C, in punctis D, &amp; E, &amp; concurrant in F. <lb/><!-- KEEP S--></s>
2863 
2864 <s>Dico F, e&longs;&longs;e centrum grauitatis propo&longs;iti trianguli. </s>
2865 
2866 <s>Quoniam enim in 13. <lb/>Aequep. <!-- REMOVE S-->probauit centrum grauitatis e&longs;&longs;e in ea linea, qu&aelig; ducta ab angulo <lb/>quouis &longs;ecat oppo&longs;itum latus bifariam, crit in linea A D, <expan abbr="centr&utilde;">centrum</expan> grauitatis. <pb pagenum="57"/><figure place="text" xlink:href="figures-la/009.01.057.1.tif"/><lb/>&longs;ed eadem ratione erit etiam in linea B E, er&shy;<lb/>go non ni&longs;i in puncto F, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> e&longs;t in vtra&shy;<lb/>que, quod erat demon&longs;trandum. </s>
2867 
2868 
2869 
2870 <s>ex quibus ap&shy;<lb/>paret, qua ratione mechanica conclu&longs;io Geo&shy;<lb/>metri&aelig; &longs;ubiaceat, dum lineari di&longs;cur&longs;u ip&longs;a <lb/>demon&longs;tratio perficitur. </s>
2871 
2872 <s>Scias pr&aelig;terea cen&shy;<lb/>trum grauitatis e&longs;&longs;e tale punctum, ex quo &longs;i &longs;u&shy;<lb/>&longs;pendatur corpus triangulare vniformis cra&longs;&shy;<lb/>&longs;itici, manet &longs;emper horizonti parallelum, &longs;i <lb/>tamen antequam &longs;u&longs;penderetur, iacebat plano horizontis, &aelig;quidi&longs;tans; <lb/><expan abbr="neq;">neque</expan> &longs;i &longs;u&longs;pen&longs;um feratur huc illud nutat, &longs;ed &longs;emper in <expan abbr="cod&etilde;">codem</expan> &longs;itu per&longs;euerat.</s></p><p type="main">
2873 
2874 <s><arrow.to.target n="marg39"/></s></p><p type="margin">
2875 
2876 <s><margin.target id="marg39"/>39</s></p><p type="main">
2877 
2878 <s>Tex. 24. <emph type="italics"/>(Veluti Arithmetica quidem quid impar, aut par; aut quadrangu&shy;<lb/>lum, aut cubus)<emph.end type="italics"/> cogno&longs;cas hinc cert&ograve; certius quadrangulum, &amp; cubum e&longs;&longs;e <lb/>&longs;pecies numerorum, &longs;icuti &longs;upra tex. <!-- REMOVE S-->9. &amp; 20. explicauimus, qu&ograve; nunc te vi&shy;<lb/>ci&longs;&longs;im, vt pr&aelig;&longs;entem locum intelligas, remittimus.</s>
2879 
2880 </p><p type="main">
2881 
2882 <s><arrow.to.target n="marg40"/></s></p><p type="margin">
2883 
2884 <s><margin.target id="marg40"/>40</s></p><p type="main">
2885 
2886 <s>Ibidem <emph type="italics"/>(Geometrica ver&ograve; quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/>verbum, irrationale, non videtur Ari&longs;t. 
2887 
2888 intellexi&longs;&longs;e proprietatem illam duo&shy;<lb/>rum linearum incommen&longs;urabilium longitudine, &amp; potentia, quia v&longs;us fui&longs;&shy;<lb/>&longs;et verbo, <foreign lang="greek">a/rrpton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio&shy;<lb/>ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latin&egrave; redditur improportionale.</s></p><p type="main">
2889 
2890 <s><arrow.to.target n="marg41"/></s></p><p type="margin">
2891 
2892 <s><margin.target id="marg41"/>41</s></p><p type="main">
2893 
2894 <s>Per verbum <emph type="italics"/>(Refrangi)<emph.end type="italics"/> &longs;eu frangi, intelligit lineam aliquam rectam, non <lb/>in directum rendere, &longs;ed in aliquo puncto frangi, &longs;eu declinari &agrave; rectitudine, <lb/>ita vt con&longs;tituat angulum.</s></p><p type="main">
2895 
2896 <s>Per verbum <emph type="italics"/>(Concurrere)<emph.end type="italics"/> intelligit, non e&longs;&longs;e parallelas, &longs;ed ad idem ali&shy;<lb/>quod punctum coire, &longs;i protrahantur.</s></p><p type="main">
2897 
2898 <s><arrow.to.target n="marg42"/></s></p><p type="margin">
2899 
2900 <s><margin.target id="marg42"/>42</s></p><p type="main">
2901 
2902 <s>Ibidem <emph type="italics"/>(Et Astrologia &longs;imiliter)<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t. 
2903 
2904 non iu&shy;<lb/>diciariam, quamuis &agrave; recentioribus hoc nomine vocetur, &longs;ed quam hodie <lb/>dicunt A&longs;tronomiam, <expan abbr="ait&qacute;">aitque</expan>; ip&longs;am con&longs;iderare quantitatem, figuram, mo&shy;<lb/>tum, &amp; locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt C&oelig;li, <lb/>&amp; Elementa.</s></p><p type="main">
2905 
2906 <s><arrow.to.target n="marg43"/></s></p><p type="margin">
2907 
2908 <s><margin.target id="marg43"/>43</s></p><p type="main">
2909 
2910 <s>Tex. 25. <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> Geometra fal&longs;a &longs;upponit, quemadmodum quidam a&longs;&longs;eruere di&shy;<lb/>centes, quod non oportet fal&longs;o vti: Geometram ver&ograve; mentiri dicentem pedalem, non <lb/>pedalem, aut rectam de&longs;criptam, non rectam <expan abbr="exist&etilde;tem">existentem</expan>: Geometra ver&ograve; nihil con&shy;<lb/>cludit e&ograve;, quod b&aelig;c e&longs;t linea, &longs;ed qu&aelig; per h&aelig;c e&longs;tenduntur)<emph.end type="italics"/> innuit his verbis eam <lb/>materiam intelligibilem, qu&aelig; e&longs;t &longs;ubiectum Geometri&aelig;: eam &longs;cilicet, qu&aelig; <lb/>&longs;ub figuris Geometricis &longs;en&longs;ibilibus, &amp; <expan abbr="plerunq;">plerunque</expan> fal&longs;is latet; nam &longs;&aelig;p&egrave; Geo&shy;<lb/>metra vtitur linea quadam &longs;en&longs;ibili pro recta, qu&aelig; ver&egrave; nec e&longs;t linea mathe&shy;<lb/>matica, nec recta; &longs;upponit aliquando talem lineam e&longs;&longs;e pedalem, qu&aelig; ve&shy;<lb/>r&egrave; non e&longs;t pedalis: Verumtamen non mentitur, quia re&longs;picit ad veram li&shy;<lb/>neam mathematicam, qu&aelig; &longs;ub illa intelligitur, &amp; qu&aelig; recta concipitur; &amp; <lb/>quidem h&aelig;c omnia ver&egrave; concipiuntur, quoniam ita e&longs;&longs;e re vera po&longs;&longs;unt.</s></p><p type="main">
2911 
2912 <s><arrow.to.target n="marg44"/></s></p><p type="margin">
2913 
2914 <s><margin.target id="marg44"/>44</s></p><p type="main">
2915 
2916 <s>Tex. 28. <emph type="italics"/>(Coaltern as ver&ograve; coincidere)<emph.end type="italics"/> per coalternas intelligendas e&longs;&longs;e pa&shy;<lb/>rallelas lineas, alias, &amp; nunc <expan abbr="quoq;">quoque</expan> monemus.</s></p><p type="main">
2917 
2918 <s><arrow.to.target n="marg45"/></s></p><p type="margin">
2919 
2920 <s><margin.target id="marg45"/>45</s></p><p type="main">
2921 
2922 <s>Tex. 29. <emph type="italics"/>(In Matbematicis ver&ograve; non est &longs;imiliter paralogi&longs;mus, quoniam me&shy;<lb/>di&ubreve; e&longs;t &longs;emper, quod duplex, de hoc enim omni, &amp; hoc rur&longs;us de alio dicitur omni)<emph.end type="italics"/><lb/>aduerte, quod quamuis nonnulli codices habeant pro, in mathematicis, in <pb pagenum="58"/>di&longs;ciplinis, idem tamen apud gr&aelig;cos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci&shy;<lb/>plm&aelig;; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. <!-- KEEP S--></s>
2923 
2924 <s>Porr&ograve; non <lb/>e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra&shy;<lb/>tione maius extremum dicitur de omni medio, &amp; rur&longs;us medium dicitur de <lb/>omni minori extremo, ac &longs;i diceret mathematic&aelig; demon&longs;trationes &longs;unt in <lb/>primo modo, qui barbar&egrave; &agrave; latinis recentioribus Barbara appellatur. </s>
2925 
2926 <s>H&aelig;c <lb/>e&longs;t autem pulcherrima mathematicarum commendatio, quippe pr&aelig;clarum <lb/>e&longs;t &agrave; laudato laudari. </s>
2927 
2928 <s>In mathematicis, inquit, non accidit &longs;imiliter para&shy;<lb/>logi&longs;mus, ide&longs;t, tam frequenter, quemadmodum in &longs;yllogi&longs;mis dialecticis, <lb/>quia modus argumentandi mathematicarum e&longs;t perfecti&longs;&longs;imus, quippe in <lb/>primo modo prim&aelig; figur&aelig;.</s></p><p type="main">
2929 
2930 <s><arrow.to.target n="marg46"/></s></p><p type="margin">
2931 
2932 <s><margin.target id="marg46"/>46</s></p><p type="main">
2933 
2934 <s>Eodem tex. <emph type="italics"/>(Contingit autem quo&longs;dam non &longs;yllogi&longs;tic&egrave; dicere, &amp; quod ex vtri&longs;&shy;<lb/>que con&longs;equentia accipiunt, quemadmodum &amp; C&aelig;neus facit, quod ignis in multi&shy;<lb/>plici proportione: etenim ignis celeriter gignitur, vt ait: &amp; h&aelig;c est proportio. </s>
2935 
2936 <s>&longs;ic <lb/>autem non e&longs;t &longs;yllog &longs;mus, ni&longs;i celerrimam proportio &longs;equatur multiplex: &amp; ignem <lb/>celerrima in motu proportio)<emph.end type="italics"/> verba illa (in multiplici proportione) gr&aelig;c&egrave; &longs;ic <lb/>&longs;e habent, <foreign lang="greek">en th pollaplasioni analogia,</foreign> quod melius redditur latin&egrave; in mul&shy;<lb/>tiplici proportione, quemadmodum fecimus, quam in multiplicata, quem&shy;<lb/>admodum in vulgata editione. </s>
2937 
2938 <s>porr&ograve; quid inter multiplicem, &amp; multipli&shy;<lb/>catam rationem inter&longs;it, optim&egrave; declarat no&longs;ter Clauius ad 4. definit. </s>
2939 
2940 <s>lib. 
2941 
2942 5. <lb/>Elem. 
2943 
2944 ex quo etiam loco pauca decerpam, qu&aelig; huic loco declarando con&shy;<lb/>ducunt. </s>
2945 
2946 <s>Proportio igitur multiplex e&longs;t habitudo inter duas quantitates in&shy;<lb/>&aelig;quales, quarum maior continet minorem, bis, vel ter, vel quater, &amp;c. </s>
2947 
2948 <s>vn&shy;<lb/>de proportio multiplex habet &longs;ub &longs;e genera infinita, quando enim maior <lb/>continet minorem bis, dicitur Dupla: quando ter, Tripla: quando quater, <lb/>Quadrupla: &amp; &longs;ic in infinitum: v. <!-- REMOVE S-->g. <!-- REMOVE S-->2. ad 1. e&longs;t proportio dupla; 3. ad 1. tri&shy;<lb/>pla; 4. ad 1. quadrupla, &amp;c. </s>
2949 
2950 
2951 
2952 
2953 
2954 <s>omnes tamen continentur &longs;ub genere multipli&shy;<lb/>cis rationis. </s>
2955 
2956 <s>porr&ograve; &longs;i qu&ecedil;piam proportio ex genere multiplici progrediatur <lb/>per plures terminos, v. <!-- REMOVE S-->g. <!-- REMOVE S-->proportio quadrupla progrediatur hoc modo, <lb/>1. 4. 16. 64. 256. &amp;c. </s>
2957 
2958 
2959 
2960 
2961 
2962 <s>fit, vt &longs;ub&longs;equentes termini mirum in modum augean&shy;<lb/>tur. </s>
2963 
2964 <s>hic vides primum ip&longs;am quadruplam rationem in di&longs;po&longs;itis terminis <lb/>progredi, quia quilibet &longs;equens terminus ad pr&aelig;cedentem e&longs;t quadruplus. <lb/></s>
2965 
2966 <s>cernis etiam in paucis terminis, quinque &longs;cilicet magnum factum e&longs;&longs;e incre&shy;<lb/>mentum, cum <expan abbr="v&longs;q;">v&longs;que</expan> ad 256. excreuerint. </s>
2967 
2968 <s>C&aelig;neus igitur dicens ignem augeri <lb/>&longs;ecundum multiplicem rationem, vnam ex pr&aelig;dictis intelligebat aliquam, <lb/>quia qu&aelig;libet illarum magnopere cre&longs;cit, &longs;i propagetur, vt ad 10. quinti <lb/>definit. </s>
2969 
2970 <s>traditur: &amp; vt paulo ante exemplo licuit per&longs;picere. </s>
2971 
2972 <s>argumentaba&shy;<lb/>tur igitur C&aelig;neus in hunc modum; quod in multiplici ratione augetur, ce&shy;<lb/>lerrim&egrave; augetur: ignis celerrim&egrave; augetur, ergo ignis in multiplici ratione <lb/>augetur, qu&aelig; argumentatio vitio&longs;a e&longs;t, ex duabus quippe affirmatiuis in &longs;e&shy;<lb/>cunda figura procedens, vt colligitur ex verbis illis tex. <emph type="italics"/>(Ex viri&longs;que con&longs;e&shy;<lb/>quentia accipiunt<emph.end type="italics"/>) ex his mathematica huius locis patere &longs;atis po&longs;&longs;unt.</s></p><p type="main">
2973 
2974 <s><arrow.to.target n="marg47"/></s></p><p type="margin">
2975 
2976 <s><margin.target id="marg47"/>47</s></p><p type="main">
2977 
2978 <s>Ibidem (<emph type="italics"/>Conuertuntur autem magis, qu&aelig;&longs;unt in mathematicis, quoniam nul&shy;<lb/>lum accidens accipiunt (m quo quidem ijs pr&aelig;&longs;t&abreve;t, qu&aelig; di&longs;putationibus traduntur) <lb/>&longs;ed definitiones<emph.end type="italics"/>) H&aelig;c e&longs;t altera mathematicarum laus, vnde earum quoque <lb/>pr&aelig;&longs;tantia elucet, quia &longs;cilicet mathematic&aelig; pro medijs vtuntur definitio&shy;<pb pagenum="59"/>nibus &longs;ubiecti, aut pa&longs;&longs;ionis, qu&aelig; nuilo modo &longs;unt accidentalia conclu&longs;ioni, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->in prima Euclidis demon&longs;tratione per definitionem &longs;ubiecti probantur <lb/>tres line&aelig; e&longs;&longs;e &aelig;quales, quia nimirum &longs;int &longs;emidiametri circulorum &aelig;qua&shy;<lb/>lium, qu&aelig; e&longs;t ip&longs;arum definitio. </s>
2979 
2980 
2981 
2982 
2983 
2984 <s>&amp; in 4. primi probantur ba&longs;is, &amp; anguli <lb/>vnius trianguli &aelig;quales e&longs;&longs;e ba&longs;i, &amp; angulis alterius trianguli per formalem <lb/>definitionem pa&longs;&longs;ionis, videlicet &aelig;qualitatis, qu&aelig; traditur in octauo axio&shy;<lb/>mate &longs;ic, qu&aelig; &longs;ibi mutuo congruunt, ea inter &longs;e &longs;unt &aelig;qualia. </s>
2985 
2986 <s>probat igitur <lb/>Euclides in quarta ba&longs;im, &amp; angulos vnius trianguli e&longs;&longs;e &aelig;qualia ba&longs;i, &amp; an&shy;<lb/>gulis alterius trianguli, quia o&longs;tendit, quod, &longs;i ba&longs;is illa huic ba&longs;i, &amp; illi an&shy;<lb/>guli hi&longs;ce angulis &longs;uperponantur, congruunt; ex qua congruentia mutua, <lb/>qu&aelig; e&longs;t &aelig;qualitatis definitio, infert &aelig;qualitatem ip&longs;arum ba&longs;ium, necnon <lb/>angulorum. </s>
2987 
2988 <s>eadem deinde &aelig;qualitatis definitione totam demon&longs;trationem <lb/>concludit, &longs;cilicet totum triangulum toti triangulo &aelig;quale e&longs;&longs;e, quia vnum <lb/>alteri congruat. </s>
2989 
2990 <s>A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in&shy;<lb/>rerpo&longs;itionem terr&aelig; inter Lunam, &amp; Solem, qu&aelig; interpo&longs;itio e&longs;t definitio <lb/>cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s>
2991 
2992 <s>huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/>Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="c&aelig;teros&qacute;">c&aelig;terosque</expan>; Mathematicas demon&shy;<lb/>&longs;trationes: ita vt merit&ograve; dixerit Ari&longs;t. Mathematicas alias omnes natura&shy;<lb/>les &longs;cientias, qu&aelig; di&longs;putabilibus rationibus traduntur ex hac parte antecel&shy;<lb/>lere. </s>
2993 
2994 <s>a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;&aelig;p&egrave; definitio&shy;<lb/>nes ad demon&longs;trandum. </s>
2995 
2996 <s>Reliqua logici expo&longs;itores declarant.</s></p><p type="main">
2997 
2998 <s><arrow.to.target n="marg48"/></s></p><p type="margin">
2999 
3000 <s><margin.target id="marg48"/>48</s></p><p type="main">
3001 
3002 <s>Tex. 30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;ph&aelig;rica &longs;it per aug&shy;<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;ph&aelig;ricum; augetur autem Luna; plan&ubreve; quod <lb/>&longs;ph&aelig;rica<emph.end type="italics"/>) Illius demon&longs;trationis, qu&aelig; ab effectu procedit, affert exemplum <lb/>ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;ph&aelig;ricam ab ef&shy;<lb/>fectu ip&longs;ius &longs;ph&aelig;ricitatis, qui e&longs;t illuminatio &longs;ph&aelig;rica: &longs;ic enim ratiocinan&shy;<lb/>tur: ea, qu&aelig; &longs;ph&aelig;ric&egrave; illuminantur &longs;unt &longs;ph&aelig;rica, Luna &longs;ph&aelig;ric&egrave; illumina&shy;<lb/>tur, ergo &longs;ph&aelig;rica e&longs;t: qu&aelig; argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/>quod ita augetur, ide&longs;t, &longs;ph&aelig;ric&egrave;, e&longs;t &longs;ph&aelig;ricum, ide&longs;t, quia lumen nou&aelig; Lu&shy;<lb/>n&aelig; augetur &longs;ph&aelig;ric&egrave;, hoc e&longs;t, ad eum modum, quo qu&aelig;uis &longs;ph&aelig;ra obiecta <lb/>corpori lumino&longs;o &longs;olet illuminari. </s>
3003 
3004 <s>illuminatio porr&ograve; Lun&aelig; in &longs;e &longs;emper e&longs;t <lb/>eadem, quia &longs;emper dimidium Lun&aelig; quod Solem a&longs;picit, illuminatur; dici&shy;<lb/>tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto &agrave; nouilunio <lb/>pars illuminata incipit quotidie magis vergere ad oculum no&longs;trum, ita vt <lb/>in dies maiorem, ac maiorem illuminationem videamus, donec opponatur <lb/>Soli, in qua oppo&longs;itione totum fer&egrave; Lun&aelig; <expan abbr="illuminat&utilde;">illuminatum</expan> con&longs;picitur. </s>
3005 
3006 <s>Vt autem <lb/>huius illuminationis non iniucundam f cias experientiam; cape &longs;ph&aelig;ram <lb/>quampiam &longs;olidam manu, cum qua recede ad medium cubiculi, &amp; pone lu&shy;<lb/>men &longs;eor&longs;um ad partem aliquam: deinde brachio exten&longs;o oppone &longs;ph&aelig;ram <lb/>lumini, quo &longs;itu nihil de illuminatione videbis, quamuis dimidium fer&egrave; il&shy;<lb/>lius illuminetur. </s>
3007 
3008 <s>po&longs;tea conuerte te ip&longs;um ibidem paulatim, ita vt aliquid <lb/>illuminationis oculo tuo appareat; &amp; videbis partem illam illuminationis, <lb/>falcat&aelig;, &longs;eu nou&aelig; Lun&aelig; &longs;imilem. </s>
3009 
3010 <s>Deinde adhuc magis te conuerte, &amp; cer&shy;<lb/>nes illuminationem dimidiat&aelig; Lun&aelig; &longs;imilem: verte adhuc te ip&longs;um donec <lb/>&longs;it &longs;ph&aelig;ra ita lumini oppo&longs;ita, vt inter ip&longs;am, &amp; lumen oculus tuus &longs;it me&shy;<lb/>dius; apparebit tunc tota illuminatio, qu&aelig; erit in&longs;tar plenilunij. </s>
3011 
3012 <s>perge ad&shy;<pb pagenum="60"/>huc te ip&longs;um conuertere, &amp; videbis paulatim lumen oculo tuo decre&longs;cere <lb/>non aliter ac in Luna &longs;ene&longs;cente. </s>
3013 
3014 <s><expan abbr="atq;">atque</expan> hoe e&longs;t &longs;ph&aelig;ric&egrave; illuminari, fierique <lb/>&longs;ph&aelig;rica illuminationis augmenta. </s>
3015 
3016 <s>cum ergo videamus Lunam eo modo lu&shy;<lb/>mine augeri, quo &longs;ph&aelig;ra, hinc ip&longs;am <expan abbr="quoq;">quoque</expan> &longs;ph&aelig;ricam-e&longs;&longs;e argumentamur.</s></p><p type="main">
3017 
3018 <s><arrow.to.target n="marg49"/></s></p><p type="margin">
3019 
3020 <s><margin.target id="marg49"/>49</s></p><p type="main">
3021 
3022 <s>Po&longs;t nonnulla (<emph type="italics"/>Vt Per&longs;pectiua ad Geometriam, &amp; Mechanica ad Stereome&shy;<lb/>tricam, &amp; Harmonica ad Arithmeticam, vt Apparentia ad A&longs;trologicam<emph.end type="italics"/>) &longs;upra <lb/>tex. <!-- REMOVE S-->20. exempla &longs;ubalternationum Per&longs;pectiu&aelig;, &amp; Mechanic&aelig; cum Geo&shy;<lb/>metria &longs;unt allata. </s>
3023 
3024 
3025 
3026 <s>hic primo notandum Stereometriam non ef&longs;e &longs;cientiam <lb/>di&longs;tinctam &agrave; Geometria, ni&longs;i &longs;icuti partem &agrave; toto: nam cum Geometria <lb/>con&longs;ideret quantitatem, &longs;ecundum tres dimen&longs;iones, longitudinem, latitu&shy;<lb/>dinem, &amp; profunditatem, oritur triplex illius diui&longs;ro, de lineis, de &longs;uperfi&shy;<lb/>ciebus, de &longs;olidis. </s>
3027 
3028 <s>pars igitur, qu&aelig; de &longs;olidis tractat, <expan abbr="pattim&qacute;">pattimque</expan>; continetur <lb/>11. 12. 13. 14. &amp; 15. Euclidis, partim aliorum Geometrarum libris, vt li&shy;<lb/>bro Archim. <!-- REMOVE S-->de Sph&aelig;ra, &amp; Cyl. <!-- REMOVE S-->&amp; &longs;imilibus, dicitur Stereometria &agrave; gr&aelig;co <lb/><foreign lang="greek">steoeov,</foreign> ide&longs;t &longs;olidum. </s>
3029 
3030 
3031 
3032 
3033 
3034 <s>Porr&ograve; cur malit Ari&longs;t. Mechanicam &longs;ubalternari Ste&shy;<lb/>reometri&aelig;, quam toti Geometri&aelig;, qua tamen, vt videre e&longs;t apud Archime&shy;<lb/>dem, innititur, fort&egrave; ea ratio e&longs;t, quia Mechanica pr&aelig;cipu&egrave; con&longs;iderat ma&shy;<lb/>chinas, qu&aelig; corpora &longs;unt, &amp; propterea pr&aelig;cipu&egrave;, &amp; prim&ograve; debet Stereome&shy;<lb/>tri&aelig;, qu&aelig; corpora pariter contemplatur, &longs;ubalternari. </s>
3035 
3036 <s>Quod ait Apparen&shy;<lb/>tia ad A&longs;irol. <!-- KEEP S--></s>
3037 
3038 <s>inteiligit per Apparentia vulgarem quandam Nautarum, &amp; <lb/>Agricolarum a&longs;tronomiam, qu&aelig; quodammodo &longs;ubaiternatur, &amp; pendet ex <lb/>&longs;cientia A&longs;trologi&aelig;; indiget enim cognitione ortus, &amp; motus a&longs;trorum, <lb/>pr&aelig;&longs;ertim Lun&aelig;, Hyadum, Pleiadum, &amp; Canis. </s>
3039 
3040 <s>Reliqua <expan abbr="v&longs;q;">v&longs;que</expan> ad &longs;inem ca&shy;<lb/>pitis optim&egrave; &agrave; Zabarella explicantur, <expan abbr="neq;">neque</expan> ad nos pertinet, cum de Mathe&shy;<lb/>maticis agant, quatenus ad Logicum &longs;pectant.</s></p><p type="main">
3041 
3042 <s><arrow.to.target n="marg50"/></s></p><p type="margin">
3043 
3044 <s><margin.target id="marg50"/>50</s></p><p type="main">
3045 
3046 <s>Po&longs;t nonnulla (<emph type="italics"/>Hic enim ip&longs;um quidem quod &longs;en&longs;itiuorum e&longs;t &longs;cire, ip&longs;um ve&shy;<lb/>r&ograve; Propter quid Mathematicorum; hi <expan abbr="namq;">namque</expan> habent cau&longs;arum demon&longs;trationes, <lb/>&amp;c.<emph.end type="italics"/>) &longs;en&longs;us e&longs;t in &longs;ubalternatis, &amp; dependentibus di&longs;ciplinis, quas &longs;en&longs;itiuas <lb/>appellat, quia de rebus &longs;en&longs;ibilibus &longs;unt, vt in Per&longs;pectiua de obiectis vifibi&shy;<lb/>libus, &amp; in Mu&longs;ica de &longs;onis cogno&longs;citur Quod, ide&longs;t effectus: cuius effectus <lb/>cau&longs;a, &longs;eu Propter quid &longs;citur auxilio Mathematicarum, ide&longs;t, traditur &agrave; <lb/>&longs;cientijs &longs;ubalternantibus. </s>
3047 
3048 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->alicuius effectus in Per&longs;pectiua cau&longs;a inqui&shy;<lb/>ritur, &amp; inuenitur ope Geometri&aelig;, cuiilla &longs;ubiacet. </s>
3049 
3050 
3051 
3052 
3053 
3054 <s>Hic obiter notandum, <lb/>Ari&longs;t. 
3055 
3056 fateri manife&longs;t&egrave; Mathematicas &longs;ubalternatas, &longs;eu medias o&longs;tendere <lb/>per cau&longs;as, quas &longs;ubalternantium ope perue&longs;tigant.</s></p><p type="main">
3057 
3058 <s><arrow.to.target n="marg51"/></s></p><p type="margin">
3059 
3060 <s><margin.target id="marg51"/>51</s></p><p type="main">
3061 
3062 <s>Et po&longs;tea (<emph type="italics"/>Se habet autem &amp; ad Per&longs;pectiuam, vt h&aelig;c ad Geometriam, alia ad <lb/>hanc, vt quo&aelig; e&longs;t de Iride ip&longs;um enim quod Naturalis e&longs;t &longs;cire, ip&longs;um vcr&ograve; Prop&shy;<lb/>ter quid Per&longs;pectiui<emph.end type="italics"/>) &longs;icut &longs;e habet, inquit, <expan abbr="&longs;ci&etilde;ti&agrave;">&longs;cienti&agrave;</expan> Naturalis de Iride ad Per&shy;<lb/>&longs;pectiuam, ita Per&longs;pectiua ad Geomettiam. </s>
3063 
3064 <s>qua ver&ograve; ratione cau&longs;a Iridis <lb/>pertineat ad opticam, <expan abbr="atq;">atque</expan> hine tandem ad Geometriam, optim&egrave; patebit <lb/>in Meteoris, cum ip&longs;ius demon&longs;trationem afferemus.</s></p><p type="main">
3065 
3066 <s><arrow.to.target n="marg52"/></s></p><p type="margin">
3067 
3068 <s><margin.target id="marg52"/>52</s></p><p type="main">
3069 
3070 <s>Tex. 37. (<emph type="italics"/>Vt &aelig;quicruri, &amp; Scaleno hoc, quod e&longs;t duobus rectis &aelig;quales habere <lb/>&longs;ecandum commune aliquod ine&longs;t<emph.end type="italics"/>) quid &longs;it habcre tres &aelig;quales duobus rectis<lb/>&longs;atis explicatum e&longs;t lib. 
3071 
3072 r. </s>
3073 
3074 <s>Priorum &longs;ecto 3. cap. 
3075 
3076 r. </s>
3077 
3078 <s>nunc igitur paraphra&longs;im<lb/>&longs;olum huius loci dabo. </s>
3079 
3080 <s>Triangnlo I&longs;o&longs;celi, &amp; Scaleno connenit pa&longs;&longs;io illa,<lb/>habere tres angulos &aelig;quales duobus rectis angulis &longs;ecundum aliquod com&shy;<pb pagenum="61"/>mune, quia illis competit, quatenus ambo &longs;unt figura qu&aelig;dam, ide&longs;t, qua&shy;<lb/>tenus <expan abbr="vtrumq;">vtrumque</expan> illorum triangulum e&longs;t; triangulo <expan abbr="namq;">namque</expan> omni primo com&shy;<lb/>petit habere tres angulos &aelig;quales duobus rectis.</s></p><p type="main">
3081 
3082 <s><arrow.to.target n="marg53"/></s></p><p type="margin">
3083 
3084 <s><margin.target id="marg53"/>53</s></p><p type="main">
3085 
3086 <s>Tex. 38. (<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, boc autem non idem <lb/>vbique, &longs;ed in pondere quidem mina, in c&abreve;tu ver&ograve; die&longs;is<emph.end type="italics"/>) Die&longs;is apud Muficos e&longs;t <lb/>pars Toni. </s>
3087 
3088 <s>Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri&shy;<lb/>mam vocem, Vt, &amp; &longs;ecundam R&egrave;, vt modo loquuntur. </s>
3089 
3090 <s>i&longs;tud interuallum <lb/>diuidunt Mu&longs;ici primum in &longs;emitonia, non tamen &aelig;qualia, &longs;ed vnum maius <lb/>altero. </s>
3091 
3092 <s>minus iterum in duas partes &aelig;quales &longs;ubdiuidunt, quarum <expan abbr="vtramq;">vtramque</expan> <lb/>veteres harmonici die&longs;im dixerunt. </s>
3093 
3094 <s>&amp; h&ecedil;c die&longs;is e&longs;t minima vox ab eis con&shy;<lb/>&longs;iderata; &amp; qu&aelig; prima cadit &longs;ub &longs;en&longs;um; &amp; propterea veluti &longs;implex prin&shy;<lb/>cipium, &amp; clementum, ex quo alia maiora interualla conftent; &amp; in quod <lb/>re&longs;oluuntur. <foreign lang="greek">die/ois</foreign> porr&ograve; gr&aelig;c&egrave; valet inter alia, diui&longs;ionem. </s>
3095 
3096 <s>igitur interual&shy;<lb/>lum i&longs;tud minimum dictum e&longs;t die&longs;is, quod &longs;it qu&aelig;dam diui&longs;io, &longs;eu &longs;egmen&shy;<lb/>turn Toni (<emph type="italics"/>Quemadmodum in pondere mina<emph.end type="italics"/>) qui de ponderibus antiquis tra&shy;<lb/>ctant, a&longs;&longs;erunt, Minam fui&longs;&longs;e maiorem libra per &longs;emunciam, &aelig;quipondera&shy;<lb/>bat enim centum drachmis: qu&aelig; refragantur huic loco. </s>
3097 
3098 <s>&longs;ed fort&egrave; <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/>Ari&longs;t. 
3099 
3100 con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>principium, cum &longs;ex millia minarum in Attico talento continerentur.</s></p><figure place="text" xlink:href="figures-la/009.01.061.1.tif"/><p type="main">
3101 
3102 <s><arrow.to.target n="marg54"/></s></p><p type="margin">
3103 
3104 <s><margin.target id="marg54"/>54</s></p><p type="main">
3105 
3106 <s>Tex. 39. <emph type="italics"/>(Si enim quod duobus rectis ine&longs;t, non in <lb/>quantum &aelig;quicrus, &longs;ed in quantum triangulus, no&shy;<lb/>&longs;cens, &amp;c.)<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha&shy;<lb/>bere tres angulos &aelig;quales duobus rectis conuenit <lb/>&aelig;quicruri, non quatenus &aelig;quicrus e&longs;t, &longs;ed quate&shy;<lb/>nus triangulus e&longs;t, &amp;c. </s>
3107 
3108 <s>quid &longs;it habere tres &aelig;qua&shy;<lb/>les duobus rectis, &amp;c. </s>
3109 
3110 <s>fus&egrave; explicatum e&longs;t in lib. 
3111 
3112 1. <lb/>Priorum &longs;ecto 3. cap. 
3113 
3114 1. qu&ograve; te nunc mitto.</s></p><p type="main">
3115 
3116 <s><arrow.to.target n="marg55"/></s></p><p type="margin">
3117 
3118 <s><margin.target id="marg55"/>55</s></p><p type="main">
3119 
3120 <s>Po&longs;t pauca <emph type="italics"/>(Ine&longs;t omni triangulo hoc quod est <lb/>duos, &amp;c.)<emph.end type="italics"/> ide&longs;t, h&aelig;c proprietas, qu&aelig; e&longs;t habere <lb/>duos angulos rectos non actu, &longs;ed per &aelig;quiualen&shy;<lb/>tiam trium angulorum trianguli. </s>
3121 
3122 <s>Vide qu&aelig; im&shy;<lb/>mediat&egrave; &longs;upra de hac re dixi, &amp; qu&ograve; te remi&longs;r.</s></p><p type="main">
3123 
3124 <s><arrow.to.target n="marg56"/></s></p><p type="margin">
3125 
3126 <s><margin.target id="marg56"/>56</s></p><p type="main">
3127 
3128 <s>Eodem tex <emph type="italics"/>(Quando igitur cognofcimes, quod&shy;<lb/>quatuor exteriores &longs;unt &aelig;quales, quoniam I&longs;o&longs;celes, <lb/>adhuc defseit, propier quid I&longs;o&longs;celes? </s>
3129 
3130 <s>quoniain trian&shy;<lb/>gulus: &amp; hoc quoniam figura rectilinea, &amp;c.)<emph.end type="italics"/> exem&shy;<lb/>plo geometrico vult o&longs;tendere demon&longs;trationem <lb/>vniuer&longs;alem e&longs;&longs;e particulari pr&aelig;&longs;tantiorem: e&longs;t <lb/>autem exemplum de pulcherrima, <expan abbr="atq;">atque</expan> admira&shy;<lb/>bili proprietate, qu&aelig; omnibus figuris rectilineis <lb/>conuenit, e&longs;t <expan abbr="&qacute;">que</expan>; huiu&longs;modi: Omnis figur&aelig; rectili&shy;<lb/>ne&aelig; anguli externi omnes &longs;imul &longs;umpti, &longs;unt &aelig;qua <lb/>les quatuor rectis angulis, qu&aelig; affectio demon&shy;<lb/>&longs;tratur in &longs;cholio 32. primi Elem. 
3131 
3132 dicuntur autern <lb/>anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo pra&longs;enti anguli externi &longs;unt, B D C, <pb pagenum="62"/>D F E, F B A, ita vt qu&aelig;libet figura tot angulos externos &longs;ortiatur, quot <lb/>habet latera; cum exproductis lateribus oriantur. </s>
3133 
3134 <s>Vt autem propo&longs;itio ve&shy;<lb/>rificetur, &longs;ingula latera ordinatim &longs;unt producenda, hoc e&longs;t, ver&longs;us eandem <lb/>partem, vt in figuris appo&longs;itis vides. </s>
3135 
3136 <s>Qu&aelig;uis igitur figura rectilinea, &longs;iue <lb/>trilatera &longs;it, &longs;iue quadrilatera, vel etiam millelatera, &amp; proinde mille quo&shy;<lb/>que angulos externos habeat, hanc tamen mirabilem proprietatem (quod <lb/>vix credi pote&longs;t) po&longs;&longs;idet, vt omnes illi anguli externi &longs;imul &longs;int &aelig;quales <lb/>quatuor rectis angulis. </s>
3137 
3138 <s>vnde tres externi anguli trianguli, &amp; quatuor exter&shy;<lb/>ni quadranguli, &amp; quinque externi <expan abbr="p&etilde;tagoni">pentagoni</expan>, &amp;c. </s>
3139 
3140 <s>&longs;unt &aelig;quales quatuor tan&shy;<lb/>tum rectis, nec aliter res &longs;e habet in figura millelatera. </s>
3141 
3142 <s>Ex quo fit, vt an&shy;<lb/>guli externi cuiu &longs;uis figur&aelig; &longs;int &aelig;quales angulis omnibus externis alterius <lb/>cuiu&longs;libet figur&aelig;. </s>
3143 
3144 <s>Ari&longs;t. 
3145 
3146 igitur inquit, quando cogno&longs;cimus, quod quatuor <lb/>angulis rectis &longs;unt &aelig;quales exteriores omnes anguli alicuius figur&aelig;, quo&shy;<lb/>niam figura illa e&longs;t triangulum &longs;calenum, adhuc talis cognitio e&longs;t defecti&shy;<lb/>ua, quia non illi competit illa pa&longs;&longs;io, quia &longs;it triangulum &longs;calenum, neque <lb/>competit &longs;caleno, quia &longs;it triangulum; &longs;ed his omnibus competit, quia &longs;unt <lb/>figur&aelig; rectiline&aelig;, cui h&aelig;c proprietas ine&longs;t primo, &amp; vniuer&longs;aliter: qui igi&shy;<lb/>tur &longs;cit, &longs;calenum habere pr&aelig;dictam affectionem, ex eo, quod &longs;it figura re&shy;<lb/>ctilinea, perfectius &longs;cit, quia nihil amplius qu&aelig;ri pote&longs;t, quia illa figura re&shy;<lb/>ctilinea illud vniuer&longs;ale e&longs;t, cui primo competit; reliquis autem per illam. <lb/></s>
3147 
3148 <s>qui igitur vniuer&longs;ale &longs;cit, perfectius &longs;cit; quod volebat Ari&longs;t. 
3149 
3150 demon&longs;trare.</s></p><p type="main">
3151 
3152 <s><arrow.to.target n="marg57"/></s></p><p type="margin">
3153 
3154 <s><margin.target id="marg57"/>57</s></p><p type="main">
3155 
3156 <s>Eodem tex. <emph type="italics"/>(Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/>&aelig;quales)<emph.end type="italics"/> nihil &longs;requentius. </s>
3157 
3158 <s>vide &longs;upra lib. 
3159 
3160 1. Priorum &longs;ecto 3. cap. 
3161 
3162 1.<!-- KEEP S--></s></p><p type="main">
3163 
3164 <s><arrow.to.target n="marg58"/></s></p><p type="margin">
3165 
3166 <s><margin.target id="marg58"/>58</s></p><p type="main">
3167 
3168 <s>Tex. 43. <emph type="italics"/>(Sed planum, quod et&longs;i e&longs;&longs;et &longs;entire triangulum, quod duobus rectis <lb/>&aelig;quales habet angulos)<emph.end type="italics"/> vide &longs;upra lib. 
3169 
3170 1. Priorum &longs;ecto 3. cap. 
3171 
3172 1.<!-- KEEP S--></s></p><p type="main">
3173 
3174 <s><arrow.to.target n="marg59"/></s></p><p type="margin">
3175 
3176 <s><margin.target id="marg59"/>59</s></p><p type="main">
3177 
3178 <s>Po&longs;t pauca <emph type="italics"/>(Quare &amp; &longs;i &longs;upra Lunam e&longs;&longs;emus, &amp; videremus obiectam terram, <lb/>non <expan abbr="vtiq;">vtique</expan> &longs;ciremus cau&longs;am eclyp&longs;is)<emph.end type="italics"/> loquitur de defectu Lun&aelig;, qui fit, quando <lb/>terra inter Lunam, &amp; Solem po&longs;ita, impedit, ne lumen Solis feratur in Lu&shy;<lb/>nam, &longs;ed efficit, vt vmbra ip&longs;ius terr&aelig; eam contegat.</s></p><p type="main">
3179 
3180 <s><arrow.to.target n="marg60"/></s></p><p type="margin">
3181 
3182 <s><margin.target id="marg60"/>60</s></p><figure place="text" xlink:href="figures-la/009.01.062.1.tif"/><p type="main">
3183 
3184 <s>Et paulo po&longs;t <emph type="italics"/>(Qutmadmod&ubreve; &longs;t vi&shy;<lb/>trum perforatum videremus, &amp; lumen <lb/>permeans, planum vtique e&longs;&longs;et propter <lb/>quid comburit)<emph.end type="italics"/> Ioquitur de ea com&shy;<lb/>bu&longs;tione, cu&aelig; fit per refractionem <lb/>media &longs;ph&aelig;ra vitrea. </s>
3185 
3186 <s>de qua Vitel&shy;<lb/>lio propo&longs;. </s>
3187 
3188 <s>48. decimi libri; non au&shy;<lb/>tem de ea, qu&aelig; fit per reflexionem <lb/>ex &longs;peculo concauo quando combu&shy;<lb/>&longs;tio fit per refractionem, cau&longs;atur &agrave; <lb/>radijs Solis vitrum permeantibus, <lb/>in quo ita franguntur, vt egredien&shy;<lb/>tes &egrave; vitro &longs;imul vniantur, ex qua <lb/>vnione ita calor intenditur, vt ibi <lb/>comburat. </s>
3189 
3190 <s>vt in appo&longs;ita figura cer&shy;<lb/>nere facile e&longs;t; in qua radij &agrave; Sole <lb/>manentes, &longs;ph&aelig;ram vitream perua&shy;<pb pagenum="63"/>dunt, <expan abbr="atq;">atque</expan> in exitu ita refraguntur, vt ad A, punctum coaceruati, ibi po&longs;&shy;<lb/>&longs;int, &longs;i quid combu&longs;tibile occurrat, comburere. </s>
3191 
3192 <s>Si igitur, inquit Ari&longs;t. 
3193 
3194 vide&shy;<lb/>remus illos radios &longs;ic permeare, &amp; refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro&shy;<lb/>pter quid incendant.<lb/><arrow.to.target n="marg61"/></s></p><p type="margin">
3195 
3196 <s><margin.target id="marg61"/>61</s></p><p type="main">
3197 
3198 <s>Ad finem tex. <!-- REMOVE S-->43. <emph type="italics"/>(Principia enim duplicia &longs;unt, ex quibus, &amp; circa quod: <lb/>qu&aelig; quidem igitur, ex quibus, communia &longs;unt: qu&aelig; autem circa quod propria, vt <lb/>numerus, magnitudo)<emph.end type="italics"/> nonnulli codices corrupt&egrave; legunt (vt numerus magni&shy;<lb/>tudine) &longs;ed ex gr&aelig;co tex. <!-- REMOVE S-->corrigendi &longs;unt, vti fecimus. </s>
3199 
3200 
3201 
3202 
3203 
3204 <s>C&aelig;terum per prin&shy;<lb/>cipia, ex quibus intelligit Dignitates, quia ex illis di&longs;currimus. </s>
3205 
3206 <s>per princi&shy;<lb/>pia ver&ograve; circa quod, intelligit Definitiones, quibus, vt apparet apud Eucli&shy;<lb/>dem, explicatur &longs;ubiectum, circa quod &longs;cientia ver&longs;atur; vt in definitioni&shy;<lb/>bus primi Elem. 
3207 
3208 docemur, quid &longs;it linea, quid triangulum, quid circulus, <lb/>quid magnitudines reliqu&aelig;, qu&aelig; &longs;unt materia, circa quam Geometria &longs;pe&shy;<lb/>culatur. </s>
3209 
3210 <s>In &longs;eptimo ver&ograve; traduntur definitiones numerorum, quid &longs;it nu&shy;<lb/>merus, quid impar, quid compo&longs;itus, quadratus, cubus, &amp; reliqu&aelig; nume&shy;<lb/>rorum &longs;pecies, qu&aelig; &longs;unt materia &longs;eptimi, octaui, &amp; noni, in quibus de Arith&shy;<lb/>metica tractatur.</s></p><p type="main">
3211 
3212 <s><arrow.to.target n="marg62"/></s></p><p type="margin">
3213 
3214 <s><margin.target id="marg62"/>62</s></p><p type="main">
3215 
3216 <s>Tex. 44. <emph type="italics"/>(Commen&longs;urabilem namq e&longs;&longs;e diametrum ver&egrave; opinari, ab&longs;urdum e&longs;t)<emph.end type="italics"/><lb/>vide, qu&aelig; de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/>lib. 
3217 
3218 1. Priorum &longs;ecto 1. cap. 
3219 
3220 23. ait igitur Ari&longs;t. 
3221 
3222 ab&longs;urdum e&longs;&longs;e opinari dia&shy;<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;t&aelig;, &longs;eu lateri eiu&longs;dem quadrati, reli&shy;<lb/>qua &longs;unt Logica.</s></p></chap><chap><p type="head">
3223 
3224 <s><emph type="italics"/>Ex Secundo Posteriorum.<emph.end type="italics"/></s></p><p type="main">
3225 
3226 <s><arrow.to.target n="marg63"/></s></p><p type="margin">
3227 
3228 <s><margin.target id="marg63"/>63</s></p><p type="main">
3229 
3230 <s>Tex. 1. <emph type="italics"/>(Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter&shy;<lb/>ram, aut Solem, aut triangulum; aliquid ver&ograve; defectum, &aelig;qualitatem, <lb/>in&aelig;qualitatem. </s>
3231 
3232 <s>&longs;i in medio, aut non)<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/>quatenus ad Mathematicum attinet, optim&egrave; declarat. </s>
3233 
3234 <s>In qu&aelig;&shy;<lb/>&longs;tionibus, &amp; demon&longs;trationibus duo &longs;unt, &longs;ubiectum, &amp; <expan abbr="pr&aelig;dicat&utilde;">pr&aelig;dicatum</expan>, <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/>cau&longs;&aelig; exi&longs;tunt, &amp; qu&aelig;runtur: v. <!-- REMOVE S-->g. <!-- REMOVE S-->Luna, terra, Sol, &amp; triangulum &longs;unt &longs;u&shy;<lb/>biectum in demon&longs;tratione, quorum pr&aelig;dicata &longs;unt, Lun&aelig; quidem, &amp; So&shy;<lb/>lis, eclyp&longs;is. </s>
3235 
3236 
3237 
3238 
3239 
3240 <s>terr&aelig; autem e&longs;&longs;e in medio mundi, quod ab A&longs;tronomis ratione <lb/>ab eclyp&longs;ibus de&longs;umpta, euidentius, quam ab alio quoquam demon&longs;tratur, <lb/>vt patet ex tractatu de &longs;ph&oelig;ra. </s>
3241 
3242 <s>in quo Zabarella non probatur, qui &longs;olum <lb/>ait, terram e&longs;&longs;e in medio mundi, &agrave; Phy&longs;icis demon&longs;trari. </s>
3243 
3244 <s><expan abbr="tri&atilde;gulum">triangulum</expan> autem, <lb/>&longs;eu angulorum ip&longs;ius <expan abbr="pr&aelig;dicat&utilde;">pr&aelig;dicatum</expan> e&longs;t &aelig;qualitas, &amp; in&aelig;qualitas: vt cum in 32. <lb/>primi Elem. 
3245 
3246 demon&longs;trat Euclides, omne triangulum habcre tres angulos <lb/>&aelig;quales duobus rectis.</s></p><p type="main">
3247 
3248 <s><arrow.to.target n="marg64"/></s></p><p type="margin">
3249 
3250 <s><margin.target id="marg64"/>64</s></p><p type="main">
3251 
3252 <s>Ibidem <emph type="italics"/>(Quid e&longs;t con&longs;onantia? </s>
3253 
3254 <s>ratio numerorum in acuto, &amp; graui, &amp;c)<emph.end type="italics"/> tan&shy;<lb/>git breuiter Ari&longs;t. 
3255 
3256 cau&longs;am formalem con&longs;onanti&aelig;, &amp; con&longs;equenter defini&shy;<lb/>tionem ip&longs;ius. </s>
3257 
3258 <s>definiunt igitur Mu&longs;ici con&longs;onantiam hoc modo; Con&longs;onan&shy;<lb/>tia e&longs;t compo&longs;itio &longs;oni grauis, &amp; acuti, qu&aelig; &longs;uauiter auribus accidit; &amp; quo&shy;<lb/>rum &longs;onorum proportio ad inuicem &longs;it &longs;icuti proportio numerorum, qui <lb/>quaternario includuntur: vt e&longs;t proportio 2. ad 1. vel 3. ad 1. vel 4. ad 1. <lb/>vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs;eunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64"/>ex <expan abbr="quinq;">quinque</expan> pr&aelig;dictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnue <lb/>tantum &longs;onus efficiatur; &longs;onus ille erit concordans, &amp; auribus gratus. </s>
3259 
3260 <s><expan abbr="atq;">atque</expan> <lb/>h&aelig;c e&longs;t &longs;ententia pri&longs;corum pr&aelig;&longs;ertim Pythagoreorum, qui propterea di&shy;<lb/>cebantnon licere Mu&longs;ico vltra quaternarium pertran&longs;ire, e&ograve; quod &longs;ol&aelig; pro&shy;<lb/>portiones, vt diximus, numerorum quaternario contentorum, concordem, <lb/>ac con&longs;onantem concentum efficere poterant: quod vt adhuc melius per&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.064.1.tif"/><lb/>cipiamus, accipe exemplum. </s>
3261 
3262 <s>Sint du&aelig; chord&aelig; <lb/>A, &amp; B, &aelig;qualis cra&longs;&longs;itici, &amp; &aelig;qu&egrave; ten&longs;&aelig;. </s>
3263 
3264 <s>qua&shy;<lb/>rum A, dupla &longs;it ip&longs;ius B, quia igitur corpora <lb/>&longs;onantia &longs;unt in dupla proportione, erunt pa&shy;<lb/>riter corum &longs;oni in ratione dupla (vt patet ex <lb/>principijs harmonic&aelig;) hoc e&longs;t, <expan abbr="eor&utilde;">eorum</expan> &longs;oni erunt, <lb/>vt 2. ad 1. quia &longs;cilicet &longs;onus maioris chord&aelig; A, erit duplus ad &longs;onum mi&shy;<lb/>noris chord&aelig; B. hoc e&longs;t, erit, vt 2. ad 1. &amp; propterea, &longs;i &longs;imul amb&aelig; chord&aelig; <lb/>pul&longs;entur, &longs;onus, quem ex duobus mixtum edent, con&longs;onans, <expan abbr="atq;">atque</expan> grati&longs;&longs;i&shy;<lb/>mus auribus no&longs;tris perueniet. </s>
3265 
3266 <s>huiu&longs;modi porr&ograve; con&longs;onantia, qu&aelig; e&longs;t in <lb/>proportione dupla, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan> omnium &longs;uaui&longs;&longs;ima e&longs;t, &agrave; gr&aelig;cis dicebatur Dia&shy;<lb/>pafon. </s>
3267 
3268 <s><expan abbr="atq;">atque</expan> h&aelig;c in pr&aelig;&longs;entia &longs;ufficiant, cum plura de his ad &longs;ectionem pro&shy;<lb/>blematum 19. qu&aelig; tota e&longs;t de Mu&longs;ica, dicenda &longs;int.</s></p><p type="main">
3269 
3270 <s><arrow.to.target n="marg65"/></s></p><p type="margin">
3271 
3272 <s><margin.target id="marg65"/>65</s></p><p type="main">
3273 
3274 <s>Tex. 2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis &aelig;quales babet)<emph.end type="italics"/> vide anno&shy;<lb/>tata lib. 
3275 
3276 1. Priorum &longs;ecto 3. cap. 
3277 
3278 1.<!-- KEEP S--></s></p><p type="main">
3279 
3280 <s><arrow.to.target n="marg66"/></s></p><p type="margin">
3281 
3282 <s><margin.target id="marg66"/>66</s></p><p type="main">
3283 
3284 <s>Eodem tex. <emph type="italics"/>(Definitiones ver&ograve; apparent omnes &longs;upponentes, &amp; accipientes <lb/>ip&longs;um quid e&longs;t, vt Mathematic&aelig;, quid vnitas, quid par, &amp; impar)<emph.end type="italics"/> alludit ad de&shy;<lb/>finitiones 7. Elem. 
3285 
3286 vbi agitur de numeris. </s>
3287 
3288 <s>Qu&aelig; ver&ograve; hoc loco de principijs <lb/>dicuntur, luculenti&longs;&longs;im&egrave; patent con&longs;ideranti definitiones, &amp; axiomata, qu&aelig; <lb/>Mathematicis demon&longs;trationibus in omnibus fer&egrave; libris pr&aelig;mittuntur; ex <lb/>quibus &longs;tatim demon&longs;trationes deriuantur.</s></p><p type="main">
3289 
3290 <s><arrow.to.target n="marg67"/></s></p><p type="margin">
3291 
3292 <s><margin.target id="marg67"/>67</s></p><p type="main">
3293 
3294 <s>Et paulo po&longs;t <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> <expan abbr="vtiq;">vtique</expan> de plano figura, non enim e&longs;t planum figura, <expan abbr="neq;">neque</expan> fi&shy;<lb/>gura planum)<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu&shy;<lb/>lus, cuius definitio e&longs;t inter definitiones primi Elem. 
3295 
3296 15. &amp; e&longs;t huiu&longs;modi: <lb/>circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, qu&aelig; periph&aelig;ria ap&shy;<lb/>pellatur, ad quam ab vno puncto eorum, qu&aelig; intra figuram &longs;unt po&longs;ita, ca&shy;<lb/>dentes omnes rect&aelig; line&aelig; inter &longs;e &longs;unt &aelig;quales: in qua quidem definitione <lb/>non pr&aelig;dicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/>&longs;au plana &longs;uperficies e&longs;t figura &longs;ecundum &longs;e, ni&longs;i terminetur; <expan abbr="neq;">neque</expan> figura e&longs;t <lb/>plana &longs;uperficies, cum plurim&aelig; &longs;int figur&aelig; curu&aelig;, &amp; pr&aelig;terea &longs;olid&aelig; quam&shy;<lb/>plurim&aelig;.</s></p><p type="main">
3297 
3298 <s><arrow.to.target n="marg68"/></s></p><p type="margin">
3299 
3300 <s><margin.target id="marg68"/>68</s></p><p type="main">
3301 
3302 <s>Ibidem <emph type="italics"/>(Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos &aelig;quales duo&shy;<lb/>bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it)<emph.end type="italics"/> ex dictis lib. 
3303 
3304 1. Priorum &longs;ecto <lb/>3. cap. 
3305 
3306 1. petatur huius loci declaratio.</s></p><p type="main">
3307 
3308 <s><arrow.to.target n="marg69"/></s></p><p type="margin">
3309 
3310 <s><margin.target id="marg69"/>69</s></p><p type="main">
3311 
3312 <s>Tex. 7. <emph type="italics"/>(Quid enim &longs;ignificat triangulum, accipit Geometra)<emph.end type="italics"/> vt manife&longs;tum <lb/>e&longs;t in 20. dednitione primi Elem.<!-- KEEP S--></s></p><p type="main">
3313 
3314 <s><arrow.to.target n="marg70"/></s></p><p type="margin">
3315 
3316 <s><margin.target id="marg70"/>70</s></p><p type="main">
3317 
3318 <s>Ibidem <emph type="italics"/>(Quod autem &longs;it, monstrat)<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="dem&otilde;&longs;tra-tione">demon&longs;tra&shy;<lb/>tione</expan> primi Elem. 
3319 
3320 vbi triangulum &aelig;quilaterum con&longs;truit, &amp; po&longs;tea probat <lb/>illud e&longs;&longs;e triangulum &aelig;quilaterum. </s>
3321 
3322 <s>Certum tamen e&longs;t, Geometram luppo&shy;<lb/>nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur, <pb pagenum="65"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="c&otilde;&longs;trni">con&longs;trni</expan>, <lb/>&amp; e&longs;&longs;e aliquod particulare triangulum, vt fit in pr&aelig;dicta demon&longs;tratione, <lb/>Euclidis.<!-- KEEP S--></s></p><p type="main">
3323 
3324 <s><arrow.to.target n="marg71"/></s></p><p type="margin">
3325 
3326 <s><margin.target id="marg71"/>71</s></p><p type="main">
3327 
3328 <s>Tex. 11. <emph type="italics"/>(Manife&longs;tum autem, &amp; &longs;ic, propter quid e&longs;t rectus in &longs;emicirculo)<emph.end type="italics"/><lb/>affert exemplum demon&longs;trationis per cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; vti &longs;olet ex <lb/>Mathematicis petitum, e&longs;t enim apud Euclidem 31. demon&longs;tratio 3. Elem. <lb/>vbi ip&longs;e o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum. </s>
3329 
3330 <s>Vbi aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t. 
3331 
3332 cui a&longs;cripta e&longs;t figura &longs;imilis huic no&longs;tr&aelig;; <lb/>in editione Clauiana. </s>
3333 
3334 <s>quod fort&egrave; non ben&egrave; aduertens Iacobus Zabarella, <lb/>alioquin in his &longs;atis oculatus incidit in errorem, dicens, &longs;e nullo pacto vi&shy;<lb/>dere medium Euclidian&aelig; demon&longs;trationis e&longs;&longs;e cau&longs;am materialem; quod <lb/>tamen nos mox aperiemus. </s>
3335 
3336 <s>per angulum in &longs;emicirculo intelligas eum, qui <lb/>fit &agrave; lineis ductis ab extremitatibus diametri, &amp; &longs;imul in quoduis punctum <lb/><figure place="text" xlink:href="figures-la/009.01.065.1.tif"/><lb/>circumferenti&aelig; coeuntibus, vt in figura <lb/>pr&aelig;&longs;enti vides lineas A C, B C, ad C, pun&shy;<lb/>ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/>A C B, qui dicitur angulus in &longs;emicircu&shy;<lb/>lo, quia de&longs;criptus e&longs;t in &longs;emicirculo A&shy;<lb/>C B. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;an&egrave; mirabilis h&aelig;c &longs;emicirculi <lb/>proprietas, cum <expan abbr="vbicunq;">vbicunque</expan> punctum C, in <lb/>periph&aelig;ria &longs;umptum fuerit, &longs;emper ta&shy;<lb/>men angulus A C B, fiat rectus. </s>
3337 
3338 <s>quod Euclides eodem pror&longs;us medio, quod <lb/>Ari&longs;t. 
3339 
3340 hic innuit, hoc modo demon&longs;trat. </s>
3341 
3342 <s>ducta enim recta D C, &agrave; centro D, <lb/>ad punctum C, exurgunt duo l&longs;o&longs;celia triangula A D C, C D B, ergo per <lb/>5. primi, anguli D C A, D A C, &longs;unt &aelig;quales: pariter anguli D C B, D B C, <lb/>&aelig;quales &longs;unt. </s>
3343 
3344 <s>&amp; quia per 32. primi, anguli D A C, D C A, &longs;imul &longs;unt &aelig;qua&shy;<lb/>les angulo externo C D B, &amp; inter &longs;e &aelig;quales, erit angulus A C D, dimidium <lb/>anguli C D B. eadem ratione probatur angulus D C B, e&longs;&longs;e dimidium an&shy;<lb/>guli C D A. ergo totus angulus A C B, dimidium erit duorum angulorum <lb/>A D C, C D B, qui per 13. primi, &longs;unt vel recti, vel duobus rectis <expan abbr="&aelig;quiual&etilde;t">&aelig;quiualent</expan>. <lb/></s>
3345 
3346 <s>Sequitur igitur, angulum A C B, in &longs;emicirculo e&longs;&longs;e dimidium duorum re&shy;<lb/>ctorum; &amp; quia omnes recti &longs;unt &aelig;quales, &longs;equitur dimidium duorum re&shy;<lb/>ctorum, nihil aliud e&longs;&longs;e, quam vnum rectum angulum, ergo angulus in &longs;e&shy;<lb/>micirculo, cum &longs;it &longs;emi&longs;&longs;is duorum <expan abbr="rector&utilde;">rectorum</expan>, erit vnus rectus angules; quod <lb/>erat probandum. </s>
3347 
3348 <s>ex quibus vides medium illud, quod Ari&longs;t. 
3349 
3350 a&longs;&longs;ump&longs;it, e&longs;&longs;e <lb/>omnino idem cum eo, quo Euclides vtitur, &longs;cilicet, e&longs;&longs;e dimidium duorum <lb/>rectorum, &amp; propterea e&longs;&longs;e rectum: quod etiam medium in toto demon&shy;<lb/>&longs;trationis decur&longs;u e&longs;t vltimum, &amp; principale, quod proxim&egrave; conclu&longs;ionem <lb/>attingit, &amp; propterea dici meretur e&longs;&longs;e medium huius demon&longs;trationis. <lb/></s>
3351 
3352 <s>C&aelig;terum, quod medium i&longs;tud &longs;it in genere cau&longs;&aelig; materialis, patet ex co, <lb/>quod e&longs;t, e&longs;&longs;e dimidium; nam e&longs;&longs;e dimidium, vel e&longs;&longs;e tertiam partem, &amp; &longs;i&shy;<lb/>milia, nihil aliud e&longs;t, quam e&longs;&longs;e partem; e&longs;&longs;e autem partem e&longs;t e&longs;&longs;e materiam <lb/>totius, etiam ex &longs;ententia ip&longs;ius Ari&longs;t. 
3353 
3354 ex hac pr&aelig;terea materia conflatur <lb/>definitio minoris extremi, vel &longs;ubiecti; dum dicitur, angulus in &longs;emicircu&shy;<lb/>lo e&longs;t dimidium duorum rectorum. </s>
3355 
3356 <s>&longs;yllogi&longs;mus enim reducitur tandem ad <pb pagenum="66"/>hanc formam, dimidium duorum rectorum e&longs;t rectus, angulus in &longs;emicir&shy;<lb/>culo e&longs;t dimidium duorum <expan abbr="rector&utilde;">rectorum</expan>, ergo angulus in &longs;emicirculo e&longs;t rectus. <lb/></s>
3357 
3358 <s>vides in minori propo&longs;itione contineri definitionem &longs;ubiecti materialem? <lb/></s>
3359 
3360 <s>ade&ograve; vt h&aelig;c &longs;it demon&longs;tratio omnibus numeris ab&longs;oluta per cau&longs;am mate&shy;<lb/>rialem, vt ben&egrave; &longs;entit Ari&longs;t. <!-- KEEP S--></s>
3361 
3362 <s>Reliqua ad logicum pertinent, etiam&longs;i per cha&shy;<lb/>racteres more mathematicorum exponantur.</s></p><p type="main">
3363 
3364 <s><arrow.to.target n="marg72"/></s></p><p type="margin">
3365 
3366 <s><margin.target id="marg72"/>72</s></p><p type="main">
3367 
3368 <s>Tex. 24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s>
3369 
3370 <s>aut propter quid apparet? </s>
3371 
3372 <s>aut propter quid <lb/>Iris? <!-- KEEP S--></s>
3373 
3374 <s>omnia enim h&aelig;r idem problemata &longs;unt genere, omnia enim &longs;unt refractio, &longs;ed <lb/>&longs;pecie altera)<emph.end type="italics"/> propter quid re&longs;onat? </s>
3375 
3376 <s>&longs;cilicet echo; propter quid apparet? <lb/></s>
3377 
3378 <s>&longs;cilicet imago in &longs;peculo. </s>
3379 
3380 <s>dicit cau&longs;am echo, imaginis in &longs;peculo, &amp; iridis <lb/>in nubibus e&longs;&longs;e eandem; nimirum refractionem; quamuis tres ill&aelig; refractio&shy;<lb/>nes, &longs;eu; vt melius loquamur, reflexiones differant &longs;pecie ab inuicem, illa <lb/>enim e&longs;t repercu&longs;&longs;io vocis; h&aelig;c reflexio &longs;peciei vi&longs;ibilis ex corpore ter&longs;o; <lb/>i&longs;ta <expan abbr="deniq;">denique</expan> radiorum Solis ex nube rorida in &longs;tato angulo repercu&longs;&longs;us. </s>
3381 
3382 <s>qua <lb/>ratione autem i&longs;ta omnia fiant, longum e&longs;&longs;et exponere, &amp; ab intelligentia <lb/>huius loci fort&egrave; alienum. </s>
3383 
3384 <s>Illud tamen non pr&aelig;tereundum, quod &longs;i propri&egrave; <lb/>cum Per&longs;pectiuis loqui velimus, dicendum e&longs;&longs;e, omnia illa e&longs;&longs;e reflexionem, <lb/>non refractionem. </s>
3385 
3386 <s>nam reflexio e&longs;t, quando linea vi&longs;ualis, per quam fertur <lb/>&longs;p&eacute;ecies in aliquod corpus ter&longs;um, impingit, ex quo deinde ad oculos refle&shy;<lb/>ctitur. </s>
3387 
3388 <s>refractio tunc e&longs;t, quando &longs;pecies obiectivi&longs;ibilis tran&longs;it per media <lb/>diuer&longs;&aelig; cra&longs;&longs;itiei., vt quando &longs;pecies lapilli per aquam prim&ugrave;m, deinde per <lb/>&aelig;erem means ad oculum peruenit; tunc enim linea, per quam &longs;pecies pro&shy;<lb/>greditur, frangitur in confinio aqu&aelig;, &amp; aeris, ita vt &longs;pecies non per vnicam <lb/>lineam rectam, &longs;ed per fractam, &longs;eu refractam in confinio illo, oculis tan&shy;<lb/>dem accidat.</s></p><p type="main">
3389 
3390 <s>In fine textus <emph type="italics"/>(Quoniam Luna deficit)<emph.end type="italics"/> non intelligit defectum illum, qui <lb/>eclyp&longs;is appellatur, &longs;ed ilium, quo paulatim lumen Lun&aelig; minus oculis no&shy;<lb/>&longs;tris apparet: decre&longs;cente enim Luna &longs;olent humida augeri.</s></p><p type="main">
3391 
3392 <s><arrow.to.target n="marg73"/></s></p><p type="margin">
3393 
3394 <s><margin.target id="marg73"/>73</s></p><p type="main">
3395 
3396 <s>Tex. 25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s>
3397 
3398 <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. <!-- REMOVE S-->13. primi Po&longs;ter. qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s>
3399 
3400 
3401 
3402 <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main">
3403 
3404 <s><arrow.to.target n="marg74"/></s></p><p type="margin">
3405 
3406 <s><margin.target id="marg74"/>74</s></p><p type="main">
3407 
3408 <s>Ibidem (<emph type="italics"/>Hic quidem forta&longs;&longs;e proportionaliter habere latera, &amp; angulos<emph.end type="italics"/>) vult <lb/>indicare, in quonam con&longs;i&longs;tat &longs;imilitudo inter duas-figuras rectilineas geo&shy;<lb/>metricas, quam &longs;imilitudinem Euclides definit. </s>
3409 
3410 <s>1. &longs;exti, &longs;ic explicat: &longs;imi&shy;<lb/>les figur&aelig; rectil&iacute;ne&aelig; &longs;unt; qu&aelig; &amp; angulos &longs;ingulos, &longs;ingulis angulis &aelig;quales <lb/>habent, <expan abbr="atq;">atque</expan> etiam latera, qu&aelig; circa angulos &aelig;quales &longs;unt proportionalia. <lb/></s>
3411 
3412 <s>vt &longs;i duo triangula appo&longs;ita habeant angulos &aelig;quales, <expan abbr="angul&utilde;">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. &amp; pr&aelig;terea latera, qu&aelig; &longs;une <pb pagenum="67"/><figure place="text" xlink:href="figures-la/009.01.067.1.tif"/><lb/>circa angulos &aelig;quales, v. <!-- REMOVE S-->g. <!-- REMOVE S-->cirea an&shy;<lb/>gulos A, &amp; D, habeant proportiona&shy;<lb/>lia, hoc e&longs;t, vt latus A B, ad latus A C; <lb/>ita &longs;it latus D E, ad latus D F; &amp; &longs;ic de <lb/>lateribus alijs circa reliquos angulos <lb/>&aelig;quales; erunt tunc pr&aelig;dicta duo tri&shy;<lb/>angula fimilia.</s>
3413 
3414 
3415 
3416 </p><p type="main">
3417 
3418 <s><arrow.to.target n="marg75"/></s></p><p type="margin">
3419 
3420 <s><margin.target id="marg75"/>75</s></p><p type="main">
3421 
3422 <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. <!-- REMOVE S-->39. &longs;ecundi Po&longs;ter. qu&aelig; huic pariter loco &longs;atisfaciunt.</s>
3423 
3424 </p><p type="head">
3425 
3426 <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head">
3427 
3428 <s><emph type="italics"/>Ex Primo Libro.<emph.end type="italics"/><!-- KEEP S--></s></p></chap><chap><p type="main">
3429 
3430 <s><arrow.to.target n="marg76"/></s></p><p type="margin">
3431 
3432 <s><margin.target id="marg76"/>76</s></p><p type="main">
3433 
3434 
3435 <s>Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;t&aelig; incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>qu&aelig; de hac re &longs;crip&longs;i lib. 
3436 
3437 
3438 1. Priorum &longs;ecto 1. cap. 
3439 
3440 23.</s></p><p type="main">
3441 
3442 <s><arrow.to.target n="marg77"/></s></p><p type="margin">
3443 
3444 <s><margin.target id="marg77"/>77</s></p><p type="main">
3445 
3446 <s>Eodem cap. (<emph type="italics"/>Similiter autem &amp; acutum; non enim idem &longs;impliciter <lb/>in omnibus dicitur: nam vox acuta quidem velox (&longs;icut dicunt, qui &longs;e&shy;<lb/>cundum numeros harmonici &longs;unt) angulus autem acutus, qui minor e&longs;trecto; gla&shy;<lb/>dius ver&ograve;, qui e&longs;t anguli acuti<emph.end type="italics"/>) affert tres &longs;pecies acuti, aliud dicens e&longs;&longs;e acu&shy;<lb/>tum, quod e&longs;t in voce acuta; aliud, quod e&longs;t in angulo acuto: aliud denique, <lb/>quod e&longs;t in gladio acuto horum enim trium acumen diuer&longs;o modo &longs;e habet. <lb/></s>
3447 
3448 <s>nam acumen vocis, &amp; &longs;oni ex celeritate motus, qua aer percu&longs;&longs;us impelli&shy;<lb/>tur; grauitatem autem ex tarditate oriri tradiderunt antiqui Mu&longs;ici om&shy;<lb/>nes: quamuis non ex &longs;ola celeritate, &amp; tarditate, &longs;ed ex alijs etiam cau&longs;is <lb/>oriri po&longs;&longs;e voluerint. </s>
3449 
3450 <s>Primus <expan abbr="omni&utilde;">omnium</expan> Architas Tarentinus, vt e&longs;t apud Por&shy;<lb/>phirium in harmonicis Ptol&aelig;mei, &amp; Zarlinum pag. </s>
3451 
3452 <s>58. complem. </s>
3453 
3454 <s>mu&longs;ica&shy;<lb/>lium, ait, &longs;i virga celerius feriat aerem, gigni motum celeriorem in aere, <lb/><expan abbr="atq;">atque</expan> hinc &longs;onum acutiorem reddi, experientia con&longs;tat: &longs;i autem eadem vir&shy;<lb/>ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o&shy;<lb/>num grauem, vt experientia docet. </s>
3455 
3456 <s>Ptol&aelig;meus deinde lib. 
3457 
3458 1. cap. 
3459 
3460 3. Harm. <lb/><!-- REMOVE S-->cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem ver&ograve; ex tardi&shy;<lb/>tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver&shy;<lb/>berat, &amp; ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/>aerem pul&longs;abit, &amp; proinde citiorem motum illi imprimet, &amp; propterea <lb/>acutiorem &longs;onum reddet. </s>
3461 
3462 
3463 
3464 <s>h&aelig;c ille. </s>
3465 
3466 <s>videmus etiam, quod cann&aelig; organo&shy;<lb/>rum maiores cum plus aeris moucant, &amp; idcirco tardius, &longs;onum grauiorem <lb/>emittunt, qu&agrave;m cann&aelig; graciliores, qu&aelig; quia parum aeris cient, &amp; ideo ce&shy;<lb/>lerius, &longs;onum acutum edunt. </s>
3467 
3468 <s>ab hac &longs;ententia po&longs;teriores Mu&longs;ici non recel&shy;<lb/>&longs;erunt, vt videre e&longs;t apud Zarlinum.<!-- KEEP S--></s></p><p type="main">
3469 
3470 <s>In quo po&longs;tea con&longs;i&longs;tat ratio acnti anguli, explicat <expan abbr="induc&etilde;s">inducens</expan> definitionem <lb/>ip&longs;ius, qu&aelig; e&longs;t inter de&longs;initiones primi Elem. 
3471 
3472 huiu&longs;modi, Angulus acutus <lb/>e&longs;t, qui minor recto e&longs;t. </s>
3473 
3474 <s>Demum explicat, cur nam gladius dicatur acutus, <lb/>quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem du&aelig; &longs;uper&shy;<lb/>ficies &longs;imul in acie gladij concurrentes efficiunt.</s></p><pb pagenum="68"/><p type="main">
3475 
3476 <s><arrow.to.target n="marg78"/></s></p><p type="margin">
3477 
3478 <s><margin.target id="marg78"/>78</s></p><p type="main">
3479 
3480 <s>Eodem cap. (<emph type="italics"/>Rur&longs;um &longs;i eorundem; qu&aelig; &longs;unt &longs;ub eodem nomine diuer&longs;&aelig; d ffe&shy;<lb/>renti&aelig; &longs;unt; vt coloris, qui e&longs;t in corporibus, &amp; in melodijs<emph.end type="italics"/>) veteres Mu&longs;ici can&shy;<lb/>tilenas omnes ad tria genera reuocarunt, videlicet Enharmonicum, Chro&shy;<lb/>maticum, &amp; Diatonicum; qu&aelig; diftinguebantur inuicem ex varia diui&longs;ione <lb/>interuallorum, ex quibus ip&longs;orum Monochordia conftabant: &longs;iue ex varijs <lb/>vocum interuallis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->quia in vno continebantur plures toni, vt in Diato&shy;<lb/>nico; in alio plures die&longs;es, vt in Enharmonico; in tertio ver&ograve; plura &longs;emito&shy;<lb/>nia, vt in Chromatico: qu&aelig; vox deducitur &agrave; chroma, gr&aelig;co, quod latinis <lb/>e&longs;t color; quare Chromaticum latin&egrave; redditur coloratum. </s>
3481 
3482 
3483 
3484 
3485 
3486 <s>Hic e&longs;t igitur <lb/>color ille, quem hic Ari&longs;t. 
3487 
3488 innuit. </s>
3489 
3490 <s>quod genus for&longs;itan &agrave; calore denomina&shy;<lb/>batur, qu&ograve;d ip&longs;ius not&aelig; mu&longs;icales e&longs;&longs;ent colorat&aelig;, vt hoc modo ab alijs ge&shy;<lb/>neribus digno&longs;ceretur. quam con&longs;uetudinem exi&longs;timat Zarlinus cap. 
3491 
3492 46. &longs;e&shy;<lb/>cund&aelig; partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi&shy;<lb/>deamus in organis, &amp; alijs huiu&longs;modi in&longs;trumentis, qu&aelig; pinnas, vulg&ograve; ta&shy;<lb/>&longs;tos, habent; illas inquam pinnas, qu&aelig; chromaticis interuallis deputat&aelig; <lb/>&longs;unt, colore nigro tinctas e&longs;&longs;e.</s></p></chap><chap><p type="head">
3493 
3494 <s><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s></p><p type="main">
3495 
3496 <s><arrow.to.target n="marg79"/></s></p><p type="margin">
3497 
3498 <s><margin.target id="marg79"/>79</s></p><p type="main">
3499 
3500 
3501 <s>Cap. 1. loco 10. (<emph type="italics"/>Si quis in&longs;ecabiles ponens lineas<emph.end type="italics"/>) nonnulli antiquorum <lb/>Philo&longs;ophorum putarunt omnia ex indiui&longs;ibilibus componi, vt Demo&shy;<lb/>critus, &amp; Leucippus, &amp; propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam ade &ograve; paruis, qu&aelig; omnino e&longs;ient in&longs;ecabiles, &longs;eu indiui&longs;ibiles: de <lb/>quibus plura in libello de line is in&longs;ecabilibus.</s>
3502 </p></chap><chap><p type="head">
3503 
3504 <s><emph type="italics"/>Libro Sexio.<emph.end type="italics"/></s></p><p type="main">
3505 
3506 <s><arrow.to.target n="marg80"/></s></p><p type="margin">
3507 
3508 <s><margin.target id="marg80"/>80</s></p><p type="main">
3509 
3510 
3511 <s>Cap. 2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudinem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem. 
3512 
3513 
3514 in&shy;<lb/>ter quas definitio line&aelig; e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">cademque</expan>; cum hac Ari&longs;totelis.<!-- KEEP S--></s></p></chap><chap><p type="head">
3515 
3516 <s><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s></p><p type="main">
3517 
3518 <s><arrow.to.target n="marg81"/></s></p><p type="margin">
3519 
3520 <s><margin.target id="marg81"/>81</s></p><p type="main">
3521 
3522 
3523 <s>Cap. 2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis qu&aelig;dam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt &amp; quoniam, qu&aelig; ad latus &longs;e&shy;<lb/>cat planum linea, &longs;imiliter diuidit &amp; lineam, &amp; locum: definitione autem dicta, <lb/>&longs;tatim manife&longs;tum e&longs;t, quod dicitur, nam eandem ablationem habent loca, &amp; linea, <lb/>&longs;ive latus plan&aelig; figur&aelig;, est autem definitio eiu&longs;dem proportionis h&aelig;c<emph.end type="italics"/>) mendos&egrave; <lb/>lugitur &agrave; nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis h&aelig;c<emph.end type="italics"/>) quos puto de&shy;<lb/>ceptos ab &aelig;quiuoco <foreign lang="greek">lsgous</foreign> quod &amp; orationem, &amp; rationem, &longs;iue proportio&shy;<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani&shy;<lb/>fe&longs;tat. </s>
3524 
3525 
3526 <s>Notandum po&longs;tea cum Alexandro (quod &amp; &longs;uperius alias commo&shy;<lb/>nui in cap. 
3527 
3528 de Priori, &amp; alibi) per verbum (De&longs;cribi) fignificari hoc loco <lb/>geometric&egrave; demon&longs;trare, quoniam Geometr&aelig; <expan abbr="n&otilde;">non</expan> ni&longs;i adhibit is de&longs;criptio&shy;<lb/>nibus, &longs;eu figutis demon&longs;trant. </s>
3529 
3530 <s>Vult autem Ari&longs;t. 
3531 
3532 exemplo mathematico <lb/>o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <expan abbr="argum&etilde;tari">argumentari</expan>, ni&longs;i prius rect&egrave; a&longs;&longs;ignetur <pb pagenum="69"/>definitio illius rei, de qua di&longs;&longs;eritur. </s>
3533 
3534 <s>Porr&ograve; exemplum mathematicum hic <lb/>allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro&shy;<lb/>po&longs;itionem; &longs;i linea ducta fuerit &aelig;quidi&longs;tans lateri vnius plani trianguli, &longs;e&shy;<lb/>cabit &amp; latera, &amp; locum, ideft &longs;uperficiem illam triangularem &longs;imiliter, ide &longs;t <lb/><figure place="text" xlink:href="figures-la/009.01.069.1.tif"/><lb/>in eadem proportione, vt in triangulo A B C, <lb/>linea D E, parallela ba&longs;i B C, &longs;ecat latera A B, <lb/>&amp; A C, in punctis D, &amp; E, in eadem ratione, <lb/>in qua etiam fecat totum triangulum, ita vt <lb/>eadem &longs;it proportio line&aelig; A D, ad D B, &amp; line&aelig; <lb/>A E, ad E C, qu&aelig; e&longs;t partium totalis trianguli <lb/>A B C, &longs;eilicet qu&aelig; e&longs;t partis A D E, ad partem <lb/>E D C, fiue ad partem D E B. quod con&longs;tat ex <lb/>&longs;ecunda 6. Elem. <!-- KEEP S--></s>
3535 
3536 <s>Inquit ergo Ari&longs;t. <!-- KEEP S--></s>
3537 
3538 <s>Si quis <lb/>vellet hoc demon&longs;trare nondum pr&aelig;mi&longs;&longs;a defi&shy;<lb/>nitione eorum, qu&aelig; habent eandem rationem, &longs;iue nondum definitione al&shy;<lb/>lata quantitatum proportionalium, hic difficile id valeret o&longs;tendere: at ve&shy;<lb/>r&ograve; allata prins definitione quantitatum proportionalium facile demon&longs;tra&shy;<lb/>bit. </s>
3539 
3540 <s>Subdit ver&ograve; Ari&longs;t. 
3541 
3542 dictam definitionem, dicens, tunc quantitates e&longs;&longs;e <lb/>proportionales, quando habent eandem ablationem, ide&longs;t, eandem diui&longs;io&shy;<lb/>nem, ide&longs;t, eadem diui&longs;io ne tantum proportionaliter de vna, quantum de <lb/>altera magnitudine re&longs;ecatur: Quemadmodum etiam Euclides loco cita&shy;<lb/>to probat, latera illius trianguli, &amp; &longs;uperficiem e&longs;&longs;e &longs;imiliter diui&longs;a, ex quo <lb/>&longs;equitur e&longs;&longs;e proportionalia. </s>
3543 
3544 <s>Porr&ograve; Euclides definit. </s>
3545 
3546 <s>&longs;eptima 5. paulo ali&shy;<lb/>ter definit quantitates proportionales e&longs;&longs;e illas, qu&aelig; eandem habent ratio&shy;<lb/>nem, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i &longs;it, vt prima ad &longs;ecundam, ita tertia ad quartam. </s>
3547 
3548 
3549 
3550 
3551 
3552 <s>ex quibus <lb/>quoad Mathematicas &longs;pectat, huic loco &longs;atisfactum &longs;it.</s></p><p type="main">
3553 
3554 <s><arrow.to.target n="marg82"/></s></p><p type="margin">
3555 
3556 <s><margin.target id="marg82"/>82</s></p><p type="main">
3557 
3558 
3559 <s>Cap. 4. loco 86. <emph type="italics"/>(Tentandum autem, &amp; ea, in qu&aelig; &longs;&aelig;pi&longs;&longs;im&egrave; incidunt di&longs;puta&shy;<lb/>tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer&shy;<lb/>citatum e&longs;&longs;e, &amp; in numeris circa capitales prompt&egrave; &longs;e habere, &amp; multum refert ad <lb/>boc, &amp; alium numerum cogno&longs;cere multiplicatum)<emph.end type="italics"/> Elementa vocabant antiqui <lb/>demon&longs;trationes faciliores, &amp; &longs;impliciores, quales propri&egrave; &longs;unt omnes, qu&aelig; <lb/>&longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele&shy;<lb/>mentis ab&longs;tru&longs;iores, &amp; difficiliores demon&longs;trationes deducebant. </s>
3560 
3561 
3562 <s><expan abbr="atq;">atque</expan> h&aelig;c <lb/>e&longs;t ratio, cur Euclides &longs;uos libros elementa nuncupauerit. </s>
3563 
3564 <s>ait igitur curan&shy;<lb/>dum e&longs;&longs;e horum elementorum cognitionem in promptu habere, quia fre&shy;<lb/>quens de ip&longs;is incidit di&longs;putatio. </s>
3565 
3566 <s>Per capitales numeros intelligo &longs;implices <lb/>ab vnitate, <expan abbr="v&longs;q;">v&longs;que</expan> ad nouem inclu&longs;iu&egrave;. </s>
3567 
3568 <s>&amp; quando ait, alium numerum cogno&shy;<lb/>&longs;cere multiplicatum, &longs;ignificat vtile vald&egrave; e&longs;&longs;e ad quotidianum v&longs;um <lb/>cogno&longs;cere, quemnam numerum producant numeri capitales, <lb/>&longs;i ad inuicem multiplicentur, quamuis huiu&longs;modi co&shy;<lb/>gnitio facilis, ac leuis &longs;it: qua de cau&longs;a vide&shy;<lb/>mus v&longs;que in hanc diem pueros diu in <lb/>Abaco memoriter perdi&longs;cen&shy;<lb/>do detineri.</s></p></chap><chap><pb pagenum="70"/><p type="head">
3569 
3570 <s><emph type="italics"/>Ex Primo Elenchorum.<emph.end type="italics"/></s></p><p type="main">
3571 
3572 <s><arrow.to.target n="marg83"/></s></p><p type="margin">
3573 
3574 <s><margin.target id="marg83"/>83</s></p><p type="main">
3575 
3576 
3577 <s>Cap. 10. <emph type="italics"/>(Nam p&longs;eudograpbi&aelig; non contentio&longs;&aelig; (&longs;ecundum enim ea, qu&aelig; <lb/>&longs;ub arte &longs;unt, captio&longs;&aelig; &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra&shy;<lb/>phia circa verum, vt Hippocratis quadratura, qu&aelig; per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; &amp; tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere &aelig;quale tentauerit, explicatum e&longs;t abund&egrave; in 2. Priorum cap. 
3578 
3579 
3580 31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib. 
3581 
3582 1. Po&longs;ter. tex. <!-- REMOVE S-->23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s>
3583 
3584 
3585 
3586 <s>Qua ratione item Hippocrates ex ijs, qu&aelig; &longs;ub arte Geometri&aelig; &longs;unt, <lb/>procederet ibi dictum e&longs;t, propter quod non e&longs;t contentio&longs;a, quamuis fallax <lb/>ip&longs;ius demon&longs;tratio: appellat enim Ari&longs;t illas demon&longs;trationes contentio&shy;<lb/>&longs;as, qu&aelig; non procedunt ex proprijs illius &longs;cienti&aelig;, in qua fiunt, &longs;ed ex com&shy;<lb/>munibus alijs &longs;cientijs: captio&longs;as ver&ograve;, &amp; &longs;ophi&longs;ticas, qu&aelig; ex proprijs &longs;cien&shy;<lb/>ti&aelig;, in qua fiunt, decipiunt. </s>
3587 
3588 <s>At ver&ograve; demon&longs;tratio, &longs;eu p&longs;eudographia Bry&longs;&shy;<lb/>&longs;onis erat contentio&longs;a, quia ex communibus, &amp; extra Geometriam petitis <lb/>argumentabatur: quemadmodum ibi explicatum e&longs;t.</s></p><p type="main">
3589 
3590 <s><arrow.to.target n="marg84"/></s></p><p type="margin">
3591 
3592 <s><margin.target id="marg84"/>84</s></p><p type="main">
3593 
3594 <s>Eodem cap. <emph type="italics"/>(Quadratura per lunulas non contentio&longs;a)<emph.end type="italics"/> inquit Hippocratis <lb/>tetragoni&longs;mum, de quo in 2. Priorum, qu&aelig; non contentio&longs;a dicitur, quia ex <lb/>proprijs Geometri&aelig; deducebatur.</s></p><p type="main">
3595 
3596 <s><arrow.to.target n="marg85"/></s></p><p type="margin">
3597 
3598 <s><margin.target id="marg85"/>85</s></p><p type="main">
3599 
3600 <s>Ibidem <emph type="italics"/>(Bry&longs;&longs;onis autem contentio&longs;a: &amp; illam quidem non e&longs;t transferre, ni&longs;i <lb/>ad Geometriam &longs;olum; eo quod ex proprijs &longs;it principijs)<emph.end type="italics"/> <expan abbr="qu&atilde;do">quando</expan> ait <emph type="italics"/>(&amp; illam qui&shy;<lb/>dem)<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s>
3601 
3602 <s>vide 2. Prior cap. 
3603 
3604 31. &amp; qu&aelig; pau&shy;<lb/>lo ante in pr&aelig;cedentibus locis diximus.</s></p><p type="main">
3605 
3606 <s><arrow.to.target n="marg86"/></s></p><p type="margin">
3607 
3608 <s><margin.target id="marg86"/>86</s></p><p type="main">
3609 
3610 <s>Ibidem <emph type="italics"/>(Hanc autem ad plures)<emph.end type="italics"/> intelligit tetragoni&longs;mum Bry&longs;&longs;onis, qui <lb/>per communia deducebatur. </s>
3611 
3612 <s>lege &longs;uperius dicta in pr&aelig;cedentibus locis hu&shy;<lb/>ius capituli.</s></p><p type="main">
3613 
3614 <s><arrow.to.target n="marg87"/></s></p><p type="margin">
3615 
3616 <s><margin.target id="marg87"/>87</s></p><figure place="text" xlink:href="figures-la/009.01.070.1.tif"/><p type="main">
3617 
3618 <s>Ad &longs;inem cap. <emph type="italics"/>(Aut vt Antiphon quadra&shy;<lb/>uit)<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon&shy;<lb/>tem in orbe quadrando, ac Hippocratem, <lb/>Ari&longs;t. 
3619 
3620 his verbis videtur &longs;ignificare, ide&longs;t, <lb/>ip&longs;um, quamuis ex proprijs Geometri&aelig;, <lb/>fal&longs;is tamen ratiocinatum e&longs;&longs;e. </s>
3621 
3622 <s>C&aelig;terum <lb/>Antiphontem in hunc modum orbem ad <lb/>quadrum redigere tenta&longs;&longs;e, tradit Simpli&shy;<lb/>cius. </s>
3623 
3624 <s>circulo quadrando in&longs;cribebat pri&shy;<lb/>m&ograve; quadratum A B C D. deinde in &longs;ingu&shy;<lb/>lis quatuor &longs;egmentis in&longs;cribebat totidem <lb/>trigona &aelig;quilatera, vt patet in ad&longs;cripta <pb pagenum="71"/>figura. </s>
3625 
3626 <s>po&longs;tea &longs;uper &longs;ingula latera horum triangulorum in reliquis &longs;egmen&shy;<lb/>tis in&longs;cribebat adhuc triangula &longs;imilia triangulo A I E. alia in&longs;uper trigona <lb/>&longs;uper latera i&longs;torum con&longs;tituebat, donec ambitus figur&aelig; illius multilater&aelig; <lb/>in circulo delinear&aelig;, circumferenti&aelig; circuli aptaretur. </s>
3627 
3628 <s>quod fieri po&longs;&longs;e ille <lb/>fals&ograve; contra Geometri&aelig; principia a&longs;&longs;umebat; e&longs;t enim principium Geome&shy;<lb/>tricum continuum e&longs;&longs;e diui&longs;ibile in infinitum, <expan abbr="neq;">neque</expan> per diui&longs;ionem ab&longs;umi <lb/>po&longs;&longs;e; cui principio aduer&longs;atur, dum putat &longs;e con&longs;umpturum rotum circu&shy;<lb/>lum, diuidendo illud in triangula &longs;emper minora; vel quia putat, lineam <lb/>curuam con&longs;tare ex minimis lineis rectis. </s>
3629 
3630 <s>Similiter igitur <expan abbr="atq;">atque</expan> Hippocra&shy;<lb/>res errauit, q&uacute;i pariter in Geometria fallebatur: Antiphon quidem contra <lb/>principia illius: Hippocrates ver&ograve; a&longs;&longs;umens fal&longs;i quidpiam in Geometria. <lb/><!-- KEEP S--></s>
3631 
3632 <s>At Bry&longs;&longs;o, eo quod per communia alijs &longs;cientijs deduceret ratiocinatio&shy;<lb/>nem propterea p&longs;eudographia Antiphontis non litigio&longs;a quidem, &longs;ed <lb/>tamen fallax extitit, non enim per communia alijs &longs;cientijs <lb/>procedat; vnde nec transferri poterat ip&longs;ius fal&longs;a de&shy;<lb/>&longs;criptio, &longs;eu demon&longs;tratio extra Geometri&aelig; li&shy;<lb/>mites, quod cau&longs;a e&longs;t contentionis.</s></p><p type="head">
3633 
3634 <s><emph type="italics"/>Logicorum locorum finis.<emph.end type="italics"/></s></p></chap><pb pagenum="72"/><chap><p type="head">
3635 
3636 <s>EX PRIMO LIBRO<lb/>PHYSICORVM.<lb/><arrow.to.target n="marg88"/></s></p><p type="margin">
3637 
3638 <s><margin.target id="marg88"/>88</s></p><p type="main">
3639 
3640 <s>Tex. 11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. &longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s>
3641 
3642 <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap. 
3643 
3644 31. de Abductione in 2. Priorum, quam inibi videas. </s>
3645 
3646 <s>hoc &longs;olum <lb/>hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua&shy;<lb/>dam pr&aelig;mi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet (in&shy;<lb/>quit Ari&longs;t.) Geometra illius deceptionem inuenire. </s>
3647 
3648 <s>Tetragoni&longs;mum autem <lb/>Antiphontis non e&longs;t Geometr&aelig; <expan abbr="c&otilde;futare">confutare</expan>, quia aduer&longs;abatur principijs Geo&shy;<lb/>metri&aelig;, &longs;upponebat enim circuli circumferentiam ex indiuiduis, <expan abbr="minimis&qacute;">minimisque</expan>; <lb/>lineis rectis componi: cuius fal&longs;am demon&longs;trationem explicatam inuenies <lb/>ad cap. 
3649 
3650 10. primi Elench. <!-- REMOVE S-->po&longs;&longs;umus addere tertiam rationem quia &longs;cilicet <lb/>Hippocrates non procedebat per communia alijs &longs;cientijs, vt videre e&longs;t ad <lb/>tex. <!-- REMOVE S-->23. primi Po&longs;ter. cap. 
3651 
3652 8. vbi ip&longs;ius p&longs;eudographiam expo&longs;ui. Quemad&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantummodo rationes eas, qu&aelig; &longs;er&shy;<lb/>uatis Geometricis principijs procedunt; non autem eas, qu&aelig; Geometri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> Parmenidem, ac Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut fallaces eorum rationes <lb/>coarguere. </s>
3653 
3654 
3655 
3656 
3657 
3658 <s>Hoc volebat Ari&longs;toteles inferre.</s></p></chap><chap><p type="head">
3659 
3660 <s><emph type="italics"/>Ex Secundo Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
3661 
3662 <s><arrow.to.target n="marg89"/></s></p><p type="margin">
3663 
3664 <s><margin.target id="marg89"/>89</s></p><p type="main">
3665 
3666 <s>Tex. 20. (<emph type="italics"/>Geometria enim de phy&longs;ica linea con&longs;iderat, &longs;ed non quatenus <lb/>e&longs;t phy&longs;ici: Per&longs;pectiua autem mathematicam quidem lineam, &longs;ed non <lb/>quatenus phy&longs;ica e&longs;t<emph.end type="italics"/>) quamuis textus hic non pertineat ad Mathe&shy;<lb/>maticum, libuit tamen illum in ordinem no&longs;trum recen&longs;ere, ope&shy;<lb/>r&aelig;pretium etenim e&longs;t ea, qu&aelig; in ip&longs;o continentur &agrave; nonnullis recentioribus <lb/>rect&egrave; intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab&shy;<lb/>&longs;tineant, ac tandem ex Ari&longs;t. 
3667 
3668 lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picu&egrave; videant. </s>
3669 
3670 <s>c&aelig;tera, qu&aelig; in pr&aelig;cedentibus locis Ari&longs;t. 
3671 
3672 de Natura Ma&shy;<lb/>thematicarum habet, &longs;unt pr&aelig;ter no&longs;trum in&longs;titutum.</s></p><p type="main">
3673 
3674 <s><arrow.to.target n="marg90"/></s></p><p type="margin">
3675 
3676 <s><margin.target id="marg90"/>90</s></p><p type="main">
3677 
3678 <s>Tex. 28. (<emph type="italics"/>Alio autem modo, &longs;orma, &amp; exemplum: b&aelig;c autem e&longs;t ratio ip&longs;ius, <lb/>quod quid erat e&longs;&longs;e, &amp; huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, &amp; omnino <lb/>numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>) vt ben&egrave; intelligas, quod in pr&aelig;&longs;enti <lb/>textu <expan abbr="mathematic&utilde;">mathematicum</expan> e&longs;t, con&longs;ule prius, qu&aelig; &longs;crip&longs;i ad tex. <!-- REMOVE S-->1. cap. 
3679 
3680 primi 2. Po&shy;<lb/>&longs;ter. <!-- REMOVE S-->&longs;uper verba illa (<emph type="italics"/>Quid e&longs;t con&longs;onantia?<emph.end type="italics"/>) vbi per&longs;picu&egrave; videbis, cur <expan abbr="con-&longs;on&atilde;ti&aelig;">con&shy;<lb/>&longs;onanti&aelig;</expan>, qu&aelig; dicitur Diapa&longs;on, e&longs;&longs;entia, &amp; definitio &longs;it ip&longs;a proportio dupla, <lb/>qu&aelig; &longs;ub his num. </s>
3681 
3682 
3683 
3684 
3685 
3686 <s>2.1. continetur: quibus per&longs;pectis facilis erit phy&longs;ico totius <lb/>loci intelligentia.</s></p><pb pagenum="73"/><p type="main">
3687 
3688 <s><arrow.to.target n="marg91"/></s></p><p type="margin">
3689 
3690 <s><margin.target id="marg91"/>91</s></p><p type="main">
3691 
3692 <s>Tex. 68. (<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo&shy;<lb/>bihbus, vt in Mathematicis, ad definitionem enim recti, aut commen&longs;urabilis, aut <lb/>alius cuiu&longs;piam reducitur vltimum<emph.end type="italics"/>) ex his manife&longs;t&egrave; videas Mathematicas <expan abbr="de-m&otilde;&longs;trare">de&shy;<lb/>mon&longs;trare</expan> per cau&longs;am formalem, cum cau&longs;am ip&longs;am ad ip&longs;um quid e&longs;t, ide&longs;t, <lb/>ad definitionem reducant. </s>
3693 
3694 <s>quorum exempla in logicis ex Mathematicis at&shy;<lb/>tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apert&egrave; manife&shy;<lb/>&longs;tat; in quo probat duos angulos A C B, A C D, e&longs;&longs;e rectos, ex definitione <lb/>ip&longs;orum, &longs;iue ex definitione line&aelig; perpendicularis A C, quod idem e&longs;t.</s></p><p type="main">
3695 
3696 <s><arrow.to.target n="marg92"/></s></p><p type="margin">
3697 
3698 <s><margin.target id="marg92"/>92</s></p><p type="main">
3699 
3700 <s>Tex 89. (<emph type="italics"/>E&longs;t autem nece&longs;&longs;arium in Mathematicis, &amp; in his, qu&aelig; &longs;ecundum <lb/>natur am fiunt qua&longs;i eodem modo; quoniam enim hocrectum e&longs;t, nece&longs;&longs;e e&longs;t, trian&shy;<lb/>gulum trcs angulos habere &aelig;quales duobus rectis; &longs;ed non, &longs;i hoc, illud; &longs;ed &longs;i hoc <lb/>non e&longs;t, <expan abbr="neq;">neque</expan> rectum e&longs;t.<emph.end type="italics"/>) cum animaduerterim non parum e&longs;&longs;e di&longs;&longs;en&longs;ionis, &amp; <lb/>difficultatis in exemplo hoc mathematico explicando, ita vt recentiores <lb/>quidam textum <expan abbr="h&utilde;c">hunc</expan> pro arbitratu &longs;uo perperam latin&egrave; verterint: ide&ograve; pri&shy;<lb/>mum ex gr&aelig;cis codicibus interpretationem hanc veram attuli. </s>
3701 
3702 <s>deinde, quia <lb/>etiam gr&aelig;ci in exemplo mathematico enodando, vel mal&egrave;, vt Simplicius; <lb/>vel ob&longs;cur&egrave; nimis, vt reliqui; Latini ver&ograve; vel nihil, vel peius mult&ograve; loquun&shy;<lb/>tur, ide&ograve; &longs;ic ego exponendum cen&longs;ui. </s>
3703 
3704 <s>cum velit Ari&longs;t. 
3705 
3706 o&longs;tendere nece&longs;&longs;ita&shy;<lb/>tem, qu&aelig; in &longs;cientijs inter pr&aelig;mi&longs;&longs;as, &longs;cu medium, &amp; conclu&longs;ionem reperi&shy;<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos &aelig;qua&shy;<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap. 
3707 
3708 1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s>
3709 
3710 <s>pro medio autem <lb/>huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/><emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/><figure place="text" xlink:href="figures-la/009.01.073.1.tif"/><lb/>A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, &amp; pro&shy;<lb/>ducatur B C, in D; tunc triangulum A B C, <lb/>habere tres angulos, A, B, &amp; A C B, &aelig;quales <lb/>duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>&longs;it perpendiculare (quod Ari&longs;t. 
3711 
3712 dicit, cum <expan abbr="re-ct&utilde;">re&shy;<lb/>ctum</expan> hoc &longs;it) erunt duo anguli deinceps A C B, <lb/>A C D, recti, ex definitione line&aelig; perpendicu&shy;<lb/>laris, cum ergo duo anguli A, &amp; B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int &aelig;quales per <lb/>32. primi, &amp; reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu&shy;<lb/>li, &amp; angulus vnus line&aelig; perpendicularis, &amp; ide&ograve; rectus; manife&longs;t&egrave; apparet, <lb/>tres angulos A, B, A C B, e&longs;&longs;e &aelig;quales nece&longs;&longs;ari&ograve; duobus rectis, ex po&longs;itio&shy;<lb/>ne illius recti, &longs;iue lateris perpendicularis, quia ex ver&ograve;, verum nece&longs;&longs;ari&ograve; <lb/>&longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/>tres angulos &aelig;quales duobus rectis, nece&longs;&longs;ari&ograve; &longs;equitur illud e&longs;&longs;e rectum, <lb/>idelt latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/>&longs;equi pote&longs;t ex ver&ograve;, &amp; fals&ograve;. </s>
3713 
3714 <s>valebit tamen h&aelig;c con&longs;e quen&shy;<lb/>tia, &longs;i triangulum non habet hanc proprietatem, ne&shy;<lb/>que illud rectum e&longs;t, ide&longs;t, <expan abbr="neq;">neque</expan> latus pr&aelig;di&shy;<lb/>ctum crit <expan abbr="perp&etilde;diculare">perpendiculare</expan>, quia fal&longs;um <lb/>non, ni&longs;i exfal&longs;o &longs;equitur.</s></p></chap><pb pagenum="74"/><chap><p type="head">
3715 
3716 <s><emph type="italics"/>Ex Tertio Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
3717 
3718 <s><arrow.to.target n="marg93"/></s></p><p type="margin">
3719 
3720 <s><margin.target id="marg93"/>93</s></p><p type="main">
3721 
3722 <s>Tex. 26. <emph type="italics"/>(Et hi quidem infinitum e&longs;&longs;e par; hoc enim compr&aelig;hen&longs;um, &amp; <lb/>ab impari terminatum tribuit ijs, qu&aelig; &longs;unt, infinitatem. </s>
3723 
3724 <s>&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numcris, circumpo&longs;it is enim Gnomoni&shy;<lb/>bus circa vnum, &amp; &longs;eor&longs;um, aliquando quidcm &longs;emper aliam fieri &longs;pe&shy;<lb/>ciem, aliquando autem vnam)<emph.end type="italics"/> vt melius percipiantur ea, qu&aelig; &longs;equuntur, lege <lb/>prius, qu&aelig; in cap. 
3725 
3726 de Motu in po&longs;t pr&aelig;dicamentis &longs;crip&longs;i de Gnomone, ad <lb/>&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu&shy;<lb/>meris Gnomones Arithmetici. </s>
3727 
3728 <s>Pythagorici enim (&agrave; quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t. 
3729 
3730 numeros impares &longs;olos appellabant Gnomones, e&ograve; quod in for&shy;<lb/>mam norm&aelig; &aelig;quilater&aelig;, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/><figure place="text" xlink:href="figures-la/009.01.074.1.tif"/><lb/>nimirum in ternario, quinario, &longs;eptenario, &amp; &longs;ic de <lb/>reliquis imparibus. </s>
3731 
3732 <s>pares autem numeri, quia ne&shy;<lb/>queunt in figuram norm&aelig; &aelig;quilater&aelig; di&longs;poni, cum <lb/>non habeant vnitatem pro angulo, &amp; paria po&longs;tea la&shy;<lb/>tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di&shy;<lb/>&longs;ponatur &longs;ic <figure place="text" xlink:href="figures-la/009.01.074.2.tif"/> non refert Gnomonem, quia lateribus in&ecedil;qualibus con&shy;<lb/>&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure place="text" xlink:href="figures-la/009.01.074.3.tif"/> quia dee&longs;t huic figur&aelig; angularis vnitas, qu&aelig; <lb/>illi nece&longs;iaria e&longs;t. </s>
3733 
3734 <s>Pythagorici igitur dicebant, numerum parem ide&ograve; e&longs;&longs;e <lb/>infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetu&aelig; diui&longs;ionis, cum <lb/>qu&aelig;libet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>parem, &amp; &longs;ubdiui&longs;ibilis po&longs;tea bifariam, &amp; &longs;ic in infinitum, vt de linea pro&shy;<lb/>blematic&egrave; probatur in 10. primi Elem. 
3735 
3736 quamuis theorematic&egrave; &longs;it axioma. <lb/></s>
3737 
3738 <s>hunc porr&ograve; numerum parem dicebant terminatum e&longs;&longs;e ab impari, quia ori&shy;<lb/>tur ex diui&longs;ione cuiu&longs;uis rei, qu&aelig; vna &longs;it, &longs;umentes vnitatem pro impari. <lb/></s>
3739 
3740 <s>&longs;ignum pr&aelig;terea huius finitatis ab impari, &amp; infinitatis &agrave; pari numero pro&shy;<lb/>cedentis, aiunt e&longs;&longs;e Gnomones, numeros &longs;cilicet impares: Gnomones enim, <lb/>ide&longs;t impares numeri vnitati additi, producunt eandem perpetu&ograve; numero&shy;<lb/>rum formam, videlicet quadratum: at ver&ograve; &egrave; contrari&ograve; numeri pares vni&shy;<lb/>tati additi, conflant perpetu&ograve; varias numerorum formas: quapropter vi&shy;<lb/>dentur numeri impares e&longs;&longs;e finitatis cau&longs;a; &longs;icut pares exaduers&ograve; infinitatis <lb/>principium. </s>
3741 
3742 <s>qu&aelig; vt melius intelligas, declaranda e&longs;t 26. propo&longs;. </s>
3743 
3744 <s>7. Arith&shy;<lb/>metices lordani, vbi i&longs;tud idem demon&longs;trat, qu&aelig; e&longs;t h&aelig;c. </s>
3745 
3746 <s>&longs;it vnitas, &amp; &longs;uo or&shy;<lb/>dine &longs;equantur impares, vt in &longs;equenti hac &longs;erie apparet 1. 3. 5. 7. 9. &amp; c. <lb/><figure place="text" xlink:href="figures-la/009.01.074.4.tif"/><lb/>&longs;i igitur vnitati addatur ternarius in Gnomo&shy;<lb/>nis modum, vt vides in prima figura, produ&shy;<lb/>cetur quaternarius numerus, qui e&longs;t numerus <lb/>quadratus (quid &longs;it quadratus numerus expli&shy;<lb/>caui in Logicis tex. <!-- REMOVE S-->9. primi Po&longs;ter.) etfi huic <lb/>quaternario addatur &longs;equens impar, qui e&longs;t <lb/>quinarius in modum Gnomonis, vt in &longs;ecunda<lb/>figura, &longs;it numerus nouenarius, qui pariter e&longs;t quadratus. </s>
3747 
3748 
3749 
3750 <s>et&longs;i huic &longs;imiliter <lb/>addatur &longs;e quens impar, nimirum &longs;eptenarius, conflabitur &longs;edenarius, qui <lb/>numerus pariter quadratus e&longs;t, vt in tertia figura, &amp; hoc modo, &longs;i in infini&shy;<pb pagenum="75"/>tum procedatur, numeri &longs;emper quadrati progignentur. </s>
3751 
3752 <s>Vides igitur, qui <lb/>ratione Gnomonum, &longs;iue imparium additione fiat &longs;emper eadem &longs;pecies, <lb/>&longs;cilicet quadratus numerus, quod &longs;ignum e&longs;t, inquiunt, imparem numerum <lb/>non infinitatis, &longs;ed finitatis e&longs;&longs;e auctorem. </s>
3753 
3754 <s>Po&longs;t pr&aelig;dictam 26. propo&longs;itio&shy;<lb/>nem Iotdani, &longs;unt aliquot propo&longs;itiones, quarum &longs;umma h&aelig;c e&longs;t: &longs;i pares <lb/>numeri ab vnitate coaceruentur; coaceruati erunt &longs;emper vari&aelig; form&aelig; nu&shy;<lb/>merorum. </s>
3755 
3756 <s>qu&aelig; &longs;ic explicantur: &longs;int ab vnitate pares di&longs;po&longs;iti ordinatim <lb/>hoc modo, 1. 2. 4. 6. &amp;c. </s>
3757 
3758 <s>&longs;i igitur vnitati binarius coaceruetur, fit numerus <lb/><figure place="text" xlink:href="figures-la/009.01.075.1.tif"/><lb/>triangularis, vt in prima figura. </s>
3759 
3760 <s>&longs;i huic ternario <lb/>coaceruetur &longs;equens par, fiet altera &longs;pecies, ni&shy;<lb/>mirum hexagonus numerus, vt in &longs;ecunda figu&shy;<lb/>ra. </s>
3761 
3762 <s>cui &longs;i &longs;equens addatur par, &longs;cilicet &longs;enarius, <lb/>fiet iterum noua numeri forma, v. <!-- REMOVE S-->g. <!-- KEEP S--></s>
3763 
3764 
3765 
3766 <s>dodecago&shy;<lb/>nus, vt in tertia figura. </s>
3767 
3768 <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s>
3769 
3770 <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. de numeris rectangulis. </s>
3771 
3772 <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main">
3773 
3774 <s><arrow.to.target n="marg94"/></s></p><p type="margin">
3775 
3776 <s><margin.target id="marg94"/>94</s></p><p type="main">
3777 
3778 <s>Tex. 31. <emph type="italics"/>(Vtuntur etiam Mathematici infinito)<emph.end type="italics"/> <expan abbr="aliqu&atilde;do">aliquando</expan> Mathematici du&shy;<lb/>cunt lineas quantumuis longas, &longs;eu indefinit&aelig; longitudinis, quas etiam in&shy;<lb/>finitas appellant: &amp; hoc modo vtuntur infinito, vt infra tex. <!-- REMOVE S-->71. ip&longs;e Ari&longs;t. <lb/>exponit. </s>
3779 
3780 
3781 
3782 <s>alio pr&aelig;terea modo vtuntur infinito, vt quando &longs;upponunt data <lb/>quauis quantitate po&longs;&longs;e &longs;umi maiorem, vel etiam minorem in infinitum, vt <lb/>patet ex 6. po&longs;tulato primi Elem. 
3783 
3784 editionis Clauian&aelig;. </s>
3785 
3786 <s>numerum <expan abbr="quoq;">quoque</expan> au&shy;<lb/>geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem. 
3787 
3788 vel demum <lb/>quando probant quamlibet lineam po&longs;&longs;e diuidi bifariam, quia hinc &longs;equitur <lb/>po&longs;&longs;e &longs;ub diuidi in <expan abbr="infinit&utilde;">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinit&utilde;">infinitum</expan> in v&longs;u e&longs;t.</s></p><p type="main">
3789 
3790 <s><arrow.to.target n="marg95"/></s></p><p type="margin">
3791 
3792 <s><margin.target id="marg95"/>95</s></p><p type="main">
3793 
3794 <s>Tex. 68. &amp; 69. plura de magnitudine, &amp; numero continent; &longs;ed qu&aelig; non <lb/>indigeant opera no&longs;tra.</s></p><p type="main">
3795 
3796 <s><arrow.to.target n="marg96"/></s></p><p type="margin">
3797 
3798 <s><margin.target id="marg96"/>96</s></p><p type="main">
3799 
3800 <s>Tex. 71. <emph type="italics"/>(Non remouet autem ratio Mathematicos &agrave; contemplatione auferens <lb/>&longs;ic e&longs;&longs;e infinitum, vt actu &longs;it ver&longs;us augmentum, vt intran&longs;ibile, <expan abbr="ncq;">ncque</expan> enim nunc in&shy;<lb/>digent infinito, <expan abbr="neq;">neque</expan> vtuntur, &longs;ed &longs;olum e&longs;&longs;e <expan abbr="quantumcunqu;">quantumcunque</expan> velint finitam)<emph.end type="italics"/> ratio <lb/>phy&longs;ica tollens infinitum actu, non e&longs;t Mathematicis impedimento, quia ip&longs;i <lb/>non vtuntur infinito actu; quam enim ip&longs;i ducunt lineam infinitam, non e&longs;t <lb/>ver&egrave; infinita, &longs;ed indefinita, eam enim quantumlibet magnam producunt, vt <lb/>po&longs;&longs;it ad demon&longs;trandum &longs;ufficere.</s></p></chap><chap><p type="head">
3801 
3802 <s><emph type="italics"/>Ex Quarto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
3803 
3804 <s><arrow.to.target n="marg97"/></s></p><p type="margin">
3805 
3806 <s><margin.target id="marg97"/>97</s></p><p type="main">
3807 
3808 <s>Tex. 120. ter in hoc textu meminit commen&longs;urabilitatis, &amp; incommen&shy;<lb/>&longs;urabilitatis, qu&aelig; e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/>primo Priorum, &longs;ecto primo, cap. 
3809 
3810 23.</s></p></chap><pb pagenum="76"/><chap><p type="head">
3811 
3812 <s><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
3813 
3814 <s><arrow.to.target n="marg98"/></s></p><p type="margin">
3815 
3816 <s><margin.target id="marg98"/>98</s></p><p type="main">
3817 
3818 <s>Tex. 6. <emph type="italics"/>(Vt media grauis ad vltimam, &amp; acuta ad primam)<emph.end type="italics"/> alludit ad or&shy;<lb/>dinem chordarum in mu&longs;icis in&longs;trumentis, vbi media chorda edit &longs;o&shy;<lb/>num, re&longs;pectu quidem vltim&aelig;, &amp; &longs;uprem&aelig; chord&aelig; grauem: re&longs;pectu ver&ograve; <lb/>prim&aelig;, &amp; infim&aelig; acutum.</s></p></chap><chap><p type="head">
3819 
3820 <s><emph type="italics"/>Ex Octauo Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
3821 
3822 <s><arrow.to.target n="marg99"/></s></p><p type="margin">
3823 
3824 <s><margin.target id="marg99"/>99</s></p><p type="main">
3825 
3826 <s>Tex. 15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib. 
3827 
3828 1. Priorum, &longs;ecto 3. cap. 
3829 
3830 1. huius rei explicationem reperies.</s></p></chap><chap><p type="head">
3831 
3832 <s><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s></p><p type="main">
3833 
3834 <s><arrow.to.target n="marg100"/></s></p><p type="margin">
3835 
3836 <s><margin.target id="marg100"/>100</s></p><p type="main">
3837 
3838 <s>Tex. 33. <emph type="italics"/>(Vt &longs;i quis minimam qu&abreve;dam e&longs;&longs;e dicat magnitudinem, hic enim <lb/>minimum introducens, maxima <expan abbr="vbiq;">vbique</expan> amoueret mathematicor&ubreve;)<emph.end type="italics"/> ide&longs;t, <lb/>&longs;i quis, vt Democritus po&longs;uerit in magnitudinibus e&longs;&longs;e minima, <lb/>&longs;eu indiui&longs;ibilia, ex quibus entia mathematica componerentur, <lb/>hic euerteret maxima mathematicorum, ide&longs;t maxime ip&longs;orum demon&longs;tra&shy;<lb/>tiones, atque etiam effata euerterentur: v. <!-- REMOVE S-->g. <!-- REMOVE S-->10. primi Elem. 
3839 
3840 qu&aelig; docet <lb/>quamlibet lineam po&longs;&longs;e diuidi bifariam nulla e&longs;&longs;et, quia linea illa, qu&aelig; con&shy;<lb/>&longs;taret ex tribus Democriti atomis, nulla ratione bifariam &longs;ecari po&longs;&longs;et. </s>
3841 
3842 
3843 
3844 
3845 
3846 <s>pa&shy;<lb/>riter totus fer&egrave; decimus liber Elem. 
3847 
3848 deceptiuus, &amp; nullus e&longs;&longs;et, &longs;i enim da&shy;<lb/>rentur ill&aelig; atomi, ex quibus <expan abbr="qu&atilde;titas">quantitas</expan> conflaretur, null&aelig; e&longs;&longs;ent line&aelig; incom&shy;<lb/>men&longs;urabiles, quandoquidem omnes communi illa, ac indiuidua, commen&shy;<lb/>&longs;urarentur. </s>
3849 
3850 <s>po&longs;tulatum <expan abbr="quoq;">quoque</expan> illud, qualibet data magnitudine &longs;umi po&longs;&longs;e <lb/>minorem pror&longs;us irritum redderetur, quia data atomo, illa minor accipi <lb/>non po&longs;&longs;et.</s></p><p type="main">
3851 
3852 <s><arrow.to.target n="marg101"/></s></p><p type="margin">
3853 
3854 <s><margin.target id="marg101"/>101</s></p><p type="main">
3855 
3856 <s>Tex. 36. <emph type="italics"/>(Sit <expan abbr="itaq;">itaque</expan> linea, in qua A G E, infinita ad partes E; &amp; alia vtrinque <lb/>infinita, in qua <foreign lang="greek">b</foreign> B; &longs;i <expan abbr="itaq;">itaque</expan> de&longs;cribat circulum linea A G E, cir ca centrum G, fe-<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.076.1.tif"/><lb/><emph type="italics"/>retur circulariter linea A G E, &longs;ecans ali&shy;<lb/>quando lineam <foreign lang="greek">b</foreign> B, tempore finito; totum <lb/>enim tempus, in quo circulariter latum <lb/>e&longs;t C&oelig;lum finitum e&longs;t, &amp; ablatum igitur, <lb/>quo &longs;ecans ferebatur; erit igitur aliqued <lb/>prmcipium, quo primum linea A G E, li&shy;<lb/>neam <foreign lang="greek">b</foreign> B, &longs;ecuit. </s>
3857 
3858 <s>&longs;ed impo&longs;&longs;ibile est; non <lb/>est igitur circulariter verti <expan abbr="infinit&utilde;">infinitum</expan>, quare <lb/><expan abbr="neq;">neque</expan> mundum, &longs;i e&longs;&longs;et infinitus)<emph.end type="italics"/> quamuis <lb/>textus hic parum &longs;it mathematicus, <lb/>quia tamen &longs;upponit figuram mathe&shy;<lb/>maticam, qu&aelig; in codicibus pariter, ac <lb/>commentarijs de&longs;ideratur, illam pla&shy;<lb/>cuit apponere. </s>
3859 
3860 <s>in qua quidem, quamuis du&aelig; line&aelig; infinit&aelig; &longs;upponantur, vna <lb/>ad alteram <expan abbr="t&atilde;tum">tantum</expan> partem in qua E: altera ver&ograve; ad <expan abbr="vtramq;">vtramque</expan> partem <foreign lang="greek">b,</foreign> &amp; B, <pb pagenum="77"/>non potuerunt tamen de&longs;cribi, ni&longs;i finit&aelig;; appo&longs;it&aelig; idcirc&ograve; &longs;unt ad partes <lb/>illas, ad quas deberent e&longs;&longs;e infinit&aelig; lineol&aelig; qu&aelig;dam infinitatem indicantes. <lb/></s>
3861 
3862 <s>debemus po&longs;tea, vt mentem Ari&longs;t. 
3863 
3864 percipiamus concipere lineam A G E, <lb/>moueri circulariter facto centro in G. qu&aelig; quia infinita &longs;upponitur ad par&shy;<lb/>tem E, &longs;ecabit nece&longs;&longs;ari&ograve; alteram <expan abbr="vtrinq;">vtrinque</expan> infinitam <foreign lang="greek">b</foreign> B, <expan abbr="illam&qacute;">illamque</expan>; nece&longs;&longs;ari&ograve; <lb/>finito tempore percurret, finito enim tempore tota mundi circulatio per&shy;<lb/>agitur, &longs;patio videlicet viginti quatuor horarum. </s>
3865 
3866 <s>ex quo Ari&longs;t. 
3867 
3868 infert mun&shy;<lb/>dum non po&longs;&longs;e e&longs;&longs;e infinit&aelig; magnitudinis; quia &longs;i mundus e&longs;&longs;et infinitus; &amp;. <lb/></s>
3869 
3870 <s>du&aelig; line&aelig; infinit&aelig;, quales &longs;unt pr&aelig;dict&aelig; in ip&longs;o, <expan abbr="atq;">atque</expan> cum ip&longs;o moueri alte&shy;<lb/>ra earum A E, intelligatur, alteram <foreign lang="greek">b</foreign> B, manentem in tempore finito, ide&longs;t, <lb/>in diurna conuer&longs;ione pertran&longs;ibit: fieri autem nequit, vt infinita magni&shy;<lb/>tudo finito tempore percurratur; quare dicendum e&longs;t, mundum e&longs;&longs;e finita <lb/>magnitudine pr&aelig;ditum.</s></p><p type="main">
3871 
3872 <s><arrow.to.target n="marg102"/></s></p><p type="margin">
3873 
3874 <s><margin.target id="marg102"/>102</s></p><p type="main">
3875 
3876 <s>Tex. 48. <emph type="italics"/>(Nihil autem refert grauitates, commen&longs;urabiles &longs;int, an incommen&shy;<lb/>&longs;ur abiles)<emph.end type="italics"/> quidnam &longs;it commen&longs;urabilitas, &amp; incommen&longs;urabilitas, expli&shy;<lb/>catum e&longs;t lib. 
3877 
3878 1. Priorum, &longs;ecto 1. cap. 
3879 
3880 23.</s></p><p type="main">
3881 
3882 <s><arrow.to.target n="marg103"/></s></p><p type="margin">
3883 
3884 <s><margin.target id="marg103"/>103</s></p><p type="main">
3885 
3886 <s>Tex. 119. <emph type="italics"/>(Est autem impo&longs;&longs;ibile, &amp; po&longs;&longs;ibile; fal&longs;um, &amp; verum, ex &longs;uppo&longs;itio&shy;<lb/>ne quidem, dico autem, vt triangulum impo&longs;&longs;ibile e&longs;t duos rectos habere, &longs;i h&aelig;c)<emph.end type="italics"/><lb/>ide&longs;t, &longs;i &longs;upponantur fal&longs;a qu&aelig;dam, qu&aelig; &longs;upponi po&longs;&longs;unt, &longs;equetur impo&longs;&longs;i&shy;<lb/>bile e&longs;&longs;e triangulum habere tres angulos &aelig;quales duobus rectis angulis, vi&shy;<lb/>de, qu&aelig; &longs;crip&longs;i lib. 
3887 
3888 1. Priorum, &longs;ecto 3. cap. 
3889 
3890 1. de hoc, quod e&longs;t, habere tres <lb/>angulos &aelig;quales duobus rectis. </s>
3891 
3892 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i in triangulo pag. </s>
3893 
3894 
3895 
3896 
3897 
3898 <s>73. producto late&shy;<lb/>re A C, in D. &longs;i &longs;upponatur externus angulus B C D, non e&longs;&longs;e &aelig;qualis duobus <lb/>internis, &amp; oppofitis A, &amp; B, nunquam poterimus eo modo, quo Euclides, <lb/>demon&longs;trare pa&longs;&longs;ionem pr&aelig;dictam de triangulo A B C. huiu&longs;modi impo&longs;&longs;i&shy;<lb/>bile, cuius oppo&longs;itum non &longs;olum po&longs;&longs;ibile, &longs;ed etiam nece&longs;&longs;arium e&longs;t, vocat <lb/>Ari&longs;t. 
3899 
3900 impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo&shy;<lb/>dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an&shy;<lb/>gulos &aelig;quales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up&shy;<lb/>po&longs;itione, impo&longs;&longs;ibile oua&longs;it.</s></p><p type="main">
3901 
3902 <s><arrow.to.target n="marg104"/></s></p><p type="margin">
3903 
3904 <s><margin.target id="marg104"/>104</s></p><p type="main">
3905 
3906 <s>Ibidem <emph type="italics"/>(Et diameter commen&longs;urabilis est co&longs;t&aelig;, &longs;i b&aelig;c)<emph.end type="italics"/> vide primo Priorum, <lb/>&longs;ecto 3. cap. 
3907 
3908 23. hoc &longs;olum nunc addendum <emph type="italics"/>(Si h&aelig;c)<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i &longs;upponamus li&shy;<lb/>neas e&longs;&longs;e compo&longs;itas ex indiui&longs;ibilibus, con&longs;ectarium erit diametrum e&longs;&longs;e <lb/>commen&longs;urabilem co&longs;t&aelig;, quia indiui&longs;ibile illud, ex quo vtraque linea con&shy;<lb/>&longs;tat, erit <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> men&longs;ura communis.</s>
3909 
3910 
3911 
3912 </p></chap><chap><p type="head">
3913 
3914 <s><emph type="italics"/>Ex Secundo de C&aelig;lo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
3915 
3916 <s><arrow.to.target n="marg105"/></s></p><p type="margin">
3917 
3918 <s><margin.target id="marg105"/>105</s></p><p type="main">
3919 
3920 <s>Tex. 24. <emph type="italics"/>(Amplius qui &longs;olida diuidunt in plana, <expan abbr="atq;">atque</expan> ex planis corpora <lb/>generant, his te&longs;tes fui&longs;&longs;e videntur: &longs;olam enim figurarum &longs;olidarum <lb/>&longs;ph&aelig;ram non diuidunt, vt non plures &longs;uperficies. </s>
3921 
3922 <s>quam vnam <expan abbr="hab&etilde;um">habenum</expan>. <lb/></s>
3923 
3924 <s>diui&longs;io enim in plana non perinde e&longs;&longs;icitur, vt qui&longs;piam <expan abbr="diuid&etilde;s">diuidens</expan> in par&shy;<lb/>tes diuidat totum, &longs;ed vt in &longs;pecie diuer&longs;a: patct igitur &longs;ph&aelig;ram e&longs;&longs;e &longs;olidarum <lb/>primam)<emph.end type="italics"/> qui &longs;olida diuidunt in plana, ca diuidunt <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> numerum &longs;uper&shy;<lb/>&longs;icierum, quibus ambiuntur, v. <!-- REMOVE S-->g. <!-- REMOVE S-->diuidunt cubum in &longs;ex &longs;uperficies, quia <lb/>cubus &longs;ex quadratis planis &longs;uperficiebus continetur: qua ratione nequcunt <pb pagenum="78"/>&longs;oh&aelig;ram in plana vlla re&longs;oluere, <expan abbr="neq;">neque</expan> in alias plures &longs;uperficies, quia &longs;ph&aelig;&shy;<lb/>ra ambitur vnica tantum &longs;uperficie &longs;ph&aelig;rica. </s>
3925 
3926 
3927 
3928 
3929 
3930 <s>quando ver&ograve; ex planis corpo&shy;<lb/>ra generant, vt facit Plato in Tim&aelig;o, accip&iacute;unt prim&ograve; triangulum &aelig;quila&shy;<lb/>terum, &amp; ex quatuor triangulis &aelig;quilateris &longs;imul compactis conficiunt py&shy;<lb/>ramidem; &amp; hoc modo alia &longs;olida &agrave; pluribus &longs;uperficiebus ambita con&longs;ti&shy;<lb/>tuunt: verum hac ratione nullo modo po&longs;&longs;unt &longs;ph&aelig;ram componere, quia <lb/>vnica tantum, <expan abbr="ea&qacute;">eaque</expan>; &longs;ph&aelig;rica &longs;uperficie compr&aelig;henditur: <expan abbr="atq;">atque</expan> hoc pacto i&longs;ti <lb/>diuidentes, &amp; componentes corpora fidem faciunt, &longs;ph&aelig;ram, cum ex nullis <lb/>componatur, &longs;olidorum e&longs;&longs;e primam.</s></p><p type="main">
3931 
3932 <s><arrow.to.target n="marg106"/></s></p><p type="margin">
3933 
3934 <s><margin.target id="marg106"/>106</s></p><p type="main">
3935 
3936 <s>Tex. 25. <emph type="italics"/>(Est autem, &amp; &longs;ecundum numerorum ordinem a&longs;&longs;ignantibus, &longs;ic po&shy;<lb/>nentibus rationabili&longs;&longs;imam, circulum quidem &longs;ecundum vnum; triangulum autem <lb/>&longs;ecundum dualitatem, quoniam duo recti. </s>
3937 
3938 <s>&longs;i autem &longs;ecundum triangulum, vnum. <lb/></s>
3939 
3940 <s>circulus non erit figura)<emph.end type="italics"/> In ordine figurarum conueniens e&longs;t, inquit, primam <lb/>facere circulum propter &longs;implici&longs;simam ip&longs;ius naturam, cum vnica, ac per&shy;<lb/>fecta circulari linea comprehendatur: <expan abbr="Triangul&utilde;">Triangulum</expan> ver&ograve; &longs;ecundam, quoniam <lb/>duo anguli recti, ide&longs;t, quia triangulum habet tres angulos &aelig;quales duobus <lb/>rectis angulis; quod fus&egrave; explicatnm e&longs;t lib. 
3941 
3942 1. Priorum, &longs;ecto 3. cap. 
3943 
3944 1. De&shy;<lb/>mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir&shy;<lb/>culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s></p><p type="main">
3945 
3946 <s><arrow.to.target n="marg107"/></s></p><p type="margin">
3947 
3948 <s><margin.target id="marg107"/>107</s></p><p type="main">
3949 
3950 <s>Tex. 31. <emph type="italics"/>(At ver&ograve;, quod aqu&aelig; &longs;uperficies talis &longs;it, manife&longs;tum e&longs;t hac &longs;uppo&longs;i&shy;<lb/>tione &longs;umpta, quod apta natura e&longs;t &longs;emper confluere aqua ad magis concauum: ma&shy;<lb/>gis autem concauum e&longs;t, quod centro propinquius est. </s>
3951 
3952 <s>ducantur ergo ex centro A,<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.078.1.tif"/><lb/><emph type="italics"/>linea A B, &amp; linea A C, &amp; producatur, in qua B C, <lb/>ducta igitur ad ba&longs;im linea, in qua A D, minor e&longs;t eis, <lb/>qu&aelig; ex centro. </s>
3953 
3954 <s>magis igitur concauus locus e&longs;t, quare <lb/>influet aqua, donec <expan abbr="vtiq;">vtique</expan> &aelig;quetur. </s>
3955 
3956 <s>&aelig;qualis e&longs;t autem eis, <lb/>qu&aelig; ex centro linea A E, quare nece&longs;&longs;e e&longs;t apud eas, qu&aelig; <lb/>ex centro, e&longs;&longs;e aquam, tunc enim quie&longs;cet. </s>
3957 
3958 <s>linea autem, <lb/>qu&aelig; eas, qu&aelig; ex centro tangit, circularis e&longs;t, &longs;ph&aelig;rica <lb/>igitur aqu&aelig; &longs;uperficies e&longs;t, in qua B E C.)<emph.end type="italics"/> toto hoc <lb/>textu lineari demon&longs;tratione probat aqu&aelig; manen&shy;<lb/>tis &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam: qu&aelig; demon&longs;tratio <lb/>per&longs;picua euadit, &longs;i &longs;igura, qu&aelig; in codicibus tam <lb/>gr&aelig;cis, quam latinis, <expan abbr="atq;">atque</expan> etiam in commentarijs de&longs;ideratur, quemadmo&shy;<lb/>dum fecimus, re&longs;tituatur. </s>
3959 
3960 <s>&longs;it igitur in pr&aelig;cedenti figura A, centrum mundi, <lb/>ex quo educantur du&aelig; rect&aelig; line&aelig; &aelig;quales A B, A C, qu&aelig; deinde alia recta <lb/>B C, coniungantur. </s>
3961 
3962 <s>educatur <expan abbr="quoq;">quoque</expan> recta alia ex centro A, qu&aelig; pertingat <lb/>ad B C, qu&aelig; ba&longs;is e&longs;t trianguli B A C, &amp; producatur vlterius quantumlibet <lb/>in E. intelligatur demum circumferentia tran&longs;ire per puncta B, &amp; C, quia <lb/>ill&aelig; du&aelig; line&aelig; A B, A C, &longs;unt &aelig;quales, qu&aelig; circumferentia alteram A D, qu&aelig; <lb/>fuit protracta, &longs;ecet in E. <!-- KEEP S--></s>
3963 
3964 <s>Iam &longs;ic argumentatur: aqua natura &longs;ua &longs;emper <lb/>de&longs;luit ad locum magis concauum, ide&longs;t, ad loca centro A, terr&aelig; propin&shy;<lb/>quiora, quale e&longs;&longs;et in figura locus D, re&longs;pectu locorum B, &amp; C, quia A D, <lb/>linea minor e&longs;t ijs, qu&aelig; ex centro educt&aelig; &longs;unt A B, A C. quapropter aqua <lb/>debet de&longs;luere ex B, ad D, vel ex C, ad idem D, donec pertingat ad E. qui <lb/>locus non e&longs;t decliuior punctis B, &amp; C. quare cum loca B, E, C, qu&aelig; &longs;unt ex&shy;<pb pagenum="79"/>trema linearum, &longs;int &aelig;qu&egrave; decliuia, nece&longs;&longs;e e&longs;t aqu&aelig; &longs;uperficiem apud ip&longs;a <lb/>con&longs;i&longs;tere, tunc enim debet quie&longs;cere, aliter nunquam quie&longs;ceret; &longs;ed vide&shy;<lb/>mus aquam manentem, &amp; quietam, ergo quie&longs;cit circa puncta B, E, C, &agrave; <lb/>centro terr&aelig; &aelig;quidi&longs;tantia, per qu&aelig; tran&longs;it linea circularis coniungens illa; <lb/>et&longs;i &longs;uperficies per eiu&longs;modi loca pertran&longs;iret, e&longs;&longs;et &longs;ph&aelig;rica: &longs;ed &longs;uper&longs;i&shy;<lb/>cies aqu&aelig; tran&longs;it per talia loca, ergo &longs;ph&aelig;rica e&longs;t. </s>
3965 
3966 <s>Huius etiam habes acu&shy;<lb/>ti&longs;&longs;imam Archimedis demon&longs;trationem initio libelli de ijs, qu&aelig; vehuntur <lb/>in aqua, quam in &longs;uam &longs;ph&aelig;ram retulit Clauius.<!-- KEEP S--></s></p><p type="main">
3967 
3968 <s><arrow.to.target n="marg108"/></s></p><p type="margin">
3969 
3970 <s><margin.target id="marg108"/>108</s></p><p type="main">
3971 
3972 <s>Tex. 46. <emph type="italics"/>(Reliquum e&longs;t orbes quidem moueri, stellas ver&ograve; quie&longs;cere, &amp; infixas <lb/>ip&longs;is orbibus ferri; &longs;olum enim &longs;ic nullum ab&longs;urdum accidit. </s>
3973 
3974 <s>celeriorem enim e&longs;&longs;e <lb/>maioris circuli velocitatem, rationabile e&longs;t circa idem centrum infixis: vt enim in <lb/>alijs maius corpus velocius fertur propria latione, &longs;ic, &amp; in circularibus: maius <lb/>enim e&longs;t eorum, qu&aelig; auferuntur ab eis, qu&aelig; ex centro, maioris circuli &longs;egmentum)<emph.end type="italics"/><lb/>ex intellectione vltim&aelig; periodi textus totius intelligentia pendet: &longs;it igitur <lb/><figure place="text" xlink:href="figures-la/009.01.079.1.tif"/><lb/>figura pr&aelig;&longs;ens, in qua cum &longs;int duo circuli concen&shy;<lb/>trici, vnus altero maior, <expan abbr="educt&aelig;&qacute;">educt&aelig;que</expan>; &longs;int ex <expan abbr="c&etilde;tro">centro</expan> du&aelig; <lb/>&longs;emidiametri A D, A E, qu&aelig; <expan abbr="vtrunq;">vtrunque</expan> circulum &longs;e&shy;<lb/>cant, apparet maius e&longs;&longs;e <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> D E, quod &egrave; ma&shy;<lb/>iori circulo &longs;emidiametri ex <expan abbr="c&etilde;tro">centro</expan> educt&aelig; auferunt, <lb/>quam &longs;egmentum B C, minoris circuli, quod ei&longs;dem <lb/>&longs;emidia metris intercipitur. </s>
3975 
3976 <s>Verumtamen &longs;i circuli <lb/>ambo &longs;imul moueantur, maior circulus &aelig;quali tem&shy;<lb/>pore maius illud &longs;patium D E, &amp; minor minus B C, <lb/>pertran&longs;ibit: idem igitur de c&oelig;le&longs;tibus orbibus di&shy;<lb/>cendum, qui quamuis omnes diurnum &longs;imul motum <lb/>ab&longs;oluunt, maiores tamen celerius conuertuntur: quo fit, vt &longs;tell&aelig; maiori&shy;<lb/>bus circulis infix&aelig;, <expan abbr="atq;">atque</expan> delat&aelig;, maiori celeritate &longs;uos cur&longs;us peragant, ne&shy;<lb/>que oportet eas, dum mouentur c&oelig;lum di&longs;&longs;ecare, quod accideret, &longs;i pro&shy;<lb/>prio motu veluti pri&longs;ces per aquam progrederentur.</s></p><p type="main">
3977 
3978 <s>H&aelig;c quidem Ari&longs;t. 
3979 
3980 con&longs;entanea ob&longs;eruationibus veterum A&longs;tronomo&shy;<lb/>rum; at ver&ograve; illis no&longs;tr&aelig; &aelig;tatis ob&longs;eruationes repugnant; pr&aelig;&longs;ertim ill&aelig;, <lb/>qu&aelig; fiunt circa &longs;tellas errantes: ex quibus fatendum e&longs;&longs;e videtur, C&oelig;lum, <lb/>qua parte Planetas continet, liquidum e&longs;&longs;e, ac per illud Planetas proprio <lb/>motu, ceu pi&longs;ces in aqua progredi. </s>
3981 
3982 <s>Tycho <expan abbr="namq;">namque</expan> Brahe, <expan abbr="alij&qacute;">alijque</expan>; plures exact&egrave; <lb/>demon&longs;trant Cometas in regione Planetarum e&longs;&longs;e, <expan abbr="eos&qacute;">eosque</expan>; motu quodam in <lb/>tran&longs;uer&longs;um moueri, quo nece&longs;&longs;ario C&ecedil;l&uacute; deberent perforare; ijdem o&longs;ten&shy;<lb/>dunt nonnullos Planetas, Martem pr&aelig;&longs;ertim, ac Venerem modo &longs;upra So&shy;<lb/>lem, modo infra a&longs;cendere, &amp; de&longs;cendere. </s>
3983 
3984 <s>Idem patet ex ob&longs;eruatione no&shy;<lb/>ua per nouum Tele&longs;copij i <expan abbr="&longs;trum&etilde;tum">&longs;trumentum</expan> in Venere facta, qu&aelig; lunulata <expan abbr="vtrinq;">vtrinque</expan> <lb/>&agrave; Sole apparet: quando nimirum e&longs;t in imo epicyclo. </s>
3985 
3986 <s><expan abbr="iterum&qacute;">iterumque</expan>; rotunda ve&shy;<lb/>luti Luna plena, cum in &longs;ummo epicyclo ver&longs;atur: qu&aelig; minim&egrave; apparerent, <lb/>ni&longs;i &longs;upra, ac infra Solem circumiret. </s>
3987 
3988 <s>His rationibus conantur ip&longs;i proba&shy;<lb/>re C&oelig;lum e&longs;&longs;e liquidum; <expan abbr="atq;">atque</expan> in eo Planetas, veluti aues in aere, permearc: <lb/>quarum &longs;olutio mihi nulla occurrit, alijs forta&longs;&longs;is occurrct.</s></p><p type="main">
3989 
3990 <s><arrow.to.target n="marg109"/></s></p><p type="margin">
3991 
3992 <s><margin.target id="marg109"/>109</s></p><p type="main">
3993 
3994 <s>Tex. 57. <emph type="italics"/>(De ordine autem ip&longs;orum, quo quidem modo &longs;ingula di&longs;ponantur, vt <lb/>qu&aelig;dam &longs;int priora, qu&aelig;dam posteriora, &amp; quomodo &longs;patijs &longs;e &abreve;<expan abbr="habe&atilde;t">habeant</expan> ad inuicem,<emph.end type="italics"/><pb pagenum="80"/><emph type="italics"/>ex ijs circa A&longs;trologiam, con&longs;ideretur: dicitur enim &longs;ufficienter)<emph.end type="italics"/> &longs;umit hoc loco <lb/>A&longs;trologiam, pro A&longs;tronomia, &longs;i iuxta recentiores loqui velimus. </s>
3995 
3996 <s>Dicit igi&shy;<lb/>tur ordinem c&oelig;lorum, ac &longs;yderum, item &longs;itum, &amp; proportiones magnitu&shy;<lb/>dinum corundem, cum per naturalis &longs;cienti&aelig; princip ia &longs;ciri nequeant, ex <lb/>rationibus A&longs;tronomorum petenda e&longs;&longs;e, apud quos i&longs;ta &longs;ufficienter <expan abbr="demon-&longs;tr&etilde;tur">demon&shy;<lb/>&longs;trentur</expan>. </s>
3997 
3998 <s>&amp; merit&ograve; quidem h&aelig;c dicuntur; po&longs;teriores enim ab Ari&longs;t. 
3999 
4000 ordines, <lb/>&longs;itus, ac magnitudines tam c&oelig;lorum, quam &longs;yderum firmis rationibus, <expan abbr="atq;">atque</expan> <lb/>inuentu peracutis demon&longs;trarunt. </s>
4001 
4002 <s>quorum princeps fuit ptol&aelig;meus; no&longs;tra <lb/>tamen &aelig;tate Tycho Brahe, qui certis ob&longs;eruationibus, quas maximo labo&shy;<lb/>re, ac &longs;umptu exantlauit, in nonnullis &agrave; Ptol&aelig;meo, ac reliquis di&longs;&longs;entjt: &longs;tan&shy;<lb/>dum autem e&longs;&longs;e recentioribus ob&longs;eruationibus apud A&longs;tronomi&aelig; peritos in <lb/>confe&longs;&longs;o e&longs;t.</s></p><p type="main">
4003 
4004 <s><arrow.to.target n="marg110"/></s></p><p type="margin">
4005 
4006 <s><margin.target id="marg110"/>110</s></p><p type="main">
4007 
4008 <s>Tex. <emph type="italics"/>(Luna autem o&longs;tenditur per ea, qu&aelig; circa vi&longs;um, quod &longs;ph&aelig;rica &longs;it: non <lb/>enim <expan abbr="vtiq;">vtique</expan> fieret accre&longs;cens, &amp; decre&longs;cens, plurim&ubreve; quidem alter a ex parte curua, <lb/>altera concaua, aut <expan abbr="vtrmq;">vtrmque</expan> curua, &longs;emel autem bipartita)<emph.end type="italics"/> ait per ea, qu&aelig; circa <lb/>vi&longs;um, ide&longs;t per opticem probari Lunam e&longs;&longs;e &longs;ph&aelig;ricam: &longs;ed con&longs;ule, qu&aelig; <lb/>primo Po&longs;ter. tex. <!-- REMOVE S-->3. de hac re &longs;crip&longs;i, &amp; plenam etiam huius loci intelligen&shy;<lb/>tiam a&longs;&longs;equeris, pr&aelig;&longs;ertim &longs;i experimentum ibi traditum inieris.</s>
4009 
4010 </p><p type="main">
4011 
4012 <s><arrow.to.target n="marg111"/></s></p><p type="margin">
4013 
4014 <s><margin.target id="marg111"/>111</s></p><p type="main">
4015 
4016 <s>Ibidem <emph type="italics"/>(Et rur&longs;us per Astrologica, quia <expan abbr="vtiq;">vtique</expan> non e&longs;&longs;ent &longs;olis eclyp&longs;es lunul&aelig; <lb/>&longs;peciem pr&aelig;&longs;eferentes. </s>
4017 
4018 <s>Quare &longs;i vnum est tale, palam e&longs;t, quod &amp; alia <expan abbr="vtiq;">vtique</expan> erunt <lb/>talia)<emph.end type="italics"/> &longs;icuti <expan abbr="pr&aelig;ced&etilde;s">pr&aelig;cedens</expan> &longs;ph&aelig;ricitatis Lun&aelig; ratio ex Per&longs;pectiua de&longs;umpta e&longs;t, <lb/>ita pr&aelig;&longs;ens ex A&longs;tronomia, ex e&ograve; enim, quod eclyp&longs;is Solis habeat figuram <lb/>lunul&aelig;, ide&longs;t, &longs;i in&longs;tar Lun&aelig; falcat&aelig;, probant A&longs;tronomi Lunam e&longs;&longs;e &longs;ph&aelig;ri&shy;<lb/>cam. </s>
4019 
4020 <s>intellige tamen partem illam Solis, qu&aelig; non eclyp&longs;atur, habere figu&shy;<lb/>ram lunul&aelig;, pars enim &agrave; Luna obumbrata non videtur, et&longs;i videretur oua&shy;<lb/>lem quandam &longs;peciem, pr&aelig;&longs;eferret: pars igitur, illa e&longs;t corniculata, quia <lb/><figure place="text" xlink:href="figures-la/009.01.080.1.tif"/><lb/>cum Solis defectio ex interpo&longs;itione Lun&aelig; inter nos, &amp; <lb/>Solem contingat, &amp; Luna &longs;it &longs;ph&aelig;rica, nece&longs;&longs;ari&ograve; &longs;ph&aelig;&shy;<lb/>ric&egrave;, &amp; circulariter Solem obumbrabit; quare pars illa <lb/>non obumbrata remanet falcata, &amp; corniculata, vt in <lb/>pr&aelig;&longs;enti figura vidcre e&longs;t; vbi cernis, Lunam Solem or&shy;<lb/>biculariter offu&longs;care in linea A D C, partem Solis de&shy;<lb/>tectam <expan abbr="content&atilde;">contentam</expan> lineis curuis A B C D, e&longs;&longs;e lunularem, <lb/>&amp; falcatam; cum ergo in hunc modum fiat Solis deli&shy;<lb/>quium, &longs;ignum certum e&longs;t, Lunam e&longs;&longs;e &longs;ph&aelig;ricam.</s></p><p type="main">
4021 
4022 <s><arrow.to.target n="marg112"/></s></p><p type="margin">
4023 
4024 <s><margin.target id="marg112"/>112</s></p><p type="main">
4025 
4026 <s>Tex. 107. <emph type="italics"/>(Quod autem dubitatur, hoc e&longs;t; videre autem non e&longs;t difficile, &longs;i pa&shy;<lb/>rum con&longs;iderauerimus, &amp; di&longs;tinxerimus, quonam modo cen&longs;eamus quantamuis ma&shy;<lb/>gnitudinem grauem ad medium ferri. </s>
4027 
4028 <s>manife&longs;tum enim e&longs;t, quod non quou&longs;que ex&shy;<lb/>tremum tangat ip&longs;um centrum; &longs;ed maior pars vincat, oportet, <expan abbr="quou&longs;q;">quou&longs;que</expan> &longs;uo medio <lb/>ip&longs;um medium compr&aelig;hendat; <expan abbr="hucn&longs;q;">hucn&longs;que</expan> enim habet propen&longs;ioncm)<emph.end type="italics"/> &longs;en&longs;us Ari&longs;to&shy;<lb/>telis e&longs;t, debere nos exi&longs;timare, quod &longs;i qu&aelig;piam grauis magnitudo de&longs;cen&shy;<lb/>dat ad centrum mundi, eam non perman&longs;uram, &longs;latim ac ip&longs;ius extremum <lb/>centrum mundi attigent; &longs;ed c&ograve; <expan abbr="v&longs;q;">v&longs;que</expan> de&longs;cen&longs;uram, <expan abbr="quou&longs;q;">quou&longs;que</expan> ip&longs;ius medium, <lb/>mundi medium, &longs;iue centrum a&longs;&longs;equutum &longs;it; maior enim ip&longs;ius pars, in qua <lb/>&longs;cilicet medium e&longs;t, minorem partem propellit, donec vtrinque &agrave; centro <lb/>mundi &aelig;qu&egrave; emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb pagenum="81"/><expan abbr="hucu&longs;q;">hucu&longs;que</expan> grauitat, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i lapis illuc de&longs;cenderet, non quie&longs;ceret &longs;tatim ac <lb/>prima ip&longs;ius pars ad mundi centrum pertingeret, &longs;ed reliqu&aelig; ip&longs;ius partes <lb/>adhuc grauitarent, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; vlterius primam partem impellerent, donec lapi&shy;<lb/>&aacute;is medium, mundi medio congrueret: quo facto lapis quie&longs;ceret. </s>
4029 
4030 
4031 
4032 
4033 
4034 <s>qu&aelig; num <lb/>vera &longs;int, vt intelligamus, oportet prius pr&aelig;mittere, iuxta Mathematicos <lb/>duplex e&longs;&longs;e medium, &longs;iue centrum cuiu&longs;uis magnitudinis: aliud enim e&longs;t <lb/>centrum molis, aliud e&longs;t centrum grauitatis. </s>
4035 
4036 <s>centrum molis e&longs;t illud pun&shy;<lb/>ctum, &agrave; quo extrema &aelig;quidi&longs;tant: centrum grauitatis e&longs;t punctum illud, &agrave; <lb/>quo extrema &aelig;que ponderant, &longs;iue &agrave; quo graue &longs;u&longs;pen&longs;um &aelig;qu&egrave; ponderat, <lb/>&longs;iue in &aelig;quilibrio manet. </s>
4037 
4038 <s>Porr&ograve; in corporibus regularibus, &longs;i vnifo mia &longs;int <lb/>idem, &amp; vnum &longs;unt centrum molis, ac centrum grauitatis: vt in &longs;ph&aelig;ra <lb/>plumbea, idem crit <expan abbr="vtrumq;">vtrumque</expan> centrum: &longs;i ver&ograve; difformia &longs;int in grauitate, <lb/>vt in &longs;ph&aelig;ra partim plumbea, partim lignea, diuer&longs;um erit centrum molis, <lb/>&agrave; centro grauitatis; illud enim erit in medio &longs;ph&aelig;r&aelig;; centrum ver&ograve; graui&shy;<lb/>tatis in parte plumbea exi&longs;tet. </s>
4039 
4040 <s>In corporibus deinde irregularibus, etiam&longs;i <lb/>&longs;int vniformis ponderis, aliud tamen e&longs;&longs;e pote&longs;t centrum molis &agrave; <expan abbr="c&etilde;tro">centro</expan> gra&shy;<lb/>uitatis, vt in corpore oblongo, cuius alterum extremum &longs;it reliquis parti&shy;<lb/>bus mult&ograve; maius, vti e&longs;t claua: vbi centrum molis erit in medio longitudi&shy;<lb/>nis clau&aelig;; centrum ver&ograve; grauitatis, erit propinquius capiti clau&aelig;. </s>
4041 
4042 <s>quando <lb/>igitur Ari&longs;t. 
4043 
4044 ait, graue de&longs;cen&longs;urum, donec ip&longs;ius medium, &longs;iue centrum, <lb/>mundi centrum attingat; ben&egrave; dicit, &longs;i de medio grauitatis intelligat; ma&shy;<lb/>l&egrave; autem &longs;i de medio molis. </s>
4045 
4046 <s>quia grauia omnia ratione centri grauitatis <lb/>ponderant, <expan abbr="neq;">neque</expan> manent; ni&longs;i ip&longs;um maneat: quare ni&longs;i ip&longs;um <expan abbr="atting&atilde;t">attingant</expan> cen&shy;<lb/>trum mundi &longs;emper grauitabunt, &amp; mouebuntur. </s>
4047 
4048 <s>Verum enim ver&ograve; ex an&shy;<lb/>tiquorum monumentis manife&longs;tum e&longs;t, Archimedem, qui mult&ograve; po&longs;t Ari&shy;<lb/>&longs;totelem floruit, primum omnium de centro grauitatis e&longs;&longs;e philo&longs;ophatum, <lb/>qua ratione dicendum e&longs;&longs;et, Ari&longs;totelem de centro, molis loquutum e&longs;&longs;e, <lb/>&amp; perinde non <expan abbr="v&longs;quequaq;">v&longs;quequaque</expan> ver&egrave;.</s></p><p type="main">
4049 
4050 <s><arrow.to.target n="marg113"/></s></p><p type="margin">
4051 
4052 <s><margin.target id="marg113"/>113</s></p><p type="main">
4053 
4054 <s>Tex. 109. <emph type="italics"/>(Pr&aelig;terea <expan abbr="quoq;">quoque</expan> &amp; per ta, qu&aelig; apparent &longs;ecundum &longs;en&longs;um, neque <lb/>enim Lun&aelig; eclyp&longs;es tales <expan abbr="haber&etilde;t">haberent</expan> deci&longs;iones; nunc enim in ijs, qu&aelig; &longs;ecundum men&shy;<lb/>&longs;em fiunt, figurationibus, omnes accipit diui&longs;iones: etenim recta fit, &amp; vtrinque <lb/>curua, &amp; concaua)<emph.end type="italics"/> probat terram e&longs;&longs;e &longs;ph&aelig;ricam ratione a&longs;tronomica, ex <lb/>Lun&aelig; eclyp&longs;ibus de&longs;umpta: nam ni&longs;i terra e&longs;&longs;et rotunda, nunquam Luna in <lb/>eclyp&longs;i haberet tales deci&longs;iones, ide&longs;t non haberet falcatas, aut lunulatas <lb/>partes illas, qu&aelig; in eclyp&longs;i ob&longs;curantur, &amp; quafi &agrave; Luna re&longs;ecantur. </s>
4055 
4056 <s>quam&shy;<lb/>uis enim &longs;ingulis men&longs;ibus Luna terminetur modo linea concaua, vt quan&shy;<lb/>do noua e&longs;t; modo recta, vt quando diuidua e&longs;t: modo vtrinque curua, vt <lb/>cum &agrave; diuidu&aelig;ad plenilunium tendit. </s>
4057 
4058 <s>quod fu&longs;ius primo Po&longs;ter. tex. <!-- REMOVE S-->30. ex&shy;<lb/>po&longs;ui. </s>
4059 
4060 
4061 
4062 <s>in eclyp&longs;ibus tamen &longs;emper curuam habet lineam illam, qu&aelig; partem <lb/>ec'yp&longs;atam de&longs;init; vt paulo po&longs;t explicabo. </s>
4063 
4064 <s>Vide precedentem textum 59. <lb/>&amp; ca, qu&aelig; ibi annotaui, <expan abbr="qu&aelig;q;">qu&aelig;que</expan> tibi propo&longs;ui, &amp; plenam huius loci intelligen&shy;<lb/>tiam a&longs;&longs;equeris. </s>
4065 
4066 <s>vide etiam, qu&aelig; mox &longs;ubdam circa huius loci reliquum.</s></p><p type="main">
4067 
4068 <s><arrow.to.target n="marg114"/></s></p><p type="margin">
4069 
4070 <s><margin.target id="marg114"/>114</s></p><p type="main">
4071 
4072 <s>Ibidem <emph type="italics"/>(Circa autem eclyp&longs;es, &longs;emper curuam habet termin&abreve;tem lmeam: qua&shy;<lb/>re qaon'am eclyp&longs;im palitur propter terr&aelig; obiectionem, terr&aelig; <expan abbr="circumfer&etilde;tia">circumferentia</expan> &longs;ph&aelig;&shy;<lb/>rica exi&longs;tens, figur&aelig; cau&longs;a erit)<emph.end type="italics"/> probat rotunditatem terr&aelig; ab eclyp&longs;i lunari, <lb/>ex eo, quod Luna &longs;ph&aelig;ric&egrave; eclyp&longs;etur, quod innuitur illis verbis, &longs;emper <pb pagenum="82"/>curuam hzbet terminantem lineam, linea &longs;cilicet, qu&aelig; terminat partem <lb/>eclyp&longs;atam &agrave; non eclyp&longs;ata, &longs;emper apparet circularis; cum autem h&aelig;c li&shy;<lb/>nea &longs;it terminus vmbr&aelig; terr&aelig;, qu&aelig; lumen obumbrat, &longs;ignum <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> e&longs;t <lb/>vmbram ip&longs;am e&longs;&longs;e rotundam; nam cum Luna deficiat propter terr&aelig; obie&shy;<lb/>ctionem inter ip&longs;am, &amp; Solem, ita, vt vmbra terr&aelig; protendatur <expan abbr="v&longs;q;">v&longs;que</expan> ad Lu&shy;<lb/>nam, <expan abbr="eam&qacute;">eamque</expan>; in omni eclyp&longs;atione, &longs;iue eclyp&longs;is &longs;it &longs;upra terram, &longs;iue infra, <lb/>ad quamlibet <expan abbr="deniq;">denique</expan> partem terr&aelig; fiat, orbiculariter eam contegit, &longs;ignum <lb/>per&longs;picuum e&longs;t terram proijcere quoquouer&longs;us vmbram rotundam, qu&aelig; vt <lb/>in &longs;ph&aelig;ra o&longs;tenditur, e&longs;t rotunda ad modum coni; cum ergo vmbra terr&aelig; <lb/>ex quauis parte proijciatur, &longs;it rotunda, cert&ograve; certius colligitur, <expan abbr="terram&qacute;">terramque</expan>; <lb/><expan abbr="quoq;">quoque</expan> ip&longs;am rotunda &longs;igura pr&aelig;ditam e&longs;&longs;e. </s>
4073 
4074 <s>hanc eandem rationem, &longs;i libue&shy;<lb/>rit, fu&longs;ius pertractatam videre poteris apud P. <!-- REMOVE S-->Clauium in &longs;ph&aelig;ra.</s>
4075 
4076 </p><p type="main">
4077 
4078 <s><arrow.to.target n="marg115"/></s></p><p type="margin">
4079 
4080 <s><margin.target id="marg115"/>115</s></p><p type="main">
4081 
4082 <s>Tex. <emph type="italics"/>(Pr&aelig;terea per astrorum apparentiam, non &longs;olum manife&longs;ium e&longs;t, quod re&shy;<lb/>tunda, &longs;ed &amp; quod magnitudine non magna &longs;it; paruo enim facto ncbis tran&longs;itu ad <lb/>meridiem, &amp; Vr&longs;am, manifa&longs;t&egrave; fit alter horizon circulus, ita vt a&longs;tra, qu&aelig; &longs;uper <lb/>caput, magnam habcant mutationem, &amp; non eadem appareant, &amp; ad Vr&longs;am, &amp; ad <lb/>meridiem tran&longs;euntibus, qu&aelig;dam enim in Acgypto quidem stell&aelig; <expan abbr="vid&etilde;tur">videntur</expan>, &amp; cir&shy;<lb/>ca Cyprum, in ijs autem, qu&aelig; ad Vr&longs;am vergunt regionibus, non <expan abbr="via&etilde;tur">viaentur</expan>. </s>
4083 
4084 <s>&amp; a&longs;tro&shy;<lb/>rum ea, qu&aelig; &longs;emper in ijs, qu&aelig; ad Vr&longs;am vergunt, apparent, in illis locis occidunt. <lb/></s>
4085 
4086 <s>Quare non &longs;olum ex his manife&longs;tum e&longs;t rotundam e&longs;&longs;e figuram terr&aelig;, &longs;ed &amp; &longs;ph&aelig;r&aelig; <lb/>non magn&aelig;: non enim tam celeriter in&longs;igne quippiam faceret, tran&longs;latis nobis ade&ograve; <lb/>parum)<emph.end type="italics"/> hic textus ei, qui &longs;ph&aelig;ram mundi audiuerit perfacilis e&longs;t: propte&shy;<lb/>rea eum breuiter &longs;ic paraphra&longs;tic&egrave; exponam. </s>
4087 
4088 <s>Terram e&longs;&longs;e rotundam, <expan abbr="atq;">atque</expan> <lb/>re&longs;pectu c&oelig;le&longs;tium corporum non magnam, &longs;ignum e&longs;t, quod facto &agrave; nobis <lb/>paruo itinere &longs;iue ad meridionalem plagam, &longs;iue ad <expan abbr="&longs;ept&etilde;trionalem">&longs;eptentrionalem</expan> (quam <lb/>Vr&longs;am dicit) magnopere mutatur horizon: quod apparet primo ex varia&shy;<lb/>tionc a&longs;trorum, nam qu&aelig; in primo loco &longs;upra no&longs;trum verticem <expan abbr="tr&atilde;&longs;ibant">tran&longs;ibant</expan>, <lb/>in &longs;ecundo loco non amplius, &longs;ed alia, <expan abbr="atq;">atque</expan> alia valde ab inuicem &longs;eiuncta <lb/><figure place="text" xlink:href="figures-la/009.01.082.1.tif"/><lb/>exfacto quamuis paruo itinere tran&longs;eunt. </s>
4089 
4090 <s>&longs;it in <lb/>pr&aelig;&longs;enti figura terra, vbi A, in qua facta parua <lb/>mutatione ex loco F, in locum G, fieret magna <lb/>mutatio <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> ver&longs;icalium B, in C, qu&aelig; mul&shy;<lb/>tum ab inuicem di&longs;tant. </s>
4091 
4092 <s>&longs;i autem terra e&longs;&longs;et <lb/>maior, v. <!-- REMOVE S-->g. <!-- REMOVE S-->circulus medius, tunc facta maio&shy;<lb/>ri mutatione ex D, in E, fieret eadem a&longs;trorum <lb/>variatio ex B, in C; &longs;ed cum nos experiamur <lb/>&longs;ieri magnam a&longs;trorum mutationem, ex parua <lb/>locorum intercapedine, &longs;ignum e&longs;t magnope&shy;<lb/>re mutari horizontem, ac proinde terram e&longs;&longs;e <lb/>rotundam, ac re&longs;pectu c&oelig;le&longs;tium corporum <lb/>paruam. </s>
4093 
4094 
4095 
4096 
4097 
4098 <s>aliud pr&aelig;terea &longs;ignum hums horizontis permutationis e&longs;t, quod <lb/>&longs;tell&aelig;, qu&aelig; in priori loco &longs;upra horizontem apparebant, mutato paululum <lb/>loco ad alterutram plagam, &longs;tatim ab&longs;conduntur; ali&aelig; ver&ograve; nou&aelig; <expan abbr="appar&etilde;t">apparent</expan> <lb/>vt in Acgypto, &amp; Cypro, &longs;tella, qu&aelig; dicitur Canobus &longs;upra horizontem <lb/>a&longs;cendit; qu&aelig; &longs;i paululum Vr&longs;am, &longs;eu &longs;eptentrionem ambulaueris, &longs;tatim <lb/>latitabit. </s>
4099 
4100 <s>Demum ciu&longs;dem cit&aelig; mutationis &longs;initoris indicium etiam &longs;it, <pb pagenum="83"/>quod regiones &longs;eptentrionales incolentibus plurima &longs;unt a&longs;tra, qu&aelig; nun&shy;<lb/>quam occidunt, quamuis horizontem leuiter per&longs;iringant, qu&aelig; tamen Cy&shy;<lb/>prijs, <expan abbr="atq;">atque</expan> Aegyptijs oriuntur, <expan abbr="atq;">atque</expan> occidunt. </s>
4101 
4102 <s>ex quibus &amp; rotunditas, &amp; <lb/>paruitas terr&aelig; colligi pote&longs;t. </s>
4103 
4104 <s>has ea&longs;dem rationes fu&longs;ius explicatas repe&shy;<lb/>ries apud P. <!-- REMOVE S-->Clauium in &longs;ph&aelig;ra.</s>
4105 
4106 </p><p type="main">
4107 
4108 <s><arrow.to.target n="marg116"/></s></p><p type="margin">
4109 
4110 <s><margin.target id="marg116"/>116</s></p><p type="main">
4111 
4112 <s>Tex. 111. <emph type="italics"/>(Quapropter existimantes eum, qui circa Herculcas columnas e&longs;t lo&shy;<lb/>cum coniungi ei, qui circa Indiam, &amp; boc modo mare vnum e&longs;&longs;e, nen admcdum <lb/>incredibilia exi&longs;timare videntur &amp;c.)<emph.end type="italics"/> exi&longs;timatores ho&longs;ce non perperam exi&shy;<lb/>&longs;tima&longs;&longs;e apert&egrave; <expan abbr="c&otilde;uincunt">conuincunt</expan> Chri&longs;tophori Columbi, Argonautarum principis <lb/>nauigationes; quibus nouus orbis repertus e&longs;t, qui inter columnas Hercu&shy;<lb/>lis, <expan abbr="atq;">atque</expan> orientalem Indiam totus vna <expan abbr="c&utilde;">cum</expan> mari Oceano Atlantico interiacet.</s></p><p type="main">
4113 
4114 <s><arrow.to.target n="marg117"/></s></p><p type="margin">
4115 
4116 <s><margin.target id="marg117"/>117</s></p><p type="main">
4117 
4118 <s>Tex. 112. <emph type="italics"/>(Matbematicorum etiam, qui circum ferenti&aelig; magnitudinemratio&shy;<lb/>cinari tentant, ad 400. dicunt ftadiorum millia, &amp;c.)<emph.end type="italics"/> quam &longs;ubtilibus rationi&shy;<lb/>bus inue&longs;tigauerint A&longs;tronomi quantitatem terr&aelig;, optim&egrave;, ac dilucid&egrave; ex&shy;<lb/>ponitur &agrave; P. <!-- REMOVE S-->Clauio in &longs;ph&aelig;ra: quem &longs;i libet, con&longs;ule, ne inani labore opu&shy;<lb/>&longs;culum i&longs;tud exere&longs;cat.</s>
4119 
4120 </p></chap><chap><p type="head">
4121 
4122 <s><emph type="italics"/>Ex Tertio de C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
4123 
4124 <s><arrow.to.target n="marg118"/></s></p><p type="margin">
4125 
4126 <s><margin.target id="marg118"/>118</s></p><p type="main">
4127 
4128 <s>Tex. 40. <emph type="italics"/>(Figur&aelig; autem omnes componuntur ex pyramidibus: rectilinea <lb/>quidem ex rectilmeis: fph&aelig;ra ver&ograve; ex octo partibus componitur)<emph.end type="italics"/> Ale&shy;<lb/>xander exiftimat, Ari&longs;totelem dicere &longs;ph&aelig;ram con&longs;tare ex octo <lb/>partibus illis, qu&aelig; de&longs;ignantur per tres circulos, quorum duo &longs;e&shy;<lb/>cant &longs;e mucu&ograve; ad angulos rectos, vt in &longs;ph&aelig;ra mundi faciunt duo coluri; <lb/>tertius ver&ograve; medios illos diuidit &aelig;quidi&longs;tanter &agrave; &longs;ectionibus <expan abbr="illor&utilde;">illorum</expan> mutuis, <lb/>quemadmodum &aelig;quator in &longs;ph&aelig;ra mundi &longs;ecat duos coluros. </s>
4129 
4130 <s>ex quibus &longs;e&shy;<lb/>ctionibus tota &longs;ph&aelig;ra in octo partes diuiditur, quibus &longs;ph&aelig;ram componi <lb/>vult Ari&longs;toteles. <!-- KEEP S--></s>
4131 
4132 <s>aduerte tamen hanc &longs;ph&aelig;r&aelig; compo&longs;itionem nullo modo <lb/>habere partes actu, cum &longs;ph&aelig;ra &longs;it vnica &longs;implici &longs;uperficie terminata; &longs;ed <lb/>qu&aelig; tantum &longs;int &agrave; pr&aelig;dictis imaginatis circulis de&longs;ignat&aelig;: at ver&ograve; ali&aelig; fi&shy;<lb/>gur&aelig;, qu&aelig; pluribus planis terminantur, vt cubus, octaedrum, &amp; &longs;imilia, qu&aelig; <lb/>Ari&longs;t. 
4133 
4134 vocat rectiliheas, quia terminantur &longs;uperficiebus rectilineis actu di&shy;<lb/>&longs;tinctis ab inuicem ex natura &longs;ua, non per no&longs;tram de&longs;ignationem, ide&ograve; re&shy;<lb/>ct&egrave; dicuntur componi ex pyramidibus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->dicimus cubum componi ex &longs;ex <lb/>pyramidibus, quia cum habeat &longs;ex ba&longs;es, cogitamus &longs;upra <expan abbr="vnamquamq;">vnamquamque</expan> il&shy;<lb/>larum &longs;ingulas pyramides erigi, quarum omnium vertices ad idem punctum <lb/>medium intra cubum imaginatum coeant. </s>
4135 
4136 
4137 
4138 
4139 
4140 <s>&amp; &longs;ic de reliquis &longs;olidis. </s>
4141 
4142 <s>qu&aelig; qua <lb/>ratione re&longs;oluantur in plures pyramides, con&longs;tat ex 10. 11. 12. &amp; 13. Ele&shy;<lb/>mentorum Euclidis, at ver&ograve; in &longs;ph&aelig;ra nullum reale compo&longs;itionis, aut di&shy;<lb/>ui&longs;ionis fundamentum reperitur.</s></p><p type="main">
4143 
4144 <s><arrow.to.target n="marg119"/></s></p><p type="margin">
4145 
4146 <s><margin.target id="marg119"/>119</s></p><p type="main">
4147 
4148 <s>Tex. <emph type="italics"/>(Ad h&aelig;c nece&longs;&longs;e e&longs;t non omne corpus e&longs;&longs;e diui&longs;ibile dicere, &longs;ed repugnare <lb/>certi&longs;&longs;i nis &longs;cientijs; nam Mathematic&aelig; ip&longs;um quide&aelig; intelligibile, accipiunt diui&shy;<lb/>&longs;ibile)<emph.end type="italics"/> ip&longs;um intelligibile, ide&longs;t, quantitatem ab&longs;tractam tam continuam, <lb/>quam di&longs;eretam, quam &longs;tatuunt Philo&longs;ophi e&longs;&longs;e &longs;ubiectam materiam ma&shy;<lb/>thematicarum. </s>
4149 
4150 <s>quam ideo appellant intelligibilem, quia cum &longs;it ab&longs;tracta <lb/>per intellectum &agrave; &longs;en&longs;ibilibus affectionibus, re&longs;tat vt &longs;it tantummodo intel&shy;<pb pagenum="84"/>lectu perceptibilis. </s>
4151 
4152 <s>Hanc eandem &longs;upponunt e&longs;&longs;e diui&longs;ibilem in infinitum, <lb/>vt &longs;upra 3. Phy&longs;. textu 31. dictum e&longs;t.</s></p><p type="main">
4153 
4154 <s><arrow.to.target n="marg120"/></s></p><p type="margin">
4155 
4156 <s><margin.target id="marg120"/>120</s></p><p type="main">
4157 
4158 <s>Tex. 66. <emph type="italics"/>(Ommn&ograve; autem eniti &longs;implicibus corporibus figur as tribuere irratio&shy;<lb/>nabile e&longs;t. </s>
4159 
4160 <s>prim&ograve; quidem, quia accidit non repleri totum; nam in planis tres figur&aelig; <lb/>videntur implere locum, Triangulus, Quadratum, &amp; Sexangulus)<emph.end type="italics"/> per &longs;implicia <lb/>corpora intelligit quatuor elementa. </s>
4161 
4162 <s>Vult enim probare quatuor elemen&shy;<lb/>ta non habere figuras illas mathematicas, quas illis Plato tribuebat, vt au&shy;<lb/>tem Ari&longs;t. 
4163 
4164 rationem prob&egrave; percipiamus, &longs;ciendum, quod implere totum, <lb/>&longs;iue locum, ill&aelig; figur&aelig; dicuntur, qu&aelig; &longs;imul &longs;uis angulis in plano quopiam ad <lb/>vnum, <expan abbr="atq;">atque</expan> idem punctum vnit&aelig; locum illum totum, qui cirea punctum il&shy;<lb/>lud con&longs;i&longs;tit, <expan abbr="c&otilde;tegunt">contegunt</expan>, ita vt nihil vacui inter ip&longs;as relinquatur. </s>
4165 
4166 <s>tales &longs;unt, <lb/>quibus fieri po&longs;&longs;unt pauimenta, oportet enim, vt &longs;imul vnit&aelig; nihil vacui in <lb/>pauimento relinquant. </s>
4167 
4168 <s>huiu&longs;modi &longs;unt triangula &aelig;quilatera (de his enim <lb/>intelligendus e&longs;t textus) quadrata, &amp; hexagona, &longs;iue &longs;exilatera regularia; <lb/><figure place="text" xlink:href="figures-la/009.01.084.1.tif"/><lb/>nam &longs;ex triangula &aelig;quilatera &longs;imul iuncta in plano paui&shy;<lb/>re po&longs;&longs;unt, vt patet in figura pr&aelig;&longs;enti; ratio huius e&longs;t, <lb/>quia omnes anguli circa idem punctum (y. </s>
4169 
4170 <s>g. <!-- REMOVE S-->A, in hac <lb/>figura) in plano, quotquot fuerint con&longs;tituti, &longs;unt &aelig;qua&shy;<lb/>les quatuor rectis, ex coroll. </s>
4171 
4172 
4173 
4174 <s>&longs;ecundo 15. primi Elemen&shy;<lb/>ti: cum igitur &longs;ex anguli, trianguli &aelig;quilateri <expan abbr="&aelig;quiuale&atilde;t">&aelig;quiualeant</expan> <lb/>quatuor rectis angulis, con&longs;tituti omnes circa punctum <lb/>A, totum locum circa illud implere po&longs;&longs;unt. </s>
4175 
4176 <s>Quadratum etiam replere lo&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.084.2.tif"/><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;intrecti, &longs;i <lb/>quatuor quadrata ad idem punctum A, copulentur, vt in <lb/>figura apparet, replebunt eadem de cau&longs;a vacuum.</s></p><p type="main">
4177 
4178 <s>Hexagonum quoque regulare, ide&longs;t &aelig;quilaterum, &amp; <lb/>&aelig;quiangulum idem pr&aelig;&longs;tare pote&longs;t; cum enim tres angu&shy;<lb/>li ip&longs;ius &aelig;quiualeant quatuor rectis, &longs;i tria hexagona ad <lb/>idem punctum A, vt in &longs;igura adaptentur, nece&longs;&longs;ari&ograve; ni&shy;<lb/>hil vacui inter ip&longs;a relinquetur, vt in figura hac o&longs;tenditur. </s>
4179 
4180 <s>pr&aelig;ter has tres <lb/><figure place="text" xlink:href="figures-la/009.01.084.3.tif"/><lb/>figuras, nulla alia reperitur, qu&aelig; i&longs;tud efficere pol&shy;<lb/>&longs;it. </s>
4181 
4182 <s>cuius demon&longs;trationem perfectam videre pote&shy;<lb/>ris in fine commentarij P. <!-- REMOVE S-->Clauij &longs;uper 4. Elem. 
4183 
4184 nos <lb/>ea tantum attingimus, qu&aelig; percipi po&longs;&longs;int ab homi&shy;<lb/>ne vix mathematicis tincto: &longs;ed tamen, qu&aelig; &longs;en&longs;um <lb/>Ari&longs;totelis patefaciunt. </s>
4185 
4186 
4187 
4188 <s>Ali&aelig; porr&ograve; figur&aelig; replen&shy;<lb/>tes locum planum, quibus aliquando Architectores <lb/>vtuntur, vel &longs;unt irregulares, vel ad pr&aelig;dictas redu&shy;<lb/>ci po&longs;&longs;unt. </s>
4189 
4190 <s>cum igitur tres tantum ex figuris planis <lb/>totum repleant, h&aelig; &longs;ol&aelig; poterunt elementis attri&shy;<lb/>bui, ac propterea non &longs;ufficient, ni&longs;i pro tribus elementis. </s>
4191 
4192 <s>quare quartum <lb/><expan abbr="ab&longs;q;">ab&longs;que</expan> figura relinquetur; quod e&longs;t ab&longs;urdum.</s></p><pb pagenum="85"/><p type="head">
4193 
4194 <s><emph type="italics"/>Admirabilis qu&aelig;dam A&pgrave;um industria.<emph.end type="italics"/></s></p><p type="main">
4195 
4196 <s>C&aelig;terum occa&longs;ione harum figurarum illud hoc loco apponere vi&shy;<lb/>&longs;um e&longs;t, quod Pappus <expan abbr="Alex&atilde;drinus">Alexandrinus</expan> initio quinti libri collectionum <lb/>mathematicarum &longs;cribit, De admirabili Apum indu&longs;tria, atque <lb/>prudentia in con&longs;truendo &longs;uas cellulas figura hexagona regulari. <lb/></s>
4197 
4198 <s>cum enim vellent omne vacuum excludere, &amp; pr&aelig;terea capaci&longs;&longs;imam <expan abbr="om-ni&utilde;">om&shy;<lb/>nium</expan> figuram habere, hexagonam accepere, qu&aelig; inter pr&aelig;dictas tres vtrum&shy;<lb/>que pr&aelig;&longs;tat, nam &amp; inane omne excludit, &amp; illarum trium capaci&longs;&longs;ima e&longs;t, <lb/>cum magis ad circularem figuram accedat: vt patet ex tractatu de figuris <lb/>I&longs;operimetris, qui e&longs;t apud Clauium in &longs;ph&aelig;ra, necnonin Geometria pra&shy;<lb/>ctica. </s>
4199 
4200 <s>hoc ide&ograve; libentius recen&longs;ui, quia animaduerti naturales hi&longs;toriogra&shy;<lb/>phos omnes latere, vel ip&longs;um Aldobrandum no&longs;trum, qui quamuis indu&shy;<lb/>&longs;trio&longs;&aelig; Apis in&longs;tar omnia delibauerit, i&longs;tud tamen de Apibus artificium tan&shy;<lb/>ta &longs;apientia plenum, ne&longs;cio quo modo pr&aelig;termi&longs;it.</s></p><p type="main">
4201 
4202 <s><arrow.to.target n="marg121"/></s></p><p type="margin">
4203 
4204 <s><margin.target id="marg121"/>121</s></p><p type="main">
4205 
4206 <s>Ibidem <emph type="italics"/>(In folidis ver&ograve; du&aelig; &longs;olum pyramis, &amp; cubus)<emph.end type="italics"/> ide&longs;t replent locum <lb/>&longs;olidum. </s>
4207 
4208 <s>nullum reperi, qui in hoc loco explicando non errauerit; nam Gr&aelig;&shy;<lb/>ci, qui alioqui &longs;olent mathematica prob&egrave; intelligere, hic omnes lap&longs;i &longs;unt, <lb/><expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; &amp; Arabes, &amp; Latinos in <expan abbr="e&atilde;dem">eandem</expan> foueam &longs;upra &longs;e mi&longs;er&egrave; traxerunt. <lb/></s>
4209 
4210 <s>communis fer&egrave; error omnium fuit, pyramides plures &longs;imul compactas po&longs;&shy;<lb/>&longs;e replere &longs;olidum locum. </s>
4211 
4212 <s>quod vt melius intelligamus, &longs;ciendum e&longs;t, reple&shy;<lb/>re locum <expan abbr="&longs;olid&utilde;">&longs;olidum</expan> nihil aliud e&longs;&longs;e, quam &longs;i plura corpora &longs;olida &longs;imul ad idem <lb/>punctum coaptata, ita con&longs;tipentur, vt totum &longs;patium, quod e&longs;t circa pun&shy;<lb/>ctum illud omnin&ograve; occupent, hoc e&longs;t, nihil vacui inter ip&longs;a relinquatur: &longs;i&shy;<lb/>cut enim pr&aelig;dict&aelig; tres &longs;igur&aelig; plan&aelig;, de quibus paul&ograve; ante, replent locum <lb/>planum, ide&longs;t &longs;uper&longs;iciem; ita cubi replent &longs;olidum, ide&longs;t &longs;oliditatem &longs;imul <lb/>vniti con&longs;tituunt, ita vt &longs;i octo cubi &longs;imul ad idem punctum <expan abbr="coapt&etilde;tur">coaptentur</expan>, con&shy;<lb/>&longs;tituant corpus &longs;olidum ex octo illius con&longs;latum, <expan abbr="nihil&qacute;">nihilque</expan>; inane inter ip&longs;os <lb/>cubos relinquatur. </s>
4213 
4214 <s>&amp; &longs;icuti plan&aelig; ill&aelig; figur&aelig; erant conficiendis pauimentis <lb/>apt&aelig;, ita &longs;olid&aelig; h&aelig; muris, qui corpora &longs;unt &longs;olida, <expan abbr="con&longs;tru&etilde;dis">con&longs;truendis</expan> idonea &longs;unt. <lb/></s>
4215 
4216 <s><expan abbr="Not&atilde;">Notam</expan> dum pr&aelig;terea, quod per pyramidem debemus intelligere pyramidem <lb/>regularem, qu&aelig; dicitur etiam Tetraedrum, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;ecunda inter <expan abbr="quinq;">quinque</expan> cor&shy;<lb/>pora regularia rectilinea, qu&aelig; alias Platonica corpora dicuntur. </s>
4217 
4218 <s><expan abbr="eorum&qacute;">eorumque</expan>; <lb/>defraitiones &longs;unt in 11. Elem. <!-- KEEP S--></s>
4219 
4220 <s>Tetraedrum autem &longs;ic definitur, e&longs;t figura &longs;o&shy;<lb/>lida &longs;ub quatuor triangulis &aelig;quilateris, <expan abbr="atq;">atque</expan> inuicem &aelig;qualious contenta: <lb/>de hac inquam e&longs;t &longs;ermo. </s>
4221 
4222 <s>quia &longs;i liceret intelligere de irregularibus figuris, <lb/>infinit&aelig; reperir entar figur&aelig; tam plan&aelig;, quam &longs;olid&aelig;, qu&aelig; vtrumque locum <lb/>complerent. </s>
4223 
4224 <s>Aduertendum tandem Ari&longs;t. 
4225 
4226 videri loqui de repletione loci <lb/>&longs;olidi, quia tran&longs;it &agrave; plan&iuml;s figuris ad &longs;olidas. </s>
4227 
4228 <s>&amp; quia &longs;i h&aelig; du&aelig; pyramis, &amp; <lb/>cubus replent locum &longs;olummedo &longs;ecundum &longs;uas &longs;uperficies, qu&aelig; &longs;unt trian&shy;<lb/>gulum, &amp; quadratum, iam de his cum proxim&egrave; ante dixi&longs;&longs;et, quid opus fui&longs;&shy;<lb/>&longs;et idem po&longs;t modum repetere. </s>
4229 
4230 <s>ad h&aelig;c &longs;i in medium &longs;olida h&aelig;c duo profert, <lb/><expan abbr="ait&qacute;">aitque</expan>; ip&longs;a replere locum, intelligens, planum, profect&ograve; non loquitur forma&shy;<lb/>liter, ide&longs;t de ip&longs;is, vt &longs;oh da &longs;unt. </s>
4231 
4232 <s>Quare Ari&longs;t. 
4233 
4234 videretur &longs;ibi non con&longs;tare, <lb/>vel perperam exi&longs;tima&longs;&longs;e plura Tetraedra complere &longs;oliditatem. </s>
4235 
4236 <s>deceptus <pb pagenum="86"/>fort&egrave; fuit Ari&longs;t. 
4237 
4238 c&ograve; quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi&shy;<lb/>bus, ver&ugrave;m ill&aelig; non &longs;unt regulares, ide&longs;t <expan abbr="n&otilde;">non</expan> &longs;unt Tetraedra, vt po&longs;tea o&longs;ten&shy;<lb/>dam. </s>
4239 
4240 <s>Verum quidem e&longs;t octo cubos &longs;imul adactos &longs;oliditatem conficere, <lb/>quia ad id nece&longs;&longs;arij &longs;unt octo anguli &longs;olidi, quos octo cubi pr&aelig;bere po&longs;&longs;unt, <lb/>cum anguli ip&longs;orum &longs;int recti, &amp; &longs;olidi. </s>
4241 
4242 <s>Verum enim ver&ograve; plures pyramides <lb/>regulares, &longs;iue plura Tetraedra non po&longs;&longs;e replere vacuum, <expan abbr="&longs;olidum&qacute;">&longs;olidumque</expan>; con&shy;<lb/>&longs;tituere, ex eo patet, quia &longs;i id pr&aelig;&longs;tarent, conflarent nece&longs;&longs;ari&ograve;, vel vnum <lb/>ex <expan abbr="quinq;">quinque</expan> corporibus regularibus, de quibus in 13. Elemen. <!-- REMOVE S-->vel aliud quod&shy;<lb/>piam; non aliud, nam, vt patet ex &longs;cholio 13. Elem. 
4243 
4244 non dantur, ni&longs;i illa. <lb/></s>
4245 
4246 
4247 
4248 <s>quinque; <expan abbr="neq;">neque</expan> vllum ex illis, quia diameter huiu&longs;modi corporis, quod com&shy;<lb/>poneretur ex illis pyramidibus, e&longs;&longs;et dupla lateris eiu&longs;dem, vt patet, quia <lb/>pyramides ill&aelig; omnes concurrerent ad centrum &longs;ph&aelig;r&aelig; illas omnes com&shy;<lb/>plectentis, quare latus vnius pyramidis &agrave; &longs;uperficie &longs;ph&aelig;r&aelig; incipiens de&longs;i&shy;<lb/>neret in centrum, ergo latus i&longs;tud e&longs;&longs;et &longs;emidiameter, quapropter tota dia&shy;<lb/>meter illius &longs;ph&ecedil;r&aelig;, &amp; con&longs;equenter huius corporis in illa in&longs;cripti, e&longs;&longs;et du&shy;<lb/>pla lateris eiu&longs;dem figur&aelig; &longs;olid&aelig; in&longs;cript&aelig;, &longs;ed nullo talis proportio diame&shy;<lb/>tri alicuius ex illis <expan abbr="quinq;">quinque</expan> &longs;olidis regularibus ad latus eiu&longs;dem reperitur, <lb/>qu&aelig; &longs;it nimirum dupla, vt patet ex vltimis demon&longs;trationibus 13. Elem. 
4249 
4250 ini&shy;<lb/>tio facto &agrave; 13. demon&longs;tratione, in quibus nulla reperitur proportio dupla <lb/>inter diametrum, &amp; latus eiu&longs;dem alicuius ex illis &longs;olidis; ex quibus mani&shy;<lb/>fe&longs;tum e&longs;t, plures regulares pyramides quouis pacto &longs;imul vnitas nullo mo&shy;<lb/>do replere locum &longs;olidum. </s>
4251 
4252 <s>cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t. 
4253 
4254 nullo <lb/>modo po&longs;&longs;e verificari de repletione &longs;olidi per plura Tetraedra, &amp; omnes <lb/>tamen commentatores auctoritate Ari&longs;t. 
4255 
4256 decepti pro ip&longs;o &longs;tarent, dubius, <lb/><expan abbr="anceps&qacute;">ancepsque</expan>; diu h&aelig;&longs;i, neque quid quam mea Minerua a&longs;&longs;erere au&longs;us &longs;um, &longs;ed P. <lb/><!-- REMOVE S-->Clauium pr&aelig;ceptorem meum per literas con&longs;ului, qui in hunc modum hu&shy;<lb/>mani&longs;&longs;im&egrave; re&longs;pondit; cubus implet locum quater &longs;umptus, ad idem enim <lb/>punctum quatuor cubi coaptantur: &longs;ic etiam pyramis &longs;exies &longs;umpta, &longs;eu &longs;ex <lb/>pyramides ad idem punctum iunct&aelig;ratione &longs;ub&longs;tantium <expan abbr="triangulor&utilde;">triangulorum</expan> &aelig;qui&shy;<lb/>laterorum. </s>
4257 
4258 
4259 
4260 <s>Verum hac ratione non videntur implere locum lolidum, fa&shy;<lb/>teor; &longs;ed tamen Ari&longs;t. 
4261 
4262 in co tex. <!-- REMOVE S-->non loquitur de repletione loci &longs;olidi. </s>
4263 
4264 
4265 
4266 <s>h&aelig;c <lb/>ip&longs;e. </s>
4267 
4268 <s>&longs;i igitur libeat Ari&longs;totelem, quod fort&egrave; Clauius intendebat defendere, <lb/>dicendum e&longs;t cum eo Ari&longs;t non loqui de repletione loci &longs;olidi: <expan abbr="neq;">neque</expan> loqui <lb/>de cubo, &amp; Tetraedro, quatenus &longs;unt corpora, &longs;ed quatenus habent &longs;uper&shy;<lb/>ficies, cubus quidem &longs;ex quadratas, Tetraedrum autem quatuor &aelig;quilate&shy;<lb/>ras &longs;uperficies, qu&aelig; du&aelig; figur&aelig;, vt &longs;upra in hoc textu vidimus, replent lo&shy;<lb/>cum: <expan abbr="atq;">atque</expan> hoc modo facimus Ari&longs;totelem non formaliter loquentem. </s>
4269 
4270 <s>ex&shy;<lb/>aduers&ograve; ne videamur magis Ari&longs;t. 
4271 
4272 quam veritatem &longs;equi, videtur dicen&shy;<lb/>dum, Ari&longs;totilem formaliter locutum e&longs;&longs;e, &amp; vt patet ex rationibus &longs;upra <lb/>allatis de repletione &longs;olidi e&longs;&longs;e intelligendum, vt etiam intellexerunt omnes <lb/>huius loci expo&longs;itores; Verumtamen ip&longs;um erra&longs;&longs;e, dum plures pyramides <lb/>replere &longs;olidum exi&longs;timauit. </s>
4273 
4274 <s>Vtrumuis dixerimus, non tamen Ari&longs;t. 
4275 
4276 ab om&shy;<lb/>ni crrore vindicabimus. </s>
4277 
4278 <s>Hoc tamen certum e&longs;t, ex pr&aelig;dictis, Gr&aelig;cos om&shy;<lb/>nes pariter, ac Latinos, illos &longs;equentes, lapos e&longs;&longs;e, a&longs;&longs;erentes duodecim py&shy;<lb/>ramides complere &longs;olidum locum, <expan abbr="atq;">atque</expan> Dodecaedrum con&longs;tituere; nam py&shy;<lb/>ramides Dodecaedron con&longs;tituentes non &longs;unt regulares, ide&longs;t, non &longs;unt Te&shy;<pb pagenum="87"/>traedra (de quibus tamen Ari&longs;t. 
4279 
4280 loquitur) vt patet ex &longs;upradictis. </s>
4281 
4282 <s>Indul&shy;<lb/>geas Lector, &longs;i hoc loco nece&longs;&longs;e fuit in Geometri&aelig; penetralia ingredi: ope&shy;<lb/>r&aelig;pretium enim e&longs;t aliquando ip&longs;is Mathematicis &longs;atisfacere. </s>
4283 
4284 <s>tu ver&ograve;, &longs;i <lb/>adeo es mathematicis imbutus, con&longs;ule po&longs;tremas demon&longs;tra. </s>
4285 
4286 <s>13. Elem. 
4287 
4288 &amp; <lb/>pr&aelig;cipu&egrave; &longs;cholium vltimum, vbi plura de his corporibus &longs;citu digni&longs;&longs;ima, <lb/><expan abbr="atq;">atque</expan> huc &longs;pectantia reperies ex his omnibus Mathematica, qu&aelig; no&longs;tr&aelig; &longs;unt <lb/>partes, per&longs;picu&egrave; &longs;atis expo&longs;uimus.</s></p><p type="main">
4289 
4290 <s>Multo po&longs;t tempore, qu&agrave;m h&aelig;c &longs;crip&longs;eram incidi fort&egrave; in cap. 
4291 
4292 38. &longs;pecu&shy;<lb/>lationem 10. Benedicti de placitis Ari&longs;t. <!-- REMOVE S--><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t. 
4293 
4294 hoc loco <lb/>erroris notari, dum a&longs;&longs;eruit duodecim pyramides replere <expan abbr="loc&utilde;">locum</expan> corporeum, <lb/>ide&longs;t, vt exponit ip&longs;e, &longs;ex pyramides &longs;uper hexagonam aliquam figuram <lb/>&longs;uperficialem, &amp; &longs;ex &longs;ub eadem, id pr&aelig;&longs;tarent, cum potius maius vacuum <lb/>remaneat ad quamlibet partium &longs;upra, &amp; infra, quam plenum. </s>
4295 
4296 
4297 
4298 <s>h&aelig;c ip&longs;e. </s>
4299 
4300 <s>&longs;ed <lb/>expo&longs;itio i&longs;ta puerili, ne dum Ari&longs;t. 
4301 
4302 ingenio pror&longs;us indigna e&longs;t: vt propte&shy;<lb/>rea exi&longs;timem ca&longs;u potius eum Ari&longs;t. 
4303 
4304 rect&egrave; reprehendi&longs;&longs;e, quam ex certa <lb/>&longs;cientia, cum illius erratum maiori errato conetur corrigere. </s>
4305 
4306 <s>Incidi po&shy;<lb/>&longs;trem&ograve; in Indicem librorum, quem Maurolyius &longs;u&aelig; Co&longs;mographi&aelig; pr&aelig;po&shy;<lb/>nit, vbi &longs;ic ait: Demon&longs;tramus autem in libello de figuris planis, <expan abbr="&longs;olidis&qacute;">&longs;olidisque</expan>; <lb/>locum replentibus, cubos per &longs;e, pyramides ver&ograve; cum octacdris compactas <lb/>dumtaxat implere locum, qua in re Auerroem erra&longs;&longs;e pueriliter manife&longs;tum <lb/>erit. </s>
4307 
4308 <s>Vides igitur tanti viri auctoritate confirmari no&longs;tram &longs;ententiam, py&shy;<lb/>ramides videlicet per &longs;e, non replere vacuum. </s>
4309 
4310 <s>cum igitur con&longs;tet vnam tan&shy;<lb/>tum ex figuris &longs;olidis, &longs;iue etiam dicas, vt perperam Ari&longs;t. &amp; alij plures exi&shy;<lb/>&longs;timarunt, replere totum &longs;olidum; nulla ratione poterunt <expan abbr="elem&etilde;ta">elementa</expan> quatuor, <lb/>quatuor diuer&longs;is figuris indui, &longs;ed vnum tantummodo, quare reliqua <expan abbr="ab&longs;q;">ab&longs;que</expan> <lb/>figura remanere nece&longs;&longs;e e&longs;&longs;et: quod e&longs;t omnino inconueniens.</s></p><p type="main">
4311 
4312 <s><arrow.to.target n="marg122"/></s></p><p type="margin">
4313 
4314 <s><margin.target id="marg122"/>122</s></p><p type="main">
4315 
4316 <s>Tex. 71 <emph type="italics"/>(Deinde &longs;i terra e&longs;t cubus &amp;c.)<emph.end type="italics"/> lege definitiones 11. Elem. 
4317 
4318 qu&aelig; &longs;unt <lb/>admodum faciles, ibi reperies de&longs;initiones quinque corporum regularium, <lb/>quorum figuras Plato elementis tribuebat: qua ver&ograve; id ratione faceret, ha&shy;<lb/>bes in &longs;ph&aelig;ra Clau. <!-- KEEP S--></s>
4319 
4320 <s>Simpl. <!-- REMOVE S-->etiam hoc loco &longs;atisfacit.</s>
4321 
4322 </p></chap><chap><p type="head">
4323 
4324 <s><emph type="italics"/>Ex Quarto de C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
4325 
4326 <s><arrow.to.target n="marg123"/></s></p><p type="margin">
4327 
4328 <s><margin.target id="marg123"/>123</s></p><p type="main">
4329 
4330 <s>Tex. 33. <emph type="italics"/>(Deinde ad &longs;imiles videtur angulos ignis quidem &longs;ur&longs;um ferri, <lb/>terra autem deor&longs;um, &amp; omnin&ograve; quod grauitatem babet, quare nece&longs;&longs;e <lb/>est ferri ad medium. </s>
4331 
4332 <s>boc autem vtrum accidit ad ip&longs;um tcrr&aelig; medium, <lb/>an ad vniuer&longs;i, quoniam idem ip&longs;orum &longs;it, alius &longs;ermo e&longs;t)<emph.end type="italics"/> cum vellet <lb/><figure place="text" xlink:href="figures-la/009.01.087.1.tif"/><lb/>probare Ari&longs;toteles dari <expan abbr="p&utilde;ctum">punctum</expan> quoddam in medio <lb/>mundi, ad quod grauia de&longs;cendant, &amp; concurrent: <lb/>&amp; &agrave; quo leuia a&longs;cendat; vtitur, pr&aelig;ter alias, etiam <lb/>ratione aliqua ex parte mathematica; qu&aelig; e&longs;t huiu&longs;&shy;<lb/>modi. </s>
4333 
4334 <s>videmus ignem, &amp; c&aelig;tera l&ecedil;uia a&longs;cendere &agrave; <lb/>terra &longs;ur&longs;um ad angulos &aelig;quales; &longs;imiliter videmus <lb/>terram, &amp; c&ecedil;tera grauia de&longs;cendere ad terram dcor&shy;<lb/>&longs;um ad angulos &aelig;quales, quod &longs;ignum e&longs;t omnia i&longs;ta <lb/>idem mundi medium re&longs;picere: v.g. <!-- REMOVE S-->&longs;it terra in &longs;igu&shy;<lb/>ra pr&aelig;&longs;enti circulus E C D, cuius medium, &longs;ine cen&shy;<pb pagenum="88"/>trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, qu&aelig; facit angulos in &longs;u&shy;<lb/>perficie terr&aelig; &aelig;quales, nimirum angulos B C D, B C E. &longs;imiliter terra per <lb/>candem lineam <expan abbr="faci&etilde;s">faciens</expan> eo&longs;dem angulos &aelig;quales de&longs;cendit. </s>
4335 
4336 
4337 
4338 <s>linea autem, qu&aelig; <lb/>facit tales angulos tendit ad centrum &longs;ph&aelig;r&aelig; A, vt patet ad &longs;en&longs;um in figu&shy;<lb/>ra, &amp; probari pote&longs;t geometric&egrave; ex primis tertij Elem. 
4339 
4340 ex quibus patet tam <lb/>l&aelig;uia, quam grauia, qu&aelig; per talem lineam ferantur, re&longs;picere centrum A, <lb/>&longs;ph&aelig;r&aelig;. </s>
4341 
4342 <s>Vtrum autem i&longs;tud centrum &longs;it idem cum <expan abbr="c&etilde;tro">centro</expan> totius mundi, alius, <lb/>inquit, e&longs;t &longs;ermo, hoc e&longs;t, ad a&longs;tronomum pertinet. </s>
4343 
4344 <s>vide igitur hac de re <lb/>pulchram de&longs;&longs;ertationem apud Clauium in &longs;ph&aelig;ra: qui probat euidenter <lb/>e&longs;&longs;e vnum, &amp; idem.</s></p><p type="main">
4345 
4346 <s><arrow.to.target n="marg124"/></s></p><p type="margin">
4347 
4348 <s><margin.target id="marg124"/>124<!-- KEEP S--></s></p><p type="main">
4349 
4350 <s><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap. 
4351 
4352 vlt. </s>
4353 
4354 <s>de C&oelig;lo. <!-- KEEP S--></s>
4355 
4356 <s>cuius loco &igrave;n-<emph.end type="italics"/></s></p><p type="main">
4357 
4358 <s><arrow.to.target n="marg125"/><lb/><arrow.to.target n="marg126"/><lb/><emph type="italics"/>terim Lector adeat Di&longs;cur&longs;um Italicum Galil&aelig;i Galil&aelig;i, de his,<emph.end type="italics"/><lb/><arrow.to.target n="marg127"/><lb/><emph type="italics"/>qu&aelig; in aqua mouentur, ac natant: ubi prop&egrave; finem, plura in hu-<emph.end type="italics"/><lb/><arrow.to.target n="marg128"/><lb/><emph type="italics"/>ius capitis explicationem affert.<emph.end type="italics"/><lb/><arrow.to.target n="marg129"/></s></p><p type="margin">
4359 
4360 <s><margin.target id="marg125"/>125</s></p><p type="margin">
4361 
4362 <s><margin.target id="marg126"/>126</s></p><p type="margin">
4363 
4364 <s><margin.target id="marg127"/>127</s></p><p type="margin">
4365 
4366 <s><margin.target id="marg128"/>128</s></p><p type="margin">
4367 
4368 <s><margin.target id="marg129"/>129</s></p></chap><chap><p type="head">
4369 
4370 <s><emph type="italics"/>Ex Lib. 2. de Generatione, &amp; Corruptione.<emph.end type="italics"/><lb/><arrow.to.target n="marg130"/><!-- KEEP S--></s></p><p type="margin">
4371 
4372 <s><margin.target id="marg130"/>130</s></p><p type="main">
4373 
4374 <s>Tex. 56. <emph type="italics"/>(ldeoqu&eacute; non prima latio cau&longs;a Generationis, &amp; Corruptionis e&longs;t, <lb/>&longs;ed qu&aelig; &longs;ecundum obliquum circulum, in hac enim &amp; continuum vnum <lb/>e&longs;t &amp; moueri duobus motibus)<emph.end type="italics"/> per primam lationem intelligit mo&shy;<lb/>tum primi mobilis, qul &longs;it &longs;uper polis mundi, quo Stell&aelig; omnes <lb/>ab oriente in occidentem rect&agrave; feruntur. </s>
4375 
4376 <s>per obliquum ver&ograve; circulum in&shy;<lb/>telligit Zodiacum, qui obliquus e&longs;t, quia poli eius &longs;unt alij &agrave; polis mundi, &amp; <lb/>quia non tendit rect&agrave; ab ortu ad occa&longs;um, &longs;ed in &longs;ph&aelig;ra mundi tran&longs;uer&shy;<lb/>&longs;us e&longs;t, &amp; deflectit &agrave; &longs;eptentrione in meridiem, quamuis non rect&agrave;, vt in <lb/>&longs;ph&aelig;ra explicari &longs;olet. </s>
4377 
4378 <s>motus ergo Planetarum, qui fit &longs;ecundum hunc cir&shy;<lb/>culum, &amp; ip&longs;e obliquus, &amp; tran&longs;uer&longs;us codem modo erit; ferrentur que per <lb/>eum &agrave; Borea ad Au&longs;trum, &amp; &egrave; conuer&longs;o; ex quo acce&longs;&longs;u, &amp; rece&longs;&longs;u efficiunt <lb/>&aelig;&longs;tatem, &amp; hyemem, item generationes, &amp; corruptiones. </s>
4379 
4380 <s>Sol porr&ograve;, &amp; pla&shy;<lb/>net&aelig;, qui motibus proprijs hunc circulum peragunt, dicuntur moueri duo&shy;<lb/>bus motibus, &amp; quidem contrarijs: quoniam dum Sol. </s>
4381 
4382 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->per Zodiacum <lb/>graditur motu proprio, interim etiam &agrave; primo mobili fertur ab ortu in oc&shy;<lb/>ca&longs;um: ex quibus duobus motibus fit vnus tantum Solis motus &longs;piralis, qui <lb/>mixtus e&longs;t, ide&longs;t, qui fit &agrave; duobus motoribus; vnde re vera Sol non mouetur <lb/>duobus motibus contrarijs re ip&longs;a di&longs;tinctis; hoc enim impo&longs;&longs;ibile e&longs;t: &longs;ed <lb/>motu mixto ex duobus, qui &longs;piralis e&longs;t, circa mundum de&longs;cribens &longs;piras ab <lb/>vno tropico ad alterum: qui, vt dixi, cau&longs;atur &agrave; duobus motoribus, qui &longs;unt <lb/>Sol ip&longs;e, mouens &longs;e ip&longs;um per Zodiacum: &amp; primum mobile mouens in&longs;u&shy;<lb/>per ip&longs;um Solem, &amp; Zodiacum ab ortu in occa&longs;um circa mundum.</s>
4383 
4384 
4385 
4386 </p></chap><pb pagenum="89"/><chap><p type="head">
4387 
4388 <s><emph type="italics"/>EX PRIMO METEORORVM.<emph.end type="italics"/></s></p><p type="main">
4389 
4390 <s><arrow.to.target n="marg131"/></s></p><p type="margin">
4391 
4392 <s><margin.target id="marg131"/>131</s></p><p type="main">
4393 
4394 <s>Svmma 1. cap. 
4395 
4396 3. <emph type="italics"/>(Moles autem terr&aelig; quanta &longs;it ad ambientes magnitudi&shy;<lb/>nes, non immamfestum, iam enim vi&longs;um est per a&longs;trologica theoremata, <lb/>quod mult&ograve; etiam quibu&longs;dam a&longs;tris est minor)<emph.end type="italics"/> Quantitas terr&aelig; non &longs;o&shy;<lb/>lum ab&longs;olut&egrave; con&longs;iderata, ab A&longs;tronomis explorata habetur, vt vi&shy;<lb/>dere e&longs;t in &longs;ph&aelig;ra Clauij; &longs;ed etiam re&longs;pectiu&egrave; con&longs;iderata, ide&longs;t re&longs;pectu <lb/>aliorum elementorum, &amp; ip&longs;orum etiam a&longs;trorum; cuius demon&longs;trationes <lb/>&longs;unt partim in libello Ari&longs;tarchi Samij, de magnitudine, &amp; di&longs;tantia Solis, <lb/>&amp; Lun&aelig;, partim apud Ptol&aelig;meum in magna Syntaxi, &longs;iue Almage&longs;to: par&shy;<lb/>tim apud Albategnium de &longs;cientia &longs;tellarum: partim demum apud Ticho&shy;<lb/>nem Brahe. </s>
4397 
4398 <s>Porr&ograve; facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra mult&ograve; maiorem, <lb/>terram ver&ograve; maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/>in figura &longs;equenti; vbi vmbra terr&aelig; e&longs;t D B E, in quam Luna nigricans im&shy;<lb/>mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro&shy;<lb/>nomi ob&longs;eruarunt vmbram terr&aelig; paul&ograve; &longs;upra Lunam pertingere, cum &longs;upe&shy;<lb/>riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ari&ograve; e&longs;&longs;e acuminatam, &longs;eu <lb/>conicam, vt figura refert. </s>
4399 
4400 <s>Cum ergo terra vmbram proijciat turbinatam, <lb/>nece&longs;&longs;ari&ograve; corpus Solis, quod ip&longs;am illuminat, eadem maior erit: quoti&shy;<lb/>diana enim experientia docemur, corpore illuminante exi&longs;tente maiore <lb/>qu&agrave; &longs;it illuminatum, vmbram proijci fa&longs;tigiatam: cum deinde Solem val&shy;<lb/>de a terra di&longs;tare certum &longs;it, optim&egrave; infertur, eum re&longs;pectu terr&aelig; e&longs;&longs;e maxi&shy;<lb/>mum: quanto enim du&aelig; line&aelig;, &longs;iue radij B A, B C. &agrave; terra ad partes Solis <lb/><figure place="text" xlink:href="figures-la/009.01.089.1.tif"/><lb/>magis elongantur, tan&shy;<lb/>to maius corpus <expan abbr="illu-min&atilde;s">illu&shy;<lb/>minans</expan> intercipiunt. </s>
4401 
4402 <s>ha&shy;<lb/>ctenus de magnitudine <lb/>terr&aelig; ad Solem. </s>
4403 
4404 <s>Cum <lb/>ver&ograve; Luna eclyp&longs;atio&shy;<lb/>nis tempore, aliquan&shy;<lb/>do non &longs;olum tota in <lb/>vmbr&aelig; vertice lateat, <lb/>ver&ugrave;m etiam <expan abbr="aliqu&atilde;do">aliquando</expan> <lb/>moram trahat, euidens <lb/>e&longs;t, eam e&longs;&longs;e mult&ograve; mi&shy;<lb/>norem illa vmbr&aelig; par&shy;<lb/>te, in quam immergi&shy;<lb/>tur; qu&aelig; pars cum &longs;it <lb/>conic&aelig; vmbr&aelig; media, <lb/>crit mult&ograve; gracilior <lb/>qu&agrave;m &longs;it ip&longs;a terra. <lb/></s>
4405 
4406 <s>Ex quo manife&longs;t&egrave; apparet, Lunam, qu&aelig; illa vmbra minor e&longs;t, e&longs;&longs;e &agrave; fortio&shy;<lb/>ri mult&ograve; minorem ip&longs;a terre&longs;tri mole. </s>
4407 
4408 <s>Atque h&aelig;c de comparatione terr&aelig; <lb/>ad Lunam. <!-- KEEP S--></s>
4409 
4410 <s>harum rerum demon&longs;trationes exactiores pertractare non e&longs;t <lb/>huius loci.</s></p><p type="main">
4411 
4412 <s><arrow.to.target n="marg132"/></s></p><p type="margin">
4413 
4414 <s><margin.target id="marg132"/>132</s></p><p type="main">
4415 
4416 <s>Eodem cap. <emph type="italics"/>(Con&longs;iderautes vtique, qu&aelig; nunc c&longs;tenduntur per Mathematica<emph.end type="italics"/><pb pagenum="90"/><emph type="italics"/>&longs;ufficienter, fort&egrave; vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>e&longs;t putare <expan abbr="vnumquodq;">vnumquodque</expan> eorum qu&aelig; feruntur e&longs;&longs;e paruum magnitudinibus, quia vi&shy;<lb/>detur a&longs;picientibus, binc nobis &longs;ic)<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, qu&aelig; <lb/>pa&longs;&longs;im apud Ari&longs;t. 
4417 
4418 occurrunt, <expan abbr="pleriq;">plerique</expan> no&longs;tr&aelig; &aelig;tatis con&longs;iderarent, qui nulla <lb/>ratione probari po&longs;&longs;e exi&longs;timant, Solem, v. <!-- REMOVE S-->g. <!-- REMOVE S-->terra e&longs;&longs;e centies &longs;exagies &longs;e&shy;<lb/>xies maiorem; &longs;ed etiam, quod peius e&longs;t, negant e&longs;&longs;e maiorem; ad demon&shy;<lb/>&longs;trationes autem a&longs;tronomicas dicunt &longs;e exi&longs;timare eas e&longs;&longs;e fallaces; at que <lb/>impo&longs;libile e&longs;&longs;e nos res adeo &agrave; nobis di&longs;taptes &longs;ufficienter perue&longs;tigare: <lb/>quanto &longs;apientius, ac prudentius eorum Magi&longs;ter Ari&longs;t. 
4419 
4420 alibi &longs;&aelig;pius, &longs;ed hoc <lb/>pr&aelig;cipu&egrave; loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/>i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia pr&aelig;ceptoris a&longs;&longs;equi poterunt.</s>
4421 
4422 
4423 
4424 </p><p type="main">
4425 
4426 <s><arrow.to.target n="marg133"/></s></p><p type="margin">
4427 
4428 <s><margin.target id="marg133"/>133</s></p><p type="main">
4429 
4430 <s>Summa 1. cap. 
4431 
4432 4. <emph type="italics"/>(Qu&aelig; igitur astrorum e&longs;t, velox quidem; long&egrave; autem: qu&aelig; <lb/>ver&ograve; Lun&aelig; deor&longs;um quidem, tarda autem: qu&aelig;autem Solis ambo h&aelig;c babet &longs;uffi&shy;<lb/>cienter)<emph.end type="italics"/> qu&aelig; igitur a&longs;trorum, ide&longs;t latio a&longs;trorum e&longs;t velox, &longs;ed procul &agrave; ter&shy;<lb/>ra; Lun&aelig; ver&ograve; latio terr&aelig; quidem proxima, tarda tamen: at ver&ograve; Solis la&shy;<lb/>tio medio modo &longs;e habet inter vtrumque, ide&longs;t, quia <expan abbr="neq;">neque</expan> nimis vt a&longs;tra di&shy;<lb/>&longs;tat, <expan abbr="neq;">neque</expan> tard&egrave; &longs;icut Luna circunfertur. </s>
4433 
4434 <s>exi&longs;timo Ari&longs;t. 
4435 
4436 loqui de motu diur&shy;<lb/>no, quia &longs;ecundum hunc a&longs;tra inerrantia &longs;unt Sole citatiora, Sol ver&ograve; ip&longs;a <lb/>Luna citior. </s>
4437 
4438 <s>Verumenimuer&ograve; illud non pr&aelig;tereundum, quod plurium inua&shy;<lb/>luerit opinio exi&longs;timantium Ari&longs;t. 
4439 
4440 his verbis, Solem &longs;upra Lunam proxim&egrave; <lb/>colloca&longs;&longs;e; quod tamen ex ip&longs;is nullo pacto deduci pote&longs;t; &longs;ed &longs;olummodo <lb/>ip&longs;um &longs;upra Lunam colloca&longs;&longs;e. </s>
4441 
4442 <s>quod &longs;i ita &longs;en&longs;i&longs;&longs;et venia dignus haberetur, <lb/>cum tunc temporis nondum fort&egrave; adinuent&aelig; e&longs;&longs;ent demon&longs;trationes ill&aelig; <lb/>a&longs;tronomic&aelig;, quibus ordo Planetarum certi&longs;&longs;im&egrave; con&longs;tat, <expan abbr="Sol&qacute;">Solque</expan>; medius in&shy;<lb/>ter Planetas collocatur. </s>
4443 
4444 <s>At ver&ograve; nulla ratione ferendi &longs;unt <expan abbr="quicunq;">quicunque</expan> no&longs;tra <lb/>hac tempe&longs;tate non &longs;olum Ari&longs;t. 
4445 
4446 ita &longs;en&longs;i&longs;&longs;e, &longs;ed etiam contra firmi&longs;&longs;imas <lb/>aftronomorum demon&longs;trationes, quibus ade&ograve; Ari&longs;t. 
4447 
4448 deferebat, vnica, vt pu&shy;<lb/>tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum &agrave; Luna locum occupare om&shy;<lb/>ni ope defendunt.</s></p><p type="main">
4449 
4450 <s><arrow.to.target n="marg134"/></s></p><p type="margin">
4451 
4452 <s><margin.target id="marg134"/>134</s></p><p type="main">
4453 
4454 <s>Summa 2. cap. 
4455 
4456 3. <emph type="italics"/>(Quod accidit circa Mercurij stellam, quia enim modicum <lb/><expan abbr="&longs;upera&longs;c&etilde;dis">&longs;upera&longs;cendis</expan>, &longs;&aelig;p&egrave; non apparet, it a vt po&longs;t tempus multum appareat)<emph.end type="italics"/> quod Mer&shy;<lb/>curius non ni&longs;i rar&ograve; con&longs;pici po&longs;&longs;it, cau&longs;a e&longs;t, quia parum &agrave; Sole elongatur, <lb/>&longs;iue ip&longs;um antecedat, &longs;iue &longs;ub&longs;equatur. </s>
4457 
4458 <s>ex quo fit, vt diu fer&egrave; &longs;imul cum So&shy;<lb/>le cit cumferatur, &amp; propterea &longs;iue oriatur, &longs;iue occidat, parum &longs;upra ho&shy;<lb/>rizontem eleuatus apparere pote&longs;t, quod Ari&longs;t. 
4459 
4460 ait modicum <expan abbr="&longs;upera&longs;c&etilde;dit">&longs;upera&longs;cendit</expan>. <lb/></s>
4461 
4462 <s>vnde fit tum propter nimiam Solis vicinitatem, cuius lumine tegitur; tum <lb/>propter vapores, qui horizonti vt plurimum incumbunt, vt rar&ograve;, &amp; po&longs;t ma&shy;<lb/>gna temporis interualla con&longs;piciatur. </s>
4463 
4464 <s>non me fugit h&aelig;c omnia ab a&longs;trono&shy;<lb/>mis per epiciclum excu&longs;ari; &longs;ed ego mediocritati eorum, in quorum gra&shy;<lb/>tiam h&aelig;c &longs;cribo, con&longs;ultum volo.</s></p><p type="main">
4465 
4466 <s><arrow.to.target n="marg135"/></s></p><p type="margin">
4467 
4468 <s><margin.target id="marg135"/>135</s></p><p type="main">
4469 
4470 <s>Eodem cap. <emph type="italics"/>(Ad au&longs;trum autem quando feratur, copiam quidem habere tal&iacute;s <lb/>humiditatis, &longs;ed quia parua e&longs;t &longs;ictio circuli, qu&aelig; &longs;uper terram, qu&aelig; autem deor&shy;<lb/>&longs;um multiplex, non po&longs;&longs;e vi&longs;um hominum fractum ferri ad Solem, <expan abbr="neq;">neque</expan> ip&longs;i tropico <lb/>au&longs;trino appropinquanti; <expan abbr="neq;">neque</expan> in &aelig;&longs;tiuis ver&longs;iombus exi&longs;tente Sole. <!-- KEEP S--></s>
4471 
4472 <s>quapropter in <lb/>lis quidem locis neque fieri cometem ip&longs;um. </s>
4473 
4474 <s>quando ver&ograve; ad Boream &longs;ubdefecerit, <lb/>accipere comam, quia magna e&longs;t circun&longs;erentia, qu&aelig; e&longs;t &longs;upra horizontem; qu&aelig; au-<emph.end type="italics"/><pb pagenum="91"/><emph type="italics"/>tem e&longs;t &longs;ubtus, pars circuli parua; facil&egrave; enim vi&longs;um hominum pertingere tunc ad <lb/>Solem)<emph.end type="italics"/> cur cometa in regione au&longs;trali vltra Solis, <expan abbr="anni&qacute;">annique</expan>; vias con&longs;titutus <lb/>non appareret, cau&longs;am referebat Hippocrates paruitatem circuli, qucm <lb/>motu diurno cometa de&longs;cribebat, ob quam ade&ograve; parum &longs;upra horizontem <lb/>attolleretur, vt <expan abbr="n&otilde;">non</expan> po&longs;&longs;et vi&longs;us no&longs;ter ab ip&longs;o ad Solem reflecti; quod &longs;ecun&shy;<lb/>dum ip&longs;um erat nece&longs;&longs;arium ad cometarum apparitionem. </s>
4475 
4476 <s>I oquitur igitur <lb/>Hippocrates de circulis, quos diurna conuer&longs;ione cometes circumducir, qui <lb/>omnin&ograve; &longs;imiles &longs;unt ijs, quos etiam Sol, <expan abbr="reliqua&qacute;">reliquaque</expan>; a&longs;tra eodem motu de &longs;i&shy;<lb/>gnant. </s>
4477 
4478 <s>qui quidem omnes in no&longs;tr a &longs;ph&aelig;ra obliqua ita &longs;e habent, vt ij, qui <lb/>&longs;unt vltra &aelig;quatorem ad Capricorm tropicum, minus &longs;upra horizontem <lb/>extent, qu&agrave;m infra de primantur, &amp; tanto minus, quanto magis ab &aelig;quato&shy;<lb/>re in auftrum recedunt: contra ver&ograve; faciunt, qui citra &aelig;quatorem ad Can&shy;<lb/>cri conuer&longs;ionem co&longs;&longs;ocantur, quanto enim magis ab &aelig;quatore in boream <lb/>remouentur, tant&ograve; eorum &longs;ectio, qu&aelig; e&longs;t &longs;upra horizontem, maior e&longs;t ea, <lb/>qu&aelig; infra horizontem latet. </s>
4479 
4480 <s>qu&aelig; quidem omnia clara &longs;unt adhibita &longs;ph&aelig;ra <lb/>materiali, quam &longs;i ad tuam poli eleuationem accommodaueris, illic&ograve; vi&shy;<lb/>debis tropici, Cancri &longs;ectionem, qu&aelig; e&longs;t &longs;upra horizontem multo maiorem <lb/>ea, qu&aelig; e&longs;t infra. </s>
4481 
4482 <s>oppo&longs;itum ver&ograve; in altero Capricorni tropico, cuius mini&shy;<lb/>mam portionem &longs;upra, maximam ver&ograve; infra horizontem exi&longs;tere videbis. <lb/></s>
4483 
4484 <s>Idem proportionaliter imaginari debes de circulis, quos cometa tam vltra <lb/>Capricornum, qu&agrave;m citra Cancrum delineat; nam eorum, qui &longs;unt vltra <lb/>Capricornum ad au&longs;trum minores adhuc &longs;ectiones &longs;upra horizontem exi&shy;<lb/>&longs;terent, qu&agrave;m opus &longs;it ad cometen &longs;pectandum. </s>
4485 
4486 <s><expan abbr="At&qacute;ue">Atque</expan> h&aelig;c cau&longs;a e&longs;t ex &longs;en&shy;<lb/>tentia Hippocr. <!-- REMOVE S-->cur in illa au&longs;trali plaga <expan abbr="n&utilde;quam">nunquam</expan> cometes effulgeat. </s>
4487 
4488 
4489 
4490 <s>&egrave; con&shy;<lb/>trario autem, quia ad boream &longs;ectiones ill&aelig; maxim&aelig; &longs;unt, <expan abbr="apt&aelig;&qacute;">apt&aelig;que</expan>; ad refra&shy;<lb/>ctionem vi&longs;us no&longs;tri v&longs;que ad Solem, idcirc&ograve; in hac mundi parte cometas <lb/>con&longs;picere &longs;olemus. </s>
4491 
4492 <s>Reliqua Vicomercatus, <expan abbr="atq;">atque</expan> Alexand. <!-- REMOVE S-->optim&egrave; expli&shy;<lb/>cant, quos tu con&longs;ule, ne actum agatur.</s>
4493 
4494 </p></chap><chap><p type="head">
4495 
4496 <s><emph type="italics"/>In cap. 
4497 
4498 4. &longs;umm&aelig; 2. lib. 
4499 
4500 1. Meteor. <!-- REMOVE S-->de Cometis.<emph.end type="italics"/><!-- KEEP S--></s>
4501 
4502 </p><p type="main">
4503 
4504 <s><arrow.to.target n="marg136"/></s></p><p type="margin">
4505 
4506 <s><margin.target id="marg136"/>136</s></p><p type="main">
4507 
4508 <s>In pr&aelig;&longs;enti cap. <!-- REMOVE S-->Ari&longs;t. &longs;uam de Cometis &longs;ententiam exponit: Come&shy;<lb/>tam nimirum infra Lunam in elementari mundo procreari, &amp; ignitum <lb/>quoddam Meteoron, ex lenta, pingui, <expan abbr="&longs;icca&qacute;">&longs;iccaque</expan>; materia &agrave; terra in &longs;u&shy;<lb/>premam aeris regionem attracta, exi&longs;tere; <expan abbr="ibi&qacute;">ibique</expan>; rapti aeris calore, <lb/>vel elementi ignis (quod illic e&longs;&longs;e putat) vicinitate, vel etiam vi a&longs;trorum <lb/>incendi, <expan abbr="atq;">atque</expan> impelli. </s>
4509 
4510 
4511 
4512 <s>Han&cacute; porr&ograve; opinionem &amp; &longs;i probabilibus tantum ra&shy;<lb/>tionibus confirmatam vulg&ograve; tamen <expan abbr="v&longs;q;">v&longs;que</expan> ad hanc diem receptam, cum fal&shy;<lb/>&longs;am e&longs;&longs;e a&longs;tronomi exi&longs;timent, non erit abs re rationes eas ex &longs;ecundo pro&shy;<lb/>gymn. </s>
4513 
4514 <s>Tichonis volumine, de&longs;umptas hic breuiter referre, quibus a&longs;trono&shy;<lb/>mus ille eos &longs;upra Lunam in &aelig;therea regione collocauit: quas quidem ra&shy;<lb/>tiones ille ex diuturnis ob&longs;eruationibus per exqui&longs;ita organa factis adinue&shy;<lb/>nit: ea&longs;que Mathematicis linearum, ac numerorum demon&longs;trationibus <lb/>explicauit.</s></p><p type="main">
4515 
4516 <s>Prima. <!-- KEEP S--></s>
4517 
4518 <s>&longs;ed vt ab auctoritate, in quam obiter incidimus <expan abbr="initi&utilde;">initium</expan> faciamus, <lb/>non e&longs;t exi&longs;timandum nonnuilos &longs;olum ex recentioribus id con&longs;tanter a&longs;&longs;e&shy;<pb pagenum="92"/>uera&longs;&longs;e, &longs;ed &longs;uperiori etiam &aelig;tate id ip&longs;um Hieron. </s>
4519 
4520 <s>Cardan. <!-- REMOVE S-->libro de &longs;ubtili&shy;<lb/>tate conatus e&longs;t, <expan abbr="neq;">neque</expan> irrito conatu, demon&longs;trare; qui pr&aelig;terea idem cum <lb/>&longs;e ip &longs;o &longs;en&longs;i&longs;&longs;e ait Albumazar. </s>
4521 
4522 
4523 
4524 <s>quibus etiam ex antiquis Seneca annumeran&shy;<lb/>dus e&longs;t. </s>
4525 
4526 <s>pr&ecedil;dicti autem recentiores omnes varijs demon&longs;trationibus ex ac&shy;<lb/>curata ob&longs;eruatione erutis illud cert&ograve; certius con&longs;irmare contendunt: <expan abbr="id&qacute;">idque</expan>; <lb/>non in vno dumtaxat, &longs;ed in <expan abbr="quinq;">quinque</expan> cometis; quorum demon&longs;trationes apud <lb/>Tychonem partim in progymn. </s>
4527 
4528 <s>partim in epi&longs;t. <!-- REMOVE S-->fu&longs;ius explicatas reperies.</s>
4529 
4530 </p><p type="main">
4531 
4532 <s>2. Quarum poti&longs;&longs;ima illa e&longs;t, qu&aelig; ex parallaxi, &longs;eu a&longs;pectus diuer&longs;itate <lb/>de&longs;umitur, certi&longs;&longs;imum enim e&longs;t lumen illud e&longs;&longs;e altero &longs;ublimius, quod mi&shy;<lb/>norem exhibet parallaxim: expertos autem &longs;e e&longs;&longs;e hi omnes, affirmant ho&shy;<lb/>&longs;ce quinque cometas mult&ograve; minorem pati parallaxim, quam Lunam; im&ograve; <lb/>quempiam minorem, qu&agrave;m Sol ip&longs;e patiatur, quo po&longs;ito manife&longs;t&egrave; conuin&shy;<lb/>ceretur eos omnes &longs;upra Lunam in &aelig;therea regione efful&longs;i&longs;&longs;e.</s></p><p type="main">
4533 
4534 <s>3. Ratio, qua etiam ante nouas ob&longs;eruationes vti &longs;olebant, de&longs;umitur <lb/>ex motu comet&aelig; diurno, quo &longs;cilicet oritur, &amp; occidit, quemadmodum c&aelig;&shy;<lb/>tera &longs;ydera, hoc e&longs;t &longs;patio 24. horarum diurnam conuer&longs;ionem circa totam <lb/>terram ab&longs;oluit. </s>
4535 
4536 <s>&longs;i igitur comete e&longs;&longs;et in &longs;ublimiori aeris regione, vbi c&aelig;te&shy;<lb/>ra ignita meteora collocantur, <expan abbr="moueretur&qacute;">mouereturque</expan>; diurno motu circa terram, &longs;e&shy;<lb/>queretur nece&longs;&longs;ari&ograve; eum tanta velocitate videri &agrave; nobis circumferri, vt po&shy;<lb/>tius fulgor quidam, &longs;eu radius pertran&longs;iens ab oriente in occidentem appa&shy;<lb/>reret, quam &longs;tella qu&ecedil;dam: <expan abbr="id&qacute;">idque</expan>; propter propinquitatem; a&longs;tra enim ob ni&shy;<lb/>miam di&longs;tantiam videntur tard&egrave; moueri, quamuis veloci&longs;&longs;im&egrave; moueantur.</s></p><figure place="text" xlink:href="figures-la/009.01.092.1.tif"/><p type="main">
4537 
4538 <s>Quod melius ex &longs;equenti figura <lb/><expan abbr="c&otilde;uincitur">conuincitur</expan>, vbi circulus interior e&longs;t <lb/>terra, cuius &longs;emidiameter A B. cir&shy;<lb/>culus ver&ograve; exterior e&longs;t comet&aelig; gy&shy;<lb/>rus, quem ip&longs;e &longs;patio 24. horarum <lb/>percurrit, qui &longs;ecundum veram pro&shy;<lb/>portionem deberet adhuc ip&longs;i terr&aelig; <lb/>propinquior, ac proinde minor e&longs;&longs;e, <lb/>iuxta aeris &longs;upremam partem. </s>
4539 
4540 <s>hori&shy;<lb/>zon e&longs;t recta D C, tangens terram in <lb/>B, vbi e&longs;t oculus no&longs;ter, qui nihil in&shy;<lb/>fra ip&longs;am D C, videre pote&longs;t; quare <lb/>&longs;i cometa 24. horarum totum gyrum <lb/>D C E, percurrit, non videbitur, ni&longs;i <lb/>quando percurret portionem D C, <lb/>&longs;upra horizontem; qu&aelig; quidem por&shy;<lb/>tio, <expan abbr="neq;">neque</expan> &longs;emihor&aelig; re&longs;ponderet, &longs;i &longs;i&shy;<lb/>gura iuxta veram proportionem con&longs;trueretur. </s>
4541 
4542 <s>experientia tamen con&longs;tat, <lb/>cometas videri &longs;upra horizontem tot horis, quot &longs;tell&aelig; fix&aelig;, &longs;ub quibus mo&shy;<lb/>uentur: non ergo e&longs;t in &longs;upremo aere. </s>
4543 
4544 <s>Quod &longs;i &longs;iat figura, in qua exterior <lb/>comet&aelig; ambitus ade&ograve; magnus &longs;it, vt ip&longs;ius portio D C, &longs;upra horizontem <lb/>exi&longs;tens, re&longs;pondeat tempori, quo cometa &longs;upra no&longs;trum pariter horizon&shy;<lb/>tem &longs;pectatur, ea figura terr&aelig; &longs;emidiametrum A B. toties multiplicabit, vt <lb/>ip&longs;i Lun&aelig; circuitui proxim&egrave; accedat.</s></p><pb pagenum="93"/><p type="main">
4545 
4546 <s>Pr&aelig;terea aiunt, quis &longs;an&aelig; mentis dixerit, Meteoron vlium ex materia <lb/>vaga, ac fluxa con&longs;tans, po&longs;&longs;e tanta pernicitate moueri, vt diurnam con&shy;<lb/>uer&longs;ionem ab&longs;oluat? </s>
4547 
4548 <s>vnde illi motus i&longs;te? </s>
4549 
4550 <s>pr&aelig;&longs;ertim cum videamus c&aelig;tera <lb/>ignita meteora e&longs;&longs;e ad modum temporanea, <expan abbr="atq;">atque</expan> euanida.</s></p><p type="main">
4551 
4552 <s>4. Comprobationem nobis &longs;uppeditant ex via, &longs;eu ductus circuli, quem <lb/>toto durationis tempore proprio cur&longs;u de&longs;ignarunt: pr&aelig;dicti <expan abbr="namq;">namque</expan> quin&shy;<lb/>que comet&aelig; motu &longs;ibi proprio, quo ab occidente non omnin&ograve; orientem <lb/>ver&longs;us, &longs;ed ad aquilonem deflectentes ab initio &longs;u&aelig; apparitionis, <expan abbr="v&longs;q;">v&longs;que</expan> ad vl&shy;<lb/>timum fiuem exqui&longs;iti&longs;&longs;im&egrave; portionem circuli maximi in c&ecedil;lo de&longs;ignarunt; <lb/>non aiiter qu&agrave;m Sol proprio motu per eclypticam in c&oelig;lo mundi &longs;ph&aelig;ram <lb/>in duo &aelig;qualia diuidentem de&longs;cribit. </s>
4553 
4554 <s>necnon aliter ac Luna &longs;uum iter per <lb/>circulum maximum c&oelig;lum bifariam diuidentem perficit. </s>
4555 
4556 <s>quapropter co&shy;<lb/>metas ho&longs;ce <expan abbr="n&otilde;">non</expan> minus quam Sol, vel Luna in ip&longs;o &aelig;there &longs;patiatos e&longs;&longs;e con&shy;<lb/>tendunt. </s>
4557 
4558 <s>qui enim, aiunt, fieri potui&longs;&longs;et, &longs;i in mundo elementari flagra&longs;&longs;ent, <lb/>vt tam regulari, <expan abbr="atq;">atque</expan> con&longs;tanti ductu circuli maximi portionem tam exact&egrave; <lb/>delinea&longs;&longs;ent, quam quidem inter elementa vagum, <expan abbr="atq;">atque</expan> in&longs;tabilem pro ma&shy;<lb/>teri&aelig; in&longs;tabilitate exercere debui&longs;&longs;ent?</s></p><p type="main">
4559 
4560 <s>5. Adde, quod in maximo hoc circulo de&longs;cribendo, etiam &longs;i in&aelig;quali ve&shy;<lb/>locitate vi&longs;i &longs;int moueri, in&aelig;qualitatem tamen illam regularem <expan abbr="vbiq;">vbique</expan> &longs;em&shy;<lb/>per &longs;eruauerunt, in principio quidem velociores, deinde &longs;ucce&longs;&longs;iu&egrave;, &amp; pro&shy;<lb/>portionaliter velocitatem illam &longs;imili analogia &longs;emper &longs;eruata <expan abbr="inhibuer&utilde;t">inhibuerunt</expan>, <lb/>nullo igitur pacto inordinatam in&aelig;qualitatem, qua &agrave; tardiore motu &longs;ubito <lb/>in celeriorem, &amp; rur&longs;us &longs;tatim ab hoc in <expan abbr="ill&utilde;">illum</expan> pro&longs;ilirent exhibuerunt: prout <lb/>omnia Meteora, qu&aelig; in mundi parte elementari ex flammanti materia ge&shy;<lb/>nerantur, talem di&longs;parem, <expan abbr="atq;">atque</expan> incon&longs;tantem motum obtinere cernuntur.</s></p><p type="main">
4561 
4562 <s>6. Argumento pr&aelig;terea e&longs;t cometas ho&longs;ce minim&egrave; elementares fui&longs;&longs;e, <lb/>quod hic eorum proprius motus, quo maximo illo tramite ferebantur, nua&shy;<lb/>quam tantus fuit, vt proprium Lun&aelig; motum, vel tardi&longs;&longs;imum ad&aelig;quauerit, <lb/>qu&aelig; quidem cum lenti&longs;&longs;ima e&longs;t plus denis gradibus vna die promouetur; <lb/>cum tamen comet&aelig; initio cum veloci&longs;&longs;imi &longs;unt non multum vltra quinos <lb/>gradus diurno motu progre&longs;&longs;i &longs;int, vt ob id long&egrave; &longs;upra Lunam cur&longs;um &longs;uum <lb/>ab&longs;olui&longs;&longs;e manife&longs;t&egrave; comprobari po&longs;&longs;it: quo enim &longs;ydera magis &agrave; terra at&shy;<lb/>tolluntur, <expan abbr="octau&aelig;&qacute;">octau&aelig;que</expan>; &longs;ph&aelig;r&aelig; propius accedunt, e&ograve; tardioribus proprijs la&shy;<lb/>tionibus proferuntur: ita vt &longs;teil&aelig; i&longs;t&aelig; c&oelig;lo ad&longs;cititi&aelig; &longs;upra Lunam admo&shy;<lb/>dum euehend&aelig; videantur. </s>
4563 
4564 <s>Quod &longs;i in &longs;uprema aeris regione con&longs;lagrarent, <lb/>qua nam ratione vn&agrave; cum toto c&oelig;lo diurnam conuer&longs;ionem ab&longs;olui&longs;&longs;ent: <lb/><expan abbr="neq;">neque</expan> enim putandum e&longs;t &longs;upremum hunc aeris limbum eadem pernecitate, <lb/>qua c&oelig;le&longs;tes orbes, verum minori admodum im&ograve; tardi&longs;&longs;im&egrave; &agrave; diurno mo&shy;<lb/>tu, &longs;i tamen eo rapitur circumduci.</s></p><p type="main">
4565 
4566 <s>7. Tandem argumentum ex ip&longs;orum duratione de&longs;umatur. </s>
4567 
4568 <s>c&aelig;tera nam&shy;<lb/>que meteora &longs;tatim <expan abbr="atq;">atque</expan> apparuerint, veluti temporanea pror&longs;us, <expan abbr="atq;">atque</expan> eua&shy;<lb/>nida extinguuntur: At ver&ograve; comet&aelig; ad men&longs;em aliquando integrum per&shy;<lb/>&longs;euerant. </s>
4569 
4570 <s>qu&igrave; igitur fieri potuerit, vt in hac corruptibili <expan abbr="m&utilde;di">mundi</expan> parte ex ma&shy;<lb/>teria ade&ograve; &longs;luxa, &amp; vaga, quam illis Ari&longs;teteles &longs;upponit, tandiu perdura&shy;<lb/>re potui&longs;&longs;ent.</s></p><p type="main">
4571 
4572 <s><expan abbr="Atq;">Atque</expan> h&aelig; &longs;unt rationes, quibus plurimi a&longs;tronomorum recentiorum, co&shy;<pb pagenum="94"/>metas ho&longs;ce motum &aelig;there&aelig; regioni conformem, contr&agrave; quam Ari&longs;t. 
4573 
4574 opi&shy;<lb/>natus e&longs;t, obtinui&longs;&longs;e, munifeftum e&longs;&longs;e volunt; ac proinde eorum locum, &amp; <lb/>cur&longs;um in c&oelig;le&longs;ti mundi parte extiti&longs;&longs;e, &longs;e comproba&longs;&longs;e exi&longs;timant: qua de <lb/>re prudentis Lectoris e&longs;to iudicium: <expan abbr="neq;">neque</expan> enim, vt ille cecinit, no&longs;trum e&longs;t, <lb/>tantas componere lites.</s></p><p type="main">
4575 
4576 <s>Verumenimuer&ograve; Peripatetica omnis &longs;chola reclamat; C&oelig;lum e&longs;t inge&shy;<lb/>nerabile, &amp; incorruptibile, mhil igitur noui c&oelig;lo pote&longs;t accidere. </s>
4577 
4578 <s>&longs;ed age <lb/>re&longs;pondent, nonne omnium a&longs;tronomorum con&longs;en&longs;u &longs;tell&aelig; tres nou&aelig; no&longs;tro <lb/>hoc &longs;&aelig;culo in c&oelig;lo toti mundo con&longs;picu&aelig; illuxerunt? </s>
4579 
4580 <s><expan abbr="eas&qacute;">easque</expan>; in octaua &longs;ph&aelig;&shy;<lb/>ra re&longs;edi&longs;&longs;e conftans e&longs;t omnium a&longs;&longs;ertio? </s>
4581 
4582 <s>quarum prior anno 1572. in con&shy;<lb/>&longs;tellatione Ca&longs;&longs;iope&aelig; apparuit. </s>
4583 
4584 <s>Secunda anno 1600. in Cygno, qu&aelig; nec dum <lb/>extinguitur. </s>
4585 
4586 <s>Tertia anno 1604. inter Sagittarij &longs;tellas vi&longs;a e&longs;t, de quibus vi&shy;<lb/>de P. <!-- REMOVE S-->Clauium in &longs;ph&aelig;ra breuiter de illis tractantem: aut &longs;i mauis, &amp; vacat, <lb/>vide quoad primam primum volumen progymna&longs;matum Tychonis Brahe, <lb/>vbi etiam aliorum a&longs;tronomorum de eadem certi&longs;&longs;imas commentationes <lb/>reperies. </s>
4587 
4588 
4589 
4590 <s>con&longs;ule etiam de reliquis duabus Ioannis Kepleri C&aelig;&longs;are&aelig; Maie&shy;<lb/>&longs;tatis Mathematici commentaria; &amp; coactus libenter fateberis noui ali&shy;<lb/>quid c&oelig;lo aduenire po&longs;&longs;e.</s></p><p type="main">
4591 
4592 <s>Po&longs;trem&ograve; tandem po&longs;&longs;et qui&longs;piam in hunc <expan abbr="mod&utilde;">modum</expan> opponere: etiam &longs;i con&shy;<lb/>&longs;tet <expan abbr="quinq;">quinque</expan> cometas c&ecedil;lo oberra&longs;&longs;e, non propterea dicemus reliquos omnes <lb/>e&longs;&longs;e pariter c&oelig;le&longs;tes, <expan abbr="nullum&qacute;">nullumque</expan>; proinde &longs;ublunarem. </s>
4593 
4594 <s>Huic memorati A&longs;tro&shy;<lb/>nomi &longs;ic re&longs;ponderent; id quidem mathematica, &amp; infallibili ratione non <lb/>colligi, im&ograve; aliquot parum infra Lunam extiti&longs;&longs;e, non omnin&ograve; negandum <lb/>videri: at ver&ograve; in &longs;uperiori aeris plaga, in tam fluxa, ac in&longs;tabili mundi par&shy;<lb/>te, cometas vnquam efful&longs;i&longs;&longs;e, nemo &longs;ibi ob allatas rationes merit&ograve; per&longs;ua&shy;<lb/>dere po&longs;&longs;e.</s></p><p type="main">
4595 
4596 <s><arrow.to.target n="marg137"/></s></p><p type="margin">
4597 
4598 <s><margin.target id="marg137"/>137</s></p><p type="main">
4599 
4600 <s>Summ&aelig; 2. cap. 
4601 
4602 5. <emph type="italics"/>(Ad h&aelig;c autem &longs;i quemadmodum o&longs;tenditur in ijs, qu&aelig; cir&shy;<lb/>ca Astrologiam &longs;peculationibus, Solis magnitudo maior e&longs;t qu&agrave;m terr&aelig;; &amp; diftax&shy;<lb/>tia mult&ograve; maior a&longs;trorum ad terram qu&agrave;m So is; &longs;icut Solis ad terram qu&agrave;m Lu&shy;<lb/>n&aelig;; non <expan abbr="vtiq;">vtique</expan> long&egrave; alicubi &agrave; terra conus, qui &agrave; Sole, conijciet radios, <expan abbr="neq;">neque</expan> vtique <lb/>vmbraterr&aelig;, qu&aelig; vocatur nox, erit apud astra; &longs;ed nece&longs;&longs;e Solem omnia a&longs;tra cir&shy;<lb/>cun&longs;picere, &amp; nulli ip&longs;orum terram ob&longs;istere)<emph.end type="italics"/> ex dictis &longs;umma 1. cap. 
4603 
4604 3. huius, <lb/>&amp; ex figura ibi de&longs;cripta, facil&egrave; e&longs;t intelligere pr&aelig;&longs;entem locum; nam cum <lb/>Sol &longs;it mult&ograve; maior terra, vt ibi probatur, ac minus di&longs;ter &agrave; terra qu&agrave;m fix&aelig; <lb/>&longs;tell&aelig;, magis tamen qu&agrave;m Luna, vt patet ex &longs;olari eclyp&longs;i, &longs;equitur nece&longs;&longs;a&shy;<lb/>ri&ograve; vmbram terr&aelig;, qu&aelig; nox e&longs;t ip&longs;a, effici turbinatam, &amp; vald&egrave; procul &agrave; ter&shy;<lb/>ra acumen coni vmbr&aelig; a&longs;cendet, &longs;ed paul&ograve; &longs;upra Lunam conus hic vmbr&aelig; <lb/>permittet radios Solis &longs;e ip&longs;um ambientes iterum &longs;imul committi, quod il&shy;<lb/>lis verbis <emph type="italics"/>(Conijciet radios)<emph.end type="italics"/> ide&longs;t committet radios expre&longs;&longs;it Ari&longs;t. 
4605 
4606 cum igi&shy;<lb/>tur vmbra apud Lunam &longs;it &longs;atis gracilis, breui &longs;upra Lunam de&longs;inet, neque <lb/>vllo pacto ad affixa &longs;ydera protendetur, <expan abbr="neq;">neque</expan> illis renebras offundet. </s>
4607 
4608 <s>quod <lb/>etiam experientia confirmat, cum nunquam a&longs;tra illa, qu&aelig; Soli opponuntur, <lb/><expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; vertex vmb &aelig; collimat, vllam <expan abbr="pati&atilde;tur">patiantur</expan> eclyp&longs;im. </s>
4609 
4610 <s>quare &longs;ine vllo ter&shy;<lb/>r&aelig; impedimento Sol pote&longs;t af&longs;ixa omuia &longs;ydera perlu&longs;lrare. </s>
4611 
4612 <s>Exactiores ha&shy;<lb/>rum rerum demon&longs;trationes &longs;unt alterius loci.</s></p><p type="main">
4613 
4614 <s><arrow.to.target n="marg138"/></s></p><p type="margin">
4615 
4616 <s><margin.target id="marg138"/>138</s></p><p type="main">
4617 
4618 <s>Eodem cap. <emph type="italics"/>(Amplius autem e&longs;t tertia qu&aelig;dam opinio de ip&longs;o, dicunt enim<emph.end type="italics"/><pb pagenum="95"/><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut &amp; &longs;tellam comatam; im&shy;<lb/>po&longs;&longs;ibile autem e&longs;t &amp; hoc, &longs;i enim videns quieuerit &amp; &longs;peculum, &amp; quod videtur <lb/>omne in eodem puncto &longs;peculi eadem apparebit <expan abbr="vtiq;">vtique</expan> pars imaginis, &longs;i autem mo&shy;<lb/>ueatur &longs;peculum, &amp; quod videtur, in eadem quidem di&longs;tantia ad videns, &amp; quie&shy;<lb/>&longs;cens; ad inuicem autem <expan abbr="neq;">neque</expan> &aelig;qu&egrave; velociter, <expan abbr="neq;">neque</expan> in eadem &longs;emper di&longs;tantia im&shy;<lb/>po&longs;&longs;ibile eandem imaginem in eadem e&longs;&longs;e parte &longs;peculi. </s>
4619 
4620 <s>Qu&aelig; autem in lactis circu&shy;<lb/>lo feruntur a&longs;tra, &amp; Sol, ad quem fit reflexio, mouentur manentibus nobis, &amp; &longs;i&shy;<lb/>militer, &amp; &aelig;qualiter ad nos di&longs;tantia; &agrave; &longs;e ip&longs;is autem non &aelig;qualiter: aliquando <lb/>enim medijs noctibus Delphin oritur, aliquando ver&ograve; diluculo. </s>
4621 
4622 <s>partes autem lactis <lb/>e&aelig;dem manent in vnoquoque; atqui non oportebat, &longs;i erat imago, &longs;ed non in ei&longs;dem <lb/>adhuc e&longs;&longs;et h&aelig;c pa&longs;&longs;io locis)<emph.end type="italics"/> in his Ari&longs;t. 
4623 
4624 confutat opinionem dicentium Gala&shy;<lb/>xiam apparere per quandam reflexionem vi&longs;us no&longs;tri ab illa parte c&ecedil;li, ceu, <lb/>ex quodam &longs;peculo ad Solem: probat autem hoc e&longs;&longs;e impo &longs;&longs;ibile ratione <lb/>de&longs;umpta ex parte Optices, qu&aelig; dicitur Catoptrica, &longs;iue &longs;pecularia, quia <lb/>tractat de vi&longs;ione reflexa, qu&aelig; fit mediante &longs;peculo, quam quidem rationem <lb/>&longs;i vellem mathematic&egrave; explicare, longa nimis, ac pr&aelig;ter in&longs;titutum fieret <lb/>tractatio. </s>
4625 
4626 <s>Pauca tamen addam, qu&aelig; Ari&longs;totelis <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> &longs;atis per&longs;picuam <lb/>reddant. </s>
4627 
4628 <s>&longs;i igitur inquit, Galaxia nihil aliud e&longs;&longs;et qu&agrave;m reflexio no&longs;tri vi&longs;us <lb/>ex illa c&oelig;li parte, in qua ip&longs;a apparet tanquam ex &longs;peculo ad Solem, ita vt <lb/>nihil aliud ip&longs;a e&longs;&longs;et, qu&agrave;m Sol vi&longs;us per reflexionem exilla c&oelig;li parte tan&shy;<lb/>quam &longs;peculo; &longs;equeretur eam non &longs;emper in eadem c&oelig;li parte apparere, <lb/>&longs;ed modo in vna, modo in alia, ita vt &longs;patio vnius anni totum c&oelig;lum perua&shy;<lb/>garetur: quod tamen non accidit. </s>
4629 
4630 <s>quod autem illud con&longs;equatur manife&shy;<lb/>&longs;tum e&longs;&longs;e pote&longs;t ex ob&longs;eruatione eorum, qu&aelig; ex &longs;peculis videntur: tunc enim <lb/>res per &longs;pe culum vi&longs;a in eadem &longs;peculi parte apparet, quando &amp; videns, &amp; <lb/>&longs;peculum, &amp; obiectum immota manent: quod &longs;i &amp; &longs;peculum, &amp; obiectum ad <lb/>inuicem accedant, vel recedant, &longs;eruata tamen eadem ab in&longs;pectore di&longs;tan&shy;<lb/>tia, nullo modo fieri pote&longs;t, vt eadem imago, in eadem &longs;peculi parte &longs;pe&shy;<lb/>ctanti videatur, ni&longs;i obiectum &longs;peculo per eandem lineam accedat, &longs;ecun&shy;<lb/>dum quam illi incidebat. </s>
4631 
4632 <s>At ver&ograve; partibus illis lactei circuli, &longs;iue a&longs;tris, qu&aelig; <lb/>in eo fulgent, Sol perpetu&ograve; accedit, vel recedit, <expan abbr="neq;">neque</expan> per lineam incidenti&aelig; <lb/><expan abbr="e&atilde;dem">eandem</expan>, &longs;eruata tamen eadem &agrave; nobis di&longs;tatia, quod quidem inde patet, quia <lb/>Delphini con&longs;tellatio, qui in ip&longs;o fer&egrave; lacte exi&longs;tit, <expan abbr="aliqu&atilde;do">aliquando</expan> medijs noctibus, <lb/>aliquando ver&ograve; mane, aliquando etiam ve&longs;peri oritur; quod inde accidit, <lb/>quia illi Sol mod&ograve; appropinquat, mod&ograve; coniungitur, mod&ograve; ab eo recedit, <lb/>quare nece&longs;&longs;e e&longs;&longs;et, vt lacteus orbis, non &longs;emper in ij&longs;dem locis, &longs;ed perpe&shy;<lb/>tu&ograve; in alijs, <expan abbr="atq;">atque</expan> alijs cernerecur, cuius tamen contrarium videmus. </s>
4633 
4634 <s>ex qui&shy;<lb/>bus con&longs;tat fal&longs;am omnin&ograve; e&longs;&longs;e eorum &longs;ententiam, qui Galaxiam per huiu&longs;&shy;<lb/>modi re&longs;lexionem fieri opinabantur. </s>
4635 
4636 <s>Qu&aelig; dicta &longs;unt de &longs;peculo, &amp; obiecto <lb/>&longs;atius e&longs;t a&longs;&longs;umpto aliquo &longs;peculo experiri, qu&agrave;m ea pluribus ob&longs;curare: qua <lb/>etiam experientia Ari&longs;t. 
4637 
4638 ratio confirmabiaur.</s></p><p type="main">
4639 
4640 <s><arrow.to.target n="marg139"/></s></p><p type="margin">
4641 
4642 <s><margin.target id="marg139"/>139</s></p><p type="main">
4643 
4644 <s>Ibidem <emph type="italics"/>(Qu&aelig; autem in lactis cir culo feruntur astra, &amp; Sol, ad quem fit refle&shy;<lb/>xio, mouentur mancntibus nobis, &amp; &longs;imiliter, &amp; &aelig;qualiter ad nos di&longs;t antia &agrave; &longs;e <lb/>ip&longs;is autem non &aelig;qualiter)<emph.end type="italics"/> qu&aelig; hic ab Ari&longs;totele dicuntur <expan abbr="n&otilde;">non</expan> &longs;unt v&longs;quequae; <lb/>vera propter apog&aelig;um, ac porig&aelig;um Solis, qu&aelig; quidem duo ab omnibus <lb/>a&longs;tronomis a&longs;&longs;eruatur: quando igitur Sol e&longs;t in apog&aelig;o, maiori multo in&shy;<pb pagenum="96"/>teruallo di&longs;tat &agrave; nobis, qu&agrave;m quando e&longs;t in perig&aelig;o, interuallum enim illud <lb/>con&longs;tat diametris terr&aelig; duobus, &amp; quadraginta, hoc e&longs;t milliarijs 208000. <lb/>fer&egrave;, ide&longs;t octonis millibus &longs;upra ducenta millia. </s>
4645 
4646 <s>qu&aelig; differentia facit vt Sol <lb/>manife&longs;t&egrave; appareat nobis minor apog&aelig;us, qu&agrave;m perig&aelig;us. </s>
4647 
4648 <s>Sol pr&aelig;terea &longs;i&shy;<lb/>militer ip&longs;is inerrantibus &longs;tellis fit tantumdem modo remotior, modo pro&shy;<lb/>pinquior: &longs;ed fort&egrave; Ari&longs;t. 
4649 
4650 i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/>per&longs;pecta erant.</s></p><p type="main">
4651 
4652 <s><arrow.to.target n="marg140"/></s></p><p type="margin">
4653 
4654 <s><margin.target id="marg140"/>140</s></p><p type="main">
4655 
4656 <s>Ibidem <emph type="italics"/>(Aliquando enim medijs noctibus Delphin oritur)<emph.end type="italics"/> vt probet, Gala&shy;<lb/>xiam non &longs;emper &longs;eruare &agrave; Sole di&longs;tantiam eandem, accipit tanquam huius <lb/>rei &longs;ignum, manife&longs;tum, quod Delphini con&longs;tellatio aliquando medijs no&shy;<lb/>ctibus oriatur &longs;upra horizontem, aliquando ver&ograve; diluculo; non ide&ograve; tamen <lb/>putes hanc rationem &longs;upponere Delphinum e&longs;&longs;e in ip&longs;o lacteo circulo, quod <lb/>tamen verum non e&longs;t, non enim e&longs;t in Galaxia, &longs;ed tamen illi proximus, vt <lb/>noctu videre e&longs;t in c&oelig;lo, vel etiam &longs;i mauis in globo a&longs;tronomico: non ta&shy;<lb/>men ob id Ari&longs;t. 
4657 
4658 ratio minus valida redditur, cum Delphinus &longs;emper Gala&shy;<lb/>xi&aelig; eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s></p><p type="main">
4659 
4660 <s><arrow.to.target n="marg141"/></s></p><p type="margin">
4661 
4662 <s><margin.target id="marg141"/>141</s></p><p type="main">
4663 
4664 <s>Summ&aelig; 2. cap. 
4665 
4666 6. Sunt qui velint Ari&longs;t. <!-- REMOVE S-->Galaxiam nihil aliud e&longs;&longs;e, qu&agrave;m <lb/>quandam refractionem lucis &longs;tellarum illarum, qu&aelig; &longs;unt in &aelig;therea Gala&shy;<lb/>xia, qu&aelig; inquam refractio fiat circa &longs;upremam aeris regionem ex occur&longs;u <lb/>exhalationum, qu&aelig; ibi perpetu&ograve; con&longs;eruantur, &amp; vi earumdem &longs;tellarum <lb/>&longs;ur&longs;um &longs;emper attrahuntur, qu&aelig; refractio fiat ad eum modum, quo halo cir&shy;<lb/>ca Solem, &amp; Lunam. <!-- KEEP S--></s>
4667 
4668 
4669 
4670 <s>&amp; quemadmodum halo, &longs;iue area omnibus <expan abbr="vndecunq;">vndecunque</expan> <lb/>a&longs;picientibus &longs;emper videntur in eodem c&oelig;li loco, hoc e&longs;t &egrave; regione Solis, <lb/>vel Lun&aelig;; &longs;imiliter Galaxia in aere omnibus <expan abbr="vndecunq;">vndecunque</expan> intuentibus appa&shy;<lb/>reat in eadem c&oelig;li parte, ide&longs;t ex aduers&ograve; eorumdem &longs;yderum, qu&aelig; c&oelig;le&shy;<lb/>&longs;tem lacteam viam conficiunt. </s>
4671 
4672 <s>Porr&ograve; qui &longs;ic mentem Ari&longs;t. 
4673 
4674 exponunt, nul&shy;<lb/>lo modo po&longs;&longs;unt &agrave; Mathematicis redargui per rationem de&longs;umptam &agrave; di&shy;<lb/>uer&longs;itate a&longs;pectus (quam po&longs;tea explicabo) quamuis phy&longs;icis rationibus re&shy;<lb/>fellantur. </s>
4675 
4676 <s>Alij &longs;unt, quorum &longs;ententia magis videtur <expan abbr="improb&atilde;da">improbanda</expan>, c&ograve; quod <lb/>Ari&longs;t. &longs;ummum Philo&longs;ophum pueriliter in a&longs;tronomia lap&longs;um fateri cogan&shy;<lb/>tur. </s>
4677 
4678 <s>Exi&longs;timant hi Galaxiam hanc Ari&longs;totelicam nihil aliud e&longs;&longs;e, qu&agrave;m ip&shy;<lb/>&longs;as tenues exhalationes in aere &longs;ubuectas, direct&egrave;que infra &longs;tellas illas la&shy;<lb/>cteum circulum in c&oelig;lo con&longs;tituentes nobis obiectas. </s>
4679 
4680 <s>qui pr&aelig;ter innumera, <lb/>ac magna ab&longs;urda &egrave; naturali Philo&longs;ophia petita, vnum maximum ex A&longs;tro&shy;<lb/>nomia, nemp&egrave; ex diuer&longs;itate a&longs;pectus de&longs;umptum, nullo modo vitare po&longs;&shy;<lb/>&longs;unt; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; huiu&longs;modi, quia &longs;i lacteus hic circulus e&longs;&longs;et in aere, non ab om&shy;<lb/>nibus, <expan abbr="neq;">neque</expan> ex omni terr&aelig; loco per eadem &longs;ydera commeare cerneretur, &longs;ed <lb/>&egrave; diuer&longs;is, &amp; pr&aelig;cipu&egrave; ab inuicem valde di&longs;&longs;itis, circa diuer&longs;a a&longs;tra &longs;e &longs;e ocu&shy;<lb/>lis no&longs;tris obijceret: at te&longs;timonio &longs;en&longs;us con&longs;tat, Galaxiam &longs;emper in eo&shy;<lb/>dem loco; <expan abbr="eadem&qacute;">eademque</expan>; &agrave; &longs;yderibus fixis di&longs;tantia albicare, erg&ograve; nullo modo <lb/>viam hanc in aere qua&longs;i pendulam fabricare debemus. </s>
4681 
4682 <s>rationem hanc di&shy;<lb/>uer&longs;itatis a&longs;pectus a&longs;tronomic&egrave; magis explicatam reperies apud Clauium <lb/>in &longs;ph&aelig;ra. </s>
4683 
4684 <s>Porr&ograve; h&aelig;c ratio quamuis adeo certa, ac no&longs;tra tempe&longs;tate vul&shy;<lb/>gata, parum tamen &agrave; nonnullis de rebus Meteorologicis commentaria con&shy;<lb/>farcinantibus intellecta, minim&egrave; eos ab&longs;terrere potuit, quin pr&aelig;dictam opi&shy;<lb/>nionem, non &longs;olum Ari&longs;toteli imponerent, verum etiam ip&longs;i <expan abbr="t&atilde;quam">tanquam</expan> veram <pb pagenum="97"/>a&longs;truerent: huiu&longs;modi patiuntur incommoda, qui <expan abbr="ab&longs;q;">ab&longs;que</expan> Mathematicarum <lb/>auxilio Philo&longs;ophiam aggrediuntur.</s></p><p type="main">
4685 
4686 <s><arrow.to.target n="marg142"/></s></p><p type="margin">
4687 
4688 <s><margin.target id="marg142"/>142</s></p><p type="main">
4689 
4690 <s>Eodem cap. <emph type="italics"/>(Ad h&aelig;c autem locus plenus e&longs;t a&longs;tris maximis, &amp; fulgidi&longs;&longs;imis, <lb/>&amp; adhuc &longs;par&longs;is vocatis)<emph.end type="italics"/> non &longs;olum viam hanc lacteam a&longs;tris plurimis refer&shy;<lb/>ti&longs;&longs;imam e&longs;&longs;e videmus, &longs;ed pr&aelig;terea eandem &longs;tellarum admodum feracem <lb/>appellare licebit, &longs;i quidem &longs;tell&aelig; omnes ill&aelig; nou&aelig;, qu&aelig; no&longs;tra tempe&longs;tate <lb/>apparuerunt, omnes in hac via exort&aelig; &longs;unt. </s>
4691 
4692 <s>prima enim anno 1572. efful&longs;it <lb/>in Ca&longs;&longs;iopea; altera anno 1600. in Cygno. </s>
4693 
4694 <s>tertia demum anno 1604. in Sa&shy;<lb/>gittario, qu&aelig; omnes con&longs;tellationes intra lacteum circulum continentur. <lb/></s>
4695 
4696 <s>Veri&longs;&longs;imum pr&aelig;terea e&longs;&longs;e hoc idem confirmatur in&longs;trumenti illius mirabi&shy;<lb/>lis auxilio, quod &longs;uperiori anno in Belgio excogitatum, &amp; po&longs;tea in Italia <lb/>&agrave; Galil&aelig;o perfectius <expan abbr="reddit&utilde;">redditum</expan> e&longs;t, <expan abbr="quod&qacute;">quodque</expan>; ip&longs;e primum Italic&egrave; Cannocchiale, <lb/>Latin&egrave; ver&ograve;, &amp; quidem apt&egrave; &agrave; Gr&aelig;cis mutuato vocabulo alius Tele&longs;copium <lb/>appellauit: hoc inquam &longs;pecillo adhibito per&longs;picuum &longs;tatim fit non &longs;olum <lb/>in via lactea innumeras &longs;tellas contineri, verum quid ip&longs;a &longs;it, cert&ograve; certius <lb/>con&longs;tat; &longs;ed &longs;atius e&longs;t ip&longs;ius Galil&aelig;i verba ex Nuncio &longs;ydereo referre: Quod <lb/>tertio inquit, loco &agrave; nobis fuit ob&longs;eruatum e&longs;t ip&longs;iu&longs;met lactei circuli e&longs;&longs;en&shy;<lb/>tia, &longs;en materies, quam Tele&longs;copij beneficio ade&ograve; ad &longs;en&longs;um licet intueri, <lb/>vt &amp; altercationes omnes, qu&aelig; per tot &longs;&aelig;cula Philo&longs;ophos excruciarunt ab <lb/>oculata certitudine <expan abbr="dirim&atilde;tur">dirimantur</expan>, <expan abbr="nos&qacute;">nosque</expan>; &agrave; verbo&longs;is di&longs;putationibus liberemur: <lb/>e&longs;t enim Galaxia nihil aliud, qu&agrave;m innumerarum &longs;tellarum coaceruatim <lb/>con&longs;itarum congeries, in <expan abbr="qu&atilde;cunq;">quancunque</expan> enim regionem illius &longs;pecillum dirigas, <lb/>&longs;tatim &longs;tellarum ingens fre quentia &longs;e &longs;e in con&longs;pectum profert, <expan abbr="quar&utilde;">quarum</expan> com&shy;<lb/>plures &longs;atis magn&aelig;, ac vald&egrave; con&longs;picu&aelig; videntur; &longs;ed exiguarum multitudo <lb/>pror&longs;us inexplorabilis e&longs;t. </s>
4697 
4698 <s>h&aelig;c ille.</s></p><p type="main">
4699 
4700 <s><arrow.to.target n="marg143"/></s></p><p type="margin">
4701 
4702 <s><margin.target id="marg143"/>143</s></p><p type="main">
4703 
4704 <s>Eodem cap. <emph type="italics"/>(Con&longs;ideretur autem &amp; circulus, &amp; qu&aelig; &longs;unt in ip&longs;o a&longs;tra ex de&shy;<lb/>&longs;criptione)<emph.end type="italics"/> id e&longs;t, con&longs;ideretur Galaxia, &amp; a&longs;tra ip&longs;ius in&longs;piciantur diligenter <lb/>ex de&longs;criptione alicuius Globi a&longs;tronomici, in quo &longs;olent A&longs;tronomi omnes <lb/>con&longs;tellationes, ac &longs;tellas &longs;uis locis reddere, <expan abbr="atq;">atque</expan> etiam lacteum ip&longs;um cir&shy;<lb/>culum graphic&egrave; effingere. </s>
4705 
4706 <s>huiu&longs;modi globum veteres &longs;ph&ecedil;ram Arat&aelig;am di&shy;<lb/>cebant ab Arato Poeta gr&aelig;co, qui <expan abbr="c&otilde;&longs;tellationes">con&longs;tellationes</expan> omnes carmine pro&longs;e quu&shy;<lb/>tus e&longs;t, ac proinde globum hunc ordine expo&longs;uit:</s></p><p type="main">
4707 
4708 <s><arrow.to.target n="marg144"/></s></p><p type="margin">
4709 
4710 <s><margin.target id="marg144"/>144</s></p><p type="main">
4711 
4712 <s>Eodem cap. <emph type="italics"/>(Spar&longs;a autem vocata)<emph.end type="italics"/> put&ograve; &longs;par&longs;a h&aelig;c &longs;ydera illa e&longs;&longs;e, qu&aelig; <lb/>recentiores informia appellant, e&ograve; quod ad aliorum a&longs;teri&longs;morum formas <lb/>minim&egrave; reuocentur.</s></p><p type="main">
4713 
4714 <s><arrow.to.target n="marg145"/></s></p><p type="margin">
4715 
4716 <s><margin.target id="marg145"/>145</s></p><p type="main">
4717 
4718 <s>Summa 4. cap. 
4719 
4720 1. <emph type="italics"/>(In A&longs;ia igitur plurimi ex Parna&longs;&longs;o vocato monte videntur <lb/>&longs;tuentes)<emph.end type="italics"/> rect&egrave; dubitat Alexander, qua ratione mons Parna&longs;&longs;us ab Ari&longs;t. 
4721 
4722 po&shy;<lb/>natur in A&longs;ia, cum cert&ograve; certius con&longs;tet, ip&longs;um in Gr&aelig;cia Europ&aelig; regione <lb/>&longs;itum e&longs;&longs;e. </s>
4723 
4724 <s>fort&egrave; legendum e&longs;t, vt vult Vicomercatus, ex Paropame&longs;&longs;o, non <lb/>autem ex Parna&longs;&longs;o, quamuis Gr&aelig;ci codices aduer&longs;entur; Paropame&longs;&longs;um <lb/><expan abbr="namq;">namque</expan> Plinius, &amp; Strabo in A&longs;ia collocant, <expan abbr="volunt&qacute;">voluntque</expan>; ip&longs;um e&longs;&longs;e iugum quod&shy;<lb/>dam montis Cauca&longs;i: Cauca&longs;um autem &longs;upra Pontum orifi, &amp; <expan abbr="v&longs;q;">v&longs;que</expan> ad Hir&shy;<lb/>canum, &amp; vltra mare per totam A&longs;iam &longs;e proferre, tradunt veteres Geo&shy;<lb/>graphi. </s>
4725 
4726 <s>vide The&longs;aurum geographicum Abrahami Ortelij. </s>
4727 
4728 <s>Strabo lib. 
4729 
4730 15. <lb/>&longs;ic: Indiam &agrave; &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/>orientale mare, qu&aelig; extrema indigen&aelig; particulatim nominant Poropami&longs;&shy;<pb pagenum="98"/>&longs;um, Emodum, Imauum, &amp; alijs nominibus: Macedones ver&ograve; Cauca&longs;um <lb/>vocant.</s></p><p type="main">
4731 
4732 <s><arrow.to.target n="marg146"/></s></p><p type="margin">
4733 
4734 <s><margin.target id="marg146"/>146</s></p><p type="main">
4735 
4736 <s>Ibidem <emph type="italics"/>(Apparet mare, quod e&longs;t extra)<emph.end type="italics"/> intelligit illud mare <expan abbr="Ocean&utilde;">Oceanum</expan>, quod <lb/>Arabiam, ac Per&longs;iam alluit, <expan abbr="Indico&qacute;">Indicoque</expan>; Oceano committitur: <expan abbr="quod&qacute;">quodque</expan>; &agrave; pri&shy;<lb/>&longs;cis Geographis Rubrum mare appellatur, cuius alterum Rubrum mare, <lb/>quod inter Africam, &amp; Arabiam &longs;e in&longs;inuat, e&longs;t quidam &longs;inus, quem nunc <lb/>communiter omnes Rubrum mare appellant. </s>
4737 
4738 <s>de illo inquam merit&ograve; intel&shy;<lb/>ligit Alexander, non de hoc Aegyptiaco, cum ex a&longs;pectu illius &agrave; monte Pa&shy;<lb/>ropame&longs;&longs;o, &longs;equatur ip&longs;um e&longs;&longs;e editi&longs;&longs;imum, quod non &longs;equeretur ex altero <lb/>ob illius propinquitatem. </s>
4739 
4740 <s>Dixit autem mare, quod e&longs;t extra, ide&longs;t extra <lb/>terram habitatam, ad di&longs;tinctionem maris Mediterranei, quod e&longs;t intra <lb/>terram habitatam, ac propterea Mediterraneum dictum e&longs;t.</s></p><p type="main">
4741 
4742 <s><arrow.to.target n="marg147"/></s></p><p type="margin">
4743 
4744 <s><margin.target id="marg147"/>147</s></p><p type="main">
4745 
4746 <s>Ibidem <emph type="italics"/>(Ex hoc igitur fluunt &amp; alij fluuij, &amp; Bactrus, &amp; Choa&longs;pes, &amp; Ara&shy;<lb/>xes. </s>
4747 
4748 <s>ab hoc autem ab&longs;cinditur Tanais pars exi&longs;tens in Meotidem paludem fluit au&shy;<lb/>tem, &amp; Indus ex ip&longs;o, omnium fluuiorum fluxio maxima)<emph.end type="italics"/> h&aelig;c omnia &longs;unt fal&longs;a, <lb/>&amp; impo&longs;&longs;ibilia; nam cum Bactrus Bactrianam regionem irriget, qu&aelig; e&longs;t vl&shy;<lb/>tra Per&longs;iam, Choa&longs;pes ver&ograve; Per&longs;iam ip&longs;am, Indus <expan abbr="deniq;">denique</expan> in India oriatur: <lb/>qu&igrave; fieri pote&longs;t, vt in Regionibus ade&ograve; inuicem di&longs;&longs;itis orti fluuij ab eodem <lb/><expan abbr="quoq;">quoque</expan> Paropame&longs;&longs;o monte ortum ducant. </s>
4749 
4750 <s>nec minus fal&longs;um e&longs;t illud de Ta&shy;<lb/>nai, quod &longs;it qua&longs;i ip&longs;ius Araxis ramus quidam, Tanais enim ex Riph&aelig;is <lb/><expan abbr="m&otilde;tibus">montibus</expan> Scythi&aelig; delabitur in Meotidem paludem long&egrave; longius ab Araxi. <lb/><!-- KEEP S--></s>
4751 
4752 <s><expan abbr="eum&qacute;">eumque</expan>; terminum inter Europam, &amp; A&longs;iam Geographi con&longs;tituunt, vnde <lb/>Diony&longs;ius Afer &longs;ic cecinit:</s></p><p type="main">
4753 
4754 <s><emph type="italics"/>Europam, <expan abbr="atq;">atque</expan> A&longs;iam Tanais di&longs;terminat amnis.<emph.end type="italics"/></s></p><p type="main">
4755 
4756 <s>ver&ugrave;m huiu&longs;modi errata Ari&longs;t. <!-- REMOVE S--><expan abbr="atq;">atque</expan> ade&ograve; Geographis illius temporis con&shy;<lb/>donanda &longs;unt, cum nondum Geographia &longs;atis exculta e&longs;&longs;et.</s>
4757 
4758 </p><p type="head">
4759 
4760 <s><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></s></p><p type="main">
4761 
4762 <s><arrow.to.target n="marg148"/></s></p><p type="margin">
4763 
4764 <s><margin.target id="marg148"/>148</s></p><p type="main">
4765 
4766 <s>Eod. <!-- REMOVE S-->cap. <emph type="italics"/>(Cauca&longs;us autem maximus mons e&longs;t eorum qui ad ori<expan abbr="&etilde;tem">entem</expan> &aelig;&longs;tiua&shy;<lb/>lem, &amp; multitudine, &amp; altitudine &longs;igna autem altitudinis quidem, quia <lb/>videtur &amp; &agrave; vocatis Profundis, &amp; &agrave; nauigantibus in Stagnum in&longs;uper il&shy;<lb/>lu&longs;trantur &agrave; Sole ip&longs;ius &longs;ummitates, v&longs;que ad tertiam partem nocte, &amp; ab <lb/>aurora, &amp; iterum a ve&longs;pera)<emph.end type="italics"/> Cauca&longs;us mons &longs;itus e&longs;t inter mare Euxinum, &amp; <lb/>Ca&longs;pium, &longs;upra Cholchidem, &amp; Iberiam regiones, vbi polus eleuatur 47. <lb/>circiter grad. <!-- REMOVE S-->ac re&longs;pectu Gr&aelig;ci&aelig;, &amp; maris Euxini vergit ad eam mundi pla&shy;<lb/>gam, vnde illis &aelig;&longs;tiuo tempore Sol oritur. </s>
4767 
4768 
4769 
4770 
4771 
4772 <s>ait Ari&longs;t. 
4773 
4774 eum e&longs;&longs;e omnium mon&shy;<lb/>tium illius plag&aelig; alti&longs;&longs;imum, quod probat prim&ograve;, quia admodum &agrave; long&egrave; <lb/>cernitur, <expan abbr="nimir&utilde;">nimirum</expan> ab illo Euxini loco, qui Profunda vocatur, e&ograve; qu&ograve;d &agrave; Nau&shy;<lb/>tis nu&longs;quam ibi fundus reperiatur. </s>
4775 
4776 <s>&amp; pr&aelig;terca &agrave; Nauigantibus in Stagnum, <lb/>&longs;iue in Meotidem paludem, qu&aelig; quidem loca minim&ugrave;m di&longs;tant a Cauca&longs;o <lb/>560. milliaribus. </s>
4777 
4778 <s>Secund&ograve;, probat il ius altitudinem ex eo, qu&ograve;d &longs;ummi&shy;<lb/>tates ip&longs;ius <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam partem nocte, &amp; ve&longs;peri &agrave; Sole illu&longs;trentur. </s>
4779 
4780 <s>Lo&shy;<lb/>cum hunc fus&egrave; pertractat eruditi&longs;&longs;imus Iacobus Mazonius &longs;ectione 3. &amp; 4. <lb/>de Comparatione Platonis, &amp; Ari&longs;t. 
4781 
4782 quo in opere plurima habet ex Mathe&shy;<lb/>maticis de&longs;umpta, quibus naturalem Philo&longs;ophiam mirific&egrave; illu&longs;trat, <expan abbr="mani-fe&longs;tum&qacute;">mani&shy;<lb/>fe&longs;tumque</expan>; reddit, qu&agrave;m nece&longs;&longs;ari&aelig; &longs;int Mathematic&aelig; ad philo&longs;ophic&aelig; veri&shy;<pb pagenum="99"/>tatis in&longs;pectionem. </s>
4783 
4784 <s>Is igitur &longs;ect. </s>
4785 
4786 <s>3. cap. 
4787 
4788 5. de hoc Ari&longs;t. 
4789 
4790 loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>multis an&longs;am dedit reprehendendi Ari&longs;t. 
4791 
4792 tanquam puerilia effutientem. </s>
4793 
4794 <s>tex&shy;<lb/>tus <expan abbr="itaq;">itaque</expan> Ari&longs;t. 
4795 
4796 duplicem habet &longs;en&longs;um; alter &agrave; quo non abhorret <expan abbr="Alex&atilde;der">Alexander</expan>; <lb/>vt tertia illa pars ad montem referatur, qua&longs;i dicat, quod antequam Sol ima <lb/>montis illu&longs;tret, illuminat illius cacumen <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam montis partem: <lb/>&longs;ed h&aelig;c Mazonij expo&longs;itio nulla e&longs;t, cuiu&longs;libet enim montis etiam medio&shy;<lb/>cris altitudinis Sol illu&longs;trat non &longs;olum tertiam partem, &longs;ed &amp; dimidium, &amp; <lb/>duas tertias, &amp; fer&egrave; totum, antequam ad planam illius ba&longs;im de&longs;cendat. <lb/></s>
4797 
4798 <s>Ego &longs;ic exponendum cen&longs;eo, vt Ari&longs;t. 
4799 
4800 dicat, mane, ide&longs;t initio Crepu&longs;culi <lb/>matutini, &amp; ve&longs;pere, ide&longs;t, in fine Crepu&longs;culi ve&longs;pertini ip&longs;ius tertiam par&shy;<lb/>tem illuminatam con&longs;pici ab ijs, quorum horizonti tunc incipit, vel de&longs;init <lb/>Crepu&longs;culum; ex quibus illi nece&longs;&longs;ari&ograve; re&longs;pectu Cauca&longs;i &longs;unt occidentales, <lb/>qu&igrave; man&egrave; hoc vident, vti &longs;unt ij, qui in Euxino, &longs;eu Ponto, &amp; Meotide naui&shy;<lb/>gant, vel loca proxima inhabitant: illi ver&ograve;, qui in fine Crepu&longs;culi ve&longs;per&shy;<lb/>tini hoc cernunt, nece&longs;&longs;ari&ograve; re&longs;pectu Cauca&longs;i erunt orientales. </s>
4801 
4802 <s>Alter huius <lb/>loci &longs;en&longs;us e&longs;t, ait Mazonius, vt non de tertia montis parte, &longs;ed de tertia <lb/>noctis portione loquatur, ita vt man&egrave;. </s>
4803 
4804 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->initio terti&aelig;, &amp; vltim&aelig; noctis <lb/>parte, cacumen Cauca&longs;i illuminetur. </s>
4805 
4806 
4807 
4808 
4809 
4810 <s>h&aelig;c ille. </s>
4811 
4812 <s>vbi animaduertendum expo&shy;<lb/>&longs;itionem <expan abbr="h&atilde;c">hanc</expan> par&ugrave;m differre &agrave; no&longs;tra mod&ograve; allata, c&ugrave;m <expan abbr="vtraq;">vtraque</expan> in idem tem&shy;<lb/>pus recidat; nam &longs;i dixerimus initio Crepu&longs;culi matutini illuminari ter&shy;<lb/>tiam partem Cauca&longs;i, tempus hoc coincidit cum initio terti&aelig; partis noctis, <lb/>quantitas enim Crepu&longs;culi in poli eleuatione 47. grad. <!-- REMOVE S-->qualem habet Cau&shy;<lb/>ca&longs;us, per totam &aelig;&longs;tatem tres horas plus minus continet, vt patet ex tabu&shy;<lb/>la quantitatis Crepu&longs;culi, qu&aelig; e&longs;t apud Nonium, &amp; apud Clauium in &longs;ph&aelig;&shy;<lb/>ra vltim&aelig; editionis; qu&aelig; quantitas reperiri geometrico calculo pote&longs;t, vt <lb/>docent Nonius, Clauius, &amp; Maginus lib. 
4813 
4814 10. primi mob. </s>
4815 
4816 
4817 
4818 <s>quod quidem trium <lb/>circiter horarum tempus e&longs;t tertia fer&egrave; noctis pars in ijs regionibus, quibus <lb/>polus eleuatur 47. grad. <!-- REMOVE S-->&longs;iue ergo dicamus id contingere initio Crepu&longs;culi, <lb/>&longs;iue initio terti&aelig; partis noctis, erit idem tempus, trium &longs;cilicet horarum. <lb/></s>
4819 
4820 
4821 
4822 <s>&longs;i ergo, inquit Mazonius, &longs;equamur priorem declarationem, nece&longs;&longs;arium <lb/>e&longs;t dicere, quod ea tertia pars montis, qu&aelig; initio auror&aelig; Solis lumine per&shy;<lb/>funditur, &longs;it ea montis altitudo, qua ip&longs;e exuperat illam aeris regionem, <lb/>vnde Crepu&longs;culum incipit apparere. </s>
4823 
4824 <s>quo po&longs;ito apt&egrave;, ac &longs;agaciter altitudi&shy;<lb/>nem Cauca&longs;i inue&longs;tigat hoc pacto. </s>
4825 
4826 <s>pr&aelig;mittit autem &longs;eptem propo&longs;itiones <lb/>apud Mathematicos manife&longs;tas, quas ego mi&longs;&longs;as facio cum non mihi nece&longs;&shy;<lb/>&longs;ari&aelig; videantur. </s>
4827 
4828 <s>po&longs;tea &longs;ic di&longs;currit; His ergo ita &longs;e habentibus, dico nos in&shy;<lb/>uenire po&longs;&longs;e viam, qua &longs;altem rudi Minerua, montis altitudinem comper&shy;<lb/>tam habeamus. </s>
4829 
4830 <s>&longs;i enim in principio Crepu&longs;culi v. <!-- REMOVE S-->g. <!-- REMOVE S-->matutini (ita enim, vt <lb/>&longs;upra annotaui intelligendus e&longs;t Ari&longs;t.) illuminatur tertia pars, nece&longs;&longs;arium <lb/>vidctur tertiam illam partem &longs;upra cam regionem collocari, ex qua Cre&shy;<lb/>pu&longs;culum in planitie apparere incipit, &longs;ed illa regio ex Alhazino, &amp; Vitell. <lb/><!-- REMOVE S-->de Crepu&longs;culis milliaribus 52. &agrave; terra recedit, ergo du&aelig; terti&aelig; montis par&shy;<lb/>tes, qu&aelig; Solem initio auror&aelig; non vident, &longs;unt 52. milliaria ad perpendicu&shy;<lb/>lum, &amp; tertia alia pars illuminata e&longs;t ad perpendiculum 26. milliaria: ita <lb/>vt totius montis altitudo perpendicularis &longs;it 78. mill. <!-- REMOVE S-->&longs;ed pap&egrave; in quos acu&shy;<pb pagenum="100"/>leos imprudens me conieci? </s>
4831 
4832 
4833 
4834 
4835 
4836 
4837 
4838 
4839 
4840 <s>rident enim hoc Ari&longs;t. 
4841 
4842 dictum Mathematici, <lb/>putant enim eum pueriliter lap&longs;um e&longs;&longs;e. </s>
4843 
4844 <s>C&aelig;terum ego pro pr&aelig;ceptoris tu&shy;<lb/>rela, dico eum &longs;equutum e&longs;&longs;e famam. </s>
4845 
4846 <s>h&aelig;c Mazonius, quorum nonnulla in&shy;<lb/>digent con&longs;ideratione cuiu&longs;modi, &longs;unt illa, quando dicit, nece&longs;&longs;arium vi&shy;<lb/>detur, quod ea pars &longs;upra eam regionem attollatur, vnde Crepu&longs;culum in <lb/>planitie apparere ineipit. </s>
4847 
4848 <s>videtur enim his verbis velle dicere, quod quan&shy;<lb/>do habitantibus planitiem, qu&aelig; e&longs;t ad pedem montis Cauca&longs;i, vel horizon&shy;<lb/>tem eiu&longs;dem, incipit Crepu&longs;culum, ij&longs;dem etiam tunc tertia montis pars <lb/>appareat illuminata; in quo &longs;en&longs;u errat po&longs;tea in colligenda montis altitu&shy;<lb/>dine, quamuis enim verum e&longs;&longs;et partem illuminatam eminere totam &longs;upra <lb/>52. milliaria, non tamen &longs;equitur ip&longs;am &longs;olam eminere, &longs;ed alia etiam pars <lb/>eminere pote&longs;t, quod &longs;ic geometric&egrave; demon&longs;trabo. </s>
4849 
4850 <s>de&longs;cribatur enim figura <lb/><figure place="text" xlink:href="figures-la/009.01.100.1.tif"/><pb pagenum="101"/>illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/>&amp; Clauius, in qua terr&aelig; globus e&longs;t F L G E, regi&ograve; vaporum, &amp; exhalatio&shy;<lb/>num M X N T. horizon a&longs;tronomicus O P. phy&longs;icus Q R, tangens terram <lb/>in puncto F, vbi etiam ponendus e&longs;t huius horizontis habitator, vn&agrave; cum. <lb/></s>
4851 
4852 <s>Cauca&longs;o F V. <!-- KEEP S--></s>
4853 
4854 <s>Sol A B C, qui initio Crepu&longs;culi infra horizontem O P, depri&shy;<lb/>mitur gr. <!-- REMOVE S-->18. vti ab A&longs;tronomis compertum e&longs;t, hoc e&longs;t, arcum D P, e&longs;&longs;e <lb/>grad. <!-- REMOVE S-->18. radius autem C I K, tangens terram, incipit illuminare halitus, <lb/>qui &longs;unt ad K, in extremo horizonte &longs;en&longs;ibili F K. quique po&longs;&longs;unt videri ab <lb/>oculo in F, ide&longs;t ab huius horizontis habitatore. </s>
4855 
4856 
4857 
4858 
4859 
4860 <s>C&aelig;ter&ugrave;m pr&aelig;dicti autho&shy;<lb/>res po&longs;t longam ratiocinationem ex calculo planorum <expan abbr="triangulor&utilde;">triangulorum</expan> tandem <lb/>o&longs;tendunt in triangulo H F K, latus H K, continere milliaria 3631. ex quo <lb/>detracta H L, &longs;emidiametro terr&aelig;, qu&aelig; e&longs;t milliar, 3579. reliqua L K, &longs;um&shy;<lb/>ma halitunm eleuatio relinquatur 52. milliar. </s>
4861 
4862 <s>quibus ab ip&longs;is demon&longs;tra&shy;<lb/>tis, &longs;i H F, terr&aelig; &longs;emidiameter, qu&aelig; continet milliar. </s>
4863 
4864 <s>3579. ponatur &longs;inus <lb/>totus 100000. &amp; latus F K, ponatur tangens anguli ad H, quem pr&ecedil;dicti au&shy;<lb/>thores probant e&longs;&longs;e grad. <!-- REMOVE S-->8. 54. erit F K, tangens partium 15659. fiat igi&shy;<lb/>tur per 2. pro. </s>
4865 
4866 
4867 
4868 <s>trjang. </s>
4869 
4870 <s>rectil. </s>
4871 
4872 <s>Clauij;<lb/><arrow.to.target n="table4"/></s></p><table><table.target id="table4"/><row><cell>vt H F, &longs;inus totus,</cell><cell>ad milliar.</cell><cell>ita tangens F K,</cell><cell>ad milliar.</cell></row><row><cell>100000.</cell><cell>3579.</cell><cell>15659.</cell><cell>560.</cell></row></table><p type="main">
4873 
4874 <s>&amp; inueniemus per auream regulam latus F K, continere milliar. </s>
4875 
4876 <s>560. quan&shy;<lb/>ta &longs;cilicet e&longs;t di&longs;tantia ab oculo no&longs;tro ad exhalationes Crepu&longs;culi initium <lb/>efficientes. </s>
4877 
4878 <s>Con&longs;ideremus iam triangulum F K V, vt ip&longs;ius latus F V, qu&aelig; <lb/>e&longs;t Cauca&longs;i altitudo, in milliaribus innote&longs;cat. </s>
4879 
4880 <s>iam ip&longs;ius latus F K, inno&shy;<lb/>tuit, angulus ver&ograve; ad F, e&longs;t rectus; at angulus ad K, &longs;ic manife&longs;tabitur; in <lb/>quadrilatero F K I H, quatuor anguli &longs;unt &aelig;quales 4. rectis ex 32. primi. </s>
4881 
4882 <s>duo <lb/>autem F, &amp; I, &longs;unt recti ex 18. 3. ergo reliqui duo H, &amp; K, &aelig;quales erunt duo&shy;<lb/>bus rectis, quorum alter H, e&longs;t gr. <!-- REMOVE S-->17. 48. vt pr&aelig;diti Mathematici <expan abbr="o&longs;t&etilde;dunt">o&longs;tendunt</expan>, <lb/>reliquus igitur ad K, erit gr. <!-- REMOVE S-->162. 12. vt compleat duos rectos. </s>
4883 
4884 
4885 
4886 
4887 
4888 <s>qui &longs;i detra&shy;<lb/>hatur &agrave; duobus rectis, qui &longs;unt deinceps ad lineam F K, reliquus angulus <lb/>F K V, erit gr. <!-- REMOVE S-->17. 48. &longs;i ergo latus F K, notum ponatur &longs;inus totus 100000. <lb/>latus ver&ograve; F V, tangens anguli noti, erit ip&longs;a 32100. fiat igitur,<lb/><arrow.to.target n="table5"/></s>
4889 
4890 </p><table><table.target id="table5"/><row><cell>vt F K, &longs;inus totus,</cell><cell>ad milliar.</cell><cell>ita F V, tangens</cell><cell>ad milliar.</cell></row><row><cell>100000.</cell><cell>560.</cell><cell>32100.</cell><cell>180.</cell></row></table><p type="main">
4891 
4892 <s><expan abbr="inueniemus&qacute;">inueniemusque</expan>; latus F V, continere milliar. </s>
4893 
4894 <s>180. cuius pars F X, qu&aelig; e&longs;t in&shy;<lb/>fra habituum altitudinem continet milliar. </s>
4895 
4896 <s>52. quibus detractis ex 180. re&shy;<lb/>manent 128. pro tota X V, qu&aelig; tota e&longs;t &longs;upra vapores, nondum tamen illu&shy;<lb/>minata. </s>
4897 
4898 <s>vnde patet Mazonium erra&longs;&longs;e in colligenda hoc modo Cauca&longs;i al&shy;<lb/>titudine, ex prima Crepu&longs;culi illuminatione in horizonte Cauca&longs;i facta, <lb/>cum ex pr&aelig;mi&longs;&longs;o calculo con&longs;tet partem montis F V, totam tunc temporis <lb/>e&longs;&longs;e tenebro&longs;am, quamuis &longs;uperet mult&ograve; regionem vaporum, contr&agrave; qu&agrave;m <lb/>ip&longs;e putabat, &longs;uperat enim eam milliar. </s>
4899 
4900 <s>128. quare du&aelig; terti&aelig; montis erunt <lb/>non 52. mill. <!-- REMOVE S-->vt ip&longs;e ait, &longs;ed mill. <!-- REMOVE S-->180. &amp; proinde tota altitudo erit mill. <!-- REMOVE S-->270. <lb/>quod &longs;an&egrave; ridiculum e&longs;t, cum nullius montis altitudo &longs;e&longs;quimilliare tran&shy;<lb/>&longs;cendat. </s>
4901 
4902 
4903 
4904 
4905 
4906 
4907 
4908 <s>Quod &longs;i &longs;equamur alteram expo&longs;itionem, vt nimirum Ari&longs;tor. <!-- REMOVE S-->lo&shy;<lb/>quatur non de tertia montis parte, &longs;ed noctis, ita vt dicat, circa initium <lb/>terti&aelig; partis noctis apicem montis illu&longs;trari, altitudo eius erit tantum&shy;<pb pagenum="102"/>modo 180. quot continet latus F V. vt vidimus, qu&aelig; quamuis illa minor &longs;it, <lb/>adhuc tamen ab&longs;urda e&longs;t.</s>
4909 
4910 </p><p type="main">
4911 
4912 <s>Si ver&ograve; dixerimus Ari&longs;t. 
4913 
4914 intelligere h&aelig;c omnia, non re&longs;pectu horizontis <lb/>Cauca&longs;i, &longs;ed alterius, cuius habitator in principio &longs;ui Crepu&longs;culi tertiam <lb/>Cauca&longs;i partem iam illu&longs;tratam videat, vti accideret &longs;i Cauca&longs;us &longs;tatuere&shy;<lb/>tur in L K, vbi incipit Crepu&longs;culum habitanti in F. tunc e&longs;&longs;et altitudo tanta, <lb/>quanta colligit Mazonius, &longs;i tamen Ari&longs;t. 
4915 
4916 intelligatur de tertia montis par&shy;<lb/>te; e&longs;t enim L K, altitudo habituum 52. mill. <!-- REMOVE S-->&amp; du&aelig; terti&aelig; montis, quare <lb/>totus mons erit 78. &longs;i autem intelligatur circa tertiam noctis partem, mon&shy;<lb/>tis apicem illuminatum videri ab habitatore F, &longs;ic altitudo eins erit tan&shy;<lb/>tummodo 52. mill. <!-- REMOVE S-->qu&aelig; tamen adhuc omnem veritatem nimium &longs;uperat. <lb/></s>
4917 
4918 
4919 
4920 
4921 
4922 <s>Cum ergo hinc inde &longs;equantur ab&longs;urda, putat Mazonium excu&longs;andum e&longs;&longs;e <lb/>Ari&longs;tot. dicendo eum &longs;equutum e&longs;&longs;e famam, <expan abbr="loquutum&qacute;">loquutumque</expan>; e&longs;&longs;e populariter. <lb/></s>
4923 
4924 
4925 
4926 <s>Verumenimuer&ograve; &longs;apientiores iudicent num rect&egrave; philo&longs;ophus, cuius e&longs;t re&shy;<lb/>condita, <expan abbr="atq;">atque</expan> abdita docere, excu&longs;etur, &longs;i dicatur, eum, popularem famam <lb/>&longs;equutum e&longs;&longs;e.</s></p><p type="main">
4927 
4928 <s>Tandem monendus mihi Lector e&longs;t, in demon&longs;tratione Magini, qu&aelig; e&longs;t <lb/>apud Mazonium &longs;ect. </s>
4929 
4930 <s>4. citati operis; a&longs;&longs;umi radium Solis tangentem terr&aelig; <lb/>globum, qui cum horizonte faciat angulum gr. <!-- REMOVE S-->18. quod fal&longs;um e&longs;t, &longs;olus <lb/>enim radius centralis, qui &agrave; centro Solis ad centrum terr&aelig; ducitur talem <lb/>facit angulum, <expan abbr="atq;">atque</expan> hac de cau&longs;a ip&longs;e colligit altitudinem no&longs;tra maiorem; <lb/>no&longs;tra e&longs;t 270. mill. <!-- REMOVE S-->&longs;ua ver&ograve; 276. vbi etiam, &longs;icut &amp; nos a&longs;&longs;umit horizon&shy;<lb/>tem Cauca&longs;i.</s>
4931 
4932 
4933 
4934 </p><p type="main">
4935 
4936 <s>Aduertendum tandem Mazonium admodum aduer&longs;antia loquutum e&longs;&longs;e, <lb/>&longs;ect. </s>
4937 
4938 <s>enim 3. demon&longs;tratin&egrave; concludit altitudinem 76. mill. <!-- REMOVE S-->&longs;ect. </s>
4939 
4940 
4941 
4942 <s>ver&ograve; 4. &longs;i&shy;<lb/>mul <expan abbr="c&utilde;">cum</expan> Magino demon&longs;tratiu&egrave; pariter colligit altitudinem eiu&longs;dem 276. m. <lb/></s>
4943 
4944 <s>qu&aelig; nimis ab innicem di&longs;crepant, cum tamen <expan abbr="vtrobiq;">vtrobique</expan> demon&longs;tret, &amp; ve&shy;<lb/>ritas &longs;it vna. </s>
4945 
4946 <s>At ver&ograve; cau&longs;a huius di&longs;crepanti&aelig; e&longs;t, qu&ograve;d &longs;ect. </s>
4947 
4948 <s>3. accipit Cre&shy;<lb/>pu&longs;culum non horizontis Cauca&longs;i, &longs;ed illius, in cuius extremitate orientali, <lb/>vbi incipit Crepu&longs;culum, Cauca&longs;us &longs;itus &longs;it, <expan abbr="di&longs;tet&qacute;">di&longs;tetque</expan>; ab habitatore 560. m. <lb/></s>
4949 
4950 <s>vt &longs;upra o&longs;tendimus. </s>
4951 
4952 <s>&longs;ect. </s>
4953 
4954 <s>ver&ograve; 4. accipit horizontem ip&longs;ius Cauca&longs;i, vt ex <lb/>figura illic de&longs;cripta videre e&longs;t. </s>
4955 
4956 <s>ex hac igitur horizontum varia &longs;uppo&longs;itio&shy;<lb/>ne, varia etiam altitudo colligitur, quamuis <expan abbr="vtrobiq;">vtrobique</expan> ex <expan abbr="vtraq;">vtraque</expan> &longs;uppo&longs;itio&shy;<lb/>ne <expan abbr="vtramq;">vtramque</expan> altitudinem rect&egrave; concludat. </s>
4957 
4958 <s><expan abbr="Atq;">Atque</expan> h&aelig;c de Cauca&longs;o &longs;ufficiant.</s></p><p type="main">
4959 
4960 <s><arrow.to.target n="marg149"/></s></p><p type="margin">
4961 
4962 <s><margin.target id="marg149"/>149</s></p><p type="main">
4963 
4964 <s>Eodem cap. <emph type="italics"/>(Ex Pyreneo autem, hic autem est mons ad occidentem &aelig;quino&shy;<lb/>ctiaiem in Gallia, flaunt l&longs;ter, &amp; Tarte&longs;&longs;us, iste quidem extra columnas, I&longs;ter au&shy;<lb/>tem per totam Europam in Pontum Euxmum)<emph.end type="italics"/> Ari&longs;t. 
4965 
4966 fort&egrave; &longs;equutus e&longs;t Herodo&shy;<lb/>tum, qui fals&ograve; tradit I&longs;trum, &longs;ine Dannbium ex Pyreneis de&longs;luere, nam Iu&shy;<lb/>ce clarius con&longs;tat ip&longs;um ex ijs Alpibus, qu&aelig; Heluetiorum montes dicuntur, <lb/>prop&egrave; Ba&longs;ileam ex Adula monte ortum ducere. </s>
4967 
4968 <s><expan abbr="neq;">neque</expan> verum e&longs;t Tarte&longs;&longs;um, <lb/>quem &amp; B&oelig;tim alij nominant ex Pyreneis de&longs;cendere. </s>
4969 
4970 <s>Tarte&longs;&longs;um hunc Ma&shy;<lb/>ginus putat e&longs;&longs;e Tagum, cui fauet vocabulorum quali&longs;cunque &longs;imilitudo. <lb/></s>
4971 
4972 <s>extra tamen columnas Herculis qui&longs;quis &longs;it in Oceanum occidentale illa&shy;<lb/>bitur. </s>
4973 
4974 <s>Igno&longs;cenda &longs;unt i&longs;ta Ari&longs;t. 
4975 
4976 tunc enim Geographia <expan abbr="nond&utilde;">nondum</expan> adoleuerat.</s></p><p type="main">
4977 
4978 <s><arrow.to.target n="marg150"/></s></p><p type="margin">
4979 
4980 <s><margin.target id="marg150"/>150</s></p><p type="main">
4981 
4982 <s>Ad finem eiu&longs;dem cap. <emph type="italics"/>(Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/>quidam fluuius, &amp; iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> &amp; hoc <pb pagenum="103"/>Ari&longs;t. 
4983 
4984 vt &longs;uperiora, ob Geographi&aelig; illius &longs;eculi imperfectionem, nu&longs;quam <lb/>enim in tota Liguria quidpiam tale reperitur.</s></p><p type="head">
4985 
4986 <s><emph type="italics"/>De Terr&aelig; rotunditate.<emph.end type="italics"/></s></p><p type="main">
4987 
4988 <s><arrow.to.target n="marg151"/></s></p><p type="margin">
4989 
4990 <s><margin.target id="marg151"/>151</s></p><p type="main">
4991 
4992 <s>Svmma 4. cap. 
4993 
4994 2. quod e&longs;t de permutatione, &amp; vici&longs;&longs;itudine aquarum, <lb/>&amp; continentis. </s>
4995 
4996 <s>Pergratum Lectori fore exi&longs;timaui, nec alienum ab <lb/>in&longs;tituto, &longs;i occa&longs;ione huius permutationis maris, ac terr&aelig;, rem ex&shy;<lb/>po&longs;uero &longs;citu digniffimam, quam pridem ob&longs;eruare c&oelig;pi, ac in dies <lb/>ob&longs;eruo, pr&aelig;&longs;ertim cum nullus pr&aelig;teritorum &longs;criptorum, quod &longs;ciam, eam <lb/>literis mandauerit: Terr&aelig; &longs;cilicet totius molem paulatim reduci ad perfe&shy;<lb/>ctam &longs;ph&aelig;ricitatem, ita vt aliquando nece&longs;&longs;e &longs;it futurum ip&longs;am &agrave; mari inun&shy;<lb/>dari, <expan abbr="atq;">atque</expan> omnin&ograve; inhabitabilem reddi. </s>
4997 
4998 <s>Prrmum igitur illud ex &longs;acris lite&shy;<lb/>ris &longs;tatuendum, orbem terr&aelig; in &longs;uo primordio fui&longs;&longs;e ab opifice rerum om&shy;<lb/>nium, figura &longs;ph&aelig;rica donatum, hoc e&longs;t <expan abbr="ab&longs;q;">ab&longs;que</expan> montium eminentijs, atque <lb/>vallium depre&longs;&longs;ionibus. </s>
4999 
5000 <s>quod patet ex eo, quia <expan abbr="t&utilde;c">tunc</expan> tota Mari obtegebatur, <lb/>ita vt minim&egrave; apta e&longs;&longs;et animantibus ad inhabitandum. </s>
5001 
5002 <s>redditam ver&ograve; ha&shy;<lb/>bitabilem, cum ip&longs;ius conditor <expan abbr="qu&atilde;dam">quandam</expan> ip&longs;ius partem humiliorem, &amp; quan&shy;<lb/>dam eminentiorem effeci&longs;&longs;et; transferendo nimirum maximam terr&aelig; por&shy;<lb/>tionem ex vno loco in alium, vnde illic maris concauitas, i&longs;tic ver&ograve; mon&shy;<lb/>tium &longs;ublimitas emer&longs;it. </s>
5003 
5004 <s>quo facto aqu&aelig; omnes in loca illa decliuiora &longs;ua <lb/>&longs;pont&egrave; rece&longs;&longs;erunt, qu&aelig; aquarum congregatio Mare appellatum e&longs;t. </s>
5005 
5006 <s>Hine <lb/>nonnulli auctores graui&longs;&longs;imi a&longs;&longs;erere non dubitarunt, montes <expan abbr="c&otilde;flatos">conflatos</expan> fui&longs;&shy;<lb/>&longs;e ex terra illa, qu&aelig; locum illum occupabat, quem po&longs;tea maria inua&longs;erunt. <lb/></s>
5007 
5008 <s>qu&aelig; cum ita &longs;int. </s>
5009 
5010 <s>&longs;equitur terram <expan abbr="n&utilde;c">nunc</expan> e&longs;&longs;e extra naturalem &longs;uam figuram, &amp; <lb/>propterea in quodam &longs;tatu violento, <expan abbr="viol&etilde;tum">violentum</expan> autem <expan abbr="null&utilde;">nullum</expan> <expan abbr="perpetu&utilde;">perpetuum</expan>. </s>
5011 
5012 <s>pr&aelig;&shy;<lb/>terea cum terra &longs;it grauior qu&agrave;m aqua, nulla ratione deberent terr&aelig; partes <lb/>&longs;uperiores a qu&aelig; &longs;uperficiem &longs;uperare, cuius tamen <expan abbr="contrari&utilde;">contrarium</expan> accidit, nam <lb/>&longs;uperficies ip&longs;a terr&aelig;, &amp; mult&ograve; magis <expan abbr="m&otilde;tana">montana</expan> loca &longs;uperficiem maris cuiu&longs;&shy;<lb/>uis non parum &longs;uperant; qu&aelig; altera violentia terr&aelig;, &amp; aqu&aelig; ine&longs;t, &amp; ide&ograve; <lb/>minim&egrave; mirum e&longs;t, im&ograve; <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> natur&aelig; vald&egrave; conueniens terram redire ad <lb/>pri&longs;tinam, ac primigeniam figuram, ex qua con&longs;ectarium erit aquam <expan abbr="quoq;">quoque</expan> <lb/>&longs;uam pariter illam &longs;ibi prim&aelig;uam recuperaturam e&longs;&longs;e figuram. </s>
5013 
5014 <s>cau&longs;am au&shy;<lb/>tem re&longs;tauratricem huius terren&aelig; <expan abbr="rot&utilde;ditatis">rotunditatis</expan> e&longs;&longs;e aquas tum pluuiales, tum <lb/>fluuiales iamdi&ugrave; ob&longs;eruauimus, vt ex &longs;equentibus ob&longs;eruationibus patebit.</s></p><p type="main">
5015 
5016 <s>Prim&ograve;, videmus flumina quotidie montium radices corrodere, ac qua&longs;i <lb/>&longs;uffodere, ita vt pa&longs;&longs;im ex hoc, vel illo monte magnas faciant ruinas, ac pr&ecedil;&shy;<lb/>cipitia, <expan abbr="atq;">atque</expan> hiac inde pr&aelig;rupti appareant montes, vt merit&ograve; legamus apud <lb/>Iob cap. 
5017 
5018 14. allunione paulatim terra con&longs;umitur. </s>
5019 
5020 <s>humum porr&ograve; illam ex <lb/>montibus delap&longs;am &longs;emper ad loca humiliora fluuij &longs;ecum detrahunt. </s>
5021 
5022 <s>Ex <lb/>continua etiam hac inter montes corro&longs;ione facta manife&longs;t&egrave; apparet, flumi&shy;<lb/>num alueos in montanis mod&ograve; e&longs;&longs;e humiliores qu&agrave;m olim, quamuis contra&shy;<lb/>rium accidat alueis &longs;luuiorum per plana decurrentium, qui mod&ograve; altiores <lb/>&longs;unt <expan abbr="qu&atilde;">quam</expan> exordio mundi, vt paul&ograve; po&longs;t <expan abbr="o&longs;t&etilde;dam">o&longs;tendam</expan>. </s>
5023 
5024 <s>Illud autem liquid&ograve; apparet <lb/>ex &longs;ignis, &longs;eu &longs;ymbolis, &longs;eu ex &longs;imilitudine terr&aelig;, aut lapidis, qu&aelig; in alti&longs;&longs;imis <lb/>fluminum ripis hinc inde pa&longs;&longs;im <expan abbr="vid&etilde;tur">videntur</expan>, qu&aelig; indicio &longs;unt montes illos iam <pb pagenum="104"/>olim fui&longs;&longs;e continuos, <expan abbr="atq;">atque</expan> vnam, <expan abbr="eandem&qacute;">eandemque</expan>; terram <expan abbr="contin&etilde;tem">continentem</expan>, antequam<lb/>flumen eos ab inuicem &longs;epararet; <expan abbr="flumen&qacute;">flumenque</expan>; ip&longs;um olim altius, vbi &longs;unt &longs;igna <lb/>illa ambula&longs;&longs;e; quemadmodum in Pyramo Cilici&aelig; amne ob&longs;eruauit Strabo, <lb/>dum libro 12. de illius ripis h&aelig;c tradit, mira pr&aelig;terea e&longs;t montis c&aelig;&longs;ura, <lb/>per quam alueus ducitur; nam quemadmodum in petris per medium &longs;ci&longs;&longs;is <lb/>contingit, alterius partis depre&longs;&longs;ioribus ita conuenire alterius partis emi&shy;<lb/>nentias, vt coniungi po&longs;&longs;int: &longs;ic videre e&longs;t imminentes flumini petras vtrin&shy;<lb/>que fer&egrave; <expan abbr="v&longs;q;">v&longs;que</expan> ad montis &longs;umma pertendentes duorum, triumu&egrave; iugerum <lb/>&longs;patio concauitates qua&longs;dam eminentijs oppo&longs;itas habere. </s>
5025 
5026 <s>h&aelig;c Strabo de <lb/>vno, quod nos in pluribus ob&longs;eruauimus. </s>
5027 
5028 <s>Pr&ecedil;terea videmus quotidie pluuias <lb/>aquas, idem quantum po&longs;&longs;unt efficere, &longs;uperficies montium, eorum maxi&shy;<lb/>m&egrave;, qui coluntur, perpetu&ograve; ab&longs;umentes, <expan abbr="atq;">atque</expan> ad loca conuallium deducen&shy;<lb/>tes. </s>
5029 
5030 <s>hinc videre e&longs;t, montes c&aelig;teris duriores, vt &longs;unt lapido&longs;i, c&aelig;teris altio&shy;<lb/>res reman&longs;i&longs;&longs;e; quippe qui magis &amp; pluuijs, &amp; fluuialibus aquis &longs;ua duritie <lb/>ob&longs;titerunt. </s>
5031 
5032 <s>idem montani incol&aelig; omnes confirmant, qui omnes aiunt &longs;ibi <lb/>hanc montium demolitionem iampridem innotui&longs;&longs;e, ex eo quod nonnulli <lb/>montes olim &longs;ibi impedimento erant, ne arcem, turremu&egrave; in vlteriore mon&shy;<lb/>te &longs;itam con&longs;picerent, quam deinde plures po&longs;t annos intermedio monte <lb/>depre&longs;&longs;o, commod&egrave; videbant. </s>
5033 
5034 <s>Ad h&aelig;c; antiqua in montium verticibus con&shy;<lb/>&longs;tituta &aelig;deficia, propterea intercidunt, quia terra hinc, &amp; inde ab aquis <lb/>paulatim confumpta, <expan abbr="deor&longs;um&qacute;">deor&longs;umque</expan>; delap&longs;a, fundamenta ip&longs;orum nuda prim&ograve; <lb/>relinquit; deind&eacute; terra etiam ip&longs;a, qua fundamenta innitebatur &longs;en&longs;im de&shy;<lb/>lap&longs;a, ip&longs;a <expan abbr="quoq;">quoque</expan> fundamenta vn&agrave; cum toto &aelig;deficio nece&longs;&longs;e e&longs;t collabi, hu&shy;<lb/>ius &longs;igna infinita propemodum videri po&longs;&longs;unt; vnum tamen, quod toti orbi <lb/>confpicuum e&longs;t, non ommittam; Capitolium videlicet Romanum, cuius <lb/>modo fundamenta tota extant, qu&aelig; olim alt&egrave; &longs;ub terram de&longs;cendebant. </s>
5035 
5036 <s>vi&shy;<lb/>de pulcherrimam hac de re tractationem apud Georgium Agricolam lib. 
5037 
5038 3. <lb/>cap. 
5039 
5040 1. qui amplius addit illud, quod &amp; mihi maxim&egrave; probatur; flumina ni&shy;<lb/>mirum producere montes, <expan abbr="colles&qacute;">collesque</expan>; hoc modo; vult enim initio mundi non <lb/>extiti&longs;&longs;e tot particulares montes ab inuicem di&longs;cretos, &longs;ed fui&longs;&longs;e perpetua <lb/>qu&aelig;dam terr&aelig; iuga eminentia quidem, &longs;ed non tot vallibus di&longs;&longs;ecta: v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->mons no&longs;ter Apenninus erat iugum, &longs;iue dor&longs;um quoddam terr&aelig; eminens <lb/>quidem, &longs;ed nullis vallibus in tot particulares colles, aut montes di&longs;&longs;ectum; <lb/>&longs;ed po&longs;tquam flumina &agrave; &longs;ummitate ip&longs;ius deor&longs;um fluere c&oelig;perunt; paula&shy;<lb/>tim corrodentes humum in dies magis, ac magis effecerunt valles, <expan abbr="atq;">atque</expan> hac <lb/>ratione in colles, <expan abbr="montes&qacute;">montesque</expan>; plurimes totus Apenninus diui&longs;us e&longs;t. </s>
5041 
5042 
5043 
5044 
5045 
5046 <s>h&aelig;c de <lb/>montibus &longs;ufficiant, nunc ad plana de&longs;cendamus.</s></p><p type="main">
5047 
5048 <s>Contrarium igitur omnin&ograve; accidere videmus in planis, quoniam e&aelig;dem <lb/>aqu&aelig;, qu&aelig; ex montibus quotidie terram &longs;ecum deducunt, eam ad humilio&shy;<lb/>ra loca, vt &longs;unt plana, &amp; campe&longs;tria, &longs;iue ibi &longs;int maria, &longs;iue arida, compor&shy;<lb/>tant, <expan abbr="eam&qacute;">eamque</expan>; ibidem deponunt. </s>
5049 
5050 <s>hinc videmus antiqua &aelig;deficia in planis locis <lb/>ex&longs;tructa, e&longs;&longs;e iam pen&egrave; tota &longs;epulta, contra quam in montanis, cuius exem&shy;<lb/>plum habes etiam Rom&aelig; prop&egrave; ip&longs;um Capitolium, in Arcu triumphali Sep&shy;<lb/>timij, qui iam fer&egrave; totus ruino&longs;a vndique terra obruitur. </s>
5051 
5052 <s>&longs;ic Pantheon. </s>
5053 
5054 <s>&longs;ic <lb/>etiam templa Epi&longs;copalia, qu&aelig; <expan abbr="plerunq;">plerunque</expan> &longs;atis peruetu&longs;ta &longs;unt, admodum <lb/>infra terram con&longs;piciuntur. </s>
5055 
5056 <s>Idem affirmant c&oelig;mentarij, &amp; architectores <pb pagenum="105"/>omnes, quibus <expan abbr="vbiq;">vbique</expan> terrarum, dum in planis &aelig;deficiorum fundamenta ex&shy;<lb/>canant, occurrit prim&ograve; terra qu&aelig;dam, quam ip&longs;i motam appellant, qu&aelig; li&shy;<lb/>gnis, ruderibus, ferramentis, numi&longs;matis, &longs;epulturis, <expan abbr="varijs&qacute;">varijsque</expan>; rebus per&shy;<lb/>mixta e&longs;t; qua eruta, reperitur terra alia, quam nunquam fui&longs;&longs;e motam, ap&shy;<lb/>paret, ex eo quod &longs;olida, ac ben&egrave; compacta &longs;it, neque vllis externis rebus, <lb/>pr&aelig;&longs;ertim artificiatis admixta, terra illa, quam motam dicunt, variam va&shy;<lb/>rijs in locis &longs;ortita e&longs;t altitudinem, prout aqu&aelig; plurimum, vel minimum <lb/>montan&aelig; terr&aelig; huc, vel illuc comportarunt: alicubi vt hic Parm&aelig; erit &longs;ex <lb/>vlnarum, alibi viginti, vt Mutin&aelig;; alibi triginta, vt Rom&aelig;, nonnullis in lo&shy;<lb/>cis. </s>
5057 
5058 <s>Comprobatur tandem h&aelig;c no&longs;tra ob&longs;eruatio ex arte illa, qua per ea&longs;&shy;<lb/>dem fluuiales aquas &longs;olent, tam loca depre&longs;&longs;iora per aggerationem paula&shy;<lb/>tim replere, <expan abbr="atq;">atque</expan> eleuare: qu&agrave;m etiam altiora per aquarum earumdem cor&shy;<lb/>ro&longs;ionem deprimere. </s>
5059 
5060 <s>qua in arte exercitati&longs;&longs;imum P. <!-- REMOVE S-->Augu&longs;tinum Spernac&shy;<lb/>ciatum no&longs;tr&aelig; Societatis videmus modo de mandato Summi Pontificis Pa&shy;<lb/>dum, ac Renum Bononien&longs;em ob aggerationem &longs;tagnantes in mari emitte&shy;<lb/>re; cui totus hic no&longs;ter di&longs;cur&longs;us maxim&egrave; probatur. </s>
5061 
5062 
5063 
5064 <s>Ex quibus omnibus &longs;e&shy;<lb/>quitur &longs;uperficiem terr&aelig; tam montium, quam planorum quotidie variari. <lb/></s>
5065 
5066 <s>illam nimirum deprimi, hanc attolli. </s>
5067 
5068 <s>vnde aliud maximum notandum &longs;e&shy;<lb/>quitur, videlicet hac tempe&longs;tate non e&longs;&longs;e eandem agrorum &longs;uperficiem, qu&aelig; <lb/>erat antiquitus, cum in montanis agris &longs;it mult&ograve; humilior, in campe&longs;tribus <lb/>ver&ograve; altior, qu&agrave;m antiqua illa, ac primigenia; quapropter mirum videri <lb/>non debet, &longs;i quorumdam locorum ade&ograve; immutata natura e&longs;t, vt qu&aelig; olim <lb/>genero&longs;a vina ferebant, vel quouis alio e&longs;&longs;ent pr&aelig;dita munere, ade&ograve; dege&shy;<lb/>nerauerint, vt &amp; vina, &amp; alia nullius mod&ograve; valoris, vel in parua copia pro&shy;<lb/>ferant. </s>
5069 
5070 <s>Quod ver&ograve; ad marium aggerationem &longs;pectat, dicimus ij&longs;dem aquis <lb/>magnam arenarum copiam perpetu&ograve; impertantibus, fieri aggerationem, <lb/>hoc e&longs;t littora quotidie magis cre&longs;cere, &longs;eu in mare ingredi, &amp; con&longs;equen&shy;<lb/>ter mare recedere. </s>
5071 
5072 <s>quod prim&ograve; Ari&longs;t. 
5073 
5074 te&longs;timonio in hoc cap. 
5075 
5076 comprobatur, <lb/>cum quo pariter &longs;entiunt veteres Geographi, &amp; Hi&longs;torici omnes. </s>
5077 
5078 <s>Ari&longs;t. 
5079 
5080 igi&shy;<lb/>tur in comprobationem huius adducit prim&ograve; magnam Aegypti aggeratio&shy;<lb/>nem; pars enim illa Aegypti, qu&aelig; Delta, <expan abbr="Nili&qacute;">Nilique</expan>; donum appellatur ab He&shy;<lb/>rodoto, ex arenis, &amp; limo, ex Aethyopi&aelig; montibus &longs;imul cum Nilo in mare <lb/>delabentibus, e&longs;t conflata, <expan abbr="atq;">atque</expan> antiquo littori addita, cui locum paulatim <lb/>mare ce&longs;&longs;it; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; propterea donum Nili appellata, quod ab ip&longs;o illuc are&shy;<lb/>nas importante &longs;it facta. </s>
5081 
5082 <s>&longs;ecundum, Ari&longs;t. 
5083 
5084 exemplum e&longs;t Ammonia Regio, <lb/>cuius humiliora loca. </s>
5085 
5086 <s>f. </s>
5087 
5088 <s>maritima, palam e&longs;t, inquit, quod aggeratione facta, <lb/>fiunt &longs;tagna, &amp; continens: &longs;uccedente autem tempore, &longs;tagnans aqua ob <lb/>nouam aggerationem de&longs;iccata e&longs;t, &amp; iam annihilata. </s>
5089 
5090 <s>tertium e&longs;t Meotidis <lb/>Paludis; At ver&ograve;, ait, &amp; qu&aelig; &longs;unt circa Meotidem Paludem creuerunt allu&shy;<lb/>uione fluuiorum tantum, vt mult&ograve; minores magnitudine naues, nunc innare <lb/>po&longs;&longs;int, qu&agrave;m anno ab hinc &longs;exage&longs;imo. </s>
5091 
5092 <s>quare ex hoc facil&egrave; e&longs;t ratiocinari, <lb/>quod &amp; prim&ograve;, vt multa &longs;tagnorum, ita &amp; hoc opus e&longs;t fluuiorum, &amp; tan&shy;<lb/>dem nece&longs;&longs;e e&longs;t totum fieri &longs;iccum. </s>
5093 
5094 <s><expan abbr="quart&utilde;">quartum</expan> e&longs;t illi Bo&longs;phorus Tracius; quod <lb/>vn&agrave; cum pr&aelig;cedentibus &longs;atius e&longs;t apud ip&longs;um, vel potius apud eius expo&longs;i&shy;<lb/>torem Vicomercatum videre, vt breuitati con&longs;ulatur. </s>
5095 
5096 <s>Accedit &amp; Plinij te&shy;<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;ed <pb pagenum="106"/>etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraci&aelig; portu 10. millia pa&longs;&longs;uum; ab <lb/>Athenarum ver&ograve; <expan abbr="quinq;">quinque</expan> millia, &amp; alijs in locis plus minu&longs;u&egrave; rece&longs;&longs;i&longs;&longs;e &longs;cri&shy;<lb/>bit. </s>
5097 
5098 <s>Huc facit locus quidam Strabonis ex lib. 
5099 
5100 12. de Pyramo Cilici&aelig; fluuio: <lb/>&longs;ic; montes ver&ograve; egre&longs;&longs;us tantum limum in mare deducit, partim ex Ca&shy;<lb/>taonia, partim ex Cilici&aelig; campis, vt huiu&longs;modi de co oraculum feratur;</s></p><p type="main">
5101 
5102 <s><emph type="italics"/>Tempus erit rapidis olim cum Pyramus vndis <lb/>In &longs;acram veniet conge&longs;io litore, Cyprum:<emph.end type="italics"/></s></p><p type="main">
5103 
5104 <s>hic enim fluuius &egrave; regione Cypri in&longs;ul&aelig; in mari influit, &amp;c. </s>
5105 
5106 <s>h&aelig;c Strabo.</s></p><p type="main">
5107 
5108 <s>Ver&ugrave;m recentiora non de&longs;unt exempla. </s>
5109 
5110 <s>Rauenna olim erat in extremo <lb/>littore &longs;ita, nunc paulatim aggeratione aucto litore, mare multum ab ea <lb/>rece&longs;&longs;it. </s>
5111 
5112 <s>Patauium pariter, vt fertur mare alluebat, quod modo 25. pa&longs;&longs;uum <lb/>millibus ab eo di&longs;tat. </s>
5113 
5114 <s>A&aelig;&longs;tuarium ip&longs;um Venetum, ob arenas &agrave; varijs &longs;lu&shy;<lb/>minibus in ip&longs;um immi&longs;&longs;as ade&ograve; fundum extulit, vt vix amplius nauigatio&shy;<lb/>ni &longs;it aptum, <expan abbr="periculam&qacute;">periculamque</expan>; &longs;it ne Venetiarum mirabilis locus, ex maritimo <lb/>fiat terre&longs;tris. </s>
5115 
5116 <s>demum exemplum &longs;it Bononien&longs;ium Renus, qui quamuis exi&shy;<lb/>guus &longs;it torrens, paucis tamen annis Padum ip&longs;um, in quem immi&longs;&longs;us fue&shy;<lb/>rat arena ita repleuit, vt &amp; &longs;ibi, &amp; Pado magno vicinorum agrorum damno <lb/>viam in mare ob&longs;truxerit. </s>
5117 
5118 <s>Cum igitur mare ob hanc adaggerationem co&shy;<lb/>gatur &longs;e quotidie magis recipere, <expan abbr="fiat&qacute;">fiatque</expan>; propterea alueus ip&longs;ius angu&longs;tior, <lb/><expan abbr="atq;">atque</expan> clatior, nece&longs;&longs;e e&longs;t etiam ip&longs;am quoque maris aquam quotidie magis <lb/>coangu&longs;tari, <expan abbr="atq;">atque</expan> attolli, &amp; aliquando futurum, vt exundare incipiat. </s>
5119 
5120 <s>quod <lb/>iam <expan abbr="pleri&longs;q;">pleri&longs;que</expan> in locis accidit, vt in littore Baltico, Danico, &amp; Hollandico, <lb/>quibus in locis &longs;unt hac tempe&longs;tate extructi pr&aelig;longi, ac pr&aelig;alti aggeres <lb/>contra maritimas innundationes: quibus antiquitus minim&egrave; fui&longs;&longs;e opus hi&shy;<lb/>&longs;toricorum, ac <expan abbr="Geographor&utilde;">Geographorum</expan> &longs;ilentium comprobat. </s>
5121 
5122 <s>Hoc igitur modo ter&shy;<lb/>ra, qua montes, <expan abbr="colles&qacute;">collesque</expan>; con&longs;tant paulatim ab aquis in maris concauitates <lb/>deportata, cau&longs;a e&longs;t, vt mare &longs;en&longs;im modo hac, modo illac, terr&aelig; &longs;uperfi&shy;<lb/>ciei &longs;uperfundatur, <expan abbr="terra&qacute;">terraque</expan>; iterum, quemadmodum exordio mundi inhabi&shy;<lb/>tabilis reddatur: quod tunc maxim&egrave; accidct cum aqu&aelig; tam fluuiales, qu&agrave;m <lb/>pluui&aelig;, &longs;uper faciem terr&aelig; perpetu&ograve; di&longs;currentes, totam illam montanam <lb/>terram in pri&longs;tinum locum, vbi ab initio fuerat, <expan abbr="vnde&qacute;">vndeque</expan>; &longs;ublata fuit, re&longs;ti&shy;<lb/>tuerint; tunc terra erit iterum rotunda, &amp; &longs;ph&aelig;rica, hoc e&longs;t &longs;u&aelig; primigeni&aelig; <lb/>iterum figur&aelig; re&longs;tituetur: quapropter mare etiam rur&longs;us &longs;icut initio mundi <lb/>totam terr&aelig; faciem <expan abbr="circumquaq;">circumquaque</expan> innundabit, quod probare volebam.</s></p><p type="main">
5123 
5124 <s><emph type="italics"/>Tantum &aelig;ui mutare potest long&aelig;ua vetu&longs;tas.<emph.end type="italics"/></s></p><p type="main">
5125 
5126 <s>Hinc nonnulla colligi po&longs;&longs;unt non minus notatu, ac &longs;citu, qu&agrave;m pr&aelig;ceden&shy;<lb/>tia digni&longs;&longs;ima, quibus Ethnicorum Philo&longs;ophorum error redarguatur, &longs;ides <lb/>ver&ograve; no&longs;tra magis roboretur: mundum nimirum ab &aelig;terno neutiquam ex&shy;<lb/>titi&longs;&longs;e, vel &longs;altem terram ab &aelig;terno non fui&longs;&longs;e hac figura pr&aelig;ditam, qua nunc <lb/>videmus, ncc mundum perpetu&ograve; duraturum. </s>
5127 
5128 <s>nam &longs;i h&aelig;c montuo&longs;a illi figu&shy;<lb/>ra ab &aelig;terno ine&longs;&longs;et, iampridem tota illa montium tubero&longs;itas fui&longs;&longs;et ab <lb/>aquis ex&aelig;&longs;a, &amp; con&longs;umpta: <expan abbr="neq;">neque</expan> &aelig;terna erit, quia &longs;ucce&longs;&longs;u temporis, vt pro&shy;<lb/>bauimus, reducetur ad rotunditatem, <expan abbr="atq;">atque</expan> &agrave; mari innun dabitur, &amp; idcirc&ograve; <lb/>inhabitabilis, vnde nece&longs;&longs;ari&ograve; mortalium genus interibit. </s>
5129 
5130 <s>Quapropter ni&longs;i <lb/>igne illo, quem &longs;acr&aelig; liter&aelig; innuunt catacly&longs;mus ille pr&aelig;ueniatur, aqua <lb/>mundus interiturus e&longs;&longs;et. </s>
5131 
5132 <s>&longs;ed de his hactenus.</s></p><pb pagenum="107"/><p type="main">
5133 
5134 <s>Quoad magnum illud Diluuium, quod Ari&longs;t. 
5135 
5136 hoc capite exi&longs;timat po&longs;t <lb/>multa &longs;ecula reuolui, hoc veritati e&longs;&longs;e con&longs;entaneum argumento &longs;unt, ac <lb/>pariter admirationi varia <expan abbr="c&otilde;chiliorum">conchiliorum</expan> genera, qu&aelig; t&ugrave;m in Apennino mon&shy;<lb/>te, t&ugrave;m in Alpibus ob&longs;eruaui; <expan abbr="&Igrave;dem&qacute;">&Igrave;demque</expan>; in alijs mundi partibus inueniri pu&shy;<lb/>to; pr&aelig;&longs;ertim in tam immen&longs;a copia, <expan abbr="atq;">atque</expan> intra vi&longs;cera montium colloca&shy;<lb/>ta, qu&aelig; nulla vis humana illuc contuli&longs;&longs;er, ni&longs;i temporibus catacly&longs;mi ebul&shy;<lb/>lientibus aquis maris &longs;uper terram facta fui&longs;&longs;et h&aelig;c varia rerum maritima&shy;<lb/>rum cum terre&longs;tribus commixtio: qu&aelig; quidem optim&egrave; ex Pomponio Mela <lb/>comprobantur, qui libro 1. de Numidia &longs;ic narrat: interius, &amp; long&egrave; &longs;atis <lb/>&agrave; litore, &longs;i fides res capit, mirum admodum, &longs;pin&aelig; pi&longs;cium, <expan abbr="Muric&utilde;">Muricum</expan>, <expan abbr="O&longs;treo-rum&qacute;">O&longs;treo&shy;<lb/>rumque</expan>; fragmenta, &longs;axi atritu, vti &longs;olent fluctibus, &amp; non differentia mari&shy;<lb/>nis, infix&aelig; cautibus anchor&aelig;, <expan abbr="alia&qacute;">aliaque</expan>; huiu&longs;modi &longs;igna, &amp; ve&longs;tigia effu&longs;i olim <lb/><expan abbr="v&longs;q;">v&longs;que</expan> ad ea loca pelagi, in campis nihil alentibus e&longs;&longs;e inuenirique narrantur. <lb/></s>
5137 
5138 <s>neque locus ille Ouid. <!-- REMOVE S-->Met. <!-- REMOVE S-->15. extra rem:</s>
5139 
5140 
5141 
5142 </p><p type="main">
5143 
5144 <s><emph type="italics"/>Vidi ego, quod fuerat olim &longs;olidi&longs;&longs;ima petra <lb/>E&longs;&longs;e fretum, vidi fact as ex &aelig;quore terras: <lb/>Et procul &agrave; Pelago conch&aelig; iacuere marin&aelig;, <lb/>Et vetus inuenta e&longs;t in montibus anchora &longs;ummis.<emph.end type="italics"/></s></p><p type="main">
5145 
5146 <s>Nos autem Chri&longs;tiani ad Noemi Diluuium i&longs;ta referre debemus.</s></p></chap><chap><p type="head">
5147 
5148 <s><emph type="italics"/>Ex Secundo Meteororum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
5149 
5150 <s><arrow.to.target n="marg152"/></s></p><p type="margin">
5151 
5152 <s><margin.target id="marg152"/>152</s></p><p type="main">
5153 
5154 
5155 <s>Cap. 1. ait multa e&longs;&longs;e maria, qu&aelig; ad inuicem non communicant. <lb/></s>
5156 
5157 
5158 <s>Eorum rubrum mare vnum e&longs;&longs;e; quod cum Oceano <expan abbr="Atl&atilde;tico">Atlantico</expan>, qui <lb/>e&longs;t extra Herculeum fretum ad occidentem parum videtur com&shy;<lb/>mi&longs;ceri &longs;iue Ari&longs;t. 
5159 
5160 pro Rubro mari intelligat Oceanum illum, qui <lb/>Arabiam, ac Per&longs;iam alluit, &longs;iue illius &longs;inum, qui Arabiam, <expan abbr="atq;">atque</expan> Aethiopiam <lb/>interluit, fal&longs;um e&longs;t ip&longs;um parum communicare cum occidentali Oceano, <lb/>vt quotidianis Lu&longs;itanorum nauigationibus ad Indos patet. </s>
5161 
5162 <s>&longs;ed merit&ograve; hoc <lb/>Ari&longs;tot. condonandum, cum tunc temporis nondum tota Africa e&longs;&longs;et cert&ograve; <lb/>circumlu&longs;trata, <expan abbr="neq;">neque</expan> iter ab Hi&longs;pania ad Indos maritimum, adeo nunc fre&shy;<lb/>quens, patefactum e&longs;&longs;et.</s>
5163 
5164 </p><p type="main">
5165 
5166 <s><arrow.to.target n="marg153"/></s></p><p type="margin">
5167 
5168 <s><margin.target id="marg153"/>153</s></p><p type="main">
5169 
5170 <s>Summ&aelig; 2. cap. 
5171 
5172 2. <emph type="italics"/>(Quapropter &amp; circa Orionis orturm maxim&egrave; fit tranquilli&shy;<lb/>tas)<emph.end type="italics"/> quando Medici, Philo&longs;ophi, Poet&aelig;, ac reliqui auctores loquuntur de <lb/>ortu a&longs;trorum fixorum, aut con&longs;tellationum, qu&aelig; &longs;unt in firmamento, vti <lb/>e&longs;t Orion (&amp; Canis, de quo po&longs;tea) intelligunt &longs;emper de ortu ip&longs;orum, qui <lb/>fit matutino tempore, quando &longs;cilicet vel &longs;imul cum Sole, vel paul&ograve; ante <lb/>Solem emergunt, ita vt videantur &agrave; nobis; qui ortus dicitur Co&longs;micus, tunc <lb/>propri&egrave;, quando &longs;imul a&longs;trum cum Sole oritur; quando autem incipit appa&shy;<lb/>rere manc ante Solem, dicitur ortus Heliacus. </s>
5173 
5174 <s>i. </s>
5175 
5176 <s>&longs;olaris, quia oritur quodam&shy;<lb/>modo ex radijs Solis, &longs;ub quibus antea latebat. </s>
5177 
5178 <s>A&longs;tra ver&ograve; incrrantia, &amp; <lb/>planet&aelig; Sole tardiores oriuntur <expan abbr="vtroq;">vtroque</expan> modo. </s>
5179 
5180 <s>nam c&ugrave;m ip&longs;a Sol, quippe il&shy;<lb/>lis velocior primum a&longs;&longs;equitur, ea &longs;uo lumine obtegit, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; hic occa&longs;us eo&shy;<lb/>rum heliacus: cum ver&ograve; eadem pr&aelig;terierit, ac po&longs;t &longs;e reliquerit fit, vt mo&shy;<lb/>tu diurno toto c&oelig;lo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliac&egrave; <lb/>oriantur: &amp; cum quotidie magis Sol ab illis recedat, ip&longs;aque magis &agrave; Sole <pb pagenum="108"/>elongentur, fit, vt quotidie magis ortum Solis anticipent, &amp; citius mane au&shy;<lb/>te Solem videantur. </s>
5181 
5182 <s><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; tanto in dies citius, vt deinde media etiam nocte <lb/>oriantur; tum ante mediam noctem po&longs;tea paul&ograve; ante occa&longs;um Solis. <!-- KEEP S--></s>
5183 
5184 <s>de&shy;<lb/>mum cum fuerint Soli oppo&longs;ita, occidente Sole oriantur, qui ortus dicitur <lb/>Ve&longs;pertinus, vel Acronicus. </s>
5185 
5186 <s>po&longs;tea oriuntur &longs;emper in die ante Solis occa&shy;<lb/>&longs;um, donec Sol ip&longs;a iterum a&longs;&longs;equatur, <expan abbr="ea&qacute;">eaque</expan>; radijs &longs;uis offu&longs;cet, quod e&longs;t he&shy;<lb/>liac&egrave; occidere; &amp; mox cum ip&longs;o Sole occumbant, quod Acronic&egrave; e&longs;t occi&shy;<lb/>dere. </s>
5187 
5188 <s>Totum porr&ograve; illud tempus, quo per diem oriuntur, non eorum ortui, <lb/>&longs;ed occa&longs;ui deputatur, e&ograve; quod non cernuntur oriri, vt &longs;equenti loco expli&shy;<lb/>cabitur. </s>
5189 
5190 <s>Qu&aelig; omnia adhibito Globo a&longs;tronomico, in quo con&longs;tellationes <lb/>omnes depict&aelig; &longs;unt, <expan abbr="eo&qacute;">eoque</expan>; ad tui poli eleuationem con&longs;tituto, appo&longs;itoque <lb/>Sole &longs;uo loco in Zodiaco, qui paulatim per Zodiacum orientem ver&longs;us gra&shy;<lb/>diatur, &amp; interim diurno motu globus conuertatur, ad &longs;en&longs;um manife &longs;ta <lb/>apparebunt. </s>
5191 
5192 <s>In &longs;umma auctores intelligunt de ortu, qui mane fit ante So&shy;<lb/>lem, quia tunc primum po&longs;t diuturnas latebras incipit apparere. </s>
5193 
5194 <s><expan abbr="n&otilde;">non</expan> autem <lb/>intelligunt de ortu Acronico, quia ante hunc ortum videbatur noctu, <expan abbr="itaq;">itaque</expan> <lb/>ortu Acronico non fit noua apparitio; ideo de hoc non intelligunt. </s>
5195 
5196 <s>fit au&shy;<lb/>tem ortus hic Orionis, heliacus, &amp; matutinus, de quo Ari&longs;t. 
5197 
5198 hoc loco, &amp; alij <lb/>auctores, no&longs;tra hac tempe&longs;tate paul&ograve; ante Solis ingre&longs;&longs;um in Cancrum, &longs;i&shy;<lb/>ue ante &longs;ol&longs;titium &aelig;&longs;tiuum circa 22. Iunij.<!-- REMOVE S--><arrow.to.target n="marg154"/></s></p><p type="margin">
5199 
5200 <s><margin.target id="marg154"/>154</s></p><p type="main">
5201 
5202 <s>Eodem cap. <emph type="italics"/>(Incertus autem, &amp; mole&longs;tus Orion e&longs;&longs;e videtur &amp; occumbens, &amp; <lb/>oriens, quia in tran&longs;mutatione temporis accidit occa&longs;us, &amp; ortus, a&longs;tate, aut hye&shy;<lb/>me, &amp; propter magnitudinem a&longs;tri dierum &longs;it aliqua pluralitas)<emph.end type="italics"/> hoc loco Vico&shy;<lb/>mercatus ex &longs;ententia a&longs;tronomorum occa&longs;um Orionis fieri autumni tem&shy;<lb/>pore, Sole Scorpionem ob&longs;idente docet, quod &amp; verba Ari&longs;t. 
5203 
5204 clar&egrave; &longs;ignifi&shy;<lb/>cant, cum dicat ortum ip&longs;ius fieri &aelig;&longs;tate; in tran&longs;mutatione ver&ograve; temporis, <lb/>videlicet in autumno fieri occa&longs;um. </s>
5205 
5206 <s>Porr&ograve; occa&longs;us hic fieri incipit primum <lb/>mane oriente Sole, <expan abbr="dicitur&qacute;">diciturque</expan>; occa&longs;us co&longs;micus, quia dum Sol e&longs;t in oriente, <lb/>Orion e&longs;t in occidente, &amp; infra orizontem cadit: deinde paul&ograve; ante Solis or&shy;<lb/>tum, &longs;ed tamen nocturno tempore, ita vt occa&longs;us eius videri po&longs;&longs;it, donec <lb/>occidat parum po&longs;t Solis occa&longs;um, &amp; tandem cum Sole ip&longs;o heliac&egrave; euane&shy;<lb/>&longs;cat. </s>
5207 
5208 <s>Scriptores autem fer&egrave; &longs;emper cum loquuntur de occa&longs;u inerrantium <lb/>&longs;yderum, de eo, qui noctu videatur, intelligunt: &longs;icuti ortum intelligunt <lb/>eum, qui noctu fit, <expan abbr="noctu&qacute;">noctuque</expan>; videtur. </s>
5209 
5210 <s>affixa <expan abbr="namq;">namque</expan> &longs;ydera per fex ferm&egrave; men&shy;<lb/>&longs;es noctu oriuntur, <expan abbr="oriri&qacute;">oririque</expan>; ea con&longs;picimus, &amp; propterea totum illud tem&shy;<lb/>pus, ortui ip&longs;orum deputamus: Reliquum ver&ograve; <expan abbr="t&etilde;pus">tempus</expan>, quo per diem oriun&shy;<lb/>tur, &amp; idcirc&ograve; ortus illorum minim&egrave; apparet, nulla ratione ortui debuit <lb/>a&longs;cribi: totum ver&ograve; tempus, quo noctu occidunt, &amp; occidere cernuntur, oc&shy;<lb/>ca&longs;ui illorum merit&ograve; attribuitur. </s>
5211 
5212 <s>&amp; <expan abbr="quemadmod&utilde;">quemadmodum</expan> temporis illius initium, <lb/>quo primo de nocte apparere incipiunt, dicitur ab&longs;olut&egrave; ortus cuiu&longs;uis &longs;y&shy;<lb/>deris; &longs;ic etiam initium temporis illius, quo primum per noctem ea occide&shy;<lb/>re videmus, &longs;impliciter occa&longs;um appellamus.</s></p><p type="main">
5213 
5214 <s><arrow.to.target n="marg155"/></s></p><p type="margin">
5215 
5216 <s><margin.target id="marg155"/>155</s></p><p type="main">
5217 
5218 <s>Eodem cap. <emph type="italics"/>(Ete&longs;i&aelig; autem flant post ver&longs;iones, &amp; Canis ortum)<emph.end type="italics"/> per ver&longs;io&shy;<lb/>nes intelligit tropicos, quod &amp; tropici etymon confirmat, <expan abbr="c&utilde;">cum</expan> tropicus idem <lb/>valeat, ac conuer&longs;iuus. </s>
5219 
5220 <s>circa Canis ortum eadem &longs;unt notanda, qu&aelig; &longs;upra <lb/>de ortu Orionis annotaui; intelligit enim eum Canis ortum, qui mane fiat <pb pagenum="109"/>primum paul&ograve; ante Solis ortum, cum &longs;cilicet incipit apparere.</s></p><p type="main">
5221 
5222 <s>Cum porr&ograve; in c&ecedil;lo &longs;it Canis maior, &amp; Canis minor, qui &amp; Procyon, ide&longs;t <lb/>Anticanis dicitur, exi&longs;timo Canem maiorem e&longs;&longs;e eum, qui vulg&ograve; Canicula <lb/>nominatur, <expan abbr="&longs;olet&qacute;">&longs;oletque</expan>; vehementes, ac noxios calores excitare. </s>
5223 
5224 <s>de quo etiam <lb/>put&ograve; Ari&longs;t. 
5225 
5226 intelligere. </s>
5227 
5228 <s>eius porr&ograve; ortus in no&longs;tra poli eleuatione quadra&shy;<lb/>ginta quinque graduum, circa diem tertium Augu&longs;ti contingit, Sole autem <lb/>10. gradum Leonis occupante. </s>
5229 
5230 <s>Ex Magini tabulis ante ephemerides.</s></p><p type="main">
5231 
5232 <s><arrow.to.target n="marg156"/></s></p><p type="margin">
5233 
5234 <s><margin.target id="marg156"/>156</s></p><p type="main">
5235 
5236 <s>Eodem cap. <emph type="italics"/>(Duobus enim exi&longs;tentibus &longs;egmentis habitabilis regionis: vno <lb/>quidem ad &longs;uperiorem polum, qui no&longs;ter e&longs;t; altero ad alterum, &amp; ad meridiem: <lb/><expan abbr="ea&qacute;">eaque</expan>, tympani &longs;peciem habeant, talem enim figuram terr&aelig; excidunt ex centro ip&longs;ius <lb/>duct&aelig; line&aelig;, &amp; faciunt duos conos, bunc quidem habentem ba&longs;im tropicum, alte&shy;<lb/>rum autem habentem ba&longs;im circulum &longs;emper manifestum, verticem autem in me&shy;<lb/>dio terr&aelig;. </s>
5237 
5238 <s>eodem autem modo ad inferiorem polum alij duo coni terr&aelig; &longs;egmenta fa&shy;<lb/>ciunt)<emph.end type="italics"/> vt ben&egrave; duas ha&longs;ce terr&aelig; portiones, quas &longs;olas habitabiles putat Ari&shy;<lb/>&longs;tot. concipias, <expan abbr="reliquaq;">reliquaque</expan> huius loci intelligas, in&longs;pice &longs;equentem figuram. <lb/><figure place="text" xlink:href="figures-la/009.01.109.1.tif"/><lb/>Maior circulus &longs;it c&oelig;lum, in quo polus L, articus; M, antarticus, ille eleua&shy;<lb/>tus &longs;upra no&longs;trum horizontem S N, 45. gradibus, i&longs;te ver&ograve; totidem infra <lb/>depre&longs;&longs;us. </s>
5239 
5240 
5241 
5242 <s><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb pagenum="110"/>diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/>X O, Capricorni, vt vides in figura. </s>
5243 
5244 <s>Terra &longs;it A B C H G F E D Z K. &agrave; cu&shy;<lb/>ius centro Z, educantur primo du&aelig; line&aelig; rect&aelig; Z R, Z S. ad circulum &longs;em&shy;<lb/>per apparentium maximum, qu&aelig; in terra tran&longs;eant per puncta B, K. &amp; iun&shy;<lb/>gatur linea B K: iam vides conum S R Z, cuius ba&longs;is e&longs;t circulus &longs;emper ap&shy;<lb/>parens S R, vertex autem Z, in centro terr&aelig;, vt ait Ari&longs;tot. <!-- KEEP S--></s>
5245 
5246 <s>educantur nunc <lb/>du&aelig; ali&aelig; rect&aelig; ad tropicum Cancri Z T, Z Q, qu&aelig; in terra faciant puncta <lb/>I, C, <expan abbr="iungatur&qacute;">iungaturque</expan>; recta I C; hic pariter vides conum alterum T Q Z, cuius ba&shy;<lb/>&longs;is e&longs;t circulus Cancri, vertex ver&ograve; centrum terr&aelig; Z. con&longs;idera iam figuram <lb/>B K I C, inter duas rectas B K, I C, &amp; duos circuli terr&aelig; arcus contentam; <lb/>hanc Ari&longs;t. 
5247 
5248 appellat tympanum vnum terr&aelig; habitabile, quod e&longs;t ad Vr&longs;am, <lb/>ide&longs;t in &longs;eptentrionali plaga, in qua &longs;umus nos: qu&aelig; quidem portio &longs;i con&longs;i&shy;<lb/>deretur vt &longs;olida, &amp; &agrave; reliqua terra pr&aelig;ci&longs;a, erit corpus rotundum, <expan abbr="vtrinq;">vtrinque</expan> <lb/>tamen duobus planis circulis ad in&longs;tar tympani terminatum: Ductis dein&shy;<lb/>de &longs;imiliter alijs quattuor lineis &agrave; centro Z, ver&longs;us polum antarticum fit al&shy;<lb/>terum tympanum H D E G, au&longs;tralis terr&aelig; habitabilis, vt in figura manife&shy;<lb/>&longs;tum e&longs;t. </s>
5249 
5250 <s>fui&longs;&longs;e autem huiu&longs;modi habitabilis terr&aelig; &longs;egmenta figur&aelig; tympa&shy;<lb/>ni &longs;imilia, optim&egrave; declarant veteres figur&aelig; geographic&aelig; Ptol&ecedil;mei, &amp; patet <lb/>etiam ex longitudine, &amp; latitudine, vt ben&egrave; ait Ari&longs;t. 
5251 
5252 quas Geographi por&shy;<lb/>tioni terr&aelig; habitabili attribuebant, longitudinem enim dixerunt eius di&shy;<lb/>men&longs;ionem ab occa&longs;u ad ortum: latitudinem autem &agrave; &longs;eptentrione in meri&shy;<lb/>diem, e&ograve; qu&ograve;d illa mult&ograve; hac longior e&longs;&longs;et. </s>
5253 
5254 <s>Ex quibus apparet habitatam <lb/>fui&longs;&longs;e veluti Zonam, terram ab occa&longs;u ad ortum pr&aelig;cingentem. </s>
5255 
5256 <s>qu&aelig; Zona <lb/>&longs;i &longs;umatur cum &longs;oliditate, quam ambit, ab Ari&longs;t. 
5257 
5258 tympano a&longs;&longs;imilatur.</s></p><p type="main">
5259 
5260 <s><arrow.to.target n="marg157"/></s></p><p type="margin">
5261 
5262 <s><margin.target id="marg157"/>157</s></p><p type="main">
5263 
5264 <s>Eodem cap. <emph type="italics"/>(H&aelig; autem habitari &longs;ol&aelig; po&longs;&longs;ibiles: &amp; <expan abbr="neq;">neque</expan> vltra ver&longs;iones; vm&shy;<lb/>bra enim non <expan abbr="vtiq;">vtique</expan> e&longs;&longs;et ad Vr&longs;am: nunc autem inhabitabilia prius fiunt loca, qu&agrave;m <lb/>&longs;ubdeficiat, aut permutetur vmbra ad meridiem. </s>
5265 
5266 <s>Qu&aelig; autem &longs;ub Vr&longs;a, &egrave; frigore <lb/>inhabitabilia)<emph.end type="italics"/> quod ait vltra ver&longs;iones, ide&longs;t intra tropicos in ip&longs;a &longs;cilicet <lb/>Zona torrida, non po&longs;&longs;e habitari, fal&longs;um e&longs;&longs;e o&longs;tendunt plurim&aelig; regiones <lb/>tam veteris, quam noui orbis, &longs;uperiori &longs;eculo patefact&aelig;, in quibus magna <lb/>in am&oelig;nitate, ac fertilitate, <expan abbr="&longs;ummis&qacute;">&longs;ummisque</expan>; delicijs viuitur. </s>
5267 
5268 <s>Quoad vmbram il&shy;<lb/>lam, intellige meridianam. </s>
5269 
5270 <s>i. </s>
5271 
5272 <s>quam Sole circa meridiem exi&longs;tente, nos qui <lb/>Boreales &longs;umus, &longs;emper ad <expan abbr="&longs;ept&etilde;trionem">&longs;eptentrionem</expan> proijcimus. </s>
5273 
5274 <s>Quod &longs;i ad meridiem <lb/>perrexerimus, occurret inhabitabilis (vt fals&ograve; putat) terra, prius quam. <lb/></s>
5275 
5276 <s>vmbra meridiana in Boream vergens deficiat. </s>
5277 
5278 <s>qu&aelig; &longs;igna &longs;unt no&longs;tram habi&shy;<lb/>tationem e&longs;&longs;e citra Zonam torridam, in Boreali parte. </s>
5279 
5280 <s>Qu&aelig; autem &longs;ub Vr&shy;<lb/>&longs;a, ide&longs;t &longs;ub polo arctico, ob nimium frigus inho&longs;pita omnin&ograve; habetur, nam</s></p><p type="main">
5281 
5282 <s><emph type="italics"/>Quod latus mundi nebul&aelig;, <expan abbr="malus&qacute;">malusque</expan>; <lb/>Iupiter vrget.<emph.end type="italics"/></s></p><p type="main">
5283 
5284 <s>Verumtamen, qu&aelig; &longs;ub <expan abbr="vtroq;">vtroque</expan> polo partes &longs;unt adhuc incognit&aelig; manent.</s></p><p type="main">
5285 
5286 <s><arrow.to.target n="marg158"/></s></p><p type="margin">
5287 
5288 <s><margin.target id="marg158"/>158</s></p><p type="main">
5289 
5290 <s>Eodem cap: <emph type="italics"/>(Fertur autem, &amp; corona &longs;ecundam hunc locum, videtur enim &longs;u&shy;<lb/>per caput e&longs;&longs;e nohis, cum fuerit &longs;ecundum meridianum)<emph.end type="italics"/> con&longs;tellatio videlicet, <lb/>qu&aelig; corona Ariadn&aelig; dicitur, h&aelig;c cum in c&oelig;lo manife&longs;t&egrave; &longs;it Borealis, <expan abbr="no-&longs;tro&qacute;">no&shy;<lb/>&longs;troque</expan>; vertici noctu, quando meridianum pertran&longs;it, incumbat: clar&egrave; indi&shy;<lb/>cat nos <expan abbr="quoq;">quoque</expan> e&longs;&longs;e Boreales.<!-- KEEP S--></s></p><p type="main">
5291 
5292 <s><arrow.to.target n="marg159"/></s></p><p type="margin">
5293 
5294 <s><margin.target id="marg159"/>159</s></p><p type="main">
5295 
5296 <s>Eodem cap. <emph type="italics"/>(Et quidem ad latitudinem <expan abbr="v&longs;q;">v&longs;que</expan> ad inhabitabilia &longs;cimus hahita-<emph.end type="italics"/><pb pagenum="111"/><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter &aelig;&longs;tum)<emph.end type="italics"/><lb/>illic autem, ide&longs;t &longs;ub Zona torrida, compertum autem e&longs;t nunc totam fer&egrave; <lb/>torridam Zonam, &amp; quidem alicubi percommod&egrave; habitari, cuius cau&longs;&aelig; &longs;unt <lb/>quatuor, qu&aelig; ip&longs;um latuerunt. </s>
5297 
5298 <s>prima <expan abbr="ea&qacute;">eaque</expan>; toti Zon&aelig; torrid&aelig; communis, <lb/>e&longs;t perpetuum &aelig;quinoctium, quo Sol tantum &longs;upra, quantum infra terram <lb/>immoratur. </s>
5299 
5300 <s>accedit, qu&ograve;d Sol nocturno tempore maxim&egrave; ad imum c&oelig;li fe&shy;<lb/>ratur, <expan abbr="plurimum&qacute;">plurimumque</expan>; ab horizonte, <expan abbr="&longs;upero&qacute;">&longs;uperoque</expan>; hemi&longs;pherio recedat. </s>
5301 
5302 <s>atque ob <lb/>hanc &longs;olam rationem Campanus in &longs;ua &longs;ph&aelig;ra Zonam hanc putat maxim&egrave; <lb/>e&longs;&longs;e habitabilem: quamuis h&aelig;c &longs;ola cau&longs;a, vt quotidiana docet experientia, <lb/>non &longs;ufficiat. </s>
5303 
5304 <s>&longs;ecunda &longs;unt pluui&aelig;, qu&aelig; alicubi quotidie &longs;tata hora decidunt. <lb/></s>
5305 
5306 <s>tertia venti, qui veluti flabella qu&aelig;dam aerem agitant. </s>
5307 
5308 <s>quarta pr&aelig;alti mon&shy;<lb/>tes perpetuis niuibus ob&longs;iti. </s>
5309 
5310 <s>qu&aelig; quatuor torridam hanc pa&longs;&longs;im refrigerant, <lb/>atque habitabilem reddunt.</s></p><p type="main">
5311 
5312 <s><arrow.to.target n="marg160"/></s></p><p type="margin">
5313 
5314 <s><margin.target id="marg160"/>160.a</s></p><p type="main">
5315 
5316 <s>Summ&aelig; 2. cap. 
5317 
5318 3. de <expan abbr="v&etilde;tis">ventis</expan> <emph type="italics"/>(Oportet autem de &longs;itu &longs;imul rationes ex de&longs;criptio <lb/>ne con&longs;iderare)<emph.end type="italics"/> ide&longs;t rationes ventorum ex de&longs;criptione, ide&longs;t in figura ali&shy;<lb/>qua, vt in &longs;equenti con&longs;iderare; &longs;olet enim Ari&longs;t. 
5319 
5320 figuras, im&ograve; demon&longs;tratio&shy;<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;&aelig;pius in Logicis <lb/>monuimus.</s></p><p type="main">
5321 
5322 <s><emph type="italics"/>De&longs;criptus &longs;it igitur, vt clarior res euadat horizontis circulus quapropter, &amp; <lb/>rotundus)<emph.end type="italics"/> vt in &longs;equenti figura circulus A G B H, de&longs;criptus horizontem <lb/>referret,</s></p><figure place="text" xlink:href="figures-la/009.01.111.1.tif"/><pb pagenum="112"/><p type="main">
5323 
5324 <s><emph type="italics"/>Oportet autem ip&longs;ius alteram portionem intelligere, qu&aelig; nobis habitatur; qu&aelig; <lb/>eodem modo diuidi poterit)<emph.end type="italics"/> ide&longs;t oportet intelligere ip&longs;ius horizontis, vel ter&shy;<lb/>r&aelig; habitat&aelig; partem, qu&aelig; quamuis rotunda non &longs;it, poterit tamen, ac &longs;i ro&shy;<lb/>tunda e&longs;&longs;et in figura circulari repre&longs;entari, <expan abbr="atq;">atque</expan> in plures partes eo modo, <lb/>quo circulus &longs;ecatur, &longs;ecari.</s></p><p type="main">
5325 
5326 <s><emph type="italics"/>Supponatur autem prim&ograve; contraria &longs;ecundum locum, e&longs;&longs;e plurimum di&longs;tantia <lb/>&longs;ecundum locum; &longs;icut &longs;ecundum &longs;peciem contraria, plurimum di&longs;tant &longs;ecundum <lb/>&longs;peciem. </s>
5327 
5328 <s>plurimum autem di&longs;tant &longs;ecundum locum, qu&aelig; per diametrum opponuntur, <lb/>&longs;it igitur vbi A, occidens &aelig;quinoctionalis, contrarius autem huic locus vltimus B, <lb/>ortus &aelig;quinoctionalis)<emph.end type="italics"/> ide&longs;t in &longs;equenti figura ducta diametro B A. in altera <lb/>ip&longs;ius extremitate vbi A. &longs;it occa&longs;us &aelig;quinoctialis, qui fit Sole exi&longs;tente in <lb/>alterutro &aelig;quinoctio; huic igitur per diametrum opponatur ortus &aelig;quino&shy;<lb/>ctialis in B. qui pariter contingit tempore &aelig;quinoctiorum: linea autem B A, <lb/>refert ip&longs;um &aelig;quatorem.</s></p><p type="main">
5329 
5330 <s><emph type="italics"/>Alia autem diameter hanc perpendiculariter &longs;ecet, cuius punctum illud, in quo <lb/>G, &longs;it Vr&longs;a: huic autem contrarium ex oppo&longs;ito illud, in quo H, meridies)<emph.end type="italics"/> h&aelig;c dia&shy;<lb/>meter erit ip&longs;a linea meridiana. </s>
5331 
5332 <s>pro Vr&longs;a ver&ograve; intelligit &longs;eptentrionem, <lb/>quod ibi &longs;it Vr&longs;&aelig; con&longs;tellatio.</s></p><p type="main">
5333 
5334 <s><emph type="italics"/>Id autem, in quo F, ortus &aelig;&longs;tiualis; in quo ver&ograve; E, occidens &aelig;&longs;tiualis)<emph.end type="italics"/> qu&aelig; duo <lb/>puncta iunguntur linea F E, qu&aelig; refert &longs;ectionem tropici, Cancri cum ho&shy;<lb/>rizonte: ortus enim, &amp; occa&longs;us &aelig;&longs;tiualis contingunt Sole Cancri tropicum <lb/>percurrente.</s></p><p type="main">
5335 
5336 <s><emph type="italics"/>Id autem, in quo D, oriens byemalis; vbi ver&ograve; C, occidens hyemalis)<emph.end type="italics"/> linea au&shy;<lb/>tem D C, erit &longs;ectio tropici Capricorni, &amp; horizontis; Sole enim hunc tro&shy;<lb/>picum attingente ortus, &amp; occa&longs;us hybernus fiunt.</s></p><p type="main">
5337 
5338 <s><emph type="italics"/>Ab F, autem ducatur diameter ad C, &amp; &agrave; D, ad E. quoniam igitur plurimum <lb/>di&longs;tantia &longs;ecundum locum, contraria &longs;unt &longs;ecundum locum: plurimum autem di&shy;<lb/>stantia, qu&aelig; &longs;ecundum diametrum; nece&longs;&longs;arium e&longs;t, &amp; flatuum hos inuicem con&shy;<lb/>trarios e&longs;&longs;e, <expan abbr="quicunq;">quicunque</expan> &longs;ecundum diametrum exi&longs;tunt. </s>
5339 
5340 <s>vocantur autem &longs;ecundum po&shy;<lb/>&longs;itionem locorum venti &longs;ic; Zephyrus quidem ab A, hoc enim e&longs;t occidens &aelig;quino&shy;<lb/>ctialis. </s>
5341 
5342 <s>Boreas autem, &amp; Aparetias &agrave; G. hic enim Vr&longs;a, contrarius autem huic <lb/>Notus ab H. <!-- KEEP S--></s>
5343 
5344 <s>Meridies enim e&longs;t hic, &agrave; quo flat, &amp; H, ip&longs;i G, contrarium e&longs;t; &longs;ecun&shy;<lb/>dum enim diametrum &longs;unt. </s>
5345 
5346 <s>Ab F, autem C&aelig;cias; hic enim oriens &aelig;&longs;tiuus e&longs;t; cui <lb/>contrarius est, non qui flat ab E, &longs;ed qui &agrave; C. Libs, i&longs;te enim ab occidente hyemali <lb/>flat; <expan abbr="est&qacute;">estque</expan>, illi contrarius, quia &longs;ecundum diametrum illi opponitur. </s>
5347 
5348 <s>Qui ver&ograve; &agrave; D, <lb/>Eurus, i&longs;te enim ab horiente hyberno flat, vicinus existens Noto, vnde &amp; &longs;&aelig;p&egrave; Eu&shy;<lb/>ronoti flare dicuntur: <expan abbr="c&otilde;trarius">contrarius</expan> autem huic, non qui &agrave; C. Libs, &longs;ed qui ab E, quem <lb/>vocant, hi quidem Arge&longs;ten, hi autem Olympium, alij ver&ograve; Scironem; iste enim ab <lb/>occidente &aelig;&longs;tiuo flat, &amp; &longs;ecundum diametrum ip&longs;i &longs;olus opponitur. </s>
5349 
5350 <s>Venti igitur, qui <lb/>&longs;ecundum diametrum po&longs;iti &longs;unt, &amp; quibus alij aduer&longs;antur, ij &longs;unt. </s>
5351 
5352 <s>Alij autem <lb/>&longs;unt, &longs;ecundum quos non &longs;unt contrarij venti, ab I, quem vocant Tra&longs;ciam, qui me&shy;<lb/>dius e&longs;t inter Argesten, &amp; Apparitiam, &agrave; K, autem, quem vocant Me&longs;en, Mtdius <lb/>enim e&longs;t C&aelig;ci&aelig;, &amp; Apareti&aelig;. </s>
5353 
5354 <s>Diameter autem K I, iuxta circulum &longs;emper con&longs;pi&shy;<lb/>cuum e&longs;&longs;e &longs;olet, non tamen exact&egrave;)<emph.end type="italics"/> ide&longs;t linea K I, &longs;olet in horizonte referre <lb/>diametrum circuli omnium &longs;emper apparentium maximi, eo quod &longs;it fer&egrave; <lb/>&longs;ub diametro illius, in qualibet enim &longs;ph&aelig;ra obliqua, ide&longs;t, in qua polus cle&shy;<pb pagenum="113"/>natur, intelligunt A&longs;tronomi circulum quendam &longs;emper apparentium ma&shy;<lb/>ximum, quem de&longs;cribunt ex ip&longs;o polo, tanquam centro, &amp; interuailo v&longs;que <lb/>ad horizontem, circa ip&longs;um polum: hunc appellant &longs;emper apparentium, <lb/>maximum, quia intra hunc alios quamplurimos concipiunt circa eundem <lb/>polum, quorum minores &longs;emper &longs;unt polo propinquiores. </s>
5355 
5356 <s>huius igitur dia&shy;<lb/>metrum vult Ari&longs;t. 
5357 
5358 per lineam, qu&aelig; &agrave; K, in I, duceretur (quamuis non exa&shy;<lb/>ct&egrave;) repre&longs;entari.</s></p><p type="main">
5359 
5360 <s><emph type="italics"/>Contrarij autem non &longs;unt his &longs;latibus, <expan abbr="neq;">neque</expan> ip&longs;i Me&longs;e, &longs;piraret enim <expan abbr="vtiq;">vtique</expan> aliquis <lb/>ab eo, in quo M. hoc enim illi e&longs;t &longs;ecundum diametrum; <expan abbr="neq;">neque</expan> Tra&longs;ci&aelig; ab N, enim, <lb/>quod punctum per diametrum aduer&longs;um illi e&longs;t, &longs;piraret. </s>
5361 
5362 <s>Ni&longs;i ab eo veniat, qui ta&shy;<lb/>men non long&egrave; progreditur ventus quidam, quem accol&aelig; Ph&aelig;niciam vocant. </s>
5363 
5364 <s>maxi&shy;<lb/>m&egrave; igitur pr&aelig;cipui, &amp; definiti venti hi &longs;unt: <expan abbr="hoc&qacute;">hocque</expan>, modo di&longs;po&longs;iti)<emph.end type="italics"/> &longs;upradicta por&shy;<lb/>r&ograve; omnia ex &longs;equenti figura optim&egrave; poterunt intelligi, quam diligenti ope&shy;<lb/>ra ad mentem Ari&longs;t. 
5365 
5366 ex gr&aelig;cis codicibus re&longs;tituere conatus &longs;um, cum ani&shy;<lb/>maduerterem figuras val d&egrave; deprauatas pa&longs;&longs;im apud <expan abbr="c&otilde;mentatores">commentatores</expan> reperiri. <lb/></s>
5367 
5368 <s>Porr&ograve; ad literam M, in figura &longs;crip&longs;i ventum Libonotum, quem Ari&longs;t. 
5369 
5370 qui&shy;<lb/>dem non ponit propter ip&longs;ius paruitatem; im&ograve; apert&egrave; dicit Hele&longs;pontum <lb/>non habere contrarium: &longs;ed feci, vt completum ventorum numerum, quem <lb/>alij tradunt, haberemus.</s></p></chap><chap><p type="head">
5371 
5372 <s><emph type="italics"/>Ex Tertio Meteororum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
5373 
5374 <s><arrow.to.target n="marg161"/></s></p><p type="margin">
5375 
5376 <s><margin.target id="marg161"/>160.b</s></p><p type="main">
5377 
5378 <s>Antequam textuum explicationem aggrediar, illud animaduerten <lb/>dum e&longs;t, <expan abbr="vbicunq;">vbicunque</expan> interpretatio antiqua vtitur verbis, refractio, <lb/>&amp; refrangere; ibi Vicomercatum in &longs;ua interpretatione merit&ograve;, <lb/>&amp; propri&egrave; v&longs;um e&longs;&longs;e verbis; reflexio, &amp; reflecti: differunt enim <lb/>vald&egrave; apud Opticos refractio, &amp; reflexio, vt etiam refrangere, &amp; reflectere. <lb/></s>
5379 
5380 <s>propterea optim&egrave; hoc loco Olympiodorus di&longs;tinguit inter <foreign lang="greek">anaxlasin, xai <lb/>diaxlasin,</foreign> reflexionem, &amp; refractionem. </s>
5381 
5382 <s>Reflexio enim fit ex repercu&longs;&longs;o, vt <lb/>quando lumen Solis incidens in aliquod &longs;peculum, inde re&longs;ilit in oppo&longs;itum <lb/>parietem, illud re&longs;ilire e&longs;t propri&egrave; per&longs;pectiuis reflecti, vnde reflexio. </s>
5383 
5384 <s>Re&shy;<lb/>fractio autem fit ex tran&longs;pectu: vt quando lapis, qui e&longs;t in aqua, emittit <lb/>fuam &longs;peciem ad oculum, qui e&longs;t in aere, tunc enim, quia &longs;pecies lapidis re&shy;<lb/>pre&longs;entatiua non tendit recta ad oculum, &longs;ed in confinio aqu&aelig;, &amp; aeris fran&shy;<lb/>gitur, dicitur fieri refractio, &amp; refrangi, in refractione igitur requiruntur <lb/>duo media, per qu&aelig; &longs;iat vi&longs;io, qu&aelig; &longs;int diuer&longs;&aelig; den&longs;itatis, vt &longs;unt aqua, &amp; <lb/>aer: vapor, exhalatio, &amp; aer: vitrum, &amp; aer, &amp;c. </s>
5385 
5386 <s>quando igitur videmus <lb/>Solem, aut Lunam per vapores, aut exhalationes fit refractio, quia den&longs;ior <lb/>e&longs;t vapor, &amp; exhalatio, quam aer.</s></p><p type="main">
5387 
5388 <s>Notandum etiam Aream, de qua mox dicam explicari po&longs;&longs;e tam per re&shy;<lb/>flexionem, qu&agrave;m per refractionem: per reflexionem, quia &longs;upponunt Philo&shy;<lb/>&longs;ophi e&longs;&longs;e in acre rorido innumcra &longs;pecula parua inuicem vald&egrave; proxima, <lb/>ide&longs;t guttulas, per quas re&longs;lectatur ad oculum no&longs;trum &longs;pecies &longs;yderis. </s>
5389 
5390 <s>per <lb/>re&longs;ractionem ver&ograve;, vt vult Vitellio, quia &longs;umit totum illum aerem humi&shy;<lb/>dum magis den&longs;um e&longs;&longs;e aere paro, qui e&longs;t circa oculos no&longs;tros, &amp; hoc modo <lb/>con&longs;tituit diucr&longs;a media in den&longs;itate, per quam fiat vi&longs;io; corpus inquam <pb pagenum="114"/>illud humidum den&longs;ius, &amp; aerem deinde circa oculum rarius. </s>
5391 
5392 <s>Vicomerca&shy;<lb/>tus igitur quamuis vtatur voce reflexionis in Halone, non tamen ex pr&aelig;di&shy;<lb/>ctis videtur reprchenden dus.</s></p><p type="main">
5393 
5394 <s><arrow.to.target n="marg162"/></s></p><p type="margin">
5395 
5396 <s><margin.target id="marg162"/>161</s></p><p type="main">
5397 
5398 <s>Summ&aelig; 2. cap. 
5399 
5400 2. De Are&aelig; figura <emph type="italics"/>(Refrangitur autem &agrave; con&longs;i&longs;tente caligine <lb/>circa Solem, aut Lunam vi&longs;us; quapropter non ex oppo&longs;ito &longs;icut iris, apparet. </s>
5401 
5402 <s><expan abbr="Vn-diq;">Vn&shy;<lb/>dique</expan> autem &longs;imiliter refracto, nece&longs;&longs;e e&longs;t circulum e&longs;&longs;e, aut circuli partem. </s>
5403 
5404 <s>ab co&shy;<lb/>dem enim &longs;igno ad idem &longs;ignum &aelig;quales frangentur &longs;uper circuli lineam &longs;emper. </s>
5405 
5406 <s>&longs;it<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.114.1.tif"/><lb/><emph type="italics"/>enim &agrave; puncto, in quo A, ad B, fracta, &amp; ea, qu&aelig; est <lb/>A C B, &amp; qu&aelig; A F B, &amp; qu&aelig; A D B, &aelig;quales autem <lb/>&amp; h&aelig; A C, A F, A D, inuiccm. </s>
5407 
5408 <s>&amp; qu&aelig; ad B, inui&shy;<lb/>cem &longs;cilicet C B, E B, D B. &amp; protrahatur A E B, <lb/>quare trianguli &aelig;quales, etenim &longs;uper &aelig;qualem, qu&aelig; <lb/>e&longs;t A E B, ducantur autem <expan abbr="perp&etilde;diculares">perpendiculares</expan> ad A E B, <lb/>ex angulis; &agrave; C, quidem, qu&aelig; e&longs;t C E; ab F, autem, <lb/>qu&aelig; e&longs;t F E; &agrave; D, autem, qu&aelig; e&longs;t D E, &aelig;quales itaque <lb/>h&aelig;, in &aelig;qualibus enim tri&abreve;gulis, &amp; in vno plano om&shy;<lb/>nes, ad rectum emm omnes ei, qu&aelig; e&longs;t A E B. &amp; ad <lb/>vnum punctum E, copulantur, circulus igitur erit <lb/>de&longs;cripta, centrum autem E. &longs;it autem B, quidem Sol, <lb/>A, autem vi&longs;us, qu&aelig; autem e&longs;t circa C D F, circun&shy;<lb/>ferentia nubes, &agrave; qua refrangitur vi&longs;us ad Solem)<emph.end type="italics"/><lb/>quia &longs;uppono Aream, &longs;iue Halonem fieri per re&shy;<lb/>fractionem, vt vult etiam Vitellio, propterea <lb/><expan abbr="pr&aelig;mitt&etilde;dum">pr&aelig;mittendum</expan> e&longs;t principium quoddam, quo tra&shy;<lb/>ctatio de refractione innititur; e&longs;t autem huiu&longs;&shy;<lb/>modi; ea, qu&aelig; <expan abbr="vid&etilde;tur">videntur</expan> per refractionem, &longs;iue &longs;ub <lb/>aliquo refractionis angulo, manentibus nobis &amp; <lb/>a&longs;tro, &amp; medio ij&longs;dem in locis, non po&longs;&longs;unt vide&shy;<lb/>ri &longs;ub diuer&longs;o angulo &agrave; priori, nec per con&longs;e<expan abbr="qu&etilde;s">quens</expan> <lb/>alibi apparere. </s>
5409 
5410 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->Sol (vt in pr&aelig;&longs;enti figura) <lb/>videatur ab oculo A, media nube C D F, &longs;ub an&shy;<lb/>gulo refractionis B C A, vel B F A, &amp; alijs &longs;imilibus angulis in eadem nube; <lb/>manente igitur oculo A, &amp; a&longs;tro B, necnon nube C D E. eodem in loco, im&shy;<lb/>po&longs;&longs;ibile e&longs;t Solem videri ab eodem oculo &longs;ub diuer&longs;o angulo &agrave; priori, nec <lb/>con&longs;equenter alibi apparere, quam in B. <!-- KEEP S--></s>
5411 
5412 
5413 
5414 
5415 
5416 <s>Nunc ad textus declarationem, in <lb/>quo continetur Geometrica demon&longs;tratio rotunditatis Are&aelig;, quam &longs;ic bre&shy;<lb/>uiter prius veteres excogitarunt: Viderunt prim&ograve; Solem in Area apparere <lb/>in orbem, &amp; con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/>con&longs;imiles, &longs;iue &aelig;quales refractionis angulos; quia diuer&longs;i anguli, diuer&longs;am <lb/>etiam <expan abbr="appar&etilde;tiam">apparentiam</expan> efficiunt: atqui con&longs;imiles, &longs;iue &aelig;quales refractionis an&shy;<lb/>gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun&shy;<lb/>ditatis huius, e&longs;t angulorum refractionis &aelig;qualitas. </s>
5417 
5418 <s>Sed iam textum Ari&longs;t. <lb/>qui geometricam huius rci continet demon&longs;trationem, explicemus. </s>
5419 
5420 <s>Suppo&shy;<lb/>nit igitur prim&ograve; Ari&longs;t. 
5421 
5422 lineas vi&longs;uales &agrave; &longs;ydere B, ad oculos no&longs;tros A, per <lb/>nubem roridam C D F, procedentes, in nube con&longs;imiliter refrangi, ide&longs;t <expan abbr="vn-diq;">vn&shy;<lb/>dique</expan> circa Solem, Lunamu&egrave; facere angulos refractionis &aelig;quales. </s>
5423 
5424 <s>quod etiam <pb pagenum="115"/>patet ex 48. 10. Vitellionis; vt in figura, in qua &longs;ydus B, oculus A, nubes <lb/>C D F, radij vi&longs;uales tres refracti in nube &longs;int B C A, B D A, B E A, facien&shy;<lb/>tes con&longs;imilem refractionem, ide&longs;t angulos refractos B C A, B D A, B E A, <lb/>&aelig;quales in punctis C, D, F: <expan abbr="atq;">atque</expan> hoc e&longs;t con&longs;imilem facere refractionem. <lb/></s>
5425 
5426 <s>Supponit &longs;ecund&ograve; lineas &agrave; &longs;ydere ad nubem, v&longs;que exten&longs;as e&longs;&longs;e &aelig;quales, vt <lb/>&longs;unt B C, B D, B F: &longs;imiliter reliquas tres &agrave; nube ad vi&longs;um A. pares e&longs;&longs;e C A, <lb/>D A, F A. his &longs;uppo&longs;itis, &longs;i deinde protrahatur recta A B, ab oculo ad &longs;ydus, <lb/>exurgunt tria triangula omnin&ograve; &aelig;qualia, &amp; &longs;imilia, cuni duo latera vnius <lb/>&longs;int &aelig;qualia duobus alterius <expan abbr="vtrunq;">vtrunque</expan> vtrique, &amp; angulus angulo, &amp; pr&aelig;terea <lb/>ba&longs;is &longs;it communis; ide&ograve; per quartam primi &longs;unt omnin&ograve; &aelig;qualia. </s>
5427 
5428 <s>ducan&shy;<lb/>tur nunc ex angulis C, D, F, tres perpendiculares ad rectam A B, qu&aelig; &longs;int <lb/>C E, D E, F E, in figura; qu&aelig; tres nece&longs;&longs;ari&ograve; erunt &aelig;quales, cum &longs;int duct&aelig; <lb/>ab angulis &aelig;qualibus &aelig;qualium triangulorum ad communem ba&longs;im, &amp; di&shy;<lb/>uident nece&longs;&longs;ari&ograve; ba&longs;im in eodem puncto E, cum diuidant triangula &aelig;qua&shy;<lb/>lia proportionaliter; <expan abbr="erunt&qacute;">eruntque</expan>; propterea h&aelig; tres rect&aelig; in eodem plano, quod <lb/>in nube concipitur ex 5. 11. Quare &longs;i concipiamus &longs;uperficiem, &longs;iue planum <lb/>delineari circa E, ad interuallum linearum &aelig;qualium C E, D E, F E, de&shy;<lb/>&longs;criptus erit circulus per 9. tertij, cuius circumferentia C D F. <!-- KEEP S--></s>
5429 
5430 <s>Ex quibus <lb/>patet tria illa puncta C, D, E, per qu&aelig; Sol tran&longs;paret e&longs;&longs;e in orbem di&longs;po&longs;i&shy;<lb/>ta. </s>
5431 
5432 <s>cau&longs;a igitur rotunditatis Are&aelig;, e&longs;t &longs;imilitudo angulorum refractionis, <lb/>quibus Sol tran&longs;paret: vel ideo rotunda e&longs;t, quia &longs;imiles anguli nece&longs;&longs;ari&ograve; <lb/>in orbem con&longs;tituuntur, vt o&longs;ten&longs;um e&longs;t. </s>
5433 
5434 <s>Eadem ratione omnia alia puncta <lb/>eiu&longs;dem <expan abbr="circ&utilde;ferenti&aelig;">circunferenti&aelig;</expan> &longs;unt puncta, per qu&aelig; Sol videtur refract&egrave;; &amp; hoc mo&shy;<lb/>do ad &longs;imilitudinem trium linearum A C B, A D B, A F B, refractarum, in&shy;<lb/>finit&aelig; <expan abbr="vndiq;">vndique</expan> intelligend&aelig; &longs;unt, quarum ali&aelig; refrangantur in circunferentia <lb/>pr&aelig;dicta, ali&aelig; ver&ograve; in alia periph&aelig;ria maiori, ali&aelig; etiam in minori, ita vt <lb/>ex tota nube fiant refractiones circulares plurim&aelig;, ex quibus in nube area <lb/>con&longs;tituatur. </s>
5435 
5436 <s><expan abbr="Atq;">Atque</expan> h&aelig;c cur Halonis figura orbicularis videatur, rationem <lb/>reddunt, <expan abbr="vna&qacute;">vnaque</expan>; textui lucem afferunt.</s></p><p type="head">
5437 
5438 <s><emph type="italics"/>Summ&aelig; 2. cap. 
5439 
5440 4. De Iridis figura.<emph.end type="italics"/></s></p><p type="main">
5441 
5442 <s><arrow.to.target n="marg163"/></s></p><p type="margin">
5443 
5444 <s><margin.target id="marg163"/>162</s></p><p type="main">
5445 
5446 <s><emph type="italics"/>Qvod autem <expan abbr="neq;">neque</expan> circulum po&longs;&longs;ibile &longs;it fieri Iridis, <expan abbr="neq;">neque</expan> maiorem &longs;emicir&shy;<lb/>culo portionem, &amp; de alijs accidentibus circa ip&longs;am, ex de&longs;criptione <lb/>erit con&longs;iderantibus manife&longs;tum)<emph.end type="italics"/> In Logicis &longs;&aelig;pius monui Ari&longs;t. 
5447 
5448 per <lb/>de&longs;criptiones intelligere geometricas demon&longs;trationes, quod <lb/>etiam hoc loco confirmatur, vbi Geometrica demon&longs;tratione quam de&longs;cri&shy;<lb/>ptionem appellat, Iridis figur&aelig; accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/>circularis, nunquam tamen circulus integer, im&ograve; <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/>maior, &longs;ed tamen &longs;emicirculo minor.</s></p><p type="main">
5449 
5450 <s><arrow.to.target n="marg164"/></s></p><p type="margin">
5451 
5452 <s><margin.target id="marg164"/>163</s></p><p type="main">
5453 
5454 <s>Ibidem <emph type="italics"/>(Hemi&longs;pberio enim exi&longs;t exte &longs;uper horizontis circulum in quo A. cen&shy;<lb/>tro autem K, alio autem quodam oriente puncto, in quo G, &longs;i line&aelig;, qu&aelig; &agrave; K, &longs;ecun&shy;<lb/>dum conum excidentes faciant velut axem lineam in qua G K, &amp; &agrave; K. ad M, co&shy;<lb/>pulat&aelig; refrangantur ab hemi&longs;ph&aelig;rio ad G, &longs;uper maiorem angulum, circuli circun&shy;<lb/>ferentiam incident line&aelig;, qu&aelig; &agrave; K, &amp; &longs;i quidem in ortu, aut in occa&longs;u a&longs;tri reflexio <lb/>fiat, &longs;emicirculus ab <expan abbr="horiz&otilde;te">horizonte</expan> a&longs;&longs;umetur &longs;uper terram factus. </s>
5455 
5456 <s>&longs;i autem &longs;upra, minor<emph.end type="italics"/><pb pagenum="116"/><figure place="text" xlink:href="figures-la/009.01.116.1.tif"/><lb/><emph type="italics"/>&longs;emper &longs;emicirculo, minus autem, <lb/>cum in meridie fuerit a&longs;trum)<emph.end type="italics"/> quod <lb/>&longs;upra monui, iterum moneo, <expan abbr="re-tin&etilde;dam">re&shy;<lb/>tinendam</expan> vocem reflexionis, <expan abbr="qu&atilde;-uis">quan&shy;<lb/>uis</expan> in antiqua tran&longs;latione lega&shy;<lb/>tur refractio, e&longs;t enim apud om&shy;<lb/>nes in confe&longs;&longs;o Iridem fieri per <lb/>reflexionem. </s>
5457 
5458 <s>E&longs;t igitur in &longs;upe&shy;<lb/>riori figura, quam textui, vt par <lb/>erat re&longs;titui, horizon G K O. cuius centrum K. in quo e&longs;t vi&longs;us no&longs;ter, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; <lb/>hemi&longs;ph&aelig;rium no&longs;trum in arcu G A M O, repr&aelig;&longs;entatum, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; nubes rori&shy;<lb/>da, in qua Iris appareat, vbi M, quod punctum M, nubem referens, in figu&shy;<lb/>ra ponitur in hemi&longs;ph&aelig;rij ambitu, quod c&oelig;lum repr&aelig;&longs;entat, cum tamen <lb/>nubes parum &agrave; terra &longs;ubuchatur; id enim ad demon&longs;trationem fer&egrave; perinde <lb/>e&longs;t. </s>
5459 
5460 <s>in oriente G, &longs;it a&longs;trum. </s>
5461 
5462 <s>&longs;i erg&ograve; line&aelig; vi&longs;uales &agrave; K, ad M, nubem tenden&shy;<lb/>tes reflectantur &longs;uper maiorem angulum M K G, ad G, erit reflexarum vna <lb/>veluti M G. <!-- KEEP S--></s>
5463 
5464 <s>Porro omnes line&aelig; viluales, qu&aelig; adnubem M, incidunt, nece&longs;&shy;<lb/>&longs;ari&ograve;, vt probabo, cadent in ambitum circularem. </s>
5465 
5466 <s>debemus enim innume&shy;<lb/>ras lineas im aginari &agrave; K, in coni figuram excidentes, cuius vertex &longs;it in K, <lb/>&amp; axis G K O, quas omnes repr&aelig;&longs;entat vna K M, <expan abbr="melius&qacute;">meliusque</expan>; repr&aelig;&longs;entabit, fi <lb/>cogitemus axem G K O, circa polos G, O, manentes circumuolui, <expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; <lb/>lineam K M, circumducere. </s>
5467 
5468 <s>in hac etiam giratione linea K M, tran&longs;ibit per <lb/>omnes illas lineas, quas imaginabamur; <expan abbr="de&longs;cribet&qacute;">de&longs;cribetque</expan>; conum, quem ill&aelig; con&shy;<lb/>formare debebant. </s>
5469 
5470 <s>In pr&aelig;dicta autem axis volutatione, extremum M, li&shy;<lb/>ne&aelig; K M, nece&longs;&longs;ari&ograve; de&longs;cribit circulum, qui e&longs;t circulus Iridis, &amp; e&longs;t ba&longs;is <lb/>memorati coni.</s></p><p type="main">
5471 
5472 <s>Si igitur oriente, vel occidente a&longs;tro fiat iris, Iris erit &longs;emicirculus, ide&longs;t <lb/>illa &longs;emi&longs;&longs;is circuli pr&ecedil;dicti (quem horizon bifariam diuidit) qu&aelig; &longs;upra ter&shy;<lb/>ram extabit. </s>
5473 
5474 <s>&longs;i autem a&longs;trum eleuatum &longs;upra horizontem fuerit, quando fit <lb/>iris, erit &longs;emper arcus Iridis &longs;emicirculo minor; <expan abbr="tunc&qacute;">tuncque</expan>; minimus <expan abbr="c&utilde;">cum</expan> a&longs;trum <lb/><expan abbr="meridian&utilde;">meridianum</expan> <expan abbr="circul&utilde;">circulum</expan> occupauerit. </s>
5475 
5476 <s>h&ecedil;c tria &longs;unt, qu&aelig; deinceps <expan abbr="prob&atilde;da">probanda</expan> recipit.</s></p><p type="main">
5477 
5478 <s><arrow.to.target n="marg165"/></s></p><p type="margin">
5479 
5480 <s><margin.target id="marg165"/>264</s></p><figure place="text" xlink:href="figures-la/009.01.116.2.tif"/><p type="main">
5481 
5482 <s>Ibidem <emph type="italics"/>(Sit enim in <expan abbr="ori&etilde;te">oriente</expan> pri&shy;<lb/>mum vbi G, &amp; refracta &longs;it K M, <lb/>ad G, &amp; planum erectum &longs;it in quo <lb/>A, &agrave; triangulo in quo G K M, cir&shy;<lb/>culus igitur erit &longs;ectio &longs;ph&aelig;r&aelig;, qui <lb/>maximus &longs;it in quo A, differet enim <lb/>mbil &longs;i quodc<expan abbr="&ubreve;q;">&ubreve;que</expan> eorum, qu&aelig; &longs;uper <lb/>G K, &longs;ecundum triangul&ubreve; K M G, <lb/>erectum fuerit planum. </s>
5483 
5484 <s>line&aelig; igitur <lb/>ab ijs, qu&aelig; G, K, duct&aelig; in bac ratio&shy;<lb/>ne non cen&longs;tituentur ad aliud, &amp; <lb/>aliud punctum, qu&agrave;m &longs;emicirculi <lb/>in quo A. <!-- KEEP S--></s>
5485 
5486 <s>Quoniam enim puncta <lb/>G, K, data &longs;unt, &amp; qu&aelig; K M, vtique data erit; &amp; qu&aelig; M G, ad M K; datam igi&shy;<lb/>tur circunferentiam tanget M, fit <expan abbr="itaq;">itaque</expan> b&aelig;c in qua M N, quare &longs;ectio circunferen-<emph.end type="italics"/><pb pagenum="117"/><emph type="italics"/>tiarum data e&longs;t. </s>
5487 
5488 <s>apud autem aliud punctum, quam ip&longs;ius M N, circunferenti&aelig;, ab <lb/>ij&longs;dem punctis, eadem ratio in eodem plano non con&longs;i&longs;tit)<emph.end type="italics"/> eorum omnium, qu&aelig; <lb/>demon&longs;tranda &longs;unt, pr&aelig;mittenda &longs;unt duo nece&longs;&longs;aria fundamenta. </s>
5489 
5490 <s>Primum <lb/>e&longs;t; ea, qu&aelig; videmus per reflexionem &longs;ub quopiam angulo, manentibus no&shy;<lb/>bis &longs;peculo, &amp; obiecto ij&longs;dem in locis, non po&longs;&longs;unt videri &longs;ub alio diuer&longs;o <lb/>angulo, nec alibi con&longs;equenter apparere. </s>
5491 
5492 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->in &longs;uperiori figura, quam <lb/>textui re&longs;tituimus exi&longs;tente Sole in G, oculo in K, &amp; nube in M. ex qua ra&shy;<lb/>dius Solis G M, re&longs;lectatur ad vi&longs;um in K, per <expan abbr="line&atilde;">lineam</expan> M K, &longs;ub angulo G M K, <lb/>impo&longs;&longs;ibile e&longs;t manentibus illis, vt dixi, videri Solem in nube M, &longs;ub diuer&shy;<lb/>&longs;o angulo &agrave; priori, nec alibi apparere. </s>
5493 
5494 
5495 
5496 
5497 
5498 <s>Alterum e&longs;t apud Opticos vulga&shy;<lb/>tum; ea &longs;cilicet, qu&aelig; per reflexionem (de quorum numero e&longs;t Iris) viden&shy;<lb/>tur, videri, tunc &longs;olum, quando angulus incidenti&aelig; fuerit &aelig;qualis angulo <lb/>reflexionis, quia tunc breui&longs;&longs;imis lineis fit vi&longs;io; quibus &longs;oli, natura (&longs;i fieri <lb/><figure place="text" xlink:href="figures-la/009.01.117.1.tif"/><lb/>pote&longs;t) vtitur. </s>
5499 
5500 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->in figura pr&aelig;&longs;enti &longs;it &longs;pe&shy;<lb/>culum C D E, obiectum A, oculus B, linea in&shy;<lb/>cidenti&aelig; e&longs;t A D, &amp; angulus pariter inciden&shy;<lb/>ti&aelig; e&longs;t A D C. linea ver&ograve; D B, e&longs;t linea refle&shy;<lb/>xionis, &amp; angulus pariter reflexionis e&longs;t B D&shy;<lb/>E, qui duo anguli ni&longs;i fuerint &aelig;quales, nun&shy;<lb/>quam videbitur obiectum A, ab oculo B, hinc <lb/>e&longs;t, quod aliquando po&longs;ito &longs;peculo, obiectum <lb/>quamuis illi aduer&longs;um, &agrave; nobis pariter ante <lb/>&longs;peculum con&longs;titutis, videri nequit, quia &longs;ci&shy;<lb/>licet in tali po&longs;itione &longs;peculi, obiecti, &amp; no&longs;tri, nulla linea incidenti&aelig;, ide&longs;t, <lb/>qu&aelig; ab obiecto in &longs;peculum tendit, facere pote&longs;t angulum cum &longs;peculo, qui <lb/>dicitur angulus incidenti&aelig;, &aelig;qualem angulo illi, quem facit linea eadem re&shy;<lb/>flexa &agrave; &longs;peculo ad oculum, quem dicunt angulum re&longs;lexionis. </s>
5501 
5502 
5503 
5504 
5505 
5506 <s>Cum ergo in <lb/>Iride videamus colorem Solis per reflexionem, tunc &longs;olum apparebit Iris, <lb/>quando Sol, nubes, &amp; oculus fuerint in ea con&longs;titutione, qua radius <expan abbr="incid&etilde;s">incidens</expan> <lb/>nubi, &amp; radius &agrave; nube repercu&longs;&longs;us faciant pares angulos. </s>
5507 
5508 <s>Et quia quando <lb/>nubes ro&longs;cida perpendiculariter opponitur Soli, &amp; nobis, po&longs;&longs;unt &longs;ieri pr&aelig;&shy;<lb/>dicti anguli &aelig;quales non in vno loco nubis, &longs;ed in pluribus, con&longs;titutis ta&shy;<lb/>men in circuli periph&aelig;ria, hinc fit, quod Solis color reflectatur ex pluribus <lb/>locis in orbem con&longs;titutis, qu&aelig; reflexio e&longs;t ip&longs;ius Iridis arcus. </s>
5509 
5510 <s>ex Vitellion <lb/>63. 10. Totam autem figur&aelig; Iridis demon&longs;trationem &longs;ic breuiter puto ad&shy;<lb/>inuentam e&longs;&longs;e. </s>
5511 
5512 <s>cum Sol in Iride videatur in orbem, <expan abbr="atq;">atque</expan> con&longs;imiliter, ne ce&longs;&shy;<lb/>&longs;e e&longs;t id prouenire ex angulis reflexionum con&longs;imilibus, &longs;iue &aelig;qualibus: di&longs;&shy;<lb/>&longs;imiles enim anguli, di&longs;&longs;imilem <expan abbr="vtiq;">vtique</expan> efficiunt Solis <expan abbr="appar&etilde;tiam">apparentiam</expan>. </s>
5513 
5514 <s>atqui con&shy;<lb/>&longs;imiles anguli, &longs;iue &aelig;quales, non ni&longs;i in orbem po&longs;&longs;unt con&longs;titui; igitur an&shy;<lb/>gulorum &aelig;qualitas cau&longs;a erit rotundationis arcus. </s>
5515 
5516 <s>h&ecedil;c e&longs;t &longs;umma totius di&shy;<lb/>&longs;cur&longs;us, quem pluribus, &amp; nimis ob&longs;cur&egrave; Ari&longs;t. 
5517 
5518 explicat.</s></p><p type="main">
5519 
5520 <s>Inquit igitur Ari&longs;t. &longs;it enim in oriente, &amp;c. </s>
5521 
5522 <s>vbi aggreditur probare vnum <lb/>ex tribus illis, qu&aelig; &longs;upra propo&longs;uit, nimirum tunc Iridem e&longs;&longs;e &longs;emicircu&shy;<lb/>lum, quando a&longs;trum fuerit in oriente, &longs;iue in horizonte, vbi G. &longs;i igitur per <lb/>triangulum G M K, intelligamus <expan abbr="plan&utilde;">planum</expan> exten&longs;um, in quo A, in figura, adeo <lb/>magnum, vt totum &longs;ecet hemi&longs;ph&aelig;rium, faciet in &longs;uperficie hemi&longs;ph&aelig;rij &longs;e&shy;<pb pagenum="118"/>ctionem, qu&aelig; erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e&shy;<lb/>cans hemi&longs;ph&aelig;rium, tran&longs;eat per <expan abbr="centr&utilde;">centrum</expan> ip&longs;ius, qu&aelig; &longs;ectio, &longs;iue circuli por&shy;<lb/>tio repr&aelig;&longs;entatur in figura, per &longs;emicirculum in quo A, &longs;iue in quo G A M&shy;<lb/>R O. nihil autem refert quodcunque intelligas planum &longs;uper axem G K O, <lb/>tran&longs;iens &longs;iue per triangulum G K M, &longs;iue per aliud illi &longs;imile. </s>
5523 
5524 <s>Pr&aelig;mitten&shy;<lb/>dum pr&aelig;terea non po&longs;&longs;e in &longs;emicirculo &longs;uperiori, quod e&longs;t planum, &amp; &longs;ectio <lb/>trianguli G K M, poni alias duas lineas. </s>
5525 
5526 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->G R, K R, ad aliud punctum, <lb/>vti e&longs;t R, qu&aelig; habeant eandem inuicem proportionem, quam habent prio&shy;<lb/>res du&aelig; G M, K M, quod probatur, quia &longs;i &longs;int vt G M, ad K M, ita G R, ad <lb/>K R, cum G R, &longs;it centro K, propinquior quam G M, erit etiam eadem G R, <lb/>longior ip&longs;a G M, per 15. 3. &amp; tamen deberet e&longs;&longs;e &aelig;qualis illi; quemadmo&shy;<lb/>dum K M, e&longs;t &aelig;qualis alteri K R; nequeunt autem du&aelig; line&aelig; in&aelig;quales inui&shy;<lb/>cem, habere eandem rationem ad duas inuicem &aelig;quales: ergo non habent <lb/>eandem rationem G M, &amp; K M, quam habent G R, &amp; K R. quod &longs;i punctum <lb/>R, &longs;umatur &longs;upra M, erit &longs;imilis <expan abbr="dem&otilde;&longs;tratio">demon&longs;tratio</expan>, &longs;i liter&aelig; M, &amp; R, loca permu&shy;<lb/>tent. </s>
5527 
5528 
5529 
5530 
5531 
5532 <s>his po&longs;itis, ait <emph type="italics"/>(Quoniam enim G, K, puncta data &longs;unt, &amp; c.)<emph.end type="italics"/> ide&longs;t data <lb/>&longs;unt po&longs;itione, cum notum &longs;it vbi &longs;int. </s>
5533 
5534 <s>G, enim e&longs;t in ortu. </s>
5535 
5536 <s>K, ver&ograve; in centro <lb/>horizontis, &longs;equitur, quod etiam linea G K, cuins ip&longs;a &longs;unt extrema, data <lb/>&longs;it, &amp; po&longs;itione, &amp; magnitudine, per 26. Datorum Euclidis. <!-- KEEP S--></s>
5537 
5538 <s>eadem quoque <lb/>ratione data erit K M, linea; &longs;iue quia e&longs;t &aelig;qualis ip&longs;i G K, &longs;iue quia per <lb/>a&longs;trolabium po&longs;&longs;umus ip&longs;ius longitudinem, &amp; po&longs;itionem inue&longs;tigare; qua&shy;<lb/>re &amp; punctum M, datum erit per 27. Datorum, quare &amp; linea G M, data <lb/>erit quoad &longs;itum, &amp; magnitudinem per 26. Datorum. <!-- KEEP S--></s>
5539 
5540 <s>Quare per primam <lb/>Datorum erit data proportio linearum G M, M K, punctum <expan abbr="itaq;">itaque</expan> M, tange t <lb/>ambitum datum, qui ba&longs;is e&longs;t coni, quem linea K M, de&longs;cribit in reuolutio&shy;<lb/>ne axis G K O, &longs;uper polis G, O. cum enim data &longs;it K M, po&longs;itu, &amp; magni&shy;<lb/>tudine, <expan abbr="ea&qacute;">eaque</expan>; &longs;it latus pr&aelig;dicti coni, &longs;equitur periph&aelig;riam, vel ambitum ba&shy;<lb/>&longs;is coni e&longs;&longs;e datum per &longs;imilem definitionem 5. definitioni Datorum. <!-- KEEP S--></s>
5541 
5542 <s>&longs;it <expan abbr="au-t&etilde;">au&shy;<lb/>tem</expan> ambitus ille in figura &longs;equenti notatus literis L M N. qui ambitus L M N, <lb/>non e&longs;t <expan abbr="concipi&etilde;dus">concipiendus</expan> in eodem plano &longs;emicirculi G A N O, quemadmodum <lb/>fals&ograve; pingitur in figura; &longs;ed debemus ip&longs;um concipere tanquam erectum ad <lb/>angulos rectos cum pr&aelig;dicto &longs;emicirculo, necnon cum horizonte G K O. <lb/><!-- KEEP S--></s>
5543 
5544 <s>Iam &longs;i <expan abbr="tri&atilde;gulum">triangulum</expan> G M K, prioris figur&aelig; circumuoluatur circa axem G K O, <lb/>punctum ip&longs;ius M, de&longs;cribit pr&aelig;dictum ambitum L M N. hunc ambitum <lb/>inquit Ariltot. <!-- REMOVE S-->linea K M, attinger, <expan abbr="erit&qacute;">eritque</expan>; hic ambitus datus, vt dictum e&longs;t. <lb/><figure place="text" xlink:href="figures-la/009.01.118.1.tif"/><lb/>Erit pr&aelig;terea &longs;ectio circunferentiarum ho&shy;<lb/>rizontis, &amp; huius amb tus data, cuius extre&shy;<lb/>ma puncta e&longs;&longs;ent L, &amp; N. &longs;i enim <expan abbr="c&otilde;cipiamus">concipiamus</expan> <lb/>in figura non &longs;olum horizontis diametrum <lb/>G K O, &longs;ed etiam circunferentiam (in qua <lb/>circunferentia e&longs;&longs;ent duo illa puncta L, &amp; N, <lb/>vt in pr&aelig;&longs;enti de&longs;criptione melius intelli ge&shy;<lb/>tur, in qua horizon G N O L, &amp; ambitus <lb/>pr&aelig;dictus e&longs;t L M N, qui debet intelligi ele&shy;<lb/>uatus &longs;upra horizontem perpendiculariter) <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb pagenum="119"/>linea N P L, cuius extrema puncta &longs;unt L, N, qu&aelig; data erunt, cum &longs;int ex&shy;<lb/>trema line&aelig; K M, circumlat&aelig;; &amp; quemadmodum dabatur &longs;uperius punctum <lb/>M. eadem ratione ex Datis, dabitur punctum N, &amp; L. quare etiam &longs;ectio <lb/>N P L, qu&aelig; inter data puncta continetur, data erit ex 26. Datorum.<!-- KEEP S--></s>
5545 
5546 </p><p type="main">
5547 
5548 <s>Illud nunc in memoriam <expan abbr="reuoc&atilde;dum">reuocandum</expan>, quod paul&ograve; ante probaui, nimirum <lb/>proportionem linearum G M, K M, non po&longs;&longs;e &longs;eruari in alijs lineis, qu&aelig; &longs;int <lb/>in eodem plano trianguli G M K, &longs;i ducantur ab ij&longs;dem punctis G, K. pote&longs;t <lb/>tamen &longs;eruari in alijs duabus, qu&aelig; cadant in pr&aelig;dictum ambitum, &longs;iue <expan abbr="cir-cunfer&etilde;tiam">cir&shy;<lb/>cunferentiam</expan> L M N, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; &longs;int in alio plano, <expan abbr="qu&atilde;">quam</expan> in plano trianguli G M K, <lb/>quod tamen tran&longs;eat per axem G K O, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vnum ex planis illis, de quibus <lb/>&longs;upra dictum e&longs;t. </s>
5549 
5550 <s>Verumenimuer&ograve; ad quid probatio h&aelig;c? </s>
5551 
5552 <s>non po&longs;&longs;e duas <lb/>alias lineas in eodem plano, &amp;c.? exi&longs;timo Ari&longs;t. 
5553 
5554 idcirc&ograve; hoc proba&longs;&longs;e, quia <lb/>&longs;i ali&aelig; du&aelig; line&aelig; habentes eandem rationem, po&longs;&longs;ent collocari in eodem <lb/>plano; e&longs;&longs;ent <expan abbr="permut&atilde;do">permutando</expan> ill&aelig; du&aelig; (in priori figura) G R, R K. <expan abbr="vtraq;">vtraque</expan> <expan abbr="vtriq;">vtrique</expan> <lb/>&aelig;quales prioribus G M, M K, per quas videtur Iris, cum enim K R, &longs;it &aelig;qua&shy;<lb/>lis ip&longs;i K M, erit, &amp; G M, &aelig;qualis ip&longs;i G R, per 7. 5. &amp; in eius &longs;cholio. </s>
5555 
5556 <s>qua&shy;<lb/>re natura ageret tam per lineas breui&longs;&longs;imas <expan abbr="ag&etilde;do">agendo</expan> per has, quam per illas, <lb/><expan abbr="hoc&qacute;">hocque</expan>; pacto perhas etiam Iris videri po&longs;&longs;et. </s>
5557 
5558 <s>cum erg&ograve; con&longs;tet non po&longs;&longs;e has <lb/>e&longs;&longs;e prioribus proportionales, &longs;ed maiorem, vel minorem, alteram illarum, <lb/>qu&agrave;m &longs;it G M, &longs;equitur, quod non faciunt angulum &aelig;qualem angulo G M K, <lb/>&longs;ub quo videtur Iris, <expan abbr="nimir&utilde;">nimirum</expan> angulum G R K, qui &longs;it &aelig;qualis angulo G M K; <lb/>habet enim Iris hunc angulum determinatum, ita vt &longs;ub maiori, vel mino&shy;<lb/>ri videri nequeat; ex 10. Bapti&longs;ta Porta. </s>
5559 
5560 <s>&longs;i autem punctum R, e&longs;&longs;et infra M, <lb/>angulus G R K, e&longs;&longs;et minor angulo Iridis G M K, &longs;i ver&ograve; &longs;upra e&longs;&longs;et maior <lb/>eodem, quod vel ad &longs;en&longs;um patere pote&longs;t in quouis circulo, <expan abbr="id&qacute;">idque</expan>; &longs;ufficiat, ne <lb/>longior euadat h&aelig;c tractatio. </s>
5561 
5562 <s>Fort&egrave; etiam addi pote&longs;t, quod alibi exi&longs;ten&shy;<lb/>te puncto R, qu&agrave;m in M, non po&longs;&longs;ent anguli incidenti&aelig;, &amp; reflexionis e&longs;&longs;e <lb/>&aelig;quales, qu&aelig; cau&longs;a e&longs;&longs;et cur &longs;ub alio angulo, quam pr&aelig;dicto G M K, Iris <lb/>non appareret.</s></p><p type="main">
5563 
5564 <s>Pr&aelig;dicta omnia &longs;unt &longs;ecundum Ari&longs;tot. di&longs;cur&longs;um, &amp; figurationem dicta, <lb/>nam &longs;ecundum veritatem po&longs;&longs;unt in eadem nube con&longs;titui plures anguli <lb/>&aelig;quales, nec tamen in eodem orbe, &longs;ed vnus &longs;upra <expan abbr="alter&utilde;">alterum</expan>; vt in figura pr&aelig;&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.119.1.tif"/><lb/>&longs;enti, &longs;i nubes e&longs;&longs;et vbi B D. <lb/>oculus in C, Sol in A. e&longs;&longs;ent <lb/>duo anguli A B C, A D C, &aelig;&shy;<lb/>quales per 33. 3. qui tamen <lb/>non &longs;unt in gyrum con&longs;tituti, <lb/>po&longs;&longs;et igitur, per <expan abbr="illor&utilde;">illorum</expan> vtrun&shy;<lb/>que Sol Iridem efficere. </s>
5565 
5566 
5567 
5568 <s>atque <lb/>animaduer&longs;io h&ecedil;c videtur ma&shy;<lb/>gni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;&longs;e, ad Iridis <expan abbr="de-mon&longs;tration&etilde;">de&shy;<lb/>mon&longs;trationem</expan> con&longs;tituendam: <lb/>cum hinc v&longs;itat&aelig; demon&longs;tra&shy;<lb/>tiones infringatur. </s>
5569 
5570 <s>Fort&egrave; confu giendum e&longs;t ad illud, quod Maurolycus, &amp; <lb/>10. Bapti&longs;ta Porta ob&longs;eruarunt; debere <expan abbr="nimir&utilde;">nimirum</expan> di&longs;tantiam ab oculo ad cen&shy;<lb/>trum Iridis e&longs;&longs;e &aelig;qualem altitudini, &longs;iue &longs;emidiametro Iridis. </s>
5571 
5572 <s>Ita vt non &longs;o&shy;<pb pagenum="120"/>lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="qu&atilde;ta">quanta</expan> requi&shy;<lb/>ritur vt angulus in orbem con&longs;tituatur, ex quo Iris po&longs;&longs;it apparere. </s>
5573 
5574 <s>h&aelig;c &agrave; <lb/>nemine hactenus animaduer&longs;a placuit addere, vt ex ijs demon&longs;tratio Iridis <lb/>omnibus numeris aliquando ab&longs;olui po&longs;&longs;it, quod infra (ni fallor, fauente <lb/>Deo) pr&aelig;&longs;tabimus.<lb/><arrow.to.target n="marg166"/></s></p><p type="margin">
5575 
5576 <s><margin.target id="marg166"/>165</s></p><p type="main">
5577 
5578 <s>Ibidem <emph type="italics"/>(Extraponatur igitur qu&aelig;dam linea, qu&aelig; D B, &amp; &longs;eindatur vt M G, ad&shy;<lb/>M K, &longs;ic qu&aelig; D, ad B, maior autem qu&aelig; M G, ea qu&agrave;m M K, quoniam &longs;uper ma&shy;<lb/>iorem angulum reflexio coni, maiori enim angulo &longs;ubtenditur trianguli M K G. <lb/><!-- KEEP S--></s>
5579 
5580 <s>Maior igitur e&longs;t &amp; ip&longs;a D, ip&longs;a B. addatur igitur ad eam, qu&aelig; B, ea in qua F, vt <lb/>&longs;it quod D, ad B, qu&aelig; B F, ad D. <!-- KEEP S--></s>
5581 
5582 <s>Deinde quod F, ad K G, qu&aelig; B, ad aliam fiat, <lb/>qu&aelig; K P. &amp; &agrave; P, ad M, copuletur qu&aelig; P M, erit igitur P. polus circuli, ad quem <lb/>line&aelig;, qu&aelig; &agrave; K, incidunt)<emph.end type="italics"/> <expan abbr="hucu&longs;q;">hucu&longs;que</expan> o&longs;tendit lineas vi&longs;uales cadere ad M, pun&shy;<lb/>ctum in Iridis periph&aelig;riam, pergit deinceps inue&longs;tigare polum, &amp; po&longs;tea <lb/>centrum eiu&longs;dem ambitus, vtraque autem exi&longs;tere in horizonte reperit, vt <lb/>hinc inferat Iridis portionem illam, qu&aelig; oriente Sole &longs;upra horizontem ap&shy;<lb/>paret, e&longs;&longs;e &longs;emicirculum, vt propo&longs;uerat. </s>
5583 
5584 <s>Differt autem polus circuli &agrave; cen&shy;<lb/>tro eiu&longs;dem circuli. </s>
5585 
5586 <s>polus e&longs;t punctum extra planum circuli, ex quo tamen <lb/>vt <expan abbr="c&etilde;tro">centro</expan> adhibito circino circuli periph&aelig;ria de&longs;cribi pote&longs;t; &longs;ic polus &aelig;qua&shy;<lb/>toris e&longs;t idem, qui polus mundi: <expan abbr="centr&utilde;">centrum</expan> ver&ograve; e&longs;t in plano &longs;ui cir culi, &longs;ic cen&shy;<lb/>trum &aelig;quatoris e&longs;t idem cum centro mundi, cum &aelig;quator per illud incedat.</s></p><p type="main">
5587 
5588 <s>Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t. 
5589 
5590 cum data &longs;it proportio linearum K M, &amp; M G, in &longs;upe&shy;<lb/>riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.120.1.tif"/><lb/>ponatur alia linea recta B D. qu&aelig; diui&shy;<lb/>datur in partes B, &amp; D. proportionales <lb/>cum lineis K M, G M, per 10. 6. cum <lb/>ergo K M, &longs;it minor qu&agrave;m G M, per 19. <lb/>primi, quia in triangulo G M K, oppo&shy;<lb/>nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor qu&agrave;m D, addatur iam ip&longs;i B. linea <lb/>nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, &amp; D, per 11. 6. <lb/>hoc ordine, vt F B, ad D. ita D, ad B. <!-- KEEP S--></s>
5591 
5592 <s>Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>B, ad aliam, qu&aelig; &longs;it K P, in eadem figura per 12. 6. &amp; &agrave; puncto P, ad M, iun&shy;<lb/>gatur recta P M. <!-- KEEP S--></s>
5593 
5594 <s>Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, &amp; in quem li&shy;<lb/>ne&aelig; &agrave; K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/>in &longs;equentibus.</s></p><p type="main">
5595 
5596 <s><arrow.to.target n="marg167"/></s></p><p type="margin">
5597 
5598 <s><margin.target id="marg167"/>166</s></p><p type="main">
5599 
5600 <s>Ibidem <emph type="italics"/>(Erit etiam, quod qu&aelig; F, ad K G. &amp; qu&aelig; B, ad K P. &amp; qu&aelig; D, ad P M. <lb/>non enim &longs;it, &longs;ed aut ad minorem, aut ad maiorem ea, qu&aelig; P M, nibil emm differet. <lb/></s>
5601 
5602 <s>&longs;it enim ad P R. eandem ergo rationem G K, &amp; K P, &amp; P R, inuicem habebunt, <lb/>quam qu&aelig; F, B, D: qu&aelig; autem F, B, D, proportionales crant, quod quidem D, ad <lb/>B. qu&aelig; F B, ad D: quare quod qu&aelig; P G, ad P R, qu&aelig; P R, ad eam, qu&aelig; P K. &longs;i igi&shy;<lb/>tur ab ijs, qu&aelig; K G, qu&aelig; G R, &amp; K R, ad R, coniungantur, coniunct&aelig; h&aelig; eandem <lb/>habebunt rationem, quam qu&aelig; G P, ad eam, qu&aelig; P R, circa eundem enim angulum <lb/>P, proportion aliter, &amp; qu&aelig; trianguli G P R, &amp; eius, qui K R P. quare &amp; qu&aelig; G R, <lb/>ad eam qu&aelig; K R, eandem rationem habebit, quam &amp; qu&aelig; G P, ad eam qu&aelig; P R, <lb/>habet autem &amp; qu&aelig; M G, ad M K, eam rationem, quam qu&aelig; D, ad eam qu&aelig; B, <lb/>quare amb&aelig; &agrave; punctis G K, non &longs;olum ad circun&longs;erentiam M N, con&longs;tituentur ean&shy;<lb/>aem habentes rationem, &longs;ed &amp; alibi, quod quidem impo&longs;&longs;ibile)<emph.end type="italics"/> incipit, vt dixi, <pb pagenum="121"/>probare P, e&longs;&longs;e polum pr&aelig;dicti ambitus, &longs;ic. </s>
5603 
5604 <s>Prim&ograve; enim &longs;ciendum in pr&aelig;&shy;<lb/>mi&longs;&longs;a con&longs;tructione e&longs;&longs;e, vt F, ad G K, &amp; B, ad K P, ita D, ad P M. nam &longs;i non <lb/>&longs;it eadem ratio D, ad P M, cum alijs pr&aelig;dictis, erit eadem ratio eiu&longs;dem D, <lb/>ad aliam maiorem, vel minorem ipfa P M. &longs;it ad minorem P R. nihil enim <lb/>refert &longs;iue dixeris habere eandem rationem ad minorem, &longs;iue ad maiorem, <lb/>ergo permutando erunt G K, K P, P R, proportionales cum F, B, D. &longs;ed li&shy;<lb/>ne&aelig; F, B, D, erant proportionales <expan abbr="compon&etilde;do">componendo</expan> hoc modo, vt F B, ad D, ita <lb/>D, ad B: quare &longs;imiliter erunt vt G P, ad P R, ita P R, ad P K. per 18. 5. &longs;i igi&shy;<lb/>tur &agrave; punctis G, &amp; K, figur&aelig; nu. </s>
5605 
5606 <s>164. <expan abbr="iung&atilde;tur">iungantur</expan> line&aelig; ad R, qu&aelig; &longs;int G R, K R, <lb/>erit vt G R, ad K R, ita G P, ad P R. quia orta <expan abbr="s&utilde;t">sunt</expan> duo <expan abbr="tri&atilde;gula">triangula</expan> G P R, K P R, <lb/>qu&aelig; habent eundem angulum ad P. &amp; latera proportionalia circa dictum <lb/>angulum. </s>
5607 
5608 <s>e&longs;t etiam vt G P, ad P R, in maiori triangulo, ita P R, ad K P, in <lb/>minori, ex con&longs;tructione, quare per 6. 6. erunt illa duo triangula &aelig;quian&shy;<lb/>gula; erg&ograve; per 4. 6. erunt latera circum &aelig;quales angulos proportionalia; <lb/>quare erit vt G P, ad P R. ita G R, ad R K: erat autem vt K M, ad G M, ita <lb/>B, ad D. &amp; ita etiam G P, ad P R; erg&ograve; per 11. 5. vt K M, ad M G. ita K R, <lb/>ad R G, intra eandem circunferentiam, &amp; in eodem plano: quod e&longs;&longs;e im&shy;<lb/>po&longs;&longs;ibile &longs;upra o&longs;tendimus, hoc autem impo&longs;&longs;ibile, &longs;equitur &longs;i neges e&longs;&longs;e vt <lb/>F, ad G K; &amp; B, ad K P, ita D, ad P M.<!-- KEEP S--></s></p><p type="main">
5609 
5610 <s><arrow.to.target n="marg168"/></s></p><p type="margin">
5611 
5612 <s><margin.target id="marg168"/>167</s></p><p type="main">
5613 
5614 <s>Ibidem <emph type="italics"/>(Quoni&abreve; igitur qu&aelig; D, <expan abbr="neq;">neque</expan> ad minorem ea, qu&aelig; P M, <expan abbr="neq;">neque</expan> ad maiorem <lb/>(&longs;imiliter enim demon&longs;ir abimus) palam e&longs;t, quod ad ip&longs;am <expan abbr="vtiq;">vtique</expan> erit, in qua P M, <lb/>quare erit, quod qu&aelig; M P, ad P K, qu&aelig; P G, ad M P. <!-- KEEP S--></s>
5615 
5616 <s>Si igitur eo in quo P, polo <lb/>vtens, di&longs;tantia autem ea, in qua P M, circulns de&longs;cribatur, omnes angulos attin&shy;<lb/>get, quos reflex&aelig; faciunt, qu&aelig; &agrave; K, G. &longs;i autem non, &longs;imiliter o&longs;tendentur eandem <lb/>babere rationem, qu&aelig; alibi, quam in &longs;emicirculo con&longs;tituuntur; quod quidem erat <lb/>impo&longs;&longs;ibile)<emph.end type="italics"/> quoniam igitur, inquit, linea D, <expan abbr="neq;">neque</expan> ad minorem, <expan abbr="neq;">neque</expan> ad ma&shy;<lb/>iorem quam P M, habet eam rationem, qu&aelig; e&longs;t ip&longs;ius F, ad G K, aut ip&longs;ius <lb/>B, ad K P. &longs;imiliter enim demon&longs;tratur ab&longs;urdum &longs;equi. </s>
5617 
5618 <s>pal&agrave;m e&longs;t, quoniam <lb/>erit D, ad P M, vt pr&aelig;dict&aelig; ad pr&aelig;dictas: quare componendo, &amp; permu&shy;<lb/>tando, erunt tandem vt G P, ad P M, ita P M, ad P K, &amp; ita G M, ad M K, <lb/>a&longs;&longs;ump&longs;imus enim in con&longs;tructione e&longs;&longs;e G M, ad M K, ita F B, ad D, &amp; D, ad <lb/>B. quare cum &longs;it vt G M, ad M K, ita F B, ad D. &amp; G P, ad P M. &amp; P M, ad <lb/>K P; erunt per 11. 5. vt G M, ad M K. ita G P, ad P M. &amp; P M, ad P K. &longs;i quis <lb/>igitur vtens puncto P, tanquam polo, &amp; interuallo P M, circulum de&longs;cribat, <lb/>omnes angulos reflexionis attinget, quos faciunt line&aelig; product&aelig; &agrave; K, &amp; re&shy;<lb/>flex&aelig; ab M, ad G. harum enim infinitam multitudinem debemus imaginari <lb/>&agrave; K, ad infinita puncta M, produci in ambitu illo con&longs;tituta, <expan abbr="re&longs;lecti&qacute;">re&longs;lectique</expan>; ad G. <lb/>&longs;i enim non attingat omnes illos angulos, &longs;equitur, vt &longs;upra, in eodem &longs;emi&shy;<lb/>circulo <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan> po&longs;&longs;e duas alias rectas proportionales prioribus G M, M K, <lb/>quod e&longs;t impo&longs;&longs;ibile. </s>
5619 
5620 <s>Porr&ograve; &longs;ub angulo G M K, linearum G M, M K, Iris <lb/>apparet: quare apparebit etiam &longs;ub alijs omnibus, qu&aelig; &agrave; punctis G K, duci <lb/>po&longs;&longs;unt ad extremum line&aelig; P M, quia erunt in eadem ratione cum illis; cum <lb/>non de&longs;inant in eundem <expan abbr="&longs;emicircul&utilde;">&longs;emicirculum</expan>, &longs;ed in ambitum Iridis M N, in quo M, <lb/>punctum imaginamur circumduci. </s>
5621 
5622 <s>Ex quibus pater P, e&longs;&longs;e polum Iridis, ex <lb/>quo per puncta M, vbi &longs;it reflexio, de&longs;cribitur arcus attingens omnes Iridis <lb/>reflexiones.</s></p><pb pagenum="122"/><p type="main">
5623 
5624 <s><arrow.to.target n="marg169"/></s></p><p type="margin">
5625 
5626 <s><margin.target id="marg169"/>168</s></p><p type="main">
5627 
5628 <s>Ibidem <emph type="italics"/>(Si igitur circumducas &longs;emicircul&ubreve;, in quo A, circa diametrum in qua <lb/>G K P, que &agrave; G, K, reflex&aelig; ad id in quo M; in omnibus planis &longs;imiliter &longs;e habebunt, <lb/>&amp; &aelig;qualem facient angulam, qui K M G, &amp; quem etiam facient angulum, qu&aelig; <lb/>K P, &amp; P M, &longs;uper eam, qu&aelig; G P, &longs;emper &aelig;qualis erit. </s>
5629 
5630 <s>Trianguli igitur &longs;uper eam, <lb/>qu&aelig; G P, &aelig;quales ei, qui G M P. con&longs;i&longs;tunt. </s>
5631 
5632 <s>horum autem perpendiculares ad idem <lb/>&longs;ignum cadent eius, qu&aelig; G P, &amp; &aelig;quales erunt, cadunt ad <foreign lang="greek">w,</foreign> centrum erg&ograve; circuli <lb/><foreign lang="greek">w</foreign> &longs;emicirculus autem, qui circa M N, ab&longs;ectus e&longs;t ab horizonte)<emph.end type="italics"/> hac vitima <lb/>textus parte concludit Iridis portionem &longs;upra horizontem a&longs;tro <expan abbr="ori&etilde;te">oriente</expan> exi&shy;<lb/>&longs;tentem e&longs;&longs;e &longs;emicirculum, hoc modo; &longs;i igitur imaginatione circumducas <lb/>&longs;emicirculum, in quo A, circa diametrum horizontis G K P, in hac circum&shy;<lb/>uolutione du&aelig; line&aelig; G M, M K, in omnibus planis con&longs;titui po&longs;&longs;ibilibus cir&shy;<lb/>ca pr&aelig;dictam diametrum, qu&aelig; &longs;upra etiam fieri &agrave; triangulis infinitis dixi&shy;<lb/>mus, &longs;ucce&longs;&longs;iu&egrave; erunt; &longs;iue percurrent &longs;imiliter omnia illa plana, &amp; facient <lb/>vbique angulum Iridis K M G, eundem: pariter du&aelig; line&aelig; K P, P M, facient <lb/>vndique eundem angulum K P M. quare omnia triangula in predictis planis <lb/>imaginata, &amp; <expan abbr="c&otilde;&longs;tituta">con&longs;tituta</expan> &longs;uper linea G P, &longs;imilia ip&longs;i G M P, &amp; &aelig;qualia erunt; <lb/>&longs;i igitur ab angulis ip&longs;orum, in quibus M, duct&aelig; &longs;int perpendiculares ad la&shy;<lb/>tus G P, omnes cadent in idem punctum <foreign lang="greek">w,</foreign> vt in figura; <expan abbr="quar&utilde;">quarum</expan> vna erit M <foreign lang="greek">w,</foreign><lb/>qu&aelig; tamen c&aelig;teras omnes repre&longs;entabit, <expan abbr="eis&qacute;">eisque</expan>; omnibus in volutatione axis <lb/>G K <foreign lang="greek">w,</foreign> coincidit; erunt autem omnes &aelig;quales, quandoquidem &longs;unt trian&shy;<lb/>gulorum &aelig;qualium. </s>
5633 
5634 <s><expan abbr="erunt&qacute;">eruntque</expan>; in eodem eiu&longs;dem circuli plano, &amp; punctum <foreign lang="greek">w,</foreign><lb/>erit centrum ip&longs;ius. </s>
5635 
5636 <s>&longs;imilia dicta &longs;unt in Halone. </s>
5637 
5638 <s>Cum erg&ograve; ip&longs;ius centrum <lb/><foreign lang="greek">a</foreign>, &longs;it in diametro horizontis G K <foreign lang="greek">w</foreign> P O, manife&longs;tum fit portionem eius, qu&aelig; <lb/>&longs;upra horizontem eminet, e&longs;&longs;e &longs;emicirculum, qui in figura notatur lineis <lb/>L M N. <!-- KEEP S--></s>
5639 
5640 <s>Atque hoc accidit Sole, vel Luna in horizonte exi&longs;tentibus; quod <lb/>erat primo loco demon&longs;trandum.</s></p><p type="main">
5641 
5642 <s>Porr&ograve; &longs;ciendum po&longs;&longs;e nos breuius polum pr&aelig;dictum inuenire, &longs;i nimirum <lb/><figure place="text" xlink:href="figures-la/009.01.122.1.tif"/><lb/>ad M, ducatur M P, faciens angulum K P M, &aelig;qua&shy;<lb/>lem angulo G M K, per 23. primi, erunt enim duo <lb/>triangula <expan abbr="&aelig;qui&atilde;gula">&aelig;quiangula</expan> G P M, K P M, angulus enim <lb/>P, e&longs;t communis, angulus ver&ograve; M K P, e&longs;t &aelig;qualis <lb/>duobus G, &amp; G M K, per 32. primi, ergo etiam <lb/>duobus ad M, &longs;iue toti G M P, &amp; reliquus K M P, <lb/>reliquo, quare per 4.6. latera circa angulos &aelig;qua&shy;<lb/>les proportionalia erunt, &amp; omologa G M, ad M K, ita G P, ad P M, qu&aelig; <lb/>&aelig;qualibus augulis &longs;ubtenduntur. </s>
5643 
5644 <s><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habcbant etiam <lb/>triangula Ari&longs;t. 
5645 
5646 in figura, de qua paul&ograve; ante dicebam. </s>
5647 
5648 <s>Verba illa <emph type="italics"/>(Qu&aelig; ali&shy;<lb/>b quam in &longs;emicirculo constituuntur)<emph.end type="italics"/> &longs;unt perperam in antiqua tran&longs;latione <lb/>tran&longs;lata, nam Gr&aelig;c&egrave; &longs;ic, <foreign lang="greek">ai alloqi tou_ hmixoxlnou/ sunisamenai,</foreign> transferenda <lb/>e&longs;&longs;ent, qu&aelig; in alio circuli loco concurrunt.</s></p><p type="main">
5649 
5650 <s><arrow.to.target n="marg170"/></s></p><p type="margin">
5651 
5652 <s><margin.target id="marg170"/>169</s></p><p type="main">
5653 
5654 <s>Ibidem <emph type="italics"/>(Iterum &longs;it horizon quidem in quo A C. oriatur autem &longs;upra hunc G, <lb/>axis autem &longs;it nunc in quo G P. <!-- KEEP S--></s>
5655 
5656 <s>Alia igitur omnia &longs;imiliter o&longs;tendentur vt &amp; prius. <lb/></s>
5657 
5658 <s>Polus autem circuli, in quo P, erit &longs;ub horizonte eo, in quo A C, eleuato puncto, <lb/>in quo G. in eadem autem &amp; polus, &amp; centrum circuli, &amp; terminantis nunc ortum, <lb/>e&longs;t enim i&longs;te, in quo G P. <!-- KEEP S--></s>
5659 
5660 <s>Quoniam autem &longs;upra diametrum, qu&aelig; A C, quod K G, <lb/>centrum vtique erit &longs;ub horizonte priori eius, in quo A C, in linea K P, in quo <foreign lang="greek">w,</foreign><emph.end type="italics"/><pb pagenum="123"/><figure place="text" xlink:href="figures-la/009.01.123.1.tif"/><lb/><emph type="italics"/>Quare minor erit &longs;uperior &longs;ectio &longs;emicir&shy;<lb/>culo, in qua S T, (nam Q S T, &longs;emicir&shy;<lb/>culus est, nunc autem inter&longs;ectus e&longs;t ab <lb/>horizonte A C; <expan abbr="itaq;">itaque</expan> Q S, di&longs;parens erit) <lb/>eleuato ip&longs;o Sole)<emph.end type="italics"/> demon&longs;trat propo&longs;i&shy;<lb/>tionem &longs;ecundam nimirum Sole &longs;upra <lb/>horizontem elcuato, ambitum Iridis <lb/>e&longs;&longs;e minorem circuli portionem, &longs;iue <lb/>&longs;emicirculo minorem. </s>
5661 
5662 <s>&longs;it igitur in fi&shy;<lb/>gura &longs;uperiori, quam textui <expan abbr="c&otilde;gruen-tem">congruen&shy;<lb/>tem</expan> re&longs;tituimus, linea A C, horizon&shy;<lb/>talis, &longs;upra quam Sol &longs;it eleuatus in <lb/>circulo altitudinis in loco G, axis au&shy;<lb/>rem coni, quem reflex&egrave; faciunt &longs;it <lb/>G K <foreign lang="greek">w</foreign> P. alia igitur omnia, qu&aelig; &longs;upra exi&longs;tente in ortu a&longs;tro o&longs;ten&longs;a &longs;unt, hic <lb/>pariter o&longs;tendi po&longs;&longs;unt, &longs;cilicet Iridem fieri tantum per lineas proportiona&shy;<lb/>les, &amp; &aelig;quales lineis G M, M K, quia Iris videri nequit, ni&longs;i in tali, ac deter&shy;<lb/>minata reflexione, &amp; angulo, vt initio &longs;uppo&longs;ui; &amp; quia line&aelig; illis propor&shy;<lb/>tionales non po&longs;&longs;unt alibi con&longs;titui, quam in ambitu circulari, &amp; in diuer&longs;is <lb/>planis, &longs;equitur, vt &longs;upra Iridem e&longs;&longs;e circularem M N L; <expan abbr="eius&qacute;">eiusque</expan>; polum P, &amp; <lb/>centrum <foreign lang="greek">w,</foreign> inueniemus &longs;imiliter in axe G K <foreign lang="greek">w</foreign> P, &amp; quia axis hic &longs;ecat hori&shy;<lb/>zontem in K, in hac vltima figura propter eleuationem Solis &longs;upra A C, in <lb/>G, &longs;equitur partem axis, in qua <foreign lang="greek">w,</foreign> &amp; P, exi&longs;tunt, infra horizontem deprimi. <lb/></s>
5663 
5664 <s>&amp; quia (vt pater ex 64. 10. Vitell.) &amp; P, polus, &amp; centrum <foreign lang="greek">w,</foreign> Iridis, &amp; cen&shy;<lb/>crum K, circuli horizontis, cuius &longs;cilicet diameter e&longs;&longs;et A K S, &amp; Sol, &longs;unt <lb/>in eadem linea G K <foreign lang="greek">w</foreign> P, &longs;i centrum Iridis <foreign lang="greek">w,</foreign> &longs;it infra horizontem, patet mi&shy;<lb/>norem circuli portionem, quam &longs;it &longs;emicirculus &longs;upra horizontem eminere, <lb/>in qua po&longs;ui literas S L T, nam Q S L T R, e&longs;t &longs;emicirculus, cuius pars con&shy;<lb/>tenta inter duos arcus Q S, &amp; T R, e&longs;t infra horizontem. </s>
5665 
5666 <s>debemus autem <lb/>hunc &longs;emicirculum, &amp; hanc portionem ip&longs;ius S L T, extantem &longs;upra hori&shy;<lb/>zontem imaginari erectam e&longs;&longs;e, vt planum ip&longs;ius circuli faciat angulos re&shy;<lb/>ctos &longs;iue &longs;it perpendiculare cum axe G K P; &amp; <expan abbr="circul&utilde;">circulum</expan> altitudinis A G M N, <lb/>modo fungi vice horizontis. </s>
5667 
5668 <s>&longs;ic enim &longs;ola portio S L T, appareret nobis, <expan abbr="e&longs;-&longs;et&qacute;">e&longs;&shy;<lb/>&longs;etque</expan>; rationabiliter con&longs;tituta. </s>
5669 
5670 <s>Ex quibus 2. Ari&longs;t. 
5671 
5672 propo&longs;itio manife&longs;ta e&longs;t.</s></p><p type="main">
5673 
5674 <s><arrow.to.target n="marg171"/></s></p><p type="margin">
5675 
5676 <s><margin.target id="marg171"/>180</s></p><p type="main">
5677 
5678 <s>Ibidem <emph type="italics"/>(Minima autem cum in meridie, quanto enim &longs;uperius G, tanto in&longs;e&shy;<lb/>rius &amp; polus, &amp; centrum circuli erit)<emph.end type="italics"/> probat tertiam propo&longs;itionem, nimi&shy;<lb/>rum Sole exi&longs;tente in meridie minimam <expan abbr="omni&utilde;">omnium</expan> e&longs;&longs;e Iridis arcus portionem: <lb/>ratio autem e&longs;t, quia tunc G, &longs;iue Sol, e&longs;t alti&longs;&longs;imus &longs;upra horizontem, &amp; <lb/>con&longs;equenter <foreign lang="greek">w;</foreign> centrum Iridis e&longs;t depre&longs;si&longs;&longs;imum, quare tunc maxima cir&shy;<lb/>culi Iridis portio ab&longs;condetur, &amp; proinde minima apparebit, quod erat vl&shy;<lb/>timo <expan abbr="dem&otilde;&longs;trandum">demon&longs;trandum</expan>. </s>
5679 
5680 <s>Non me latet has Ari&longs;t. 
5681 
5682 figurationes e&longs;&longs;e apud Olym&shy;<lb/>piodorum nonnullis obiectionibus obnoxias, &longs;ed cum facil&egrave; dilui po&longs;&longs;int, &amp; <lb/>etiam &longs;i non diluantur, &longs;aluetur tamen veritas Ari&longs;totelic&aelig; demon&longs;tratio&shy;<lb/>nis, breuitati &longs;tudens, con&longs;ult&ograve; eas pr&aelig;termitto.</s></p><p type="main">
5683 
5684 <s>Aduertendum pr&aelig;terea Vicomercatum inordinat&egrave; citare librum Dato&shy;<lb/>rum Euclidis, &amp; <expan abbr="quandoq;">quandoque</expan> etiam mal&egrave; citare Euclidem ip&longs;um. </s>
5685 
5686 <s>peius ver&ograve; <pb pagenum="124"/>faciunt ij, qui has demon&longs;trrationes <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla libri Datorum mentione ex&shy;<lb/>plicare conantur, cum manife&longs;t&egrave; illo innitantur.</s></p><p type="main">
5687 
5688 <s>C&aelig;terum &longs;i quis breues, ac dilucidas harum rerum demon&longs;trationes re&shy;<lb/>quirat, is legat 74. 75. 76. propo&longs;itiones 10. Vitell. <!-- REMOVE S-->vel &longs;equentem no&longs;tram <lb/>de Iride additionem. </s>
5689 
5690 
5691 
5692 <s>ego enim longiorem hanc, <expan abbr="atq;">atque</expan> impeditam Ari&longs;t. 
5693 
5694 tra&shy;<lb/>ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e&shy;<lb/>quutus &longs;um.<!-- KEEP S--></s></p><p type="main">
5695 
5696 <s><arrow.to.target n="marg172"/></s></p><p type="margin">
5697 
5698 <s><margin.target id="marg172"/>181</s></p><p type="main">
5699 
5700 <s>Ibidem <emph type="italics"/>(Quod autem in minoribus quidem diebus ijs, qui po&longs;t &aelig;quinoctium au&shy;<lb/>tumnale <expan abbr="c&otilde;tingit">contingit</expan> &longs;emper fieri Iridem: in longioribus aurem diebus ijs qui ab &aelig;qui&shy;<lb/>noctio altero, ad &aelig;quinoctium alterum circa meridiem non fit Iris, can&longs;a est, quia <lb/>qu&aelig; ad Vr&longs;am &longs;ectiones omnes maiores &longs;unt &longs;emicirculo, &amp; &longs;emper ad maiores quod <lb/>autem e&longs;t occultum, paruum: qu&aelig; autem ad &aelig;quatoris meridiem &longs;ectiones, qu&aelig; qui&shy;<lb/>dem &longs;upra &longs;ectio, parua; qu&aelig; autem &longs;ub terra magna, &amp; &longs;emper maiores, qu&aelig; lon&shy;<lb/>gius. </s>
5701 
5702 <s>quare in ijs, qui ad &aelig;&longs;tiuas ver&longs;iones diebus propter magnitudinem &longs;ectionis, <lb/>antequam veniat G, ad medium &longs;ectionis, infra iam p&oelig;nitus fit P; propterea quod <lb/>long&egrave; di&longs;tat &agrave; terra meridies propter magnitudinem &longs;ectionis. </s>
5703 
5704 <s>In ijs autem diebus, <lb/>qui ad hyemates ver&longs;iones, quia non mult&ubreve; &longs;unt &longs;upra terram &longs;ectiones cir culorum, <lb/>contrarium nece&longs;&longs;arium fieri, modicum enim eleuato in quo G, in meridie fit Sol)<emph.end type="italics"/><lb/>qu&aelig;rit cur po&longs;t &aelig;quinoctium autumnale v&longs;que ad vernum, hoc e&longs;t hyemali <lb/>tempore, Iris appareat etiam Sole meridiem occupante: reliquo autem <lb/>tempore &aelig;&longs;tiuo, quod e&longs;t ab &aelig;quinoctio verno ad autumnale appareat tan&shy;<lb/>tum Sole vel in ortu, aut occa&longs;u exi&longs;tente, vel parum &longs;upra terram &longs;ublato. <lb/></s>
5705 
5706 <s>cau&longs;a autem huius refert in &longs;ectiones parallelorum circulorum, quos Sol <lb/>diurno motu inter <expan abbr="vtrunq;">vtrunque</expan> <expan abbr="tropic&utilde;">tropicum</expan> de&longs;cribit: nam &longs;ectiones parallelorum, <lb/>qui &longs;unt ad Vr&longs;am, ide&longs;t in parte &longs;ph&aelig;r&aelig; Boreali, qui omnes &longs;unt inter &aelig;qua&shy;<lb/>torem, &amp; tropicum Cancri; &longs;ectiones inquam horum circulorum, qu&aelig; &longs;unt <lb/>&longs;upra horizontem, maiores &longs;unt &longs;ectionibus infra horizontem depre&longs;&longs;is, &amp; <lb/>&longs;emper e&ograve; maiores, qu&ograve; propiores &longs;unt Cancro, ita vt magna yald&egrave; &longs;it ea <lb/>portio, qu&aelig; e&longs;t &longs;upra terram, exigua ver&ograve; admodum, qu&aelig; infra (intelligan&shy;<lb/>tur h&aelig;c in &longs;ph&aelig;ra obliqua, cuius polus eleuetur grad. <!-- REMOVE S-->45. circiter) quare <lb/>quando a&longs;trum G, con&longs;cenderit meridiem, ade&ograve; P, polus Iridis, &amp; etiam <foreign lang="greek">w,</foreign><lb/>centrum eius infra terram deprimitur, vt aut nihil, aut in&longs;en&longs;ibile quid de <lb/>Iridis ambitu &longs;upra terram eleuari po&longs;&longs;it, contrarium accidit in parallelis <lb/>meridionalibus, quia eorum &longs;ectiones &longs;uperiores &longs;unt &longs;emper inferioribus <lb/>minores, quapropter etiam &longs;i a&longs;trum ad meridiem eleuetur, parum tamen <lb/>attollitur, &amp; con&longs;equenter centrum <foreign lang="greek">w,</foreign> Iridis parum infra horizontem <lb/>de&longs;cendit, ac propterea etiam in meridie pars ip&longs;ius &longs;atis ma&shy;<lb/>gna con&longs;picitur. </s>
5707 
5708 
5709 
5710 <s>qu&aelig; omnia adhibita &longs;ph&aelig;ra materia&shy;<lb/>li, eaque a&longs;tronomic&egrave; ad &longs;uam eleuationem <lb/>accommodata, nullo negotio li&shy;<lb/>cebit intueri.</s></p><pb pagenum="125"/><p type="head">
5711 
5712 <s><emph type="italics"/>Additio de Iride.<emph.end type="italics"/></s></p><p type="main">
5713 
5714 <s>Cvm &longs;uperior Ari&longs;tot. de Iride tractatio ob&longs;cura, ac tricis pluribus <lb/>impedita eua&longs;erit, <expan abbr="cum&qacute;">cumque</expan>; aliorum etiam demon&longs;trationes aliqua <lb/>ex parte vacilient, vi&longs;um e&longs;t breuiter expeditam, <expan abbr="atq;">atque</expan> ab&longs;olutam <lb/>ip&longs;ius apponere demon&longs;trationem. </s>
5715 
5716 
5717 
5718 <s>Cum igitur in c&oelig;le&longs;ti arcu <lb/>duo poti&longs;&longs;imum &longs;int, qu&aelig; &longs;ui admiratione <expan abbr="Philo&longs;ophor&utilde;">Philo&longs;ophorum</expan> animos in &longs;ui con&shy;<lb/>templationem alliciant, colores, &longs;cilicet, &amp; figura: nos mirabilem illam co&shy;<lb/>lorum triadem, tanquam alienam, phy&longs;icis relinquentes, de figura ip&longs;ius iu&shy;<lb/>re mathematico di&longs;&longs;eremus: rotunditatis &longs;cilicet Iridis cau&longs;am opticis ra&shy;<lb/>tionibus venabimur, cur aliquando &longs;emicirculus, aliquando &longs;emicirculo mi&shy;<lb/>nor appareat. </s>
5719 
5720 <s>vt igitur ordine procedamus.</s></p><p type="main">
5721 
5722 <s>Primo loco aduertendum e&longs;t tria ad Iridis vi&longs;ionem e&longs;&longs;e nece&longs;&longs;aria, So&shy;<lb/>lem, oculum, &amp; nubem tenuem, ac ro&longs;cidam, qu&aelig; &longs;cilicet minutis guttulis <lb/>iam &longs;cateat; hac enim ratione guttul&aelig; ill&aelig; innumera erunt veluti parua <lb/>&longs;pecula, qu&aelig; lumen Solis ob paruitatem imperfecto quodam modo repre&shy;<lb/>&longs;entare po&longs;&longs;int, ex tali enim repre&longs;entatione Iris apparet. </s>
5723 
5724 <s>qu&aelig; tria debent <lb/>e&longs;&longs;e ita di&longs;po&longs;ita, vt Sol, oculus, &amp; centrum Iridis &longs;int in eadem recta linea <lb/>con&longs;tituta, <expan abbr="oculus&qacute;">oculusque</expan>; medium locum, inter Solem, &amp; Iridis <expan abbr="c&etilde;trum">centrum</expan> obtineat, <lb/>vt in prima figura videre e&longs;t, in qua Sol vbi A, oculus in C. nubes ver&ograve; <lb/>G H L E, in qua apparet Iris in arcu E B F, quem debemus concipere e&longs;&longs;e <lb/>in rece&longs;&longs;u, vt pictores aiunt, depictum. </s>
5725 
5726 <s>i. </s>
5727 
5728 <s>non in hoc &longs;itu, &amp; ouali figura, &longs;ed <lb/><figure place="text" xlink:href="figures-la/009.01.125.1.tif"/><lb/>e&longs;&longs;e perfect&egrave; &longs;emicircularem, <expan abbr="habere&qacute;">habereque</expan>; talem po&longs;itionem, vt pars ip&longs;ius B F, <lb/>&longs;it citra chartam eleuata, <expan abbr="ip&longs;i&qacute;">ip&longs;ique</expan>; perpendicularis, pars ver&ograve; E B, vltra pagi&shy;<pb pagenum="126"/>nam rect&agrave; recedat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; diameter Iridis E F, faciat angulos rectos cum <lb/>linea horizontali A C L, in quo &longs;itu oculo C, totus ex oppo&longs;ito direct&egrave; &longs;pe&shy;<lb/>ctaretur, non aliter ac Iridem ip&longs;am con&longs;picere &longs;olemus. </s>
5729 
5730 <s>Quod autem ne&shy;<lb/>ce&longs;&longs;aria &longs;it nubes ro&longs;cida, pulcherrima hac experientia <expan abbr="c&otilde;probatur">comprobatur</expan>: &longs;i enim <lb/>in Sole po&longs;iti ore aquam efflantes leui a&longs;pergine aerem Soli, ac nobis ad&shy;<lb/>uer&longs;um irroremus, actutum Iridis arcum guttulis illis, quamuis volitanti&shy;<lb/>bus inh&aelig;rcntem &longs;umma voluptate &longs;pectabimus. </s>
5731 
5732 <s>Quod pr&aelig;terea oculus no&shy;<lb/>&longs;ter, cum Iridem videmus, medius &longs;it inter Solem, &amp; Iridis centrum, expe&shy;<lb/>rimento diuturno, manife&longs;tum e&longs;t.</s></p><p type="main">
5733 
5734 <s>Secund&ograve;, notandum e&longs;t, arcum per reflexionem fieri: quod quidem pri&shy;<lb/>mo eadem experientia, qua pr&aelig;cedens conclu&longs;io confirmatur: deinde, quia <lb/>Iridem &longs;emper in oppo&longs;ita Soli, ac nobis parte <expan abbr="c&otilde;&longs;picimus">con&longs;picimus</expan>; quemadmodum <lb/>in eadem figura o&longs;tenditur, quod aliter qu&agrave;m per reflexionem fieri nequit.</s></p><p type="main">
5735 
5736 <s>Terti&ograve;, &longs;ciendum e&longs;t ex Maurolyco, &amp; 10. Bapti&longs;ta Porta, tantam e&longs;&longs;e di&shy;<lb/>&longs;tantiam C D, ab oculo ad centrum arcus, quanta e&longs;t altitudo, &longs;eu &longs;emidia&shy;<lb/>meter D B, ob&longs;eruarunt enim ip&longs;i angulos D C B, &amp; C B D, e&longs;&longs;e &longs;emirectos, <lb/>&amp; proinde &aelig;quales, &amp; con&longs;equenter duo latera C D, D B, trianguli C D B, <lb/>per 6. 1. &aelig;qualia &longs;unt.</s></p><p type="main">
5737 
5738 <s>Quart&ograve;, con&longs;iderandum e&longs;t lineas A B, A D, ob maximam Solis ab Iride <lb/>di&longs;tantiam in&longs;en&longs;ibiliter differre; &amp; ide&ograve; &longs;upponi po&longs;&longs;unt &aelig;quidi&longs;tantes, <lb/>quare angulus A B C, qui &aelig;qualis e&longs;t alterno B C D, &longs;umi pote&longs;t ab&longs;que vllo <lb/>errore pro &longs;emirecto. </s>
5739 
5740 <s>hic autem angulus A B C, dicitur angulus reflexionis <lb/>Iridis, &longs;ub tali enim reflexione lumen Solis occurrens nubi in B, reflectitur <lb/>ad oculum C.<!-- KEEP S--></s></p><p type="main">
5741 
5742 <s>Quint&ograve;, &longs;equitur ex pr&aelig;dictis arcum videri &longs;emper &longs;ub &longs;tato, ac determi&shy;<lb/>nato reflexionis angulo, &longs;cilicet &longs;ub &longs;emirecto, <expan abbr="neq;">neque</expan> po&longs;&longs;e per alium videri. <lb/></s>
5743 
5744 <s>quod etiam probari pote&longs;t ex Ari&longs;t. 
5745 
5746 quia nimirum videmus arcum apparere <lb/>con&longs;imiliter in ambitu circulari, erg&ograve; nece&longs;&longs;ari&ograve; apparebit <expan abbr="vbiq;">vbique</expan> in toto il&shy;<lb/>lo ambitu per con&longs;imilem reflexionem, &longs;iue per &aelig;quales reflexionis angulos, <lb/>pro quibus omnibus vnus cernitur in figura angulus A B C.<!-- KEEP S--></s></p><p type="main">
5747 
5748 <s>Sext&ograve;, ad Iridis vi&longs;ionem, pr&aelig;ter ea, requiri aeris rorantis multiplica&shy;<lb/>tionem; &longs;icuti enim nebulam videre nequimus, ni&longs;i aer exhalatione illa in&shy;<lb/>fectus multus &longs;it ante oculum no&longs;trum: &longs;ic etiam exi&longs;timo ad Iridis appari&shy;<lb/>tionem, opus e&longs;&longs;e plurima nube rore&longs;cente, vt ex multiplicatione guttula&shy;<lb/>rum, quarum ali&aelig; po&longs;t alias &longs;int, totus tandem Iris appareat. </s>
5749 
5750 <s>quia pauc&aelig; <lb/>guttul&aelig;, etiam &longs;i qu&aelig;libet illarum aliquid Iridis efficeret, ob paruitatem <lb/>tamen illarum, nulla arcus figura &longs;pectaretur. </s>
5751 
5752 <s>Quod &longs;i ante oculum pluri&shy;<lb/>m&aelig; &longs;int in toto aere ali&aelig; po&longs;t alias, tunc &longs;e mutu&ograve; iuuantes, obiectum &longs;atis <lb/>&longs;en&longs;ibile, quoc Iris e&longs;t, efficere po&longs;&longs;unt. </s>
5753 
5754 <s>Adde, quod etiam ex tali guttula&shy;<lb/>rum multiplicatione, aer opacatur, qu&aelig; opacatio plurimum iuuat ad Iri&shy;<lb/>dem &longs;pectandam.</s></p><p type="main">
5755 
5756 <s>Septim&ograve;, Iridis rotundationis cau&longs;am ex pr&aelig;mi&longs;&longs;is con&longs;tare poti&longs;&longs;imum <lb/>ex duabus. </s>
5757 
5758 <s>prim&ograve;, ex angulo reflexionis determinato, qui videlicet &longs;it fer&egrave; <lb/>&longs;emirectus. </s>
5759 
5760 <s>&longs;ecund&ograve;, ex paribus di&longs;tantijs C D, D B, huiu&longs;modi enim plures <lb/>anguli, qui ad Iridem &longs;unt nece&longs;&longs;arij (debent enim &longs;ingul&aelig; Iridis partes &longs;ub <lb/>huiu&longs;modi angulo repre&longs;entari) non po&longs;&longs;unt aliter qu&agrave;m in gyrum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, <pb pagenum="127"/>quem gyrum optim&egrave; concipiemus, &longs;i imaginemur triangulum A B C, cir&shy;<lb/>cumuerti circa lineam horizontalem A C L, fixam, tanquam circa axem. </s>
5761 
5762 <s>in <lb/>hac enim conuer&longs;ione angulus Iridis B, de&longs;cribet circulum, qui erit Iris, &amp; <lb/>pertr an&longs;ibit omnes angulos, qui in tali Solis, oculi, ac nubis &longs;itu, arcum ef&shy;<lb/>ficere &longs;unt idonei.</s></p><p type="main">
5763 
5764 <s>Sed contra pr&aelig;dicta de angulo Iridis determinato eadem nobis obijcies, <lb/>qu&aelig; nos &longs;upra ad finem numeri 164. Ari&longs;t. &amp; alijs obiecimus, plures <expan abbr="nimi-r&utilde;">nimi&shy;<lb/>rum</expan> po&longs;&longs;e con&longs;titui angulos &aelig;quales angulo Iridis B, in plano trianguli A B C, <lb/>qui non &longs;int in eodem orbe con&longs;tituti, in quo &longs;unt omnes anguli B. <!-- KEEP S--></s>
5765 
5766 <s>Iridem <lb/>reflectentes, <expan abbr="quiq;">quique</expan> reflexionem faciant ad eundem oculum C, vnde &longs;equitur <lb/>pr&aelig;dictam Iridis altitudinem non e&longs;&longs;e, vti diximus, determinatam, cum <lb/>po&longs;&longs;it angulus B, alios &longs;ibi &aelig;quales tam &longs;upra, qu&agrave;m infra habere, qua ra&shy;<lb/>tione deberet etiam Iris, &amp; altius, &amp; inferius apparere.</s></p><p type="main">
5767 
5768 <s>Huic dubitationi re&longs;pondeo, quod quamuis huiu&longs;modi plures anguli <lb/>&aelig;quales fiant, non tamen Iridis generationi ob&longs;tant, quinim&ograve; ad eam vald&egrave; <lb/>nece&longs;&longs;arij &longs;unt; <expan abbr="c&utilde;">cum</expan> enim omnes &longs;int in <expan abbr="circunfer&etilde;tia">circunferentia</expan> circuli A C D B, quar&shy;<lb/>t&aelig; figur&aelig; num. </s>
5769 
5770 <s>164. qu&aelig; modo in&longs;picienda e&longs;t, vt &longs;unt in ea anguli A D C, <lb/>A B C; qu&aelig; circunferentia ob &longs;ui circuli immen&longs;itatem ad &longs;en&longs;um e&longs;t in&longs;tar <lb/>line&aelig; rect&aelig;, fit vt omnes illi anguli t&agrave;m qui &longs;upra B, qu&agrave;m qui infra &longs;unt, <lb/>&longs;int quoad &longs;en&longs;um in eadem recta C D B, ante vi&longs;um proten&longs;a, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; Iris, qui <lb/>apparet in D, &amp; in B, &amp;c. </s>
5771 
5772 <s>ob medij rorantis multiplicationem vnam <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> <lb/>oculo Iridem repre&longs;entet. </s>
5773 
5774 <s>locus tamen, in quo apparet, &amp; vbi e&longs;t angulus <lb/>B, qui propri&egrave; Iridis appellatur, e&longs;t in tanta di&longs;tantia &agrave; centro arcus, quan&shy;<lb/>ta e&longs;t ab eodem centro ad oculum, vt &longs;upra dictum e&longs;t.</s></p><p type="main">
5775 
5776 <s>Quod ver&ograve; alibi extra circunferentiam illius circuli, poni nequeat angu&shy;<lb/>lus &aelig;qualis angulo B, pr&aelig;&longs;entis figur&aelig;, qui re&longs;lectat ad C. patet &longs;ic, &longs;it enim <lb/>angulus A N O, &longs;emirectas, &amp; ide&ograve; &aelig;qualis angulo B, erunt ergo B C, N O, <lb/>parallel&aelig;, quare non concurrent amb&aelig; ad C, &longs;ed altera ad E, altera ver&ograve; ad <lb/>O, qu&aelig; propterea oculo in O, po&longs;ito Iridem efficeret, non autem oculo C: <lb/><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; oculus C, &amp; oculus O, viderent diuer&longs;os arcus. </s>
5777 
5778 <s>eodem modo o&longs;tendi <lb/>pote&longs;t, <expan abbr="neq;">neque</expan> in &longs;uperiori parte nubis vbi P, con&longs;titui po&longs;&longs;e angulum &aelig;qualem <lb/>angulo B, qui oculo C, Iridem valeat o&longs;tendere. </s>
5779 
5780 <s>Ex quibus &longs;atis patefacta <lb/>e&longs;t cau&longs;a rotunditatis arcus, angulus &longs;cilicet determinatus cum di&longs;tantia&shy;<lb/>rum C D, D B, paritate, necnon cum medij rorantis &longs;ufficienti multiplica&shy;<lb/>tione. </s>
5781 
5782 <s>Ex his etiam Iridis definitio in hunc modum concinnari pote&longs;t, Iris <lb/>e&longs;t arcus multicolor in nube rorida, ex radiorum Solis, aut Lun&aelig; reflexio&shy;<lb/>ne &longs;ab &longs;tatuto angulo effulgens.</s></p><p type="main">
5783 
5784 <s>Octauo loco Problemata nonnulla re&longs;oluemus.</s></p><pb pagenum="128"/><p type="head">
5785 
5786 <s><emph type="italics"/>Problema Primum.<emph.end type="italics"/></s></p><p type="head">
5787 
5788 <s>Cur oriente, aut occumbente Sole, Iris &longs;emicirculus e&longs;t?</s></p><p type="main">
5789 
5790 <s>Cau&longs;a huius h&aelig;c e&longs;t; &longs;upra enim dictum e&longs;t, in omni Iridis appari&shy;<lb/>tione tria h&aelig;c, Solem, oculum, &amp; Iridis centrum e&longs;&longs;e in eadem re&shy;<lb/>cta linea, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in linea A C D, pr&aelig;cedentis figur&aelig;, cum igitur Sol <lb/>tam oriens, quam occidens &longs;it in horizonte, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in A, horizontis <lb/>puncto, &longs;imiliter oculus &longs;it in C, horizontis centro, con&longs;ectarium e&longs;t, cen&shy;<lb/>trum etiam Iridis D, e&longs;&longs;e pariter in horizontis &longs;uperficie, quare &longs;ecabitur <lb/>ab horizonte per centrum, vnde etiam &longs;equitur ip&longs;ius Iridis portionem <lb/>E B F, qu&aelig; &longs;upra horizontem extat e&longs;&longs;e &longs;emicirculum. </s>
5791 
5792 
5793 
5794 
5795 
5796 
5797 
5798 
5799 
5800 <s>Quod &longs;i horizon non <lb/>ob&longs;taret, <expan abbr="integr&utilde;">integrum</expan> Iris compleret orbem, <expan abbr="cerneretur&qacute;">cernereturque</expan>; toto ambitu B F M E.<!-- KEEP S--></s></p><p type="head">
5801 
5802 <s>An <expan abbr="quando&qacute;">quandoque</expan>; maior &longs;emicirculo appareat?</s></p><p type="head">
5803 
5804 <s><emph type="italics"/>Problema Secundum.<emph.end type="italics"/></s></p><p type="main">
5805 
5806 <s>Maior quidem, im&ograve; etiam integer circulus, &longs;ed ab oculo in &longs;ummitate <lb/>montis con&longs;tituto, <expan abbr="Sole&qacute;">Soleque</expan>; iam multum eleuato videri pote&longs;t, vt in <lb/>hac &longs;ecunda figura cernitur, vbi euecto Sole ad locum E, &longs;upra horizontem <lb/><figure place="text" xlink:href="figures-la/009.01.128.1.tif"/><lb/>A B, poterit oculus in vertice montis C, po&longs;itus Iridem F G H I, comple&shy;<lb/>tam videre, quia infra lineam E C D, in qua exi&longs;tunt Sol, oculus, &amp; Iridis <lb/>centrum, nihil e&longs;t ad partes D, vbi nubes irrorat, quod Iridis apparitioni <lb/>&longs;it impedimento.</s></p><pb pagenum="129"/><p type="head">
5807 
5808 <s>Cur quanto Sol altior e&longs;t, tanto inferior, <expan abbr="tanto&qacute;">tantoque</expan>; &longs;emicir&shy;<lb/>culo minor appareat Iris?<!-- KEEP S--></s></p><p type="head">
5809 
5810 <s><emph type="italics"/>Problema Tertium.<emph.end type="italics"/></s></p><p type="main">
5811 
5812 <s>Qvia eleuato Sole ad E, vt in hac tertia figura, nece&longs;&longs;ario centrum Iri&shy;<lb/>dis D, infra horizontem A B, deprimetur, cum in eadem recta E C D. <lb/><figure place="text" xlink:href="figures-la/009.01.129.1.tif"/><lb/>Sol E, oculus C, <expan abbr="centr&utilde;&qacute;">centrunque</expan>; Iridis D, exi&longs;tant: vnde nece&longs;&longs;ari&ograve; &longs;equitur Iridis <lb/>portionem F G H, &longs;upra horizontem extantem, &longs;emicirculo minorem e&longs;&longs;e.</s></p><p type="head">
5813 
5814 <s>Cur Iris in&longs;equentes fugit, fugientes ver&ograve; in&longs;equitur?</s></p><p type="head">
5815 
5816 <s><emph type="italics"/>Problema Quartum.<emph.end type="italics"/></s></p><p type="main">
5817 
5818 <s>Pvlcherrimum i&longs;tud ph&aelig;nomenon primus omnium Philippus Mend&aelig;us <lb/>Platonis di&longs;cipulus, ob&longs;eruauit; Cuius ratio e&longs;t, quia arcus non ni&longs;i &longs;ub <lb/>determinato angulo, di&longs;tantijs etiam illis paribus, ac tandem idone a a&longs;per&shy;<lb/>gino&longs;&aelig; nubis multiplicatione &longs;pectatur; quapropter &longs;i quis per aerem to&shy;<lb/>tum <expan abbr="vndiq;">vndique</expan> ro&longs;cidum inambulet, <expan abbr="vbicunq;">vbicunque</expan> illi anguli, <expan abbr="ill&aelig;&qacute;">ill&aelig;que</expan>; conditiones af&shy;<lb/>fuerint Iris apparebit: quod &longs;i in aperta planitie obequitans arcu con&longs;pe&shy;<lb/>cto, additis equo calcaribus citatum cur&longs;um ad eum direxerit, fugientem <lb/>ante &longs;e Iridem &longs;umma cum iucunditate mirabitur.</s></p><p type="main">
5819 
5820 <s>Ex dictis pr&ecedil;tere a patet, &longs;impliciter nimis eos hallucinari, qui exi&longs;timant <lb/>in plana, aut concaua nubis &longs;uperficie Iridem tantummodo apparere po&longs;&longs;e.</s></p><pb pagenum="130"/><p type="head">
5821 
5822 <s>Curlunares Irides fiunt rariores?</s></p><p type="head">
5823 
5824 <s><emph type="italics"/>Problema Quintum.<emph.end type="italics"/></s></p><p type="main">
5825 
5826 <s>Qvoniam iuxta plenilunia tantum, cum &longs;cilicet Luna plurimo lumine <lb/>abundat, quod Iridem efficere debet, contingunt: pr&aelig;terea quia cum <lb/>lunare lumen debile &longs;it, ni&longs;i ali&aelig; cau&longs;&aelig; perfect&aelig; admodum concur&shy;<lb/>rant, quod rar&ograve; accidit, Iris nullo modo effulgere valet. </s>
5827 
5828 <s>Hactenus de Iri&shy;<lb/>dis figura &longs;it &longs;atis.</s></p><p type="head">
5829 
5830 <s><emph type="italics"/>Summa 2. cap. 
5831 
5832 5. De Parelio.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
5833 
5834 <s><arrow.to.target n="marg173"/></s></p><p type="margin">
5835 
5836 <s><margin.target id="marg173"/>182</s></p><p type="main">
5837 
5838 <s>Textus <emph type="italics"/>(Fiunt autem vt diximus, &amp; Virg&aelig;, &amp; Parelia in ortu, &amp; oc&shy;<lb/>ca&longs;u, &amp; nec &longs;upra Solem, nec infra, &longs;ed ex lateribus, nec prop&egrave; admo&shy;<lb/>dum, nec procul omnin&ograve;. </s>
5839 
5840 <s>propinquam enim concretionem Sol di&longs;&longs;oluit: <lb/>&longs;i autem procul ab&longs;it, a&longs;pectus non reflectetur, &longs;i enim &agrave; paruo &longs;peculo <lb/>procul protenditur imbecillus fit. </s>
5841 
5842 <s>quare, &amp; Coron&aelig; &egrave; regione Solis non fiunt. </s>
5843 
5844 <s>&longs;i igi&shy;<lb/>tur &longs;upra fuerit, &amp; proxima; eam Sol di&longs;&longs;oluet: &longs;i ver&ograve; procul a&longs;pectus minor <lb/>quam vt reflecti po&longs;&longs;it in Solem non-incidet; &agrave; latere autem fieri pote&longs;t, vt &longs;pecu&shy;<lb/>lum ita distet &agrave; Sole, vt non &longs;oluatur, &amp; a&longs;pectus totus ad eum perueniat, eo quod <lb/>ad terram dum fertur, qua&longs;i per immen&longs;um feratur, peruenire nequeat. </s>
5845 
5846 <s>&longs;ub Sole <lb/>ver&ograve; non fit, quia cum ad terram propius acce&longs;&longs;erit &agrave; Sole di&longs;&longs;oluitur, cum medium <lb/>c&oelig;li tenuerit a&longs;pectus di&longs;trahitur. </s>
5847 
5848 <s>omnin&ograve; ne &agrave; latere quidem, Sole medium c&oelig;li <lb/>tenente, efficitur, quia a&longs; pectus &longs;ub terram non fertur, quare exiguus ad &longs;peculum <lb/>producitur, &amp; qui reftectitur pror&longs;us imbecillis redditur)<emph.end type="italics"/> ibi <emph type="italics"/>(propinquam enim <lb/>concretionem Sol di&longs;&longs;oluit)<emph.end type="italics"/> rationes, quas affert circa Parelia videntur (auda&shy;<lb/>cter loquar) admodum debiles. </s>
5849 
5850 <s>pr&aelig;&longs;ens ea e&longs;t, vt Parelium non fiat prop&egrave; <lb/>Solem, quia illa nubis concretio, qu&aelig; Parelio nece&longs;&longs;aria e&longs;t, nequit adeo So&shy;<lb/>li propinqua e&longs;&longs;e, quia nimirum Sol ob propinquitatem eam di&longs;&longs;olueret; &longs;ed <lb/>quis non videt eam nubem, quam vulg&ograve; exi&longs;timamus e&longs;&longs;e Soli propinquam, <lb/>&longs;eu qua&longs;i inter nos, &amp; Solem tantum, im&ograve; etiam minus aliquando &agrave; Sole ve&shy;<lb/>r&egrave; di&longs;tare, qu&agrave;m alia, qu&agrave;m vulg&ograve; remotiorem &agrave; Sole putabimus? </s>
5851 
5852 <s>pr&aelig;te&shy;<lb/>rea omnes nubes no&longs;tri horizontis re vera &aelig;quidi&longs;tare &agrave; Sole certum e&longs;t, ob <lb/>maximam enim Solis di&longs;tantiam totus no&longs;ter horizon phy&longs;icus e&longs;t in&longs;en&longs;i&shy;<lb/>bilis quantitatis ad Solem, &amp; vnius puncti vicem gerit.</s></p><p type="main">
5853 
5854 <s>Ibi ver&ograve; <emph type="italics"/>(Si autem procul ab&longs;it, &amp;c.)<emph.end type="italics"/> reddit rationem, cur parelium non <lb/>appareat in nube &agrave; Sole valde remota &longs;ecundum vulgarem &aelig;&longs;timationem, <lb/>vnde vulgarem etiam rationem affert, ait enim, nubem illam e&longs;&longs;e veluti &longs;pe&shy;<lb/>culum Solis repre&longs;entatiuum, &longs;peculum autem t&agrave;m long&egrave; &agrave; Sole po&longs;itum, <lb/>reddi debile, &amp; proptere&aacute; non po&longs;&longs;e Solis imaginem referre: Ver&ugrave;m ratio <lb/>h&aelig;c nulla e&longs;&longs;e videtur, quis enim ignorat non propterea e&longs;&longs;e remotius &agrave; So&shy;<lb/>le, quamuis maiorem habere videatur &agrave; Sole lateralem di&longs;tantiam, vt pau&shy;<lb/>l&ograve; ante dixi? </s>
5855 
5856 <s>Eandem rationem illi dubitationi accommodat, cur <expan abbr="neq;">neque</expan> vi&shy;<lb/>deatur &longs;upra Solem, quamuis non ei quadret, pote&longs;t enim aliqua nubes vi&shy;<pb pagenum="131"/>deri &longs;upra Solem, qu&aelig; tamen remotior &longs;it &agrave; Sole, quam illa, in qua Parclium <lb/>gignitur. </s>
5857 
5858 <s>Ait po&longs;tea <emph type="italics"/>(A latere autem, &amp;c.)<emph.end type="italics"/> cur appareat in nube fatis Soli <lb/>&agrave; latere vicina, in di&longs;tantiam &agrave; Sole refert: &longs;ed qu&aelig; dudum dicta &longs;unt, i&longs;tud <lb/><expan abbr="quoq;">quoque</expan> refellunt. </s>
5859 
5860 <s>Verba illa <emph type="italics"/>(Eo quod ad terram dum fertur qua&longs;i per immen&longs;um <lb/>feratur, peruenire nequeat)<emph.end type="italics"/> videntur alieno loco dicta; &longs;imilia pr&aelig;cedentibus <lb/>&longs;unt reliqua, pr&aelig;&longs;ertim qu&aelig; ibi <emph type="italics"/>(Sub Sole ver&ograve; non fit, quia cum ad terram pro&shy;<lb/>pius acce&longs;&longs;erit)<emph.end type="italics"/> cur non videatur infra Solem, rationem quandam, qu&aelig; fort&egrave; <lb/>inanis e&longs;t reddit; nunquid enim non po&longs;&longs;umus tam infra Solem, qu&agrave;m &longs;upra <lb/>ita &longs;peculum accommodare, vt Solem no&longs;tris vi&longs;ibus remittat? </s>
5861 
5862 <s>huic cert&egrave; <lb/>Optice tota repugnat. </s>
5863 
5864 <s>Cum igitur Mathematica ratione h&aelig; rationes non <lb/>con&longs;i&longs;tant, alias alij excogitent. </s>
5865 
5866 <s>Mirum tamen e&longs;t, omnes, quos viderim <lb/>commentatores, eas tanquam optimas admittere.</s></p><p type="head">
5867 
5868 <s><emph type="italics"/>In quarto Meteororum nihil Mathematicum occurrit.<emph.end type="italics"/></s></p></chap><chap><p type="head">
5869 
5870 <s><emph type="italics"/>EX LIB. PRIMO DE ANIMA.<emph.end type="italics"/></s></p><p type="main">
5871 
5872 <s><arrow.to.target n="marg174"/></s></p><p type="margin">
5873 
5874 <s><margin.target id="marg174"/>183</s></p><p type="main">
5875 
5876 <s>Tex. 11. <emph type="italics"/>(Videtur autem non &longs;olum ip&longs;um quid e&longs;t cogno&longs;cere vtile e&longs;&longs;e <lb/>ad cogno&longs;cendas cau&longs;as accidentium &longs;ub&longs;tantijs: &longs;icut in Mathemati&shy;<lb/>cis quid rectum, &amp; quid obliqaum, aut quid linea, &amp; planum, ad co&shy;<lb/>gno&longs; cendum quot rectis, trianguli anguli &longs;unt &aelig;quales)<emph.end type="italics"/> quid &longs;it <expan abbr="vnum-quodq;">vnum&shy;<lb/>quodque</expan> ex pr&aelig;dictis patet tum ex definitionibus primi Elem. 
5877 
5878 tum ex com&shy;<lb/>mentarijs ip&longs;arum; quamuis autem ibi non definiatur <expan abbr="rect&utilde;">rectum</expan>, nec obliquum <lb/>in genere, definitur tamen linea recta, &amp; obliqua, &amp; plana &longs;uperficies, &longs;iue <lb/>planum, ex quibus facil&egrave; definitio recti, &amp; obliqui colligi pote&longs;t: qu&aelig; defi&shy;<lb/>nitiones nece&longs;&longs;ari&aelig; &longs;unt ad cogno&longs;cendum quot rectis angulis &aelig;quales &longs;int <lb/>tres anguli cuiufuis trianguli. </s>
5879 
5880 <s>vide qu&aelig; de hac &aelig;qualitate &longs;crip&longs;i lib, primo <lb/>Priorum, &longs;ecto 3. cap. 
5881 
5882 1.<!-- KEEP S--></s></p><p type="main">
5883 
5884 <s><arrow.to.target n="marg175"/></s></p><p type="margin">
5885 
5886 <s><margin.target id="marg175"/>184</s></p><p type="main">
5887 
5888 <s>Tex. 13. <emph type="italics"/>(Si igitur e&longs;t aliqua anim&aelig; operatio, aut pa&longs;&longs;io propria, continget vti&shy;<lb/>que ip&longs;am &longs;eparari: &longs;i ver&ograve; nulla e&longs;t propria ip&longs;ius non vtique erit &longs;eparabilis. </s>
5889 
5890 <s>&longs;ed <lb/>&longs;icut recto in quantum rectum multa accidunt, vt tangere &aelig;neam &longs;ph&aelig;ram &longs;ecun&shy;<lb/>dum punctum, non tamen tanget hoc, rectum ip&longs;um &longs;eparatum: in&longs;eparabile enim, <lb/>&longs;i quidem cum corpore quodam &longs;emper e&longs;t)<emph.end type="italics"/> Propo&longs;itio 2. tertij Elem. 
5891 
5892 &pacute;robat li&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.131.1.tif"/><lb/>neam rectam, duo qu&aelig;libet puncta <expan abbr="qu&atilde;tumuis">quantumuis</expan> pro&shy;<lb/>pinqua in circuli ambitu a&longs;&longs;umpta coniungentem <lb/>cadere intra circulum. </s>
5893 
5894 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->puncta A B, quantum&shy;<lb/>uis &longs;ibi inuicem propinqua fnerint, attamen &longs;i line a <lb/>A B, ea coniungat, ip&longs;a cadet intra circulum, &amp; <lb/>veluti chorda &longs;ubtendet arcum A B, quantulum&shy;<lb/>cunque. </s>
5895 
5896 
5897 
5898 
5899 
5900 <s>ex qua demon&longs;tratione colligitur in corol&shy;<lb/>lario eius lineam rectam tangentem circulum ip&shy;<lb/>&longs;um in vnico puncto tangere. </s>
5901 
5902 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->rectam C D, tan&shy;<lb/>gere circulum in puncto E. &longs;i enim dixeris tangere <lb/>in duobus admodum propinquis, vt in E F, tunc non erit amplius tangens, <lb/>&longs;ed &longs;ecans, quia vt modo dixi, pars line&aelig; rect&aelig;, qu&aelig; <expan abbr="c&otilde;iungeret">coniungeret</expan> puncta E F, <pb pagenum="132"/>intra circulum per &longs;ecundam pr&aelig;allegatam caderet, quod e&longs;t ab&longs;urdum, <lb/>quia contra hypothe&longs;im, cum &longs;upponamus illam &longs;ol&ugrave;m tangere, non autem <lb/>&longs;ecare circulum. </s>
5903 
5904 
5905 
5906 
5907 
5908 <s>Ex hac Euclidis doctrina Theodo&longs;ius primo &longs;ph&aelig;ricorum, <lb/>propo&longs;itione 3. probat planum, &longs;iue &longs;uperficiem planam tangere &longs;ph&aelig;ram <lb/>in vnico puncto, vt hoc loco innuit Philo&longs;ophus. <!-- KEEP S--></s>
5909 
5910 <s>probat autem hac fer&egrave; ra&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.132.1.tif"/><lb/>tione. </s>
5911 
5912 <s>&longs;it &longs;ph&aelig;ra A B C, qu&aelig; tangat quodpiam planum <lb/>in duobus punctis A, B, &longs;i fieri pote&longs;t. </s>
5913 
5914 <s>per qu&aelig; duo pun&shy;<lb/>cta intelligatur ducta recta linea A B, intelligatur <expan abbr="eti&atilde;">etiam</expan> <lb/>circulus A B C, qui &longs;ecet &longs;ph&aelig;ram per centrum C. &amp; <lb/>per puncta A, B, ergo ex demon&longs;tratis ab Euclide li&shy;<lb/>nea A B, qu&aelig; coniungit puncta A B, cadet intra pr&aelig;di&shy;<lb/>ctum circulum; &longs;ed linea h&aelig;c e&longs;t in plano tangente ex <lb/>&longs;uppo&longs;itione, circulus ver&ograve; in &longs;ph&aelig;ra; erg&ograve; cum linea <lb/>cadat intra circulum, cadet etiam nece&longs;&longs;ari&ograve; planum <lb/>in quo e&longs;t linea, &amp; cum linea cadat intra circulum, cadet etiam nece&longs;&longs;ari&ograve; <lb/>intra &longs;ph&aelig;ram; <expan abbr="idem&qacute;">idemque</expan>; faciet planum, quod eam nece&longs;&longs;ari&ograve; &longs;equatur, erg&ograve; <lb/>planum &longs;ecat &longs;ph&aelig;ram, non autem tangit, quod e&longs;t ab&longs;urdum, quia contra <lb/>hypothe&longs;im, &longs;upponunt autem Mathematici, entia h&aelig;c mathematica e&longs;&longs;e <lb/>perfecta, qualia in &longs;ublunaribus fort&egrave; non reperiuntur; &aelig;nea enim &longs;ph&aelig;ra <lb/>nulla erit perfect&egrave; rotunda, vel planum aliquod perfect&egrave; complanatum, vt <lb/>ip&longs;i &longs;upponunt, e&ograve; quod materi&aelig; imperfectio, ac ruditas id nequaquam pa&shy;<lb/>tiatur. </s>
5915 
5916 <s>quare cum huiu&longs;inodi entia non reperiantur ab&longs;tracta ab impura hac <lb/>materia, nullum erit inquit Ari&longs;t. 
5917 
5918 ab&longs;tractum planum, quod po&longs;&longs;it mathe&shy;<lb/>matic&egrave;, <expan abbr="atq;">atque</expan> ade&ograve; in vnico puncto mathematico &longs;ph&aelig;ram tangere. </s>
5919 
5920 <s><expan abbr="hucu&longs;q;">hucu&longs;que</expan> <lb/>nece&longs;&longs;aria &longs;unt mathematica ad huius loci <expan abbr="intelligenti&atilde;">intelligentiam</expan>. </s>
5921 
5922 <s>ex quibus ea etiam, <lb/>qu&aelig; ad phy&longs;icum &longs;pectant manife&longs;ta fiunt, nimirum &longs;icut entia mathemati&shy;<lb/>ca &agrave; materia non exi&longs;tunt &longs;eparata, quia &longs;ic nullam haberent operationem; <lb/>ita etiam anima, &longs;i nullam habet propriam operationem non exi&longs;tet &agrave; cor&shy;<lb/>pore &longs;eparata.</s></p></chap><chap><p type="head">
5923 
5924 <s><emph type="italics"/>Ex Secundo de Anima.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
5925 
5926 <s><arrow.to.target n="marg176"/></s></p><p type="margin">
5927 
5928 <s><margin.target id="marg176"/>185</s></p><p type="main">
5929 
5930 <s>Tex. 12. <emph type="italics"/>(Non enim &longs;olum ip&longs;um, quod&longs;it, oportet definitiuam rationem <lb/>oftendere, &longs;icut plures definitionum dicunt, &longs;ed &amp; cau&longs;am ine&longs;&longs;e, &amp; ap&shy;<lb/>parere. </s>
5931 
5932 <s>nunc autem, vt conclu&longs;iones rationes definitionum &longs;unt, vt quid <lb/>tetragoni&longs;mus? </s>
5933 
5934 <s>&aelig;quale altera parte longiori rectangulum &aelig;quilaterum <lb/>e&longs;&longs;e, talis autem definitio ratio conclu&longs;ionis. </s>
5935 
5936 <s>dicens autem, quod tetragoni&longs;mus e&longs;t <lb/>medij inuentio rei cau&longs;am dicit)<emph.end type="italics"/> aggre&longs;&longs;urus Ari&longs;t. 
5937 
5938 anim&aelig; definitionem pr&aelig;&shy;<lb/>mittit duplicem e&longs;&longs;e definitionem, alteram &longs;cilicet, qu&aelig; explicat &longs;olum rei <lb/>e&longs;&longs;entiam, quam dicunt formalem definitionem; alteram ver&ograve;, qu&aelig; pr&aelig;te&shy;<lb/>rea explicat etiam rei cau&longs;am, quam dicunt cau&longs;alem definitionem: vtram&shy;<lb/>que autem exemplo Geometrico explicat.</s></p><p type="main">
5939 
5940 <s>In cap. 
5941 
5942 igitur de relatione plura &longs;crip&longs;i de tetragoni&longs;mo, &longs;eu qua dratio&shy;<lb/>ne circuli, qu&aelig; huc &longs;pectant. </s>
5943 
5944 <s>propterea nunc tantum propria huius loci <expan abbr="de-clar&atilde;da">de&shy;<lb/>claranda</expan> re&longs;tant. </s>
5945 
5946 <s>loquitur igitur hic Philo &longs;ophus non de quadratione circuli, <pb pagenum="133"/>&longs;ed figur&aelig; rectiline&aelig; illius, qu&aelig; dicitur Altera parte longior, qualis e&longs;t pr&aelig;&shy;<lb/>&longs;ens figura A B C D, cuius quadrand&aelig; ratio e&longs;t huiu&longs;modi. </s>
5947 
5948 <s>per 13. 6. inue&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.133.1.tif"/><lb/>niatur recta linea media proportionalis inter <lb/>duo latera figur&aelig; A B, B C, <expan abbr="ea&qacute;">eaque</expan>; &longs;it B D, in &longs;e&shy;<lb/>quenti figura. </s>
5949 
5950 <s>e&longs;&longs;e autem mediam proportio&shy;<lb/>nalem nihil aliud e&longs;t quam ita e&longs;&longs;e A B, ad B D, <lb/>&longs;icut B D, ad B C. <expan abbr="dicitur&qacute;">diciturque</expan>; media proportio&shy;<lb/>nalis, quia in hac habitudine medium locum obtinet. </s>
5951 
5952 <s>quadratum autem li&shy;<lb/>ne&aelig; B D, &aelig;quale e&longs;t rectangulo dato A B C D, per 17.6. Inuentio porr&ograve; hu&shy;<lb/>ius medi&aelig; proportionalis, quia facilis e&longs;t, &amp; &longs;citu iucunda, eam &longs;ic habeto. <lb/><figure place="text" xlink:href="figures-la/009.01.133.2.tif"/><lb/>accipe duo latera A B, &amp; B C, <expan abbr="quadr&atilde;di">quadrandi</expan> rectan&shy;<lb/>guli, <expan abbr="ea&qacute;">eaque</expan>; in directum con&longs;titue, vt vnicam re&shy;<lb/>ctam con&longs;tituant A C, vt apparet in figura; de&shy;<lb/>inde diui&longs;a tota A C, bifariam in E, facto cen&shy;<lb/>tro in E, de&longs;cribe &longs;emicirculum &longs;uper lineam <lb/>A C, demum &agrave; puncto B, in quo duo latera con&shy;<lb/>iunguntur, erigatur linea perpendicularis <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>ad periph&aelig;riam, qu&aelig; &longs;it B D. h&aelig;c enim B D, e&longs;t media proportionalis inter <lb/>latera A B, B D, quam nimirum habitudinem habet A B, ad B D, eam quo&shy;<lb/>que obtinet B D, ad B C. <!-- KEEP S--></s>
5953 
5954 <s>Quadratum igitur huius B D, hoc e&longs;t quadratum, <lb/>cuius quatuor latera &longs;iut &aelig;qualia line&aelig; B D, quale e&longs;t pr&aelig;&longs;ens, &aelig;quale erit <lb/><figure place="text" xlink:href="figures-la/009.01.133.3.tif"/><lb/>dato &longs;uperiori rectangulo A B C D, <expan abbr="atq;">atque</expan> hoc modo per&shy;<lb/>acta erit quadratio, &longs;eu tetragoni&longs;mus dati quadrilateri <lb/>A B C D. <!-- KEEP S--></s>
5955 
5956 <s>Vides igitur, qua ratione quadratum con&longs;ti&shy;<lb/>tuatur &aelig;quale dato quadrilatero; &amp; qua rationem inuen&shy;<lb/>tio illius medi&aelig; proportionalis &longs;it cau&longs;a quadratur&aelig; re&shy;<lb/>ctanguli, &amp; proinde &longs;i quis dicat quadrationem hanc e&longs;&longs;e <lb/>effectionem rectanguli &aelig;quilateri, ide&longs;t quadrati, &aelig;qualis dato quadrilate&shy;<lb/>ro, hic definitionem formalem &longs;olum afferet: qu&aelig; definitio, vt dixit in Lo&shy;<lb/>gicis, e&longs;t in&longs;tar conclu&longs;ionis. </s>
5957 
5958 <s>&longs;i quis ver&ograve; dicat tetragoni&longs;mum hunc quadri&shy;<lb/>lateri dati e&longs;&longs;e medi&aelig; pr&aelig;dict&aelig; inuentionem cau&longs;alem afferet definitionem, <lb/>cum rei cau&longs;am dicat. </s>
5959 
5960 <s>Aduerte 10. Grammaticum immerit&ograve; accu&longs;are Ale&shy;<lb/>xandrum, quod dicat quadrationem hanc per inuentionem medi&aelig; propor&shy;<lb/>tionalis tradi in 2. Elem. 
5961 
5962 nam ver&egrave; in 14. 2. traditur talis inuentio, quam&shy;<lb/>uis enim ibi nulla fiat expre&longs;&longs;a mentio huiu&longs;modi medi&aelig;, in ip&longs;a tamen ea<lb/>reperitur, ac per eam figur&aelig; rectiline&aelig; quadrantur: quod patet ex figura <lb/>14. pr&aelig;dict&aelig;, qu&aelig; eadem e&longs;t cum figura 13. 6. qua docemur pr&aelig;dictam in&shy;<lb/>uentionem.</s></p><p type="main">
5963 
5964 <s><arrow.to.target n="marg177"/></s></p><p type="margin">
5965 
5966 <s><margin.target id="marg177"/>186</s></p><p type="main">
5967 
5968 <s>Tex. 86. <emph type="italics"/>(Acutum mouet &longs;en&longs;um in tempore pauco mult&ugrave;m: graue autem in <lb/>multo par&ugrave;m; non igitur velox e&longs;t acutum, graue autem tardum, fed fit illius qui&shy;<lb/>dem propter velocitatem motus huiu&longs;modi, huius autem propter tarditatem)<emph.end type="italics"/> vide <lb/>qu&aelig; de hac re primo topic. </s>
5969 
5970 <s>cap. 
5971 
5972 13. dicta &longs;unt, illa enim omnia in hunc lo&shy;<lb/>cum quadrant. </s>
5973 
5974 <s>Verum occurrit illa dubitatio; quod cum Ari&longs;t. 
5975 
5976 ibi dicat <lb/><emph type="italics"/>(Vox acuta quidem velox)<emph.end type="italics"/> hic autem <emph type="italics"/>(Non igitur velox e&longs;t acutum<emph.end type="italics"/>) repugnan&shy;<lb/>tia dicere videtur. </s>
5977 
5978 <s>cui dubitationi &longs;ic occurrendum; vt dicamus ibi Philo&shy;<lb/>&longs;ophum dicere vocem acutam e&longs;&longs;e velocem, quatenus acumen vocis oritur <pb pagenum="134"/>ex velocitate motus aerem impellentis. </s>
5979 
5980 <s>hic ver&ograve; di&longs;tinguere acutum &agrave; ve&shy;<lb/>loci, tanquam effectum &agrave; cau&longs;a.</s></p><p type="main">
5981 
5982 <s><arrow.to.target n="marg178"/></s></p><p type="margin">
5983 
5984 <s><margin.target id="marg178"/>187</s></p><p type="main">
5985 
5986 <s>Tex. 159. <emph type="italics"/>(Apparent autem, &amp; fal&longs;a, de quibus &longs;imul exi&longs;timationem veram <lb/>habet, vt apparet &longs;ol vnius pedis, per&longs;ua&longs;um autem e&longs;t, eum maiorem e&longs;&longs;e babitata)<emph.end type="italics"/><lb/>habitata, ide&longs;t terra habitata. </s>
5987 
5988 <s>Vide, qu&aelig; cap. 
5989 
5990 3. &longs;umm&aelig; 1. primi Meteor. <lb/><!-- KEEP S--></s>
5991 
5992 <s>Item capite 5. &longs;umm&aelig; 2. de Solis magnitudine &longs;crip&longs;i, ea enim huic loco <lb/>abund&egrave; &longs;atisfaciunt.</s></p></chap><chap><p type="head">
5993 
5994 <s><emph type="italics"/>Ex Tertio de Anima.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
5995 
5996 <s><arrow.to.target n="marg179"/></s></p><p type="margin">
5997 
5998 <s><margin.target id="marg179"/>188</s></p><p type="main">
5999 
6000 <s>Tex. 21. <emph type="italics"/>(Vt incommen&longs;urabile, &amp; diameter)<emph.end type="italics"/> vide, qu&aelig; de incom&shy;<lb/>men&longs;uratione diametri, &amp; co&longs;t&aelig; &longs;cripta &longs;unt lib. 
6001 
6002 1. Priorum, cap. <lb/>23. vnde &longs;atis huic loco fieri pote&longs;t.</s></p><p type="main">
6003 
6004 <s><arrow.to.target n="marg180"/></s></p><p type="margin">
6005 
6006 <s><margin.target id="marg180"/>189</s></p><p type="main">
6007 
6008 <s>Tex 25. <emph type="italics"/>(Punctum autem, &amp; omnis diui&longs;io, &amp; &longs;ic indiui&longs;ibile mon&shy;<lb/>&longs;tratur &longs;i cut priuatio)<emph.end type="italics"/> punctum enim cum &longs;it terminus line&aelig;, e&longs;t negatio vl&shy;<lb/>terioris line&aelig; <emph type="italics"/>(Et omnis diui&longs;io)<emph.end type="italics"/> innuit his verbis pr&aelig;ter punctum, lineam <lb/>etiam, &amp; &longs;uperficiem, nam quemadmodum punctus oritur ex diui&longs;ione li&shy;<lb/>ne&aelig;, ita linea ex diui&longs;ione &longs;uperficiei, &amp; &longs;uperficies ex diui&longs;ione corporis. <lb/></s>
6009 
6010 <s>&amp; quamuis punctum, linea, &longs;uperficies, &longs;int indiui&longs;ibilia, mon&longs;trantur ta&shy;<lb/>men quatenus &longs;unt priuationes, &longs;eu negationes, illud vlterioris line&aelig;, i&longs;ta <lb/>vlterioris &longs;uperficiei, h&aelig;c tandem vlterioris corporis.</s></p><p type="main">
6011 
6012 <s><arrow.to.target n="marg181"/></s></p><p type="margin">
6013 
6014 <s><margin.target id="marg181"/>190</s></p><p type="main">
6015 
6016 <s>Tex. 32. <emph type="italics"/>(Sit igitur vt A, quidem album, ad B, quod nigrum; &longs;ic C, ad D; qua&shy;<lb/>re &amp; permutatim)<emph.end type="italics"/> ide&longs;t, quare &amp; permutando (vt aiunt Geometr&aelig;) erit vt <lb/>A, ad C, ita B, ad D, hunc argumentandi modum &agrave; permutata proportio&shy;<lb/>ne explicaui in primo Po&longs;ter. cap. 
6017 
6018 5. tex. <!-- REMOVE S-->13. dicitur etiam alterna ratio; <lb/>&amp; definitur ab Euclide definitione 12, 5.<!-- KEEP S--></s>
6019 
6020 </p></chap><chap><p type="head">
6021 
6022 <s><emph type="italics"/>Ex Libro de Sen&longs;u.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6023 
6024 <s><arrow.to.target n="marg182"/></s></p><p type="margin">
6025 
6026 <s><margin.target id="marg182"/>191</s></p><p type="main">
6027 
6028 <s>Cap, 6. <emph type="italics"/>(Et qui in Die&longs;i &longs;onus latet, quamuis continuum exi&longs;tentem audit <lb/>omnem cantum, di&longs;t antia enim eius ad extremos &longs;onos latet)<emph.end type="italics"/> quid &longs;it <lb/>Die&longs;is apud Mu&longs;icos explicatum e&longs;t primo Po&longs;ter. tex. <!-- REMOVE S-->38. cum <lb/>autem Die&longs;is &longs;it minima di&longs;tantia, &longs;eu vt loquuntur Mu&longs;ici, mini&shy;<lb/>mum <expan abbr="interuall&utilde;">interuallum</expan> inter duas voces, hinc fit vt h&aelig;c minima di&longs;tantia inter ex&shy;<lb/>tremos &longs;onos non exaudiatur, quemadmodum nec minima particula alicu&shy;<lb/>ius magni corporis &agrave; long&egrave; vi&longs;i <expan abbr="n&otilde;">non</expan> percipitur, &longs;ed latetinter extrema illius.</s>
6029 
6030 </p><p type="main">
6031 
6032 <s><arrow.to.target n="marg183"/></s></p><p type="margin">
6033 
6034 <s><margin.target id="marg183"/>192</s></p><p type="main">
6035 
6036 
6037 <s>Cap. 8. <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> magis e&longs;t &longs;entire &longs;implex exi&longs;tens, qu&agrave;m mixtum, velut <lb/>vinum non temperatum, qu&agrave;m temperatum; &amp; mel, &amp; colorem, &amp; neten &longs;olam. <lb/></s>
6038 
6039 
6040 <s>qu&agrave;m in diapa&longs;on, quia ob&longs;curant &longs;e inuicem)<emph.end type="italics"/> nete apud veteres mu&longs;icos erat <lb/>in mu&longs;icis in&longs;trumentis omnium chordarum acuti&longs;&longs;ima, cuiu&longs;modi apud <lb/>nos e&longs;t, quam vulg&ograve; canto appellant. </s>
6041 
6042 <s>Hypate ver&ograve; erat chorda omnium <lb/>graui&longs;&longs;ima, qualis e&longs;t ea, quam modo Ba&longs;&longs;o vocant. </s>
6043 
6044 <s>h&aelig; du&aelig; &longs;imul pul&longs;at&aelig; <lb/>edebant conionantiam, qu&aelig; Diapa&longs;on dicitur, &amp; vulg&ograve; octaua. </s>
6045 
6046 <s>ex quibus <lb/>&longs;en&longs;us verberum Ari&longs;t. 
6047 
6048 manife&longs;tus e&longs;t.</s></p><pb pagenum="135"/><p type="main">
6049 
6050 <s><arrow.to.target n="marg184"/></s></p><p type="margin">
6051 
6052 <s><margin.target id="marg184"/>193</s></p><p type="main">
6053 
6054 <s>Eodem cap. <emph type="italics"/>(Velut Diapa&longs;on, &amp; Diapente)<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa&shy;<lb/>&longs;on, explicaui in primo Po&longs;ter. tex. <!-- REMOVE S-->1. Diapente ver&ograve; e&longs;t con&longs;onantia ex duo&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.135.1.tif"/><lb/>bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>3. ad 2. qu&aelig; dicitur &longs;e&longs;quialtera. </s>
6055 
6056 
6057 
6058 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;int du&aelig; <lb/>chord&aelig; &aelig;qualis cra&longs;fitiei, <expan abbr="atq;">atque</expan> &aelig;qu&egrave; ten&longs;&aelig;: vna <lb/>tamen habeat ad alteram proportionem &longs;e&longs;&shy;<lb/>quialteram, vt in figura apparet; &longs;i &longs;imul pul&shy;<lb/>&longs;entur, edent con&longs;onantiam Diapente. <!-- KEEP S--></s>
6059 
6060 
6061 
6062 
6063 
6064 <s>vulg&ograve; autem quinta.</s></p></chap><chap><p type="head">
6065 
6066 <s><emph type="italics"/>Ex Libro de Memoria, &amp; remini&longs;centia.<emph.end type="italics"/></s></p><p type="main">
6067 
6068 <s><arrow.to.target n="marg185"/></s></p><p type="margin">
6069 
6070 <s><margin.target id="marg185"/>194</s></p><p type="main">
6071 
6072 
6073 <s>Cap. 1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis &aelig;quales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos &aelig;qua&shy;<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s>
6074 
6075 
6076 <s>lege annotata primo <lb/>Po&longs;ter. &longs;ecto 3. cap. 
6077 
6078 1.<!-- KEEP S--></s></p><p type="main">
6079 
6080 <s><arrow.to.target n="marg186"/></s></p><p type="margin">
6081 
6082 <s><margin.target id="marg186"/>195</s></p><p type="main">
6083 
6084 
6085 <s>Cap. 3. <emph type="italics"/>(Sunt facil&egrave; remini&longs;cibilia, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> habent ordinationem aliquam, <lb/>vt mathemata)<emph.end type="italics"/> h&ecedil;c Philo&longs;ophus dicensfp ectabat ad mirabilem illam, ac per&shy;<lb/>petuam de mon&longs;trationum connexionem, qua Geometr&aelig; omnes, &amp; pr&aelig;ci&shy;<lb/>pu&egrave; Euclides opera &longs;ua ab initio ad finem v&longs;que, diuino plan&egrave; ingenij acu&shy;<lb/>mine deduxerunt.</s>
6086 </p></chap><chap><p type="head">
6087 
6088 <s><emph type="italics"/>Ex Libro de Somnijs.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6089 
6090 <s><arrow.to.target n="marg187"/></s></p><p type="margin">
6091 
6092 <s><margin.target id="marg187"/>196</s></p><p type="main">
6093 
6094 
6095 <s>Cap. 2. <emph type="italics"/>(Cur autem fallimur, cau&longs;a e&longs;t, quoniam non &longs;olum cum &longs;en&longs;ibile <lb/>mouetur apparent qu&aelig;libet, &longs;ed etiam cum &longs;en&longs;us ip&longs;e mouetur, &longs;i eodem <lb/>modo moueatur, quemadmodum &agrave; &longs;en&longs;ibili. </s>
6096 
6097 
6098 <s>dico autem velut terra vi&shy;<lb/>detur nauigantibus moueri, dummodo vi&longs;us ab alio)<emph.end type="italics"/> reddit rationem, <lb/>cur nauigantibus videatur terra ip&longs;a moueri, ac retrocedere, non autem <lb/>ip&longs;i nauigantes, quin potius ip&longs;i fibi &longs;tare videantur. </s>
6099 
6100 <s>cau&longs;am igitur eam e&longs;&shy;<lb/>&longs;e ait, quia ex motu nauis, terra ip&longs;a manente, accidit, vt eodem modo im&shy;<lb/>mutetur &longs;en&longs;us vi&longs;us, ac &longs;i terra ip&longs;a moueretur, vi&longs;us ver&ograve; quie&longs;ceret. <lb/></s>
6101 
6102 <s>At cur eodem modo afficitur &longs;en&longs;us? </s>
6103 
6104 <s>Per&longs;pectiuirationem e&longs;&longs;e dicunt, quia <lb/>ea, qu&aelig; circa oculum &longs;unt, vt nauis, &amp; ea, qu&aelig; in naui &longs;unt, non mutant &longs;i&shy;<lb/>tum re&longs;pectu oculi, quemadmodum facerent, &longs;i nos ip&longs;i &longs;ine naui progrede&shy;<lb/>remur. </s>
6105 
6106 <s>arbores autem, &amp; reliqua, qu&aelig; in terra &longs;unt, variant &longs;itum re&longs;pectu <lb/>oculi, non &longs;ecus, ac &longs;i ip&longs;&aelig; arbores retro deferrentur. </s>
6107 
6108 <s>propterea igitur vi&longs;us <lb/>tunc arbores remeare iudicat, quia qu&aelig; circa oculum &longs;unt re&longs;pectu ip&longs;ius <lb/>oculi non mouentur, &longs;iue non variant &longs;itum ad ip&longs;um; ex variatione enim <lb/>&longs;itus rei re&longs;pectu oculi, percipimus cuiu&longs;uis rei localem motum.</s></p><p type="main">
6109 
6110 <s><arrow.to.target n="marg188"/></s></p><p type="margin">
6111 
6112 <s><margin.target id="marg188"/>197</s></p><p type="main">
6113 
6114 
6115 <s>Cap. 3. <emph type="italics"/>(Quemadmodum igitur, &longs;i quem lateat &longs;uppo&longs;itus oculo digitus, non <lb/>&longs;olum app trebit, &longs;ed etiam putabitur duo, quod e&longs;t vnum. </s>
6116 
6117 
6118 <s>Si ver&ograve; non lateat appa&shy;<lb/>rebit quidem, non putabitur tamen)<emph.end type="italics"/> e&longs;t h&aelig;c optica deceptio, qu&aelig; tunc accidit, <lb/>cum aliquod obiectum intuentes, interim digito alterum oculum &longs;ur&longs;um <lb/>pellimus, ita vt oculi propterea varient &longs;itum re&longs;pectu obiecti, &longs;iue non eo&shy;<pb pagenum="136"/>dem &longs;itu vterque obiectum intueatur, hoc e&longs;t, vt optici aiunt, axes vi&longs;uales <lb/>non amplius concurrunt &longs;imul in rem vi&longs;am. </s>
6119 
6120 <s>Vnde &longs;equitur &longs;peciem rei in&shy;<lb/>tentionalem oculis vario &longs;itu affectis imprimi, ac proinde eam eundem &longs;i&shy;<lb/>tum in vtroque oculo minim&egrave; obtinere, &longs;ed ea, qu&aelig; oculo &agrave; &longs;uo naturali <lb/>&longs;latu dimoto accidit ab altera alterius oculi differt; quapropter vario <lb/>ctiam modo, duplici nimirum, obiectum repre&longs;entant. </s>
6121 
6122 <s>atque h&aelig;c <lb/>ip&longs;a cau&longs;a e&longs;t, cur illud, quod vnum tantum e&longs;t, duo tamen <lb/>emoto oculorum altero, videatur. </s>
6123 
6124 <s>Vide Alhaze&shy;<lb/>num lib. 
6125 
6126 3. propo&longs;it. </s>
6127 
6128 <s>11. &amp; 12. &amp; infra <lb/>Problem. 7. &longs;ectionis 31.</s></p></chap><pb pagenum="137"/><chap><p type="head">
6129 
6130 <s>EX PRIMO<lb/>METAPHYSICAE.</s></p><p type="main">
6131 
6132 <s><arrow.to.target n="marg189"/></s></p><p type="margin">
6133 
6134 <s><margin.target id="marg189"/>198</s></p><p type="main">
6135 
6136 <s>Capite 1. <emph type="italics"/>(Cirea Aegyptum Mathematic&aelig; artes constitut&aelig; &longs;unt; illic <lb/>enim gens Sacerdotum vacare permittitur)<emph.end type="italics"/> Notanda maxim&egrave; no&shy;<lb/>bilis Mathematicarum origo, cum ab Aegyptiorum Sacerdoti&shy;<lb/>bus te&longs;te Philo&longs;opho fuerint adinuent&aelig;, quibus occa&longs;ionem pr&aelig;&shy;<lb/>buit anniuer&longs;aria agrorum ob Nili innundationem, diui&longs;io: cum enim iam <lb/>perplures dimetiendorum agrorum rationes repert&aelig; fui&longs;&longs;ent, Sacerdotes <lb/>ip&longs;i, quibus per otium licebat, illarum praxium demon&longs;tr ationes c&oelig;perunt <lb/>perue&longs;tigare, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; paulatim po&longs;tea Geometria amplius exculta adoleuit; <lb/>qu&aelig; deinde ij&longs;dem ad res a&longs;tronomicas per&longs;crutandas <expan abbr="adium&etilde;to">adiumento</expan> fuit, <expan abbr="hac&qacute;">hacque</expan>; <lb/>ratione reliquas etiam in mathematicas inciderunt.</s></p><p type="main">
6137 
6138 <s><arrow.to.target n="marg190"/></s></p><p type="margin">
6139 
6140 <s><margin.target id="marg190"/>199</s></p><p type="main">
6141 
6142 
6143 <s>Cap. 2. <emph type="italics"/>(Sicut de pr&aelig;&longs;tigio&longs;is, qu&aelig; per &longs;e mouentur, illi qui nondum &longs;peculati <lb/>&longs;unt cau&longs;am<emph.end type="italics"/>) verbis illis (<emph type="italics"/>Qu&aelig; per &longs;emouentur<emph.end type="italics"/>) vnica dictio <expan abbr="Gr&aelig;care&longs;p&otilde;det">Gr&aelig;care&longs;pondet</expan>, <lb/>Automata. <!-- KEEP S--></s>
6144 
6145 
6146 <s>erant autem Automata apud veteres Gr&ecedil;cos machin&aelig; qu&ecedil;dam, <lb/>qu&aelig; &agrave; Mathematicis Mechanic&aelig; artis occultis quibu&longs;dam ingenijs, ea arte <lb/>con&longs;truebantur, vt &agrave; &longs;eip&longs;is de loco ad locum, ac &longs;i viu&aelig; e&longs;&longs;ent &longs;pont&egrave; pro&shy;<lb/>grederentur; vnde, &amp; automata, qua&longs;i &longs;pontanca dicebantur. </s>
6147 
6148 <s>Extat adhuc <lb/>de huiu&longs;modi machinis liber Heronis Alexandrini, quem nuper ex gr&aelig;co <lb/>latinum reddidit docti&longs;&longs;imus Abbas Gua&longs;tallenfis. </s>
6149 
6150 <s>de huiu&longs;modi artificio&longs;is <lb/>operibus, quibus &longs;&aelig;p&egrave; pri&longs;ci ita admirationi fuere, vt pr&aelig;&longs;tigia qu&aelig;dam ar&shy;<lb/>tificium ignorantibus, viderentur, intelligit hoc loco Ari&longs;t.<!-- KEEP S--></s></p><p type="main">
6151 
6152 <s><arrow.to.target n="marg191"/></s></p><p type="margin">
6153 
6154 <s><margin.target id="marg191"/>200</s></p><p type="main">
6155 
6156 
6157 <s>Cap. 3. (<emph type="italics"/>Aut de &longs;ol&longs;titijs<emph.end type="italics"/>) quid &longs;ol&longs;titium, cur dicatur &longs;ol&longs;titium, &amp; cur Sol <lb/>in <expan abbr="vtroq;">vtroque</expan> topico, quoad dierum incrementum, ac decrementum, &amp; quoad <lb/>eleuationem eius, aut depre&longs;&longs;ionem meridianam, videatur moras trahere, <lb/>quamuis no&longs;trum &longs;it explicare, ob rei tamen facilitatem omittantur. </s>
6158 
6159 
6160 <s>Hoc <lb/>tantum &longs;cias velim &longs;ol&longs;titiorum cau&longs;am e&longs;&longs;e Zodiaci ad Tropicos longio&shy;<lb/>rem adh&aelig;&longs;ionem, ide&longs;t, qu&ograve;d Zodiacus prop&egrave; contactum tropicorum ab ijs <lb/>parum recedat, cum ergo Sol motu proprio &longs;emper per Zodiacum inam&shy;<lb/>bulet, fit vt ip&longs;e <expan abbr="quoq;">quoque</expan> pariter modicum &agrave; tropicis remoueatur, im&ograve; pluri&shy;<lb/>mum &longs;ecus illos incedat, ita vt eo tempore, quo ad eos paulatim accedit, <lb/>aut ab eis paulatim recedit, qua&longs;i &longs;tare, &longs;iue quie&longs;cere apud eo&longs;dem videa&shy;<lb/>tur: <expan abbr="atq;">atque</expan> hinc etiam quantitas <expan abbr="dier&utilde;">dierum</expan>, ac noctium videatur fer&egrave; nihil variari; <lb/>&amp; noua elcuatio, aut depre&longs;&longs;io Solis &longs;upra horizontem nuila fer&egrave; appareat.</s></p><p type="main">
6161 
6162 <s><arrow.to.target n="marg192"/></s></p><p type="margin">
6163 
6164 <s><margin.target id="marg192"/>201</s></p><p type="main">
6165 
6166 <s>Ibidem (<emph type="italics"/>Aut de diametri incommen&longs;ur abilitate, admirabile enim omnibus vi&shy;<lb/>detur, &longs;i quid, cum non &longs;it minimum non men&longs;uretur, decet autem in contrarium, <lb/>&amp; in melius &longs;ecundum prouerbium con&longs;umare, quemadmod&ubreve; in his fit, cum di&longs;cant, <lb/>nihil enim magis vir Geometricus admiraretur, qu&agrave;m &longs;i diamcter commen&longs;urabi&shy;<lb/>lis &longs;ieret<emph.end type="italics"/>) vide qu&aelig; de hac commen&longs;urabilitate &longs;crip&longs;i lib. 
6167 
6168 1. Priorum, &longs;ect. </s>
6169 
6170 <s>1. <lb/>cap. 
6171 
6172 1. Videtur inquit mirum &agrave; principio Geometriam aggredienti diame&shy;<lb/>trum, &amp; latus eiu&longs;dem quadrati non commen&longs;urari, cum in neutro eorum <lb/>detur minimum, &longs;eu indiui&longs;ibile, videtur enim omne diui&longs;ibile po&longs;&longs;e men&longs;u&shy;<pb pagenum="138"/>rari. </s>
6173 
6174 <s>po&longs;tea tamen cum in Geometria ver&longs;atus fuerit, maxim&egrave; admirare&shy;<lb/>tur, &longs;i audiret diametrum e&longs;&longs;e lateri commen&longs;urabilem.</s></p><p type="main">
6175 
6176 <s><arrow.to.target n="marg193"/></s></p><p type="margin">
6177 
6178 <s><margin.target id="marg193"/>202</s></p><p type="main">
6179 
6180 <s>Summa 2. cap. 
6181 
6182 3. (<emph type="italics"/>Pythagorici primi Mathematicis operam dedere, h&aelig;c pr&aelig;po&shy;<lb/>nebant, &amp; in cis enutriti, eorum principia, entium <expan abbr="quoq;">quoque</expan> cunctorum putant e&longs;&longs;e <lb/>principia<emph.end type="italics"/>) vtinam no&longs;trates Philo&longs;ophi Pythagoricos imitarentur; enimue&shy;<lb/>r&ograve; mult&ograve; melius &amp; &longs;ibi, &amp; Philo&longs;ophi&aelig; con&longs;ulerent. </s>
6183 
6184 <s>At ver&ograve; non &longs;ine ma&shy;<lb/>gno artium, <expan abbr="atq;">atque</expan> di&longs;ciplinarum omnium di&longs;pendio &agrave; plurimis hac tempe&shy;<lb/>&longs;tate de&longs;pectui habentur; &longs;ed quid mirum cum quas &longs;cientiarum omnium <lb/>alumni Pythagorei omnibus &longs;cientijs anteferebant; eas no&longs;tri &longs;eculi quam&shy;<lb/>plures omnibus alijs facultatibus po&longs;thabeant.</s></p><p type="main">
6185 
6186 <s><arrow.to.target n="marg194"/></s></p><p type="margin">
6187 
6188 <s><margin.target id="marg194"/>203</s></p><p type="main">
6189 
6190 <s>Tex. 47. (<emph type="italics"/>Qui Geometriam di&longs;cit aliqua pr&aelig;&longs;cire contingit<emph.end type="italics"/>) ide&longs;t definitio&shy;<lb/>nes, po&longs;tulata, axiomata, qu&aelig; &longs;unt tria principiorum genera, ex quibus to&shy;<lb/>ta Geometria deducitur.</s></p></chap><chap><p type="head">
6191 
6192 <s><emph type="italics"/>Ex Secundo Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6193 
6194 <s><arrow.to.target n="marg195"/></s></p><p type="margin">
6195 
6196 <s><margin.target id="marg195"/>204</s></p><p type="main">
6197 
6198 <s>Tex. 14. (<emph type="italics"/>Quantam ver&ograve; vim con&longs;uetudo habeat, leges declar ant, in qui&shy;<lb/>bus fabulo&longs;a, ac puerilia plus po&longs;&longs;unt propter con&longs;uetudinem, qu&agrave;m &longs;i <lb/>ea cogno&longs;ceremus<emph.end type="italics"/>) per leges intelligit cantilenas illas, quas vete&shy;<lb/>res Mu&longs;ici leges appellabant, e&ograve; qu&ograve;d eas &longs;olas, c&aelig;teris abroga&shy;<lb/>tis liceret lata lege decantari. </s>
6199 
6200 <s>Vide declarationem problematis 15. &amp; 28. <lb/>&longs;ect. </s>
6201 
6202 <s>19. <expan abbr="problemat&utilde;">problematum</expan> vbi <expan abbr="tanqu&atilde;">tanquam</expan> in proprio loco i&longs;ta fu&longs;ius pertractabuntur.</s></p></chap><chap><p type="head">
6203 
6204 <s><emph type="italics"/>Ex Tertio Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6205 
6206 <s><arrow.to.target n="marg196"/></s></p><p type="margin">
6207 
6208 <s><margin.target id="marg196"/>205</s></p><p type="main">
6209 
6210 <s>Tex. 3. Verba huius textus, cum &longs;atis per&longs;picua &longs;int, ac parum ma&shy;<lb/>thematicis indigeant, omittenda duxi. </s>
6211 
6212 <s>Quod ad mathematicas <lb/>attinet, ait, eas non demon&longs;trare, nec per cau&longs;am finalem, nec <lb/>per efficientem (quod intelligendum e&longs;t de Mathematicis puris, <lb/>&amp; &longs;peculatiuis nam mathematic&aelig; practic&aelig; reliquas etiam cau&longs;as, efficien&shy;<lb/>tem, &amp; finalem nece&longs;&longs;ari&ograve; habere debent, quapropter &longs;ophi&longs;ta quidam no&shy;<lb/>mine Ari&longs;tippus, eas irridebat, <expan abbr="atq;">atque</expan> adeo illiberalibus, ac &longs;edentarijs arti&shy;<lb/>bus po&longs;thabebat, qu&aelig; cau&longs;am efficientem, quia &longs;cilicet operantur, &amp; fina&shy;<lb/>lem &longs;cilicet qu&aelig;&longs;tum &longs;ibi proponunt. </s>
6213 
6214 <s>fuit autem i&longs;te ex Plutarcho, &amp; Laer&shy;<lb/>tio primus, qui pacto pretio doceret, <expan abbr="philo&longs;ophiam&qacute;">philo&longs;ophiamque</expan>; faceret qu&aelig;&longs;tuo&longs;am: <lb/><expan abbr="ideo&qacute;">ideoque</expan>; mathematicas paruipendebat, qu&ograve;d neglecta cau&longs;a efficiente, nihil <lb/>efficerent; &amp; finali, nihil lucrarentur. </s>
6215 
6216 <s>videas igitur quales &longs;int pulcherrima&shy;<lb/>rum facultatum contemptores, ij nimirum, qui philo&longs;ophi&aelig;, aut lucri, aut <lb/>ambitionis cau&longs;a dant operam. </s>
6217 
6218 <s>Quod autem Mathematic&aelig; nihil efficiant, <lb/><expan abbr="nihil&qacute;">nihilque</expan>; lucrentur, ne videamur vtile paruifacere, e&longs;t omnin&ograve; fal&longs;um: &longs;unt <lb/>enim plures mathematic&aelig; practic&aelig;, qu&aelig; innumera, <expan abbr="atq;">atque</expan> <expan abbr="admir&atilde;da">admiranda</expan> efficiunt <lb/>opera, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; magnos qu&aelig;&longs;tus quotidie faciunt. </s>
6219 
6220 <s>huiu&longs;modi &longs;unt Geometria <lb/>practica, qua men&longs;urationes omnes vel &longs;olo vi&longs;u perficiuntur. </s>
6221 
6222 <s>Arithmeti&shy;<lb/>ca, cuius v&longs;us qu&agrave;m lat&egrave; patet? </s>
6223 
6224 <s>Mu&longs;ica practica, qua quotidie ip&longs;i oblecta&shy;<pb pagenum="139"/>mur; <expan abbr="Deo&qacute;">Deoque</expan>; Optimo Maximo laudes debitas concinimus. </s>
6225 
6226 <s>Mechanica pra&shy;<lb/>ctica, cuius ope ingentia pondera, vel exigua vi, <expan abbr="inuita&qacute;">inuitaque</expan>; natura &longs;u&longs;g; <expan abbr="de&qacute;">deque</expan>; <lb/>commouentur. </s>
6227 
6228 <s>Per&longs;pectiua, qu&aelig; Pictoribus, &amp; Architectoribus adeo in&longs;er&shy;<lb/>uit, vt <expan abbr="ab&longs;q;">ab&longs;que</expan> ea nihil ferm&egrave; audeant. </s>
6229 
6230 <s>A&longs;tronomia tandem, &longs;i in praxim de&shy;<lb/>ducatur, ex vna &longs;olum eclyp&longs;ium pr&aelig;dictione, quantam vniuer&longs;o orbi ad&shy;<lb/>mirationem parit? </s>
6231 
6232 <s>mitto hanc &longs;olam dierum, men&longs;ium, &amp; annorum di&longs;tri&shy;<lb/>butionem, ac temporum emendationem exhibere, rem ade&ograve; Reipublic&aelig; <lb/>Chri&longs;tian&aelig; nece&longs;&longs;ariam.</s></p><p type="main">
6233 
6234 <s><arrow.to.target n="marg197"/></s></p><p type="margin">
6235 
6236 <s><margin.target id="marg197"/>206</s></p><p type="main">
6237 
6238 <s>Eodem tex. <!-- REMOVE S-->3. (<emph type="italics"/>Item &amp; in c&aelig;teris tunc &longs;cire vnumquodque arbitramur torum, <lb/>quorum &longs;unt demonstrationes, cum quid e&longs;t &longs;ciamus, vt puta quid tetragoni&longs;mus, <lb/>qu&ograve;d inuentio medi&aelig;<emph.end type="italics"/>) eadem reperies &longs;uperius in &longs;ecundo de Anima, tex. <!-- REMOVE S-->12. <lb/>fu&longs;ius explicata.</s>
6239 
6240 
6241 
6242 </p><p type="main">
6243 
6244 <s><arrow.to.target n="marg198"/></s></p><p type="margin">
6245 
6246 <s><margin.target id="marg198"/>207</s></p><p type="main">
6247 
6248 <s>Tex. 8. (<emph type="italics"/>Si enim in hoc differret &longs;olum Geometria &agrave; Geod&aelig;&longs;ia, quod h&aelig;c quidem <lb/>eorum e&longs;t, qu&aelig; &longs;entimus, illa ver&ograve; non &longs;en&longs;ibilium e&longs;t<emph.end type="italics"/>) Geod&aelig;&longs;ia e&longs;t pars Geo&shy;<lb/>metri&aelig; practic&aelig;, ea &longs;cilicet, qu&aelig; circa diui&longs;ionem &longs;uperficierum ver&longs;atur. <lb/></s>
6249 
6250 <s>audi Pedia&longs;mum de men&longs;uratione: Terr&aelig; inquit men&longs;uratio in duas partes <lb/>diuiditur, Geometriam &longs;cilicet, &amp; Geod&aelig;&longs;iam: Are&aelig; <expan abbr="namq;">namque</expan> &longs;ecundum ar&shy;<lb/>tem men&longs;uratio, &amp; terr&aelig; men&longs;uratio e&longs;t, &amp; merit&ograve; Geometria vocatur. <lb/></s>
6251 
6252 <s>Vnius ver&ograve;, &amp; eiu&longs;dem are&aelig;, &longs;eu loci diui&longs;io inter diuer&longs;as per&longs;onas, parti&shy;<lb/>tio qu&aelig;dam e&longs;t terr&aelig;, &amp; iure optimo Geod&aelig;&longs;ia appellatur. </s>
6253 
6254 <s>h&aelig;cille. </s>
6255 
6256 <s>dicitur <lb/>autem Geod&aelig;&longs;ia &agrave; <foreign lang="greek">gea</foreign>, terra, &amp; <foreign lang="greek">da/iw</foreign>, diuido. </s>
6257 
6258 <s>Vocabulum tamen i&longs;tud Geo&shy;<lb/>d&aelig;&longs;i&aelig; fuit po&longs;tea ad latiorem tran&longs;latum &longs;ignificationem: extat enim Geo&shy;<lb/>d&aelig;&longs;ia Heronis Mechanici antiqui &longs;criptoris, quampridem Baroccius lati&shy;<lb/>nitate donauit, qu&aelig; quidem ars e&longs;t eadem cum Geometria practica, cum <lb/>non &longs;olum diui&longs;iones, &longs;ed men&longs;urationes omnes etiam per dioptricam f&shy;<lb/>cultatem, &longs;eu per lineas vi&longs;uales doceat inue&longs;tigare.</s></p></chap><chap><p type="head">
6259 
6260 <s><emph type="italics"/>Ex Quarto Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6261 
6262 <s><arrow.to.target n="marg199"/></s></p><p type="margin">
6263 
6264 <s><margin.target id="marg199"/>208</s></p><p type="main">
6265 
6266 <s>Tex. 4. <emph type="italics"/>(Philo&longs;ophus <expan abbr="namq;">namque</expan> e&longs;t, vt ille, qui Mathematicus dicitur, &amp; <lb/>b&aelig;c enim habet partes: ac prima qu&aelig;dam, &amp; &longs;ecunda &longs;cientia e&longs;t: c&aelig; <lb/>ter&aelig; <expan abbr="quoq;">quoque</expan> con&longs;equenter in mathematibus<emph.end type="italics"/>) inter mathematicas pri&shy;<lb/>m&aelig; &longs;cienti&aelig; &longs;unt Geometria, &amp; Arithmetica, quia ip&longs;&aelig; &agrave; c&aelig;teris <lb/>nulla ratione dependent; im&ograve; c&aelig;ter&aelig; ip&longs;is innituntur, qu&aelig; &longs;ecund&aelig; hoc lo&shy;<lb/>co appellantur, h&aelig; &longs;unt Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia. <!-- KEEP S--></s>
6267 
6268 <s>illas <lb/>duas recentiores &longs;ubalternantes, has ver&ograve; &longs;ecundas &longs;ubalternatas vocant. <lb/></s>
6269 
6270 <s>Exempla &longs;ubalternationum varia attuli in Logicis tex. <!-- REMOVE S-->20. &amp; 23. primi Po&shy;<lb/>&longs;ter. <!-- REMOVE S-->vbi clar&egrave; licet intueri quid &longs;it &longs;ubalternatio, vnde etiam pr&aelig;&longs;ens lo&shy;<lb/>cus illu&longs;tratur.</s>
6271 
6272 
6273 
6274 </p><p type="main">
6275 
6276 <s><arrow.to.target n="marg200"/></s></p><p type="margin">
6277 
6278 <s><margin.target id="marg200"/>209</s></p><p type="main">
6279 
6280 <s>Tex. 28. (<emph type="italics"/>Vti diametrum commen&longs;urabilem e&longs;&longs;e<emph.end type="italics"/>) legenda &longs;unt ea, qu&aelig; libro <lb/>primo Priorum, &longs;ecto 1. cap. 
6281 
6282 23. de hac commen&longs;urabilitate, &amp; incommen&shy;<lb/>&longs;urabilitate tractata &longs;unt.</s></p></chap><pb pagenum="140"/><chap><p type="head">
6283 
6284 <s><emph type="italics"/>Ex Quinto Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6285 
6286 <s><arrow.to.target n="marg201"/></s></p><p type="margin">
6287 
6288 <s><margin.target id="marg201"/>210</s></p><p type="main">
6289 
6290 <s>Tex. 2. (<emph type="italics"/>Alia ver&ograve; cau&longs;a e&longs;t forma, &amp; exemplar: h&aelig;c autem e&longs;t ratio ip&shy;<lb/>&longs;ius quid erat e&longs;&longs;e, &amp; borum genera, vt ip&longs;ius Diapa&longs;on duo ad vnum, <lb/>&amp; &longs;impliciter numerus, &amp; partes, qu&aelig; in ra ione &longs;unt<emph.end type="italics"/>) affert exem&shy;<lb/>plum cau&longs;&aelig; formalis ex Mu&longs;ica petitum; <expan abbr="ait&qacute;">aitque</expan>; cau&longs;am formalem <lb/>illius con&longs;onanti&aelig;, qu&aelig; Diapa&longs;on dicitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; omnium perfecti&longs;&longs;ima, e&longs;&longs;e <lb/>duplam proportionem, ide&longs;t, qu&aelig; e&longs;t inter duo, &amp; vnum, id, quod omnes <lb/>Mu&longs;ici <expan abbr="fat&etilde;tur">fatentur</expan>. </s>
6291 
6292 <s>quod vtinelius intelligas, repete, qu&aelig; in 2. Po&longs;ter. ad tex. <!-- REMOVE S-->1. <lb/>&longs;cripta &longs;unt: necnon qu&aelig; in libro de Sen&longs;u in cap. 
6293 
6294 8. Amplius inquit can&longs;am <lb/>formalem genericam eiu&longs;dem Diapa&longs;on e&longs;&longs;e numerum, &amp; partes numeri, <lb/>&longs;ub numero enim continentur &amp; duo, &amp; vnum. </s>
6295 
6296 
6297 
6298 <s>Occurrit hoc loco vnum <lb/>magnopere notandum, videlicet tam con&longs;onantias, quam di&longs;&longs;onantias ha&shy;<lb/>bere proportiones numerorum, hoc tamen di&longs;crimine, quod con&longs;onanti&aelig; <lb/>habent &longs;ol&ugrave;m proportiones numerorum eorum, qui quaternario continen&shy;<lb/>tur, ex veterum pr&aelig;&longs;ertim Pythagoreorum &longs;ententia, qui propterea vltra <lb/>quaternarium progredi vetabant. </s>
6299 
6300 <s>Recentiores tamen y&longs;que ad &longs;enarium <lb/>procedunt, quippe, qui omnes vocum con&longs;onantias admittunt, qu&aelig; pro&shy;<lb/>portionibus numerorum &longs;enario contentorum pr&aelig;dit&aelig; &longs;int. </s>
6301 
6302 <s>Di&longs;&longs;onanti&aelig; <lb/>ver&ograve; &longs;eoundum pri&longs;cos habent proportiones numerorum extra quaterna&shy;<lb/>rium progredientium, iuxta no&longs;tros autem extra &longs;enarium. </s>
6303 
6304 <s>qua de re pluri&shy;<lb/>bus Zarlinus colloquio 2. definit. </s>
6305 
6306 <s>3.<!-- KEEP S--></s></p><p type="main">
6307 
6308 <s><arrow.to.target n="marg202"/></s></p><p type="margin">
6309 
6310 <s><margin.target id="marg202"/>211</s></p><p type="main">
6311 
6312 <s>Tex. 3. <emph type="italics"/>(Partes <expan abbr="quoq;">quoque</expan> totius<emph.end type="italics"/>) ide&longs;t &longs;unt inateria; loquitur enim de cau&longs;a <lb/>materiali. </s>
6313 
6314 <s>libuit locum hunc annotare in gratiam Geometricarum demon&shy;<lb/>&longs;trationum, quorum media &longs;&aelig;p&egrave; &longs;unt ex cau&longs;a materiali &longs;umpta, quod ta&shy;<lb/>men non ita ab omnibus ob&longs;eruatur, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim probant affe ctio&shy;<lb/>nem quampiam de aliquo &longs;ubiecto, ex eo, quod &longs;ubiectum illud &longs;it, vel di&shy;<lb/>midium alicuius, vel duplum, vel reliquum, vel tertia pars, &amp; his &longs;imilia, <lb/>erit talis ratio in genere cau&longs;&aelig; materialis. </s>
6315 
6316 <s><expan abbr="neq;">neque</expan> e&longs;t cur recentiores quidam, <lb/>naturalibus &longs;cientijs a&longs;&longs;ueti, negent huiu&longs;modi materiam veram e&longs;&longs;emate&shy;<lb/>riam, ac proinde neq, Geometricas demon&longs;trationes veras e&longs;&longs;e demon&longs;tra&shy;<lb/>tiones; dicendum enim talem quidem materiam non e&longs;&longs;e veram materiam <lb/>phy&longs;icam, &amp; proinde illas demon&longs;trationes <expan abbr="n&otilde;">non</expan> e&longs;&longs;e veras naturales demon&shy;<lb/>&longs;irationes, e&longs;&longs;e tamen veram materiam intelligibilem, qu&aelig; Geometri&aelig; &longs;u&shy;<lb/>bijcitur, &amp; proinde demon&longs;trationes illas veras e&longs;&longs;e demon&longs;trationes Geo&shy;<lb/>metricas; id quod Ari&longs;t. &longs;&aelig;pius in libris Po&longs;ter, apert&egrave; &longs;ignificat, tum a&longs;&longs;er&shy;<lb/>tionibus, tum exemplis quamplurimis. </s>
6317 
6318 <s>Quapropter cauendum e&longs;t illis, ne <lb/>ingrati animi notam incurrant, dum pulcherrimam artem re&longs;olutoriam, <lb/>quam Ari&longs;t. &agrave; Mathematicis acceptam omnibus &longs;cientijs accommodauit <lb/>(vt initio Priorum o&longs;ten&longs;um e&longs;t) eam ip&longs;i ita alijs facultatibus adaptent, vt <lb/>Mathematicis ip&longs;is, ex quibus orta, &amp; &longs;ub quibus adoleuit, pulla ratione <lb/>conuenire poi&longs;it. </s>
6319 
6320 <s>De hac materia fu&longs;ius infra in additamento de natura Ma&shy;<lb/>thematicarum.</s></p><p type="main">
6321 
6322 <s><arrow.to.target n="marg203"/></s></p><p type="margin">
6323 
6324 <s><margin.target id="marg203"/>212</s></p><p type="main">
6325 
6326 <s>Tex. 3. (<emph type="italics"/>Et ip&longs;ius Diapa&longs;on duplum, &amp; numerus<emph.end type="italics"/>) &longs;cilicet cau&longs;&aelig; formales <lb/>&longs;unt, quemadmodum &longs;upra tex. <!-- REMOVE S-->2. huius cap. 
6327 
6328 explicatum e&longs;t.</s>
6329 
6330 </p><pb pagenum="141"/><p type="main">
6331 
6332 <s><arrow.to.target n="marg204"/></s></p><p type="margin">
6333 
6334 <s><margin.target id="marg204"/>213</s></p><p type="main">
6335 
6336 <s>Tex. 4. (<emph type="italics"/>Similiter autem figurationum <expan abbr="quoq;">quoque</expan> elementa dicuntur, ac &longs;impliciter <lb/>demon&longs;trationum prim&aelig; enim demon&longs;trationes, qu&aelig; in pluribus demonstr ationbus <lb/>in&longs;unt, h&aelig;c elementa demon&longs;trationum dicuntur<emph.end type="italics"/>) verbo (<emph type="italics"/>Figurationum<emph.end type="italics"/>) &longs;iue <expan abbr="de-&longs;cription&utilde;">de&shy;<lb/>&longs;criptionum</expan>, Ari&longs;t, intelligere demon&longs;trationes Geometricas, &longs;&aelig;pius dictum <lb/>e&longs;t, pr&aelig;&longs;ertim in Logicis, &amp; ex hoc loco pariter confirmatur. </s>
6337 
6338 <s>Ex hoc por&shy;<lb/>r&ograve; loco illud innote&longs;cit dignum, quod pr&aelig;cipu&egrave; &agrave; Mathematico non igno&shy;<lb/>retur, qu&aelig; nam &longs;int demon&longs;trationes ill&aelig;, qu&aelig; nomine <expan abbr="elementor&utilde;">elementorum</expan> debeant <lb/>appelllari, necnon cau&longs;a cur Euclides &longs;uum opus elementa nuncupauerit, <lb/>&longs;unt enim ill&aelig;, qu&aelig; in pluribus demon&longs;trationibus in&longs;unt, ide&longs;t, qu&aelig; &longs;&aelig;pius <lb/>in alijs demon&longs;trationibus citantur, vti &longs;unt pr&aelig;cipu&egrave; &longs;ex priores libri Eu&shy;<lb/>clidis: <expan abbr="atq;">atque</expan> hac ratione elementa appellantur.</s></p><p type="main">
6339 
6340 <s><arrow.to.target n="marg205"/></s></p><p type="margin">
6341 
6342 <s><margin.target id="marg205"/>214</s></p><p type="main">
6343 
6344 <s>Tex. 12. <emph type="italics"/>(Principium <expan abbr="itaq;">itaque</expan> &longs;cibilis, circa <expan abbr="vnumquodq;">vnumquodque</expan> ip&longs;um vnum, non e&longs;t au&shy;<lb/>tem idem in cunct is generibus vnum, &longs;ed hic quidem die&longs;is, hic ver&ograve; vocalis, aut <lb/>muta)<emph.end type="italics"/> ide&longs;t, in Mu&longs;ica quidem principium omnium, &amp; elementum e&longs;t die&shy;<lb/>&longs;is, qu&aelig; e&longs;t minima vox, aut &longs;onus, qui &longs;ub Mu&longs;ici con&longs;iderationem cadat. <lb/></s>
6345 
6346 <s>Porr&ograve; ad tex. <!-- REMOVE S-->38. primi Po&longs;ter. de die&longs;i plura &longs;unt dicta.</s>
6347 
6348 </p><p type="main">
6349 
6350 <s><arrow.to.target n="marg206"/></s></p><p type="margin">
6351 
6352 <s><margin.target id="marg206"/>215</s></p><p type="main">
6353 
6354 <s>Tex. 17. <emph type="italics"/>(Veluti diametrum commen&longs;urabilem e&longs;&longs;e impo&longs;&longs;ibile est)<emph.end type="italics"/> huius expo&shy;<lb/>&longs;itionem inuenies 1. Priorum, &longs;ecto 1. cap. 
6355 
6356 23.</s></p><figure place="text" xlink:href="figures-la/009.01.141.1.tif"/><p type="main">
6357 
6358 <s><arrow.to.target n="marg207"/></s></p><p type="margin">
6359 
6360 <s><margin.target id="marg207"/>216</s></p><p type="main">
6361 
6362 <s>Tex. eodem <emph type="italics"/>(Metaphoric&egrave; autem, qu&aelig; in Geometria po&shy;<lb/>tentia dicitur)<emph.end type="italics"/> potentiam vnius line&aelig; appellant Geometr&aelig; <lb/>quadratum illius, ide&longs;t quadratum &longs;uper ip&longs;am con&longs;tru&shy;<lb/>ctum. </s>
6363 
6364 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->quadratum in quo C, dicitur potentia line&aelig; <lb/>D B, quia &longs;uper illam con&longs;tructum e&longs;t.</s>
6365 
6366 
6367 
6368 </p><p type="main">
6369 
6370 <s><arrow.to.target n="marg208"/></s></p><p type="margin">
6371 
6372 <s><margin.target id="marg208"/>217</s></p><p type="main">
6373 
6374 <s>Tex. 34. (<emph type="italics"/>Quemadmodum dicitur diametrum e&longs;&longs;e commen&longs;urabilem<emph.end type="italics"/>) vide an&shy;<lb/>notata 1. Priorum, fecto 1. cap. 
6375 
6376 23.</s></p><p type="main">
6377 
6378 <s><arrow.to.target n="marg209"/></s></p><p type="margin">
6379 
6380 <s><margin.target id="marg209"/>218</s></p><p type="main">
6381 
6382 <s>Tex. 35. (<emph type="italics"/>Vt triangulo duos rectos habere<emph.end type="italics"/>) ide&longs;t affectio trianguli e&longs;t habe&shy;<lb/>re tres angulos &aelig;quales duobus rectis angulis. </s>
6383 
6384 <s>Vide declarationem huius <lb/>lib. 
6385 
6386 primo Priornm, &longs;ecto 3. cap. 
6387 
6388 1.<!-- KEEP S--></s></p></chap><chap><p type="head">
6389 
6390 <s><emph type="italics"/>Ex Sexto Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6391 
6392 <s><arrow.to.target n="marg210"/></s></p><p type="margin">
6393 
6394 <s><margin.target id="marg210"/>219</s></p><p type="main">
6395 
6396 <s>Tex. 1. (<emph type="italics"/>Mathematicorum quoque principia, elementa, &amp; cau&longs;&aelig; &longs;unt<emph.end type="italics"/>) <lb/>notanda &longs;unt h&aelig;c aduer&longs;us quo&longs;dam, qui negant in Mathemati&shy;<lb/>cis cau&longs;as reperiri, vt hinc <expan abbr="quoq;">quoque</expan> illis &longs;cientiam auferant. </s>
6397 
6398 <s>enim&shy;<lb/>uer&ograve; apert&egrave; patet eos falli ex toto hoc Ari&longs;t. 
6399 
6400 di&longs;cur&longs;u.</s></p></chap><chap><p type="head">
6401 
6402 <s><emph type="italics"/>Ex Nono Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6403 
6404 <s><arrow.to.target n="marg211"/></s></p><p type="margin">
6405 
6406 <s><margin.target id="marg211"/>220</s></p><p type="main">
6407 
6408 <s><emph type="italics"/>Vt &longs;i quis dicat diametrum po&longs;&longs;e commen&longs;arari, non tamen commen&longs;u&shy;<lb/>rabitur<emph.end type="italics"/>) &amp; paul&ograve; infra (<emph type="italics"/>Commen&longs;urari enim impo&longs;&longs;ibile e&longs;t<emph.end type="italics"/>) expo&longs;i&shy;<lb/>tionem horum reperies 1. Priorum, &longs;ecto 1. cap. 
6409 
6410 23.</s></p><p type="main">
6411 
6412 <s><arrow.to.target n="marg212"/></s></p><p type="margin">
6413 
6414 <s><margin.target id="marg212"/>221</s></p><p type="main">
6415 
6416 <s>Tex. 20. (<emph type="italics"/>De&longs;eriptiones <expan abbr="quoq;">quoque</expan> actu inueniuntur, diuidentes nanque <lb/>inuenirent, quod &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife&longs;i &egrave; e&longs;&longs;ent, nunc autem in&longs;unt potentia, cur <lb/>triangulus duo recti? </s>
6417 
6418 <s>quia qui circa vnum punctum anguli duobus rectis &aelig;quales<emph.end type="italics"/><pb pagenum="142"/><emph type="italics"/>&longs;unt, &longs;i igitur qu&aelig; ad latus educeretur, videnti mox e&longs;&longs;et manife&longs;tum<emph.end type="italics"/>) per de&longs;cri&shy;<lb/>ptiones, vel figurationes, vel de&longs;ignationes intelligendas e&longs;&longs;e demon&longs;tra&shy;<lb/>tiones Geometricas &longs;&aelig;pius &longs;upra dictum e&longs;t, &amp; pariter ex hoc loco com&shy;<lb/>probatur. </s>
6419 
6420 <s>Dicit igitur, quod demon&longs;trationes &longs;uas Geometr&aelig; inueniunt, <lb/>reducendo ad actum ea, qu&aelig; erant in potentia, diuidentes enim educunt in <lb/>actum, figuras, angulos, lineas, &amp; c&aelig;tera huiu&longs;inodi, qu&aelig; prius &longs;ol&ugrave;m erat <lb/>in potentia, ex quibus po&longs;tea &longs;uas demon&longs;trationes perficiunt (<emph type="italics"/>Cur triangu&shy;<lb/>lus duo recti<emph.end type="italics"/>) affert exemplum eius, quod proxim&egrave; dixerat, &longs;cilicet Geome&shy;<lb/>tras demon&longs;trare producendo ad actum entia qu&aelig;dam Mathematica, quod <lb/>exemplum, vt intelligas ijs opus habes, qu&aelig; primo Priorum, &longs;ecto 3. cap. 
6421 
6422 1. <lb/>con&longs;cripta &longs;unt (<emph type="italics"/>Cur triangulus duo recti?<emph.end type="italics"/>) ide&longs;t, cur triangulus habet tres <lb/>angulos &aelig;quales duobus rectis angulis (<emph type="italics"/>Quia qui circa vnum punctum anguli <lb/>duobus rectis angulis &aelig;quales &longs;unt<emph.end type="italics"/>) ni&longs;i hoc dictum ad bonum trahatur &longs;en&longs;um, <lb/><figure place="text" xlink:href="figures-la/009.01.142.1.tif"/><lb/>fal&longs;um e&longs;t, nam omnes anguli, qui circa vnum <lb/>punctum, v. <!-- REMOVE S-->g. <!-- REMOVE S-->A, &longs;unt con&longs;tituti, &aelig;quales &longs;unt <lb/>non duobus, vt e&longs;t in textu, &longs;ed quatuor rectis, <lb/>vt patet ex corollario 2. 15. primi Elem. 
6423 
6424 quot&shy;<lb/>quot enim anguli con&longs;tituantur ad punctum A, <lb/>omnes &longs;imul erunt &aelig;quales quatuor rectis, quos <lb/>faciunt pr&aelig;&longs;entes line&aelig; B C, D E. vniuer&longs;i enim <lb/>illi congruent his quatuor rectis: &longs;ed Ari&longs;t. &longs;en&shy;<lb/>&longs;us e&longs;t omnes angulos ad ea&longs;dem partes con&longs;ti&shy;<lb/>tutos, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad partes &longs;uperiores line&aelig; B C, e&longs;&longs;e <lb/>&aelig;quales duobus rectis B A D, D A C, vt o&longs;tenditur in 13. primi, necnon <lb/>etiam patere pote&longs;t ex corollario 2. 15. eiu&longs;dem. </s>
6425 
6426 
6427 
6428 
6429 
6430 
6431 
6432 
6433 
6434 <s>tales &longs;unt quatuor anguli <lb/>ad &longs;uperiores partes line&aelig; B C, &amp; ad punctum A, con&longs;tituti, qui, vt patet, <lb/><figure place="text" xlink:href="figures-la/009.01.142.2.tif"/><lb/>&longs;unt &aelig;quales duobus rectis B A D, D A C, <lb/>tales etiam &longs;unt in hac &longs;ecunda figura tres <lb/>anguli B C A, A C D, D C E, qui quidem <lb/>&aelig;quales &longs;unt duobus rectis angulis. </s>
6435 
6436 <s>hoc <lb/>&longs;en&longs;i&longs;&longs;e Ari&longs;t. 
6437 
6438 patet ex demon&longs;tratione 32. <lb/>primi, qu&aelig; demon&longs;trat <expan abbr="memorat&atilde;">memoratam</expan> ab Ari&shy;<lb/>&longs;tot. trianguli affectionem, &amp; ad quam <lb/>propterea ip&longs;e &longs;pectabat, cuius figura e&longs;t <lb/>eadem cum hac &longs;ecunda, in qua Euclides o&longs;tendit pr&aelig;dictos tres angulos <lb/>&aelig;quari duobus rectis. </s>
6439 
6440 
6441 
6442 <s>&longs;ubdit po&longs;tea, &longs;i igitur linea C D, qu&aelig; ad latus A B, <lb/>parallela e&longs;t in potentia, educeretur in actum, videnti mox e&longs;&longs;et manife&longs;tum <lb/>tres angulos trianguli A B C, e&longs;&longs;e pares duobus rectis. </s>
6443 
6444 <s>ducta enim C D, pa&shy;<lb/>rallela lateri B A, apparet &longs;tatim angulus A, &aelig;qualis angulo A C D, &amp; an&shy;<lb/>gulus B, angulo D C E; cum reliquus ver&ograve; <expan abbr="tri&atilde;guli">trianguli</expan> angulus B C A, &longs;it apud <lb/>pr&aelig;dictos duos ad idem punctum C, con&longs;tit utus; <expan abbr="atq;">atque</expan> omnes hi tres duobus <lb/>rectis &aelig;quentur, mox in&longs;picienti talem figur ationem manife&longs;tum fit tres an&shy;<lb/>gulos illius trianguli e&longs;&longs;e duobus rectis &aelig;qu ales.</s></p><p type="main">
6445 
6446 <s><arrow.to.target n="marg213"/></s></p><p type="margin">
6447 
6448 <s><margin.target id="marg213"/>222</s></p><p type="main">
6449 
6450 <s>Ibidem (<emph type="italics"/>Cur in &longs;emicirculo vniuer&longs;aliter rectus? </s>
6451 
6452 <s>quia &longs;i tres &aelig;quales, &amp; qu&aelig; <lb/>ba&longs;is e&longs;t duo, &amp; qu&aelig; ex medio &longs;upra stat recta, videnti manifestum erit ei, qui illud <lb/>&longs;ciat<emph.end type="italics"/>) In 2. Po&longs;ter. tex. <!-- REMOVE S-->11. inuenies hu ius loci expo&longs;itionem. </s>
6453 
6454 
6455 
6456 <s>nunc &longs;ol&ugrave;m <pb pagenum="143"/><figure place="text" xlink:href="figures-la/009.01.143.1.tif"/><lb/>h&aelig;c addenda &longs;unt. </s>
6457 
6458 <s>Re&longs;pondet Ari&longs;t. 
6459 
6460 qu&aelig;&shy;<lb/>&longs;ito pr&ecedil;cedenti, cur &longs;cilicet angulus in &longs;e&shy;<lb/>micirculo &longs;it rectus, qualis e&longs;t in figura <lb/>angulus A C B, <expan abbr="dicit&qacute;">dicitque</expan>; cau&longs;am e&longs;&longs;e, quia <lb/>in figura tres line&aelig; &longs;unt &aelig;quales, du&aelig; ni&shy;<lb/>mirum, in quas ba&longs;is B A, diuiditur, qu&aelig; <lb/>&longs;unt B D, D A, &amp; tertia, qu&aelig; ex medio <lb/>ba&longs;is erigitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; D C, cum omnes &longs;int <lb/>&longs;emidia metri ciu&longs;dem circuli. </s>
6461 
6462 <s>educta <expan abbr="itaq;">itaque</expan> linea D C, de potentia in actum, <lb/>&longs;i cuipiam trium harum linearum &aelig;qualitas innote&longs;cat, continu&ograve; ei etiam <lb/>manife&longs;tum erit angulum A C B, in &longs;emicirculo, e&longs;&longs;e rectum. </s>
6463 
6464 <s>quia &longs;tatim ap&shy;<lb/>parent duo i&longs;o&longs;celia B D C, A D C, quorum anguli ad ba&longs;es B C, A C, &longs;unt <lb/>&aelig;quales inuicem; &amp; anguli duo ad D, &longs;unt dupli duorum <expan abbr="angulor&utilde;">angulorum</expan> A C D, <lb/>D C B, ex quibus conflatur totus angulus A C B, ergo duo anguli ad D, &longs;unt <lb/>dupli anguli B C A, &longs;ed duo anguli ad D, &longs;unt &aelig;quales duobus rectis, ergo <lb/>duo recti &longs;unt dupli anguli A C B, ergo angulus B C A, e&longs;t dimidium duo&shy;<lb/>rum rectorum. </s>
6465 
6466 <s>cum autem omnes recti &longs;int &aelig;quales, con&longs;ectarium e&longs;t dimi&shy;<lb/>dium duorum rectorum e&longs;&longs;e angulum rectum. </s>
6467 
6468 <s>patet igitur, qua ratione ex <lb/>ductu linearum pr&aelig;dictarum actu, manife&longs;tum fiat angulum in &longs;emicirculo <lb/>A C B, e&longs;&longs;e rectum. </s>
6469 
6470 <s>ne mireris &longs;i vulgatam tran&longs;lationem antiquam non <lb/>&longs;um &longs;equutus, indigebat enim correctione, quam iuxta gr&aelig;cum exem&shy;<lb/>plar adhibui.</s></p><p type="main">
6471 
6472 <s><arrow.to.target n="marg214"/></s></p><p type="margin">
6473 
6474 <s><margin.target id="marg214"/>223</s></p><p type="main">
6475 
6476 <s>Tex. 22. (<emph type="italics"/>Vt puta &longs;i triangulum non putet mutari, non opinabitur modo duos <lb/>rectos habere, modo non, mutaretur enim<emph.end type="italics"/>) quia nimirum huius habemus &longs;cien&shy;<lb/>tiam per demon&longs;trationem 32. primi Elementorum. <!-- KEEP S--></s>
6477 
6478 <s>quomodo autem tri&shy;<lb/>angulus habeat duos rectos, ide&longs;t tres angulos &aelig;quales duobus rectis angu&shy;<lb/>lis, explicatum e&longs;t primo Priorum, &longs;ecto 3. cap. 
6479 
6480 1.<!-- KEEP S--></s></p><p type="main">
6481 
6482 <s><arrow.to.target n="marg215"/></s></p><p type="margin">
6483 
6484 <s><margin.target id="marg215"/>224</s></p><p type="main">
6485 
6486 <s>Ibidem (<emph type="italics"/>Verum aliquid quidem, aliquid ver&ograve; non, vt puta parem numerum <lb/>primum nullum e&longs;&longs;e; aut quo&longs;dam quidem, quo&longs;dam ver&ograve; non<emph.end type="italics"/>) definitione 11. <lb/>7. Elem. 
6487 
6488 &longs;ic numerus ille, qui &agrave; Mathematicis dicitur primus, definitur, pri&shy;<lb/>mus numerus e&longs;t, quem vnitas &longs;ola metitur, vnde patet inter numeros pa&shy;<lb/>res &longs;olum binarium e&longs;&longs;e primum, cum ip&longs;um &longs;ola vnitas bis replicata men&shy;<lb/>&longs;uraret. </s>
6489 
6490 <s>quaternarium autem, &longs;enarium, &amp;c. </s>
6491 
6492 <s>pares, non e&longs;&longs;e primos, cum <lb/>eos non &longs;ola vnitas, &longs;ed alius numerus metiatur: quaternarium enim bina&shy;<lb/>rius bis replicatus men&longs;urat: &longs;enarium men&longs;urat &amp; binarius, &amp; ternarius: <lb/>quare verum erit exi&longs;timare inter pares numeros aliquos e&longs;&longs;e primos, ide&longs;t <lb/>binarium, aliquos ver&ograve; non, ide&longs;t c&aelig;teros pares vltra binarium.</s></p></chap><chap><p type="head">
6493 
6494 <s><emph type="italics"/>Ex Decimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6495 
6496 <s><arrow.to.target n="marg216"/></s></p><p type="margin">
6497 
6498 <s><margin.target id="marg216"/>225</s></p><p type="main">
6499 
6500 <s>Tex. 4. (<emph type="italics"/>Ac etiam motum &longs;implici, &amp; veloti&longs;&longs;imo motu men&longs;urant, mi&shy;<lb/>nimum enim tempus hic habet. </s>
6501 
6502 <s>quapropter in A&longs;trologia tale vn&ubreve; prin&shy;<lb/>cipium, &amp; men&longs;ura e&longs;t. </s>
6503 
6504 <s>motum enim &aelig;qualem, &amp; veloci&longs;&longs;ini&ubreve; &oelig;li &longs;up&shy;<lb/>ponunt, ad quem c&aelig;teros tudicant<emph.end type="italics"/>) intelligit motum diureum, quam <lb/>primo c&oelig;lo, &longs;eu mobili a&longs;eribunt, hic enim veloci&longs;&longs;imus e&longs;t omnium reli&shy;<pb pagenum="144"/>quorum c&oelig;le&longs;tium motuum, ac &longs;impliciffimus, &amp; vald&egrave; vniformis, ac regu&shy;<lb/>laris, &amp; propterea minimum habet tempus, ide&longs;t tempus vnius diei natura&shy;<lb/>lis, quo tempore totum primum mobile circulationem integram perficit. <lb/></s>
6505 
6506 <s>per minimum tempus, po&longs;&longs;uut etiam intelligi partes diei, qu&aelig; &longs;unt hor&aelig;, &amp; <lb/>horarum partes. </s>
6507 
6508 <s>con&longs;iderant hunc motum in circulo &aelig;qu&agrave;toris, quia &aelig;qua&shy;<lb/>tor motu primi mobilis, &longs;eu diurno vniformiter, ae maxim&egrave; regulatiter <lb/>mouetur: hac de cau&longs;a hunc motum tanquam reliquorum men&longs;uram, ac <lb/>normam merit&ograve; a&longs;&longs;ump&longs;erunt.</s></p><p type="main">
6509 
6510 <s><arrow.to.target n="marg217"/></s></p><p type="margin">
6511 
6512 <s><margin.target id="marg217"/>226</s></p><p type="main">
6513 
6514 <s>Ibidem <emph type="italics"/>(Et in Mu&longs;ica Die&longs;is primus &longs;en&longs;ibilis &longs;onus, quia minimum)<emph.end type="italics"/> ide&longs;t mi&shy;<lb/>nimum interuallum, quod &agrave; Mu&longs;icis con&longs;ideretur, e&longs;t men&longs;ura maiorum in&shy;<lb/>teruallorum. </s>
6515 
6516 <s>ad tex. <!-- REMOVE S-->38. primi Po&longs;ter. &longs;atis dictum e&longs;t de Die&longs;i, qu&aelig; videas.</s>
6517 
6518 </p><p type="main">
6519 
6520 <s><arrow.to.target n="marg218"/></s></p><p type="margin">
6521 
6522 <s><margin.target id="marg218"/>227</s></p><p type="main">
6523 
6524 <s>Eodem tex. <!-- REMOVE S-->&longs;ed cap. 
6525 
6526 3. <emph type="italics"/>(Nox &longs;emper autem men&longs;ura numero vnum e&longs;t, verum <lb/>aliquando plura, vt puta die&longs;es du&aelig;, non quidem &longs;ecundum cuditum, &longs;ed in ratio&shy;<lb/>nibus, &amp; voces plures, quibus men&longs;uramus, &amp; diameter duobus men&longs;uratur, &amp; la&shy;<lb/>tus, &amp; omnes magnitudines)<emph.end type="italics"/> ita corrigenda e&longs;t antiqua tran&longs;latio. </s>
6527 
6528 
6529 
6530 <s>quid die&longs;is <lb/>dictum &longs;it ad tex. <!-- REMOVE S-->38. primi Po&longs;ter. quando autem ait <emph type="italics"/>(Vt puta du&aelig; die&longs;es)<emph.end type="italics"/><lb/>ide&longs;t du&aelig; die&longs;es &longs;unt men&longs;ura vnius interualli mu&longs;ici, qui tonus appellatur: <lb/>qu&aelig; quidem du&aelig; die&longs;es non &longs;unt men&longs;ura &longs;en&longs;ibilis, qu&aelig; &longs;cilicet auribus per&shy;<lb/>cipiatur, &longs;ed tantummod&ograve; exi&longs;tunt in numerorum proportionibus, ibi per <lb/>intellectum excogitatis, quando ait <emph type="italics"/>(Et voces plures quibus men&longs;uramus)<emph.end type="italics"/><lb/>quando vtimur eodem interuallo, &longs;iue eadem voce ad cantus men&longs;uram, <lb/>tunc &longs;unt plures men&longs;ur&aelig; numero, quamuis vna tantum &longs;pecie. Ait <emph type="italics"/>(Et dia&shy;<lb/>meter duobus men&longs;uratur)<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->duobus &longs;emidiametris: vel duobus pedibus. <lb/></s>
6531 
6532 
6533 
6534 
6535 
6536 
6537 
6538 <s>&amp; latus pariter quadrati, duobus. </s>
6539 
6540 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->pedibus mensuratur; eode<expan abbr="m&qacute;">mque</expan>; mo&shy;<lb/>do reliqu&aelig; omnes magnitudines po&longs;&longs;unt ab eadem men&longs;ura &longs;&aelig;ipius replica&shy;<lb/>ta men&longs;urari.</s>
6541 
6542 
6543 
6544 </p><p type="main">
6545 
6546 <s><arrow.to.target n="marg219"/></s></p><p type="margin">
6547 
6548 <s><margin.target id="marg219"/>228</s></p><p type="main">
6549 
6550 <s>Eodem tex. <emph type="italics"/>(Semper autem men&longs;ura eiu&longs;dem generis e&longs;t, magnitudinum nam&shy;<lb/>que magnitudo, &amp; &longs;ecundum vnumquedque, longitudinis longitudo<emph.end type="italics"/>) ex his ratio <lb/>manife&longs;ta apparet, cur Geometr&aelig; practici men&longs;urent longitudines per ali&shy;<lb/>quam longitudinem, vt puta per vlnam, digitum, vnciam, &amp;c. </s>
6551 
6552 <s>&longs;uperficies <lb/>etiam per aliquam &longs;uperficiem, &longs;ed qu&aelig; &longs;it quadrata, vt puta per vlnam qua&shy;<lb/>dratam, palmum quadratum, &amp;c. </s>
6553 
6554 <s>corpora <expan abbr="quoq;">quoque</expan> per corpus, quod tamen <lb/>&longs;it cubus, vt per vlnam cubicam, palmum cubicum, vnciam cubicam, &amp;c.</s></p><p type="main">
6555 
6556 <s><arrow.to.target n="marg220"/></s></p><p type="margin">
6557 
6558 <s><margin.target id="marg220"/>229</s></p><p type="main">
6559 
6560 <s>Tex. 11. <emph type="italics"/>(Similia ver&ograve; &longs;i cum non &longs;int eadem &longs;impliciter, nec &longs;ecundum &longs;ab&longs;t an&shy;<lb/>tiam &longs;ubiectam in d. <!-- KEEP S--></s>
6561 
6562 <s>fferentia &longs;ecundum formam eadem &longs;it: quemadmodum quadra&shy;<lb/>tum maius minori &longs;imile e&longs;t, &amp; line&aelig; in&aelig;quales, h&aelig; enim &longs;imiles quidem, ver&ubreve; non <lb/>c&aelig;dem &longs;impliciter &longs;unt)<emph.end type="italics"/> Prima definitio &longs;exti definit &longs;imiles figuras eas e&longs;&longs;e, <lb/>qu&aelig; &longs;unt &aelig;quiangul&aelig; inuicem, &amp; qu&aelig; habent latera proportionalia circa <lb/>&aelig;quales angulos. </s>
6563 
6564 <s>cum erg&ograve; quadratum maius, &amp; minus &longs;int &aelig;quiangula, <lb/>quia habent omnes angulos rectos; &amp; pr&aelig;terea habeant latera circa &aelig;qua&shy;<lb/>les angulos proportionalia, &longs;icut enim latera maioris quadrati circa vnum <lb/>angulum rectum &longs;unt in proportione &aelig;qualitatis; ita <expan abbr="quoq;">quoque</expan> latera minoris <lb/>circa vnum angulum rectum &longs;unt illis proportionalia, cum &longs;int inuicem pa&shy;<lb/>riter in proportione &aelig;qualitatis, erunt nece&longs;&longs;ari&ograve; &longs;imilia h&aelig;c duo quadrata. <lb/></s>
6565 
6566 <s>du&aelig; ctiam, exempli gratia, line&aelig; rect&aelig; &longs;unt inuicem &longs;imiles, quamuis vna <lb/>&longs;it maior altera.</s></p><pb pagenum="145"/><p type="main">
6567 
6568 <s><arrow.to.target n="marg221"/></s></p><p type="margin">
6569 
6570 <s><margin.target id="marg221"/>230</s></p><p type="main">
6571 
6572 <s>Eodem tex. <emph type="italics"/>(Tertium &longs;icut illa, qu&aelig; in Mathematicis)<emph.end type="italics"/> tertium &longs;cilicet mo&shy;<lb/>dum diuer&longs;i, ponit in entibus Mathematicis, &longs;icut enim po&longs;uit idem e&longs;&longs;e in <lb/>Mathematicis, quando du&aelig; figur&aelig; &longs;unt &longs;imiles, &amp; &aelig;quales: ita ex oppo&longs;ito <lb/>diuer&longs;um erit in Mathematicis, quando du&aelig; figur&aelig; fuerint di&longs;&longs;imiles, &amp; in&shy;<lb/>&aelig;quales, <expan abbr="dicentur&qacute;">dicenturque</expan>; diuer&longs;&aelig;, in quo con&longs;i&longs;tat &longs;imilitudo figurarum dictum <lb/>e&longs;t in pr&aelig;cedenti expo&longs;itione.</s></p></chap><chap><p type="head">
6573 
6574 <s><emph type="italics"/>Ex Vndecimo Metaphy&longs;i&aelig;.<emph.end type="italics"/></s></p><p type="main">
6575 
6576 <s><arrow.to.target n="marg222"/></s></p><p type="margin">
6577 
6578 <s><margin.target id="marg222"/>231</s></p><p type="main">
6579 
6580 <s>Svmma r. </s>
6581 
6582 <s>cap. 
6583 
6584 2. <emph type="italics"/>(Si quis ver&ograve; lineas, aut qu&aelig; has &longs;equuntur, dico autem <lb/>primas &longs;uperficies principia e&longs;&longs;e ponat. </s>
6585 
6586 <s>b&aelig;c non &longs;unt &longs;ub&longs;tanti&aelig; &longs;eparabiles, <lb/>ver&ugrave;m &longs;ectiones, &amp; diui&longs;iones, ill&aelig; quidem in &longs;uperficierum, h&aelig;c ver&ograve; cor&shy;<lb/>porum, puncta ver&ograve; linearum &longs;unt, &amp; etiam ip&longs;arum earumdem termini; <lb/>h&aelig;c autem omnia in alijs &longs;unt, &amp; nihil &longs;eparabile e&longs;t)<emph.end type="italics"/> ait puncta oriri ex &longs;ectio&shy;<lb/>ne line&aelig;, quamuis &longs;int etiam termini illius; lineas ver&ograve; oriri ex diui&longs;ione <lb/>&longs;uperficierum, quamuis &longs;int etiam termini illarum. </s>
6587 
6588 <s>&longs;uperficies <expan abbr="quoq;">quoque</expan> oriri <lb/>ex diui&longs;ione corporum, quamuis &longs;int etiam termini, illorum. </s>
6589 
6590 <s>H&aelig;c placuit <lb/>annotare propter <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan> conuenientiam <expan abbr="c&utilde;">cum</expan> ijs, qu&aelig; &agrave; Geometris traduntur.</s></p><p type="main">
6591 
6592 <s><arrow.to.target n="marg223"/></s></p><p type="margin">
6593 
6594 <s><margin.target id="marg223"/>232</s></p><p type="main">
6595 
6596 <s>Summa 3. cap. 
6597 
6598 2. <emph type="italics"/>(Vt puta &longs;ub Cane fiat frigus)<emph.end type="italics"/> ideft &longs;ub ortum Canis c&oelig;&shy;<lb/>l&aelig;&longs;tis, &longs;eu Canicul&aelig;. <!-- KEEP S--></s>
6599 
6600 <s>Vide qu&aelig; libro &longs;ecundo Meteororum, &longs;umma 2. cap. 
6601 
6602 2. <lb/>de hac &longs;tella &longs;crip&longs;imus.</s></p></chap><chap><p type="head">
6603 
6604 <s><emph type="italics"/>Ex Duodecimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6605 
6606 <s><arrow.to.target n="marg224"/></s></p><p type="margin">
6607 
6608 <s><margin.target id="marg224"/>233</s></p><p type="main">
6609 
6610 <s>Tex. 44. <emph type="italics"/>(Pluralitatem ver&ograve; lationum ex peculiari&longs;&longs;ima Philo&longs;ophie <lb/>Mathematicarum &longs;cientiarum, videlicet ex A&longs;tronomia con&longs;iderandum <lb/>est: h&aelig;c enim de &longs;ub&longs;tantia &longs;en&longs;ibili quidem, ac &longs;empiterna &longs;peculatur)<emph.end type="italics"/><lb/>pluralitatem nimirum c&oelig;le&longs;tium motuum petendam e&longs;&longs;e a&longs;&longs;erit <lb/>ex pr&aelig;cipua totius Philo&longs;ophi&aelig; parte, quam ait e&longs;&longs;e A&longs;tronomiam. </s>
6611 
6612 <s>dignum <lb/>porr&ograve; con&longs;ideratione e&longs;t, quanti faciat Ari&longs;t. Mathematicas di&longs;ciplinas, ac <lb/>pr&aelig;cipu&egrave; &longs;yderalem &longs;cientiam.</s></p><p type="main">
6613 
6614 <s><arrow.to.target n="marg225"/></s></p><p type="margin">
6615 
6616 <s><margin.target id="marg225"/>234</s></p><p type="main">
6617 
6618 <s>Tex. 45. <emph type="italics"/>(Eudoxus igitur Solis, &amp; Lun&aelig; lationem po&longs;uit fieri &agrave; tribus orbibus, <lb/>quorum primus quidem e&longs;&longs;et, qui inerrantium &longs;iellarum; &longs;ecundus ver&ograve; &longs;ecunduns <lb/>id, quod per medium Zodiacum; tertius tandem, &longs;ecundum quem qui in latitudine <lb/>Zodiaci obliquatur. </s>
6619 
6620 <s>in maiori autem latitudine obliquari eum &longs;ecundum quem Lu&shy;<lb/>na, qu&agrave;m eum &longs;ecundum quem Sol &longs;ertur)<emph.end type="italics"/> Eudoxi tempore nondum &longs;atis ex&shy;<lb/>culta fuerat A&longs;tronomia, vt propterea minim&egrave; mirandum &longs;it, eum hoc lo&shy;<lb/>co imperfecta admodum circa c&ecedil;le&longs;tia tradere. </s>
6621 
6622 <s>omittit enim in Sole orbem <lb/>motum augis conficientem; necnon duos eccentricos, qui &longs;olis anomaliam, <lb/><expan abbr="atq;">atque</expan> eccentricitatis variationem excu&longs;ant. </s>
6623 
6624 <s>attribuit pr&aelig;terea Soli motum <lb/>quendam in latitudinem, quod fal&longs;um e&longs;t omnin&ograve;, cum Sol perpetu&ograve; direct&egrave; <lb/>&longs;ub eclyptica incedat. </s>
6625 
6626 <s>In Luna pariter plures nece&longs;&longs;arios illi orbes ad motus <lb/>ip&longs;ius &longs;aluandos pr&aelig;termittit. </s>
6627 
6628 <s>Ex &longs;ententia tamen Tychonis Brahe hos or&shy;<lb/>bes, ac circulos tanquam ab inuicem di&longs;tinctos abrogare debemus.</s></p><pb pagenum="146"/><p type="main">
6629 
6630 <s><arrow.to.target n="marg226"/></s></p><p type="margin">
6631 
6632 <s><margin.target id="marg226"/>235</s></p><p type="main">
6633 
6634 <s>Tex. 46. <emph type="italics"/>(Errantium ver&ograve; &longs;tellarum <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> in quatuor &longs;ph&aelig;ris, quarura <lb/>primam quidem, &amp; &longs;ecundam eandem illis e&longs;&longs;e: etenim, qu&aelig; fix arum eft eam illam <lb/>e&longs;&longs;e, qu&aelig;omnes fert: at cam, qu&aelig; &longs;ub ip&longs;a ordinata e&longs;t, ac qu&aelig; &longs;ecuxdum Zodiacum <lb/>lationem habet, communem omnibus e&longs;&longs;e. </s>
6635 
6636 <s>Terti&aelig; ver&ograve; omnium polos in eo, quod <lb/>per medium Zodiacum e&longs;t. </s>
6637 
6638 <s>Quart&aelig; autem lationem &longs;ecundum eum, qui obliquatus <lb/>ad medusm eius e&longs;t; e&longs;&longs;e ver&ograve; terti&aelig; &longs;ph&aelig;r&aelig; polos aliarum quidem proprios, Veneris <lb/>autem, &amp; Mercurij eo&longs;dem)<emph.end type="italics"/> pergit tradere theoriam reliquorum errantium <lb/><expan abbr="quinq;">quinque</expan> &longs;yderum, &longs;ecundum mentem Eudoxi, qui propri&egrave; Planet&aelig; dicuntur: <lb/>Sol autem, &amp; Luna hoc nomine non e&longs;t complexus, eo quod ip&longs;a mereantur <lb/>potius duo mundi luminaria appellari, qu&agrave;m cum c&ecedil;teris &longs;tellis in ordinem <lb/>redigi. </s>
6639 
6640 <s>Reliquis igitur <expan abbr="quinq;">quinque</expan> erronibus &longs;ingulis quatuor &longs;ph&aelig;ris attribue&shy;<lb/>bat, quarum prima, &amp; &longs;ecunda eodem modo &longs;e habebant, ac in Sole, &amp; Lu&shy;<lb/>na, etenim octaua &longs;ph&aelig;ra, &longs;eu firmamentum, quod affixa &longs;ibi &longs;ydera differt <lb/>communicabat, &longs;ecundum ip&longs;um reliquis inferioribus &longs;ph&aelig;ris motum &longs;uum <lb/>peculiarem, videlicet diurnum, quo ab oriente in occidentem tota c&ecedil;li ma&shy;<lb/>china conuertebatur. </s>
6641 
6642 <s>fecundam eam facit, qu&aelig; Planetas omnes &longs;ecundum <lb/>Zodiaci longitudinem ab occidente in <expan abbr="ori&etilde;tem">orientem</expan> vehebat, qu&aelig; pariter eodem <lb/>modo &longs;e habet in &longs;ingulis. </s>
6643 
6644 <s>Tertiam ver&ograve; eam confinxit, cuius poli e&longs;&longs;ent in <lb/>eclyptica, in quibus cita, ab eclyptica vltr&ograve;, <expan abbr="citro&qacute;">citroque</expan>; dilataretur. </s>
6645 
6646 <s>Quartam <lb/>demum po&longs;uit, qu&aelig; tertiam bifariam &longs;ecaret, <expan abbr="eam&qacute;">eamque</expan>; tali motu cieret, ne ab <lb/>eclyptica plus iu&longs;to ver&longs;us mundi polos exorbitaret. </s>
6647 
6648 <s>porr&ograve; in reliquis vo&shy;<lb/>luit polos tertij orbis e&longs;&longs;e peculiares, Veneri autem, &amp; Mercurio eo&longs;dem <lb/>e&longs;&longs;e, ide&longs;t e&longs;&longs;e in eadem linea. </s>
6649 
6650 <s>Ex mente igitur Eudoxi c&oelig;le&longs;tes orbes in <lb/>vniuer&longs;um 27. numerantur, in Sole &longs;imul, ac Luna 6. in reliquis quinque er&shy;<lb/>rantibus 20. <expan abbr="atq;">atque</expan> octau&aelig; &longs;ph&aelig;r&aelig; 1. Non me later, has Eudoxi po&longs;itiones, <lb/>ob ratas po&longs;teriorum a&longs;tronomorum ob&longs;eruationes non &longs;ub&longs;i&longs;tere. </s>
6651 
6652 <s>at ver&ograve; <lb/>hic non ip&longs;ius placita, &longs;ed pr&aelig;cipu&egrave; textus intelligentiam per&longs;equor.</s></p><p type="main">
6653 
6654 <s><arrow.to.target n="marg227"/></s></p><p type="margin">
6655 
6656 <s><margin.target id="marg227"/>236</s></p><p type="main">
6657 
6658 <s>Tex. 47. <emph type="italics"/>(At Calippus &longs;itum quidem &longs;ph&aelig;rarum eundem Eudoxo ponebat, hoe <lb/>e&longs;t di&longs;tantiarum ordinem. </s>
6659 
6660 <s>pluralitatem autem &longs;tell&aelig; quidem Iouis, ac Saturni ean&shy;<lb/>dem illi attribuebat. </s>
6661 
6662 <s>Solis ver&ograve;, &amp; Lun&aelig; duas adbuc putabat &longs;ph&aelig;ras addendas <lb/>e&longs;&longs;e, &longs;i quis eorum, qu&aelig; &longs;en&longs;ibilitcr apparent, can&longs;as a&longs;&longs;ignare debeat. </s>
6663 
6664 <s>C&aelig;teris ve&shy;<lb/>r&ograve; errantium vnicuique vnam. </s>
6665 
6666 <s>nece&longs;&longs;e ver&ograve; e&longs;&longs;e, &longs;i debent omnes &longs;imul po&longs;it&aelig;, qu&aelig; <lb/>apparent reddere, &longs;ecundam <expan abbr="vnamquamq;">vnamquamque</expan> errantium alteras &longs;ph&aelig;ras vna paucie&shy;<lb/>res e&longs;&longs;e, qu&aelig; reuoluant, &amp; ad idem po&longs;itione &longs;emper primam eius astri &longs;ph&aelig;ram, <lb/>quod inferius ordinatum e&longs;t, con&longs;tituant. </s>
6667 
6668 <s>boc enim modo &longs;ol&ugrave;m contingit errantium <lb/>lationem omnia facere. </s>
6669 
6670 <s>C&ugrave;migitur, in quibus ip&longs;a quidem feruntur &longs;ph&aelig;ris, h&aelig; <lb/>quidem octo, b&aelig;ver&ograve; <expan abbr="vigintiquinq;">vigintiquinque</expan> &longs;int. </s>
6671 
6672 <s>horum &longs;ane non oportet illas &longs;olas reuo&shy;<lb/>lai, in qui&ograve;us fertur, quod infim&egrave; ordinatum e&longs;t. </s>
6673 
6674 <s>qu&aelig; quidem duarum &longs;ph&aelig;rarum <lb/>primas reuoluant, &longs;ex erunt. </s>
6675 
6676 <s>qu&aelig; ver&ograve; pe&longs;teriorum quatuor, &longs;exdecim. </s>
6677 
6678 <s>cunctarum <lb/>ver&ograve; numerus, t&ugrave;m earum qu&aelig; ferunt, t&ugrave;m qu&aelig; reuoluunt eas, quinquaginta quin&shy;<lb/>que. </s>
6679 
6680 <s>qu&ograve;d &longs;i Lun&aelig;, &amp; Soli, non addat aliquis quos diximus motus, omnes &longs;ph&aelig;r&aelig; <lb/>erunt &longs;eptem, &amp; quadraginta. </s>
6681 
6682 <s>pluralitas <expan abbr="itaq;">itaque</expan> &longs;ph&aelig;rarum tanta &longs;it)<emph.end type="italics"/> textum hunc <lb/>per paraphra&longs;im &longs;ic explico; Calippus igitur eundem quidem ordinem, at&shy;<lb/>que di&longs;tantiam &longs;ph&aelig;rarum cum Eudoxo ponebat: <expan abbr="eandem&qacute;">eandemque</expan>; pluralitatem <lb/>orbium mouentium Saturnum, ac Jouem; quatuor <expan abbr="nimir&utilde;">nimirum</expan> <expan abbr="vnicuiq;">vnicuique</expan> eorum. <lb/></s>
6683 
6684 <s>&longs;ed putabat &longs;oli duas addendas, ac Lun&aelig; &longs;imiliter, &longs;i quis eorum <expan abbr="appar&etilde;tias">apparentias</expan> <pb pagenum="147"/>&longs;aluare vellet. </s>
6685 
6686 <s>c&aelig;teris ver&ograve; errantium, Marti, Veneri, &amp; Mercurio <expan abbr="vnicuiq;">vnicuique</expan> <lb/>vnam. </s>
6687 
6688 <s>nece&longs;&longs;e pr&aelig;terea exi&longs;timabat e&longs;&longs;e, vt pr&aelig;dict&aelig; omnes &longs;ph&aelig;r&aelig; &longs;imul <lb/>apparentias omnes excu&longs;arent, addendas e&longs;&longs;e alias &longs;ingulis planetis toti&shy;<lb/>dem &longs;ph&aelig;ras vna minus, quas Reuoluentes appellabat; ita vt qui quatuor <lb/>Mouentes &longs;ph&aelig;ras habuif&longs;et, tribus pr&aelig;terea reuoluentibus opus haberet: <lb/>qu&aelig; &longs;ph&aelig;r&aelig; reuoluentes id pr&aelig;&longs;tabant, vt qua&longs;i priores Mouentes ita in of&shy;<lb/>ficio continerent, vt priori po&longs;itioni a&longs;trum, quod interiori orbi affigebur <lb/>&longs;uo tempore re&longs;tituerent, vt Alexander exponit. </s>
6689 
6690 <s>hoc enim &longs;olummodo po&longs;&shy;<lb/>&longs;ibile putabat omnes errantium lationes nos imitari po&longs;&longs;e. </s>
6691 
6692 <s>Cum igitur mo&shy;<lb/>uentes &longs;ph&aelig;r&aelig; ill&aelig; quidem Saturni, ac Iouis &longs;int octo; reliquorum ver&ograve; vi&shy;<lb/>gintiquinque, nam reliqui Planet&aelig; <expan abbr="quinq;">quinque</expan> &longs;inguli &longs;ph&aelig;ras <expan abbr="quinq;">quinque</expan> mouentes <lb/>habent, qu&aelig; omnes &longs;imul numerum <expan abbr="vigintiquinq;">vigintiquinque</expan> explent: quarum omnium <lb/>&longs;ol&aelig; inferiores, quibus a&longs;trum affixum volebat, non indigebant reuoluente, <lb/>&longs;equitur duorum &longs;uperiorum Saturni, &amp; Iouis, quorum octo erant mouen&shy;<lb/>tes, &longs;ex debere e&longs;&longs;e reuoluentes. </s>
6693 
6694 <s>Inferiorum ver&ograve; quatuor planetarum re&shy;<lb/>uoluentes erunt &longs;exdecim: &longs;ed hoc loco Ari&longs;t. 
6695 
6696 memoria fallit, deberet enim <lb/>dicere, reliquorum <expan abbr="quinq;">quinque</expan> planetarum reuoluentes erunt vigint&igrave;, &longs;unt enim <lb/>planet&aelig; &longs;eptem, quorum Saturno, ac Ioui &longs;upremis &longs;ex reuoluentes attri&shy;<lb/>buit habita ratione &longs;ph&aelig;ratum mouentium; reliquis igitur <expan abbr="quinq;">quinque</expan> planetis <lb/>habita ratione &longs;uorum orbium mouentium, 25. cum &longs;inguli habeant <expan abbr="quinq;">quinque</expan> <lb/>mouentes, habebunt ex pr&aelig;lcripto Calippi &longs;inguli 4. reuoluentes; ac pro&shy;<lb/>inde 20. in vniuer&longs;um erunt reuoluentes. </s>
6697 
6698 <s>Omnium igitur &longs;ph&aelig;rarum tam <lb/>mouentium, qu&agrave;m reuoluentium &longs;ummam ait, &longs;ed perperam, e&longs;&longs;e quinqua&shy;<lb/>gintaquinque; cum enim mouentes Saturni, &amp; Iouis &longs;int 8. reliquorum au&shy;<lb/>tem 25. reuoluentes ver&ograve; Saturni, &amp; Iouis &longs;int 6. reliquorum autem, vt ip&shy;<lb/>&longs;e memoria fal&longs;us ponit, &longs;exdecim, conflant quidem &longs;ummam pr&aelig;dictam, <lb/>&longs;ed illi in memoria reuocandus e&longs;t, planeta ille, quem oblitus e&longs;t, cuius &longs;unt <lb/>quatuor reuoluentes, qui prioribus additi &longs;ph&aelig;rarum errantium numerum <lb/>quinquaginta nouem con&longs;tituent: quibus etiam addenda e&longs;t octaua &longs;ph&aelig;ra, <lb/>&longs;eu firmamentum, quod inerrantium &longs;edes e&longs;t, non enim &longs;olum errantium, <lb/>&longs;ed omnium c&oelig;le&longs;tium orbium numerum inue&longs;tigare volebat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; e&longs;&longs;ent <lb/>omnes &longs;ecundum Calippum &longs;ph&ecedil;r&aelig; &longs;exaginta. </s>
6699 
6700 <s>Quod &longs;i Lun&aelig;, &amp; Soli non ad&shy;<lb/>dantur &longs;ingulis duo mouentes, vt facit Calippus, <expan abbr="neq;">neque</expan> con&longs;equenter quatuor <lb/>illis debiti reuoluentes non erunt omnes, 55. ver&ugrave;m, detractis octo pr&aelig;di&shy;<lb/>ctis, erunt tantum 47. &longs;eu vt melius loquatur non erunt in vniuer&longs;um, 60. &longs;ed <lb/>52. tantum. </s>
6701 
6702 <s>Hactenus de numero c&oelig;lorum.</s></p></chap><chap><p type="head">
6703 
6704 <s><emph type="italics"/>Ex Decimotertio Metaphy&longs;ic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6705 
6706 <s><arrow.to.target n="marg228"/></s></p><p type="margin">
6707 
6708 <s><margin.target id="marg228"/>237</s></p><p type="main">
6709 
6710 <s>Svmma 1. cap. 
6711 
6712 3. <emph type="italics"/>(Qui dicunt Mathematicas &longs;cientias nihil de bono, vel <lb/>pulchro dicere, fal&longs;um dicunt. </s>
6713 
6714 <s>dicunt. </s>
6715 
6716 <s>n. </s>
6717 
6718 <s>&amp; maxim&egrave; <expan abbr="o&longs;t&etilde;dunt">o&longs;tendunt</expan>. </s>
6719 
6720 <s>nam &amp; &longs;i non <lb/>nominant, quia tamen opera, &amp; rationes ostendunt, non ne dicunt de eis? <lb/></s>
6721 
6722 <s>pulchra <expan abbr="namq;">namque</expan> maxim&egrave; &longs;pecies &longs;unt, ordo, commen&longs;uratio, &amp; definu&ubreve;, qu&aelig; <lb/>maxim&egrave; &agrave; Mathematicis &longs;cientijs o&longs;tenduntur, &amp;c.)<emph.end type="italics"/> placuit h&aelig;c in Mathemati&shy;<lb/>carum commendationem, ac defen&longs;ionem apponere, cum non de&longs;int hac <lb/>no&longs;tra tempe&longs;tate ageometrcti complures, qui cas libenter &longs;ugillare &longs;olent.</s></p></chap><pb pagenum="148"/><chap><p type="head">
6723 
6724 <s><emph type="italics"/>IN MECHANICAS QV&AElig;STIONES.<emph.end type="italics"/></s></p><p type="main">
6725 
6726 <s>Qvidquid Mathematicum in his qu&aelig;&longs;tionibus occurret, illud, vt <lb/>plurimum per paraphra&longs;im exponemus, ita tamen, vt tex. <!-- REMOVE S-->Ari&longs;t. <lb/>&amp; figur&aelig; textui re&longs;pondentes per eam, quantum fieri poterit re&shy;<lb/>&longs;tituantur, &amp; &longs;i qu&aelig; &longs;e offerent difficilia, pro viribus &longs;oluantur. <lb/></s>
6727 
6728 
6729 
6730 <s>E&longs;t autem nonnullis in locis textus tam gr&aelig;cus, qu&agrave;m latinus ade&ograve; corrup&shy;<lb/>tus, ac deprauatus, vt nullo modo emendari queat.</s></p><p type="head">
6731 
6732 <s><emph type="italics"/>Caput Primum.<emph.end type="italics"/></s></p><p type="head">
6733 
6734 <s>Qu&aelig; &longs;it artis Mechanic&aelig; facultas.</s></p><p type="main">
6735 
6736 <s><arrow.to.target n="marg229"/></s></p><p type="margin">
6737 
6738 <s><margin.target id="marg229"/>238</s></p><p type="main">
6739 
6740 <s>Eorum, qu&aelig; miraculo &longs;unt, alia quidem natura contingunt, <expan abbr="&longs;unt&qacute;">&longs;untque</expan>; ea, <lb/>quorum ignorantur cau&longs;&aelig;: alia ver&ograve; &longs;unt, qu&aelig; pr&aelig;ter naturam per <lb/>artificium aliquod ad hominum vtilitatem perficiuntur, in multis <lb/><expan abbr="namq;">namque</expan> natura ei, quod nobis v&longs;ui e&longs;&longs;e pote&longs;t, contrarium facit, quod <lb/>inde oritur, quia natura eundem &longs;emper, ac &longs;implicem &longs;eruat modum: quod <lb/>autem nobis vtile e&longs;t, plurimas &longs;ubit varietates. </s>
6741 
6742 <s>quando igitur quippiam <lb/>pr&aelig;ter naturam facere opportuerit, illud, quod faciendum e&longs;t, difficultate <lb/>&longs;ua nos remoratur, <expan abbr="arte&qacute;">arteque</expan>; propterea indigemus. </s>
6743 
6744 <s>quamobrem eam artis <lb/>partem, qu&aelig; huiu&longs;modi &longs;uccurrit difficultatibus, Mechanicam appellamus. <lb/></s>
6745 
6746 <s>C&aelig;ter&ugrave;m optim&egrave; Antiphon Poeta in hunc modum cecinit;</s></p><p type="head">
6747 
6748 <s><emph type="italics"/>Arte &longs;uperamus ea, in quibus &agrave; natura vincimur.<emph.end type="italics"/></s></p><p type="main">
6749 
6750 <s>Quemadmodum accidit, cum minora &longs;uperant maiora, &amp; qu&aelig;cunque exi&shy;<lb/>guam vim habentia, magna tamen mouent pondera, &amp; omnia fer&egrave; illa, qu&aelig; <lb/>&longs;ub ea cadunt problemata, qu&aelig; mechanica nuncupari <expan abbr="&longs;ol&etilde;t">&longs;olent</expan>. </s>
6751 
6752 <s>&longs;unt autem h&aelig;c <lb/><expan abbr="neq;">neque</expan> naturalibus omnin&ograve; qu&aelig;&longs;tionibus eadem, <expan abbr="neq;">neque</expan> &longs;eiugata valde: ver&ugrave;m <lb/>mathematicarum contemplationum, <expan abbr="naturaliumq;">naturaliumque</expan> communia. </s>
6753 
6754 <s>Po&longs;tea in <lb/>gr&aelig;cis codicibus h&aelig;c &longs;equuntur (<foreign lang="greek">to\ men ga\r w_c di\a twn maqhmatixw_n dh/log: to\ <lb/>de pevi\o\, di\a tw_n fuszxw_n</foreign>) ide&longs;t, &longs;i quidem quomodo &longs;int, &longs;eu qua ratione <lb/>exi&longs;tant, manife&longs;tum e&longs;t per Mathematica: illud ver&ograve; circa quod ver&longs;antur, <lb/>hoc e&longs;t obiectum, de quo pertractant Mechanic&aelig; qu&aelig;&longs;tiones per &longs;cientias <lb/>phy&longs;icas habetur, ide&longs;t res naturalis e&longs;t; e&longs;t enim pondus, &amp; vis, aut poten&shy;<lb/>tia pondus ip&longs;um mouens, quatenus quanta &longs;unt; &longs;iue dixeris e&longs;t quantitas <lb/>ponderum, <expan abbr="atq;">atque</expan> potentiarum. </s>
6755 
6756 <s>Mathematic&aelig; enim medi&aelig;, de quorum nu&shy;<lb/>mero e&longs;t facultas Mechanica, con&longs;iderant quantitatem rei alicuius <lb/>determinat&aelig;, &longs;ic A&longs;tronomia circa c&oelig;le&longs;tium corporum, <expan abbr="mo-tuum&qacute;">mo&shy;<lb/>tuumque</expan>; quantitates, Per&longs;pectiua circa linearum vi&longs;ua&shy;<lb/>lium; Mu&longs;ica circa &longs;onorum quantitates ver&shy;<lb/>&longs;antur. </s>
6757 
6758 <s>qu&aelig; placuit annotare, vt &longs;cien&shy;<lb/>ti&aelig; huius naturam per&longs;pectam <lb/>haberemus.</s></p><pb pagenum="149"/><p type="head">
6759 
6760 <s>De dignitatibus, <expan abbr="admirandis&qacute;">admirandisque</expan>; Circuli proprietatibus.</s></p><p type="head">
6761 
6762 <s><emph type="italics"/>Cap. 
6763 
6764 Secundum.<emph.end type="italics"/></s></p><p type="main">
6765 
6766 <s><arrow.to.target n="marg230"/></s></p><p type="margin">
6767 
6768 <s><margin.target id="marg230"/>239</s></p><p type="main">
6769 
6770 <s>Cvm vellet Ari&longs;t. 
6771 
6772 mirabilium effectuum, quos in Mechanicis admi&shy;<lb/>ramur, cau&longs;am referre in circulum: merit&ograve; ante omnia de admi&shy;<lb/>randa ip&longs;ius circuli natura di&longs;&longs;erit, quo minus mirum deinde vi&shy;<lb/>deatur pr&aelig;dictas mirabiles-operationes exip&longs;o procedere. </s>
6773 
6774 <s>quan&shy;<lb/>doquidem exadmiranda cau&longs;a admirabiles effectus prodire debeant. </s>
6775 
6776 <s>qua&shy;<lb/>lia &longs;unt ea, qu&aelig; circa yectem, cum magna <expan abbr="omni&utilde;">omnium</expan> admiratione contingunt. <lb/></s>
6777 
6778 <s>videmus enim exiguam pror&longs;us vim ingens pondus, quod <expan abbr="ab&longs;q;">ab&longs;que</expan> vecte mini&shy;<lb/>m&egrave; mouere po&longs;&longs;et, addito etiam ip&longs;ius vectis pondere, facil&egrave; <expan abbr="quocunq;">quocunque</expan> vo&shy;<lb/>luerit propellere. </s>
6779 
6780 <s>quod quidem auditu ab&longs;urdum foret, ni&longs;i vi&longs;u con&longs;taret. <lb/></s>
6781 
6782 <s>omnium autem huiu&longs;modi cau&longs;&aelig; principium circulus obtinet: &amp; hoc qui&shy;<lb/>dem merit&ograve;, ex admirabili enim, quippiam mirandum accidere rationi <lb/>omnin&ograve; con&longs;entaneum eft.</s></p><p type="main">
6783 
6784 <s>Prim&ograve; igitur maxim&egrave; admirandum e&longs;t contraria &longs;imul fieri, aut exi&longs;tere:<lb/>circulus tamen ex contrarijs e&longs;t con&longs;titutus, oritur enim circulus ex com&shy;<lb/>moto, &amp; manente, qu&aelig; quidem naturaliter &longs;untinuicem contraria. </s>
6785 
6786 <s>&longs;it au&shy;<lb/>tem circulus ex commoto, &amp; manente, quia oritur ex circumuolutione <lb/>vnius rect&aelig; line&aelig;, cuius alterum extremum fixum manet, alterum ver&ograve; cir&shy;<lb/>cumagitur; quamobrem i&longs;th&aelig;c cernentes minus admirari <expan abbr="c&otilde;uenit">conuenit</expan> reliquas, <lb/>qu&aelig; in ip&longs;o &longs;unt contrarietates. </s>
6787 
6788 <s>cuiu&longs;modi e&longs;t h&aelig;c, quod cum linea, qu&aelig; cir&shy;<lb/>culi orbem complectitur, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; circunferentia appellatur, nullam habeat <lb/>latitudinem, ei tamen contraria quodammodo in&longs;unt, concauum &longs;cilicet, <lb/>&amp; curuum; qu&aelig; quidem eo modo &longs;unt contraria, quo etiam magnum, &amp; pa&shy;<lb/>ruum, horum enim medium e&longs;t &aelig;quale; illorum ver&ograve; rectum. </s>
6789 
6790 <s>&amp; &longs;icuti quan&shy;<lb/>do magnum, &amp; paruum inuicem commutantur, ita vt quod magnum e&longs;t fiat <lb/>paruum, quod ver&ograve; paruum fiat magnum, nece&longs;&longs;e e&longs;t, vt perueniant ad <lb/>&aelig;quale priu&longs;quam ad extremum alterutrum; ita linea curua antequam fiat <lb/>concaua, debet prius fieri recta: &amp; ex concaua, vt tran&longs;eat ad conuexam, <lb/>&amp; circularem, debet &longs;imiliter prius e&longs;&longs;e recta.</s></p><p type="main">
6791 
6792 <s>Alterum contrarium, quod circulo ine&longs;t, e&longs;t &longs;imul <expan abbr="c&otilde;trarijs">contrarijs</expan> motibus mo&shy;<lb/>neri: &longs;imul enim ad anteriorem mouetur locum, &amp; ad po&longs;teriotem. </s>
6793 
6794 <s>&amp; eo&shy;<lb/>dem modo linea illa, qu&aelig; ex vno extremo manens, ex altero ver&ograve; circum&shy;<lb/>lata circulum de&longs;cribit, &longs;e habet; contraria enim &longs;imul contipet, primum <lb/>&longs;cilicet, &amp; extremum. </s>
6795 
6796 <s>Ex quo enim primo loco circumagi incipit ad eun&shy;<lb/>dem rur&longs;us po&longs;trem&ograve; reuertitur, ita, vt primum ip&longs;ius, &amp; po&longs;tremum idem <lb/>&longs;int; quapropter, vt prius dicebamus non e&longs;t inconueniens, ip&longs;um circulum <lb/>miraculorum omnium e&longs;&longs;e principium. </s>
6797 
6798 <s>Admiranda igitur ea, qu&aelig; circa li&shy;<lb/>bram &longs;iunt, ad circulum <expan abbr="t&atilde;quam">tanquam</expan> cau&longs;am referuntur, qu&aelig; ver&ograve; circa vectem <lb/>ad ip&longs;am libram: alia autem fer&egrave; omnia, qu&aelig; circa mechanicas contingunt <lb/>motiones, ad vectem reducuntur.</s></p><p type="main">
6799 
6800 <s>Pr&aelig;ter pr&aelig;dicta aliud tandem mirum ip&longs;i ine&longs;t, quia nimirum cum innu&shy;<lb/>mera &longs;int puncta in vna <expan abbr="eadem&qacute;">eademque</expan>; linea, qu&aelig; &longs;emidiameter e&longs;t, omnia tamen <pb pagenum="150"/>quando &longs;emidiameter circa centrum mouetur, quamuis cum ip&longs;a mouean&shy;<lb/>tur, in&aelig;quali veiocitate mouentur; Nam punctum illud &longs;emper velocius <lb/>mouetur, quod remotius e&longs;t &agrave; centro circuli, &longs;eu &agrave; manente &longs;emidiametri <lb/>termino, &amp; proinde illud tardius, quod centro proximius e&longs;t. </s>
6801 
6802 <s><expan abbr="Atq;">Atque</expan> ex hac <lb/>mira circuli proprietate, <expan abbr="pleraq;">pleraque</expan> miraculorum accidunt circuli motioni&shy;<lb/>bus, vt in &longs;equentibus qu&aelig;&longs;tionibus manife&longs;tum erit.</s></p><p type="main">
6803 
6804 <s>Quoniam autem &longs;ecundum contrarias &longs;imul motiones mouetur circulus, <lb/>&amp; alterum quidem diametri extremum vbi A, in figura pr&aelig;&longs;enti antror&longs;um <lb/><figure place="text" xlink:href="figures-la/009.01.150.1.tif"/><lb/>mouetur; alterum ver&ograve; vbi B, retror&shy;<lb/>&longs;um, efficiunt nonnulli, vt ab vnica mo&shy;<lb/>tione multi contrari&ograve; &longs;imul mouean&shy;<lb/>tur denticulati circuli: vt &longs;unt ij, quos <lb/>in locis proponunt &longs;acris, quorum alij <lb/>&longs;unt &aelig;nei, alij ferrei. </s>
6805 
6806 <s>&longs;i enim circulus <lb/>A B, alterum circulum C D, contige&shy;<lb/>rit, mota diametro A B, ita vt A, an&shy;<lb/>tror&longs;um eat, commouebit alteram dia&shy;<lb/>metrum C D, ita vt C, retror&longs;um, hoc e&longs;t in contrarium ip&longs;i A, veniat, in <lb/>contrarium igitur mouebitur &longs;ecundus circulus C D, ad circulum A B, &amp; <lb/>rur&longs;us circulus E F. in contrarium ip&longs;i C D, commouebitur ab ip&longs;o C D, ob <lb/>eandem rationem. </s>
6807 
6808 <s>eodem etiam modo &longs;i plures fuerint, idem facient vno <lb/>&longs;olo tanquam primo motore <expan abbr="c&otilde;moto">commoto</expan>. </s>
6809 
6810 <s>hanc igitur circuli naturam animad&shy;<lb/>uertentes Architecti, in&longs;trumentum artificios&egrave; <expan abbr="fabric&atilde;t">fabricant</expan>, motus principium <lb/>occultantes, vt machin&aelig; &longs;ol&ugrave; manife&longs;tum &longs;it illud, quod admirationem <lb/>parit, cau&longs;a ver&ograve; lateat: quod genus machinarum Automata dicebantur, <lb/>quia &longs;pont&egrave; &agrave; &longs;e ip&longs;is mouebantur.</s></p><p type="main">
6811 
6812 <s>In primis igitur, qu&aelig; circa libram accidunt, dubitare faciunt, quamnam <lb/>ob cau&longs;am maiores libr&aelig; minoribus &longs;int exactiores: huius autem rei prin&shy;<lb/>cipium e&longs;t illud, quod &longs;upra innuimus, quod &longs;cilicet, qu&aelig; &agrave; centro plus di&shy;<lb/>&longs;tat linea, &longs;iue qu&aelig; longior e&longs;t, eadem vi commota citius fertur, quam illa, <lb/>qu&aelig; minus &agrave; centro di&longs;tat, &longs;eu qu&aelig; minor e&longs;t. </s>
6813 
6814 <s>Porr&ograve; citius bifariam dicitur; <lb/>&longs;iue enim in minori tempore &aelig;quale pertran&longs;it &longs;patium: &longs;iue in &aelig;quali tem&shy;<lb/>pore, maius conficit interuallum; citius feci&longs;&longs;e dicitur. </s>
6815 
6816 <s>&longs;i autem du&aelig; line&aelig; <lb/>circa idem centrum moueantur vna maior, &amp; altera minor in &aelig;quali tem&shy;<lb/>pore; maior maiorem circulum de&longs;cribet, quam minor; quia circulus &agrave; ma&shy;<lb/>iori de&longs;criptus, alterum &agrave; minori delineatum circumple ctetur, <expan abbr="atq;">atque</expan> intra &longs;e <lb/>continebit; maius autem e&longs;t continens, qu&agrave;m <expan abbr="cont&etilde;tum">contentum</expan>. </s>
6817 
6818 <s>horum autem cau&shy;<lb/>&longs;a, quoniam qu&aelig; circulum de&longs;cribit linea, duabus fertur lationibus, qu&aelig; nul&shy;<lb/>lam inuicem obtinent analogiam: quod antequam probemus, &longs;ciendum <lb/>e&longs;t, quod, quidquid duobus motibus inuicem proportionatis, mouetur, ne&shy;<lb/>ce&longs;&longs;e e&longs;t, quod motu exillis mixto progrediatur per lineam rectam, qu&aelig; dia&shy;<lb/>meter e&longs;t quadrilateri, cuius latera habeant illam proportionem, quam <lb/>duo illi motus. </s>
6819 
6820 <s>&longs;it enim in figura proportio lateris A B, ad latus A C, quam <lb/>ctiam habent duo motus, &longs;ecundum quos latum quodpiam feratur, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; la&shy;<lb/>tum illud A, &amp; feratur motu vno ver&longs;us B, per lineam A B, altero ver&ograve; mo&shy;<lb/>tu feratur ver&longs;us C. quod fiet &longs;i cogitemus latus A B, <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan> ver&longs;us M C, <pb pagenum="151"/><figure place="text" xlink:href="figures-la/009.01.151.1.tif"/><lb/>ip&longs;i &aelig;quidi&longs;tanter, dum punctum A, mouetnr <lb/>ad B. his duabus lationibus A, latum. </s>
6821 
6822 <s>nece&longs;&longs;a&shy;<lb/>ni&ograve; motu mixto progre dietur per diametrum <lb/>A M, quod &longs;ic probari pote&longs;t; &longs;it iam A, mo&shy;<lb/>tum primo motu <expan abbr="v&longs;q;">v&longs;que</expan> ad D, linea ver&ograve; ex &longs;e&shy;<lb/>cundo motu &longs;it in G F E, quo motu punctum <lb/>A, quod erat in D, <expan abbr="tract&utilde;">tractum</expan> erit in F. quod pun&shy;<lb/>ctum e&longs;t in diametro A M, quoniam enim mo&shy;<lb/>uetur duobus motibus, cum lineis A B, A C, proportionalibus, motus au&shy;<lb/>tem <expan abbr="hucu&longs;q;">hucu&longs;que</expan> &longs;unt A D, A E, qu&aelig; debent e&longs;&longs;e proportionales, cum A B, A C <lb/>compleatur rectangulum A D F E, erunt &longs;imiliter proportionalia F E, D E, <lb/>cum &longs;int &aelig;qualia duobus D A, A E, quare per 26. 6. cum quadrilaterum <lb/>paruum A D F E, &longs;it &longs;imile toti A B M C, erit A M, <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> diameter, erg&ograve; <lb/>punctum F, in quo e&longs;t A, e&longs;t in diametro A M. eodem modo, de quouis pun&shy;<lb/>cto in linea A B, ad quod A, perueniat, probabitur ab altero motu de&longs;cen&shy;<lb/>di&longs;&longs;e v&longs;que ad diametrum. </s>
6823 
6824 <s>&longs;emper erg&ograve; latum A, per rectam A M, diame&shy;<lb/>trum quadrilateri, cum illis motibus proportionalibus progreditur, quod <lb/>probandum erat. </s>
6825 
6826 <s>&egrave; conuers&ograve; manife&longs;tum etiam e&longs;t, quod &longs;i quid &longs;ecundum <lb/>diametrum duabus fertur lationibus, eas lationes e&longs;&longs;e proportionales late&shy;<lb/>ribus quadrilateri, cuius e&longs;t illa diameter, &longs;i enim ill&aelig; lationes non &longs;unt la&shy;<lb/>teribus proportionales, latum illud non feretur &longs;ecundum diametrum il&shy;<lb/>lam, &longs;ed &longs;ecundum aliam alterius quadrilateri.</s></p><p type="main">
6827 
6828 <s>Quod &longs;i quid duabus lationibus nullam habentibus proportionem per&shy;<lb/>petu&ograve; ferratur, impo&longs;&longs;ibile e&longs;t ip&longs;um motu mixto lineam rectam de&longs;cribere. <lb/></s>
6829 
6830 <s>&longs;i enim dixeris illud po&longs;&longs;e de&longs;cribere rectam lineam, tunc circa rectam il&shy;<lb/>lam tanquam diametrum de&longs;cribam quadrilaterum, &amp; po&longs;tea o&longs;tendam, vt <lb/>proxim&egrave; o&longs;ten&longs;um e&longs;t, illud latum e&longs;&longs;e &longs;ecundum laterum illius proportio&shy;<lb/>nem, quare impo&longs;&longs;ibile e&longs;t id, quod mouetur duabus lationibus nullam in&shy;<lb/>uicem rationem habentibus, ferri per lineam rectam: quapropter <expan abbr="dic&etilde;dum">dicendum</expan> <lb/>e&longs;t hoc modo <expan abbr="lat&utilde;">latum</expan>, nece&longs;&longs;ari&ograve; ferri circulariter, &longs;iue per lineam circularem. <lb/></s>
6831 
6832 <s>Quod autemea, qu&aelig; de&longs;cribit circulum linea, dum altero eins manente <lb/>extremo circumagitur, duabus &longs;imul feratur lationibus, ex quibus motus <lb/>orbicularis oriatur, manife&longs;tum e&longs;t ex &longs;uperioribus, quia &amp; antror&longs;um, &amp; <lb/>retror&longs;um impellitur; t&ugrave;m etiam, quia &longs;i rect&agrave; tenderet recta <expan abbr="de&longs;crib&etilde;s">de&longs;cribens</expan> cir&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.151.2.tif"/><lb/>culum, nunquam ad diametri perpendiculum <lb/>perueniret, &longs;ed tamen peruenit, ita vt &longs;it ip&longs;a <lb/>&agrave; centro perpendicularis diametro. </s>
6833 
6834 <s>&longs;it circuli <lb/>figura A B C D, in qua extremum diametri <lb/>B, feratur ad alterum extremum vbi D, per <lb/>ip&longs;ius diametri B D, circumuolutionem circa <lb/>centrum F, nece&longs;&longs;e e&longs;t aliquando B, perueniat <lb/>ad C. &longs;i igitur B, feretur duabus lationibus <lb/>aliquo modo proportionatis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->vt e&longs;t pro&shy;<lb/>portio lateris B E, ad E C, latus, &longs;equeretur <lb/>ex demon&longs;tratis ip&longs;um B, ferri per <expan abbr="rect&atilde;">rectam</expan> B C, <lb/>qu&aelig; diameter e&longs;&longs;et quadrilateri B E C G. &longs;ed <pb pagenum="152"/>quia in nu&longs;la proportione fertur, propterea per circularem lineam B E C, <lb/>progreditur ad C, ita vt ip&longs;a diameter B D, in po&longs;itione A C, fiat perpendi&shy;<lb/>cularis priori diametro B D. ex quibus &longs;equitur eam moueri duobus moti&shy;<lb/>bus nullam rationem habentibus; quod erat intentum.</s>
6835 
6836 
6837 
6838 </p><p type="main">
6839 
6840 <s>Hoc modo Ari&longs;t. 
6841 
6842 probare conatur, lineam circulum de&longs;cribentem, dua&shy;<lb/>bus ferri lationibus, qu&aelig; nullam habeant analogiam: Yer&ugrave;m, vt liber&egrave; fa&shy;<lb/>tear nullo modo mihi videtur intentum a&longs;&longs;equi, nam <expan abbr="neq;">neque</expan> ex dictis pater, <lb/>ip&longs;am duobus motibus ferri, quibus opus e&longs;&longs;et: neque patet eos (quamuis <lb/>concedantur) nullam inuicem habere analogiam: qui enim fieri pote&longs;t, vt <lb/>duo motus reperiantur, qu&igrave; nulla &longs;e mutu&ograve; habitudine re&longs;piciant? </s>
6843 
6844 <s>Pr&aelig;te&shy;<lb/>rea &longs;i B, ferretur illis motibus, non &longs;equitur debere moueri per lineam cir&shy;<lb/>cularem, cum pr&aelig;ter lineam rectam &longs;int plures curu&aelig;, qu&aelig; tamen non &longs;unt <lb/>circulares, vt &longs;unt &longs;ectiones parabolic&aelig;, &amp; line&aelig; &longs;pirales. </s>
6845 
6846 <s>Deinde pergit.</s></p><p type="main">
6847 
6848 <s><arrow.to.target n="marg231"/></s></p><p type="margin">
6849 
6850 <s><margin.target id="marg231"/>241</s></p><p type="main">
6851 
6852 <s>Vt autem cau&longs;a appareat, cur ea, qu&aelig; &agrave; centro longior e&longs;t linea velocius <lb/>moueatur, &longs;iue quod in eadem &longs;emidiametro remotiora puncta &agrave; <expan abbr="c&etilde;tro">centro</expan> ve&shy;<lb/>locius moueantur, vt &longs;upra dictum e&longs;t, &longs;ciendum e&longs;t, Quod &longs;i duo mouean&shy;<lb/>tur ab eadem potentia, quorum vnum &agrave; quopiam alio mouente plus repel&shy;<lb/>latur &agrave; motu priori, alterum ver&ograve; minus, rationi <expan abbr="c&otilde;&longs;entaneum">con&longs;entaneum</expan> e&longs;&longs;e, tardius <lb/>moueri id, quod plus, eo quod minus impeditur; quod videtur accidere <lb/>maiori, &amp; minori illarum, qu&aelig; &agrave; centro egre&longs;&longs;&aelig; circulos delineant. </s>
6853 
6854 <s>quoniam <lb/>enim propius e&longs;t manenti eius, qu&aelig; minor e&longs;t extremum, qu&agrave;m extremum <lb/>maioris, propterea plus &agrave; centro, cui propius e&longs;t, retrahitur &agrave; priori mo&shy;<lb/>tu, <expan abbr="hinc&qacute;">hincque</expan>; motus eius tardior redditur, ide&longs;t, quia centro propius e&longs;t; hinc <lb/>fit, vt extremum illud de&longs;cribat lineam circularem quidem, &longs;ed tamen <lb/>curuiorem quam de&longs;cribat extremum longioris line&aelig;, qu&aelig; circulum minus <lb/>curuum, &longs;eu magis ad rectam lineam accedentem delineat. </s>
6855 
6856 <s>omni quidem <lb/>igitur line&aelig; circulum de&longs;cribenti i&longs;tud accidit, vt duobus feratur motioni&shy;<lb/>bus; vna quidem, qu&aelig; illi naturalis, ac &longs;ecundum circunferentiam, qua re&shy;<lb/>ct&agrave; tenderet ni&longs;i impediretur: altera ver&ograve;, qu&aelig; illi innaturalis, qua in tran&longs;&shy;<lb/>uer&longs;um agitur, &longs;eu &longs;ecus centrum, ob quam cogitur in gyrum duci, minor <lb/>autem linea &longs;ecundum hanc motionem innaturalem plus fertur, qu&agrave;m ma&shy;<lb/>ior, ide&longs;t plus ip&longs;ius progre&longs;&longs;io inflectitur in orbem; quia enim e&longs;t centro <lb/><figure place="text" xlink:href="figures-la/009.01.152.1.tif"/><lb/>vicinior, quod quodammodo retra&shy;<lb/>hit &agrave; motu naturali, propterea ma&shy;<lb/>gis vincitur, qu&agrave;m remotior. </s>
6857 
6858 <s>Quod <lb/>ex his erit <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan>. </s>
6859 
6860 <s>&longs;it circulus vbi <lb/>B C E D, &amp; alter in eo minor, vbi <lb/>N M O P, circa idem centrum A. &amp; <lb/>proijciantur diametri in magno qui&shy;<lb/>dem C D, B E, in minori ver&ograve; M O, <lb/>N P. &amp; altera parte longius quadri&shy;<lb/>laterum compleatur D K R C. &longs;i igi&shy;<lb/>tur &longs;emidiameter A B, circumacta <lb/>de&longs;cribit circulum maiorem, reuer&shy;<lb/>titur tandem ad locum B A, vnde di&shy;<lb/>gre&longs;&longs;a e&longs;t. </s>
6861 
6862 <s>&longs;imiliter M A, circumuoluta <pb pagenum="153"/>redibit ad priorem po&longs;itionem in M A. <!-- KEEP S--></s>
6863 
6864 <s>Tardius autem fertur M A, qu&agrave;m <lb/>B A, vt dictum e&longs;t, quia maior illi fit retractio &agrave; recta progre&longs;&longs;ione. </s>
6865 
6866 <s>Sit igi&shy;<lb/>tur linea A B, mota v&longs;que ad locum A L F, &amp; &agrave; puncto L, ducatur L Q, per&shy;<lb/>pendicularis ip&longs;i A B, in minori circulo. </s>
6867 
6868 <s>&amp; rur&longs;us ducatur L S, parallela ei&shy;<lb/>dem A B, &amp; &agrave; puncto S, in maiori circulo ducatur S T, perpendicularis ei&shy;<lb/>dem B A, necnon F X. erunt igitur S T, L Q, latera rectanguli T L, &aelig;qualia <lb/>per 34. primi. </s>
6869 
6870 <s>erit po&longs;tea B T, minor quam M Q, quia &aelig;quales rect&aelig; S T, <lb/>L Q, duct&aelig; &agrave; circunferentia ad diametrum perpendiculares in circulis in&shy;<lb/>&aelig;qualibus, ea qu&aelig; e&longs;t in maiori circulo minorem re&longs;ecat diametri portio&shy;<lb/>nem, qu&agrave;m qu&aelig; in minori.</s></p><p type="main">
6871 
6872 <s>In quanto autem tempore ip&longs;a A L, lata e&longs;t per circunferentiam M L, in <lb/>tanto temporis &longs;patio in maiori circulo B, extremum ip&longs;ius B A, latum erit <lb/>per maiorem arcum qu&agrave;m &longs;it B S; iam con&longs;ideraudum e&longs;t motus vtriu&longs;que <lb/>line&aelig; in hoc ca&longs;u &aelig;quales e&longs;&longs;e, &longs;unt enim de&longs;cripti per lineas &aelig;quales T S, <lb/>Q L, qu&aelig; &longs;unt rect&aelig;; tam enim linea B A, qu&agrave;m M A, naturali motu recta <lb/>tenderet, vt dictum e&longs;t, <expan abbr="peragra&longs;&longs;et&qacute;">peragra&longs;&longs;etque</expan>; illa rectam T S: h&aelig;c ver&ograve; rectam Q L. <lb/><!-- KEEP S--></s>
6873 
6874 <s>Verum lationes innaturales &longs;unt impares, latio enim B T, breuior e&longs;t M <expan abbr="q.">que</expan> <lb/>quantitate autem B T, retracta e&longs;t B A, &agrave; motu &longs;ibi naturali, &amp; recto: quan&shy;<lb/>titate ver&ograve; M Q, retracta e&longs;t M A, vnde apparet motu hoc violento magis <lb/>retractam e&longs;&longs;e minorem M A, qu&agrave;m maiorem B A, quod erat primo de&shy;<lb/>clarandum.</s></p><p type="main">
6875 
6876 <s>Quod autem ob id A B, maior c&ecedil;lerius mota &longs;it motu naturali, qu&agrave;m mi&shy;<lb/>nor M A, pal&agrave;m fiet. </s>
6877 
6878 <s>quia enim oportet <expan abbr="vtramq;">vtramque</expan> lineam maiorem, &amp; mi&shy;<lb/>norem eadem vi motam, confeci&longs;&longs;e binos illos motus proportionales, ide&longs;t <lb/>ita &longs;e debet habere motus naturalis maioris ad motum innaturalem eiu&longs;&shy;<lb/>dem, quemadmodum &longs;e habet motus naturalis minoris ad motum innatu&shy;<lb/>ralem eiu&longs;dem: Oportet ergo, vt &longs;i A B, &amp; A M, &longs;unt eadem vi commot&aelig;, <lb/>vt &longs;it eadem ratio T S, ad Q L, qu&aelig; e&longs;t B T, ad M Q, non e&longs;t autem, vt o&longs;ten&shy;<lb/>&longs;um e&longs;t; ergo linea A B, eadem vi commota, ac M A, conficit plu&longs;quam <lb/>B S, &longs;ed nece&longs;&longs;ari&ograve; peruenit ad F. hoc enim in puncto erunt pr&aelig;dicti motus <lb/>proportionales, vt oportet, erit enim motus naturalis in maiori perpendi&shy;<lb/>cularis F X, &amp; innaturalis B X, in minori ver&ograve; naturalis L Q, innaturalis <lb/>M <expan abbr="q.">que</expan> quod &longs;i ducantur rect&egrave; B F, M L, apparebunt duo triangula &aelig;quian&shy;<lb/>gula B X F, M Q L, &amp; erunt per 4. 6. vt F X, ad B X. ita L Q, ad M Q, &amp; <lb/>permutando erunt etiam vt F X, ad L Q, ita B X, ad M <expan abbr="q.">que</expan> ide&longs;t, vt motus <lb/>naturalis ad naturalem, ita innaturalis ad innaturalem. </s>
6879 
6880 <s>In alio autem lo&shy;<lb/>co pr&aelig;ter F, non erunt e&aelig;dem proportiones.</s></p><p type="main">
6881 
6882 <s>Ex quibus patere &longs;atis pote&longs;t, cur A B, longior &agrave; centro velocius mouea&shy;<lb/>tur qu&agrave;m minor M A, &longs;eu cur puncta eiu&longs;dem B A, velocius vertuntur, quo <lb/>longius ab&longs;unt &agrave; centro A, ide&longs;t maiorem arcum B F, peractum e&longs;&longs;e &agrave; B, <lb/>qu&agrave;m &longs;it arcus M L, peractus ab M, quod erat o&longs;tendendum.</s></p><p type="main">
6883 
6884 <s>Atque hic e&longs;t di&longs;cur&longs;us ille Ari&longs;t. 
6885 
6886 quo putat &longs;e cau&longs;am aperui&longs;&longs;e, cur lon&shy;<lb/>gior &longs;emidiameter velocius moueatur: quod num rect&egrave; attigerit, non puto <lb/>oper&aelig;pretium e&longs;&longs;e hoc loco di&longs;cutere, pr&aelig;&longs;ertim cum ad naturalem Philo&shy;<lb/>&longs;ophum &longs;pectet.</s></p><p type="main">
6887 
6888 <s>Mihi tamen maxim&egrave; con&longs;iderandum videtur hoc ip&longs;um quod a&longs;&longs;eruit, &amp; <pb pagenum="154"/>ex &longs;e patet, remotiores &longs;cilicet partes diametrorum &agrave; centro velocius mo&shy;<lb/>ueri, qu&agrave;m viciniores; ex hac enim maiori velocitate &longs;equitur maiore etiam <lb/>vi moueri, vnde &amp; potenti&aelig; mouenti in extremo eius vis augebitur, &amp; plus <lb/>poterit quam &longs;ola &longs;ine vecte, e&longs;t enim vectis du&aelig; &longs;emidiametri altera alte&shy;<lb/>ram longior; ex quibus fort&egrave; apparet vnde vectis vires oriantur.</s></p><p type="main">
6889 
6890 <s>His igitur tanquam huius Mechanic&aelig; facultatis principijs po&longs;itis, ad va&shy;<lb/>rias Qu&aelig;&longs;tiones di&longs;cutiendas accedit.</s></p><p type="head">
6891 
6892 <s><emph type="italics"/>QV&AElig;STIO PRIMA<emph.end type="italics"/></s></p><p type="head">
6893 
6894 <s><emph type="italics"/>De Libra.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6895 
6896 <s><arrow.to.target n="marg232"/></s></p><p type="margin">
6897 
6898 <s><margin.target id="marg232"/>242</s></p><p type="main">
6899 
6900 <s>Cvr autem maiores libr&aelig; minoribus &longs;int exactiores, pal&agrave;m e&longs;t ex <lb/>pr&aelig;mi&longs;&longs;is principijs. </s>
6901 
6902 <s>con&longs;iderare enim oportet, quod in motu li&shy;<lb/>br&aelig; de&longs;cribitur quidam circulus, cuius diameter &longs;unt ip&longs;a libr&aelig; <lb/>brachia, centrum ver&ograve; e&longs;t fpartum, &longs;iue trutina; hoc enim pun&shy;<lb/>ctum in motu libr&aelig; manet: duo ver&ograve; brachia &longs;unt veluti du&aelig; &longs;emidiametri <lb/><figure place="text" xlink:href="figures-la/009.01.154.1.tif"/><lb/>&agrave; centro exeuntes, vt in figura cerne&shy;<lb/>re e&longs;t, in qua centrum, &longs;iue &longs;partum <lb/>e&longs;t vbi C, reliqua &longs;unt manife&longs;ta. </s>
6903 
6904 <s>In <lb/>eadem porr&ograve; figura libra maior &longs;it <lb/>A B. minor ver&ograve; circa idem &longs;partum <lb/>C, &longs;it F G. <!-- KEEP S--></s>
6905 
6906 <s>Iam vt pr&aelig;mi&longs;&longs;um e&longs;t, ea&shy;<lb/>dem vi, vel eodem onere in lance B, <lb/>po&longs;ito, mouebitur velocius brachium <lb/>libr&aelig; maioris, qu&agrave;m minoris &longs;it ma&shy;<lb/>ior tran&longs;lata ad <expan abbr="loc&utilde;">locum</expan> D E, erg&ograve; com&shy;<lb/>mota e&longs;t per arcum B E, vel A D. <!-- KEEP S--></s>
6907 
6908 <s>Minor autem libra acta e&longs;&longs;et per mino&shy;<lb/>rem arcum G I, vel F H, melius autem apparet arcus B E, maior, quam mi&shy;<lb/>nor G I, <expan abbr="atq;">atque</expan> hoc e&longs;t, qu&ograve;d maiores libras exactiores facit. </s>
6909 
6910 <s><expan abbr="hinc&qacute;">hincque</expan>; etiam e&longs;t, <lb/>qu&ograve;d nonnulla pondera in minimis libris ade&ograve; paruam brachiorum aper&shy;<lb/>tionem faciant, vt &aelig;gr&egrave; percipi po&longs;&longs;it; in magnis ver&ograve; propter brachiorum <lb/>longitudinem vald&egrave; &longs;en&longs;ibilem efficiant. </s>
6911 
6912 <s>qu&aelig;dam ver&ograve; ben&egrave;, &amp; in magnis, <lb/>&amp; in paruis apparent, &longs;ed tamen &longs;emper melius in magnis ob dictam ratio&shy;<lb/>nem. </s>
6913 
6914 <s>Quamobrem machinantur ij, qui purpuram vendunt, vt pendendo <lb/>defraudent, tum in medio libr&aelig; non ponentes &longs;partum, vt hoc modo bra&shy;<lb/>chium ex vna parte longius factum facilius moueatur, &amp; proinde &agrave; minori <lb/>purpur&aelig; pondere; tum etiam <expan abbr="plumb&utilde;">plumbum</expan> in lancem illam infundentes inquam <lb/>merces imponitur, vel partem illam lancis, quam magis grauitare cu&shy;<lb/>piunt ex ligno radici proximo, vel ex nodo&longs;o facientes: lignum <lb/>enim, quod radici proximum e&longs;t, graue admodum e&longs;t, <lb/>quemadmodum etiam nodus; quia nodus e&longs;t, <lb/>qu&aelig;dam radix. </s>
6915 
6916 <s><expan abbr="Atq;">Atque</expan> h&aelig;c e&longs;t huius pri&shy;<lb/>m&aelig; qu&aelig;&longs;tionis paraphra&longs;is.</s></p><pb pagenum="155"/><p type="head">
6917 
6918 <s><emph type="italics"/>QV&AElig;STIO SECVNDA<emph.end type="italics"/></s></p><p type="head">
6919 
6920 <s><emph type="italics"/>De Libra<emph.end type="italics"/></s></p><p type="main">
6921 
6922 <s><arrow.to.target n="marg233"/></s></p><p type="margin">
6923 
6924 <s><margin.target id="marg233"/>243</s></p><p type="main">
6925 
6926 <s><emph type="italics"/>Cvr &longs;i quidem &longs;ur&longs;um fuerit &longs;partum, quando deor&longs;um lato pondere, qui&longs;&shy;<lb/>piam id amouet, rur&longs;um a&longs;cendit libra? </s>
6927 
6928 <s>Si autem deor&longs;um constitutum <lb/>fuerit, non a&longs;cendit, &longs;ed manet? </s>
6929 
6930 <s>An quia &longs;ur&longs;um &longs;parto quidem exi&longs;ten&shy;<lb/>te plus libr&aelig; extra perpendiculum fit, &longs;partum enim e&longs;t perpendiculum, <lb/>quare nece&longs;&longs;e est deor&longs;um ferri id, quod plus est, donec a&longs;cendat, qu&aelig; bifariam li&shy;<lb/>bram diuidit ad ip&longs;um perpendicul&ubreve;, cum onus incumbat ad libr&aelig; partem tractam.<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.155.1.tif"/><lb/><emph type="italics"/>&longs;it libra vbi recta B C, &longs;partum autem <lb/>A D: hoc igitur &longs;ur&longs;um erecto, perpendi&shy;<lb/>culum erit vbi A D M. &longs;i igitur in ip&longs;o B, <lb/>ponatur onus, B, quidem de&longs;cendet vbi E; <lb/>C, autem a&longs;cendat vbi H, quamobrem ea, <lb/>qu&aelig; bifariam libram &longs;ecat, prim&ograve; quidem <lb/>erit D M, ip&longs;ius perpendiculi; incumben&shy;<lb/>te autem onere erit D G, quare libr&aelig; ip&shy;<lb/>&longs;ius vbi E H, quod extra A M, perpendi&shy;<lb/>culum e&longs;t, vbi e&longs;t D D H, maius e&longs;t dimidio. </s>
6931 
6932 <s>&longs;i igitur amoueatur onus ab ip&longs;o E, ne&shy;<lb/>ce&longs;&longs;e e&longs;t H, deor&longs;um ferri, minus enim e&longs;t ip&longs;um E D. &longs;i quidem igitur &longs;ur&longs;um ha&shy;<lb/>buerit &longs;partum, propter hoc a&longs;cendit libra. </s>
6933 
6934 <s>&longs;i autem deor&longs;um fuerit, id quod &longs;ub&shy;<lb/>stat, contrarium facit; plus enim dimidio fit libr&aelig;, qu&aelig; deor&longs;um e&longs;t, pars, qu&agrave;m <lb/>quod perpendiculum &longs;ecet; quapropter non a&longs;cendit, pars enim eleuata leuior e&longs;t.<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.155.2.tif"/><lb/><emph type="italics"/>&longs;it libra vbi N G, perpendiculum autem <lb/>K L M, bifariam igitur &longs;ecatur N G. im&shy;<lb/>po&longs;ito autem onere in ip&longs;o N, erit quidem <lb/>N, vbi O, ip&longs;um autem G, vbi R; K L, au&shy;<lb/>tem vbi K P, quare maius e&longs;t L P O, qu&agrave;m <lb/>L R, ip&longs;o P L. <!-- KEEP S--></s>
6935 
6936 <s>Ablato igitur onere, ne&shy;<lb/>ce&longs;&longs;e e&longs;t manere; incumbit enim, ceu onus <lb/>exce&longs;&longs;us medietatis in quo P L.)<emph.end type="italics"/> Aduer&shy;<lb/>te textum gr&aelig;cum e&longs;&longs;e mendo&longs;um, la&shy;<lb/>tinum vero mendo&longs;i&longs;&longs;imum. </s>
6937 
6938 <s>Ego partim ex certa rei intelligentia, vti vi&shy;<lb/>des re&longs;titui. </s>
6939 
6940 <s><expan abbr="Idem&qacute;">Idemque</expan>; circa figuras pr&aelig;&longs;titi. </s>
6941 
6942 <s>Porr&ograve; quoniam Piccolomineus, <lb/>&amp; &longs;i plurimum, vt ip&longs;e fatetur, in&longs;udauerit, non tamen &longs;olutionem huius <lb/>qu&aelig;&longs;tionis e&longs;t a&longs;&longs;ecutus, eam tibi ex Mechanicis Guidibaldi tradam. </s>
6943 
6944 <s>Ari&longs;t&shy;<lb/>igitur ponit duas libr&aelig; &longs;pecies, &longs;iue potius duas eiu&longs;dem libr&aelig; po&longs;itiones, <lb/>vnam, qu&aelig; haber &longs;partum, &longs;iue perpendiculum &longs;upra; alteram, qu&aelig; infra. <lb/><figure place="text" xlink:href="figures-la/009.01.155.3.tif"/><lb/>vt in pr&aelig;&longs;enti figura, &longs;it libra B C, cuius <lb/>&longs;partum, &longs;iue perpendiculum A D, &longs;it &longs;ur&shy;<lb/>&longs;um, ita vt in puncto A, &longs;it affixum perpen&shy;<lb/>diculum, &amp; circa idem punctum A, tan&shy;<lb/>quam circa centrum tota libra circum&shy;<lb/>uertatur. </s>
6945 
6946 <s>h&aelig;c e&longs;t prima libr&aelig; collocatio. </s>
6947 
6948 <s>&longs;it deinde libra B C, cuius &longs;partum, <lb/>&longs;iue perpendiculum A D, &longs;it deor&longs;um, vt in altera figura, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; circa pun&shy;<pb pagenum="156"/><figure place="text" xlink:href="figures-la/009.01.156.1.tif"/><lb/>ctum A, tanquam circa <expan abbr="centr&utilde;">centrum</expan>, aut axem <lb/>ita fixum, vt ip&longs;i libr&aelig; conuer&longs;io innita&shy;<lb/>tur, qu&aelig; e&longs;t altera libr&aelig; po&longs;itio. </s>
6949 
6950 <s>Qu&aelig;rit <lb/>igitur, cur &longs;i in libra &longs;ur&longs;um <expan abbr="hab&etilde;te">habente</expan> per&shy;<lb/>pendiculum, &amp; centrum, ponatur ex vna <lb/>parte onus quodpiam, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in parte B, vt in prima textus figura factum e&longs;t, <lb/>libra de primo &longs;itu B C, mouetur ad &longs;itum E H, &longs;ed tamen ablato pondere <lb/>reuertitur &longs;ua &longs;pont&egrave; ad pri&longs;tinum &longs;itum B C. &longs;i autem in libra, cuius per&shy;<lb/>pendiculum, ac centrum deor&longs;um &longs;it, vt in &longs;ecunda figura textus, pondus <lb/>imponatur, ip&longs;a quidem &agrave; &longs;itu B C, ad &longs;itum O R, transferretur; verumta&shy;<lb/>men ablato onere, <expan abbr="n&otilde;">non</expan> amplius ad priorem po&longs;itionem, vti prior, reucrtitur.</s>
6951 
6952 
6953 
6954 </p><p type="main">
6955 
6956 <s>Huic qu&aelig;&longs;tioni, vt re&longs;pondeat, tacit&egrave; &longs;upponit omne graue tendere de&shy;<lb/>or&longs;um, hoc pacto, vt centrum grauitatis ip&longs;ius tendat per lineam rectam <lb/>ad mundi centrum ab ip&longs;o grauitatis centro protractam, quam lineam Di&shy;<lb/>rectionis Recentiores appellant. </s>
6957 
6958 <s>&longs;ciendum autem centrum grauitatis e&longs;&longs;e <lb/>punctum quoddam in quolibet graui, ex quo &longs;i graue illud &longs;u&longs;pendatur, &longs;em&shy;<lb/>per manet in &aelig;quilibrio, nec vnquam po&longs;itionem re&longs;pectu &longs;uarum partium <lb/>mutat, quamuis ita &longs;u&longs;pen&longs;um huc illuc transferatur. </s>
6959 
6960 <s>Ita Pappus Alexan&shy;<lb/>drinus initio octaui libri Mathematicarum collectionum. </s>
6961 
6962 <s>Totius igitur li&shy;<lb/>br&aelig; ab&longs;que onere centrum grauitatis e&longs;&longs;et circa punctum D, quod e&longs;&longs;et di&shy;<lb/>&longs;tinctum &agrave; centro circumuolutionis A. quod grauitatis centrum, &longs;emper <lb/>quantum fieri pote&longs;t, &longs;i nihil ob&longs;tet, centro mundi appropinquat; &amp; propte&shy;<lb/>rea facit, vt prior libra &longs;ine onere &longs;u&longs;pen&longs;a in A, in &aelig;quilibrio, atque hori&shy;<lb/>zonti parallela permaneat, &longs;tante enim D, centro mundi maxim&egrave; propin&shy;<lb/>quo, &longs;iue in loco humillimo, erit inter punctum A, &amp; centrum mundi, ac <lb/>con&longs;equenter in linea directionis. </s>
6963 
6964 <s>qu&aelig; linea directionis in prima figura <lb/>textus e&longs;&longs;et eadem cum perpendiculo A D M, manente libra &longs;ine pondere <lb/>horizonti parallela; in <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> autem figura textus coincideret pariter cum <lb/>perpendiculo K L M, antequam libra ob impo&longs;itum onus ab &aelig;quilibrio di&shy;<lb/>moueretur. </s>
6965 
6966 <s>per hanc enim lineam centrum grauitatis libr&aelig;, quod e&longs;t prop&egrave; <lb/>puncta D, &amp; L, tenderet ad mundi centrum, &longs;i libra liber&egrave; ad centrum mun&shy;<lb/>di dilaberetur. </s>
6967 
6968 <s>his pr&aelig;mi&longs;&longs;is &longs;ic qu&aelig;&longs;tioni &longs;atisfacit, &amp; prim&ograve; prim&aelig; parti, <lb/>quando nimirum &longs;partum &longs;upern&egrave; collocatum e&longs;t. </s>
6969 
6970 <s>Ratio igitur, cur tunc li&shy;<lb/>bra amoto pondere ad horizontis &aelig;quilibrium reuertatur e&longs;t, quia pondus <lb/>libr&aelig; impo&longs;itum in altera tantum libr&aelig; parte, grauitando impellit libram <lb/>ad alium &longs;itum E H, ita vt maior pars libr&aelig; con&longs;tituatur ex altera parte li&shy;<lb/>ne&aelig; directionis prioris A D M, in qua etiam parte exi&longs;tit centrum granita&shy;<lb/>tis libr&aelig; ip&longs;ius, e&longs;t enim circa D, quod centrum vi ponderis incumbentis in <lb/>E, cogitur paul&ugrave;m a&longs;cendere, <expan abbr="atq;">atque</expan> contra ip&longs;ius naturalem inclinationem &agrave; <lb/>mundi centro recedere, vt &longs;i in libra B C, appendatur onus in B, vt in pri&shy;<lb/>ma textus figura; B, de&longs;cendet ad E, &amp; C, a&longs;cendet ad H, &amp; centrum graui&shy;<lb/>tatis D, paul&ugrave;m a&longs;cendet &agrave; centro mundi, &amp; linca A D M, qu&aelig; libram bi&shy;<lb/>fariam &longs;ecabat modo tran&longs;lato perpendiculo in A D G, non amplius cam <lb/>bifariam &longs;ecabit; &longs;ed libr&aelig; E H, maior pars erit vltra perpendiculum A D&shy;<lb/>M, qu&aelig; maior pars e&longs;t D D H.<!-- KEEP S--></s></p><p type="main">
6971 
6972 <s>Si igitur nunc onus amoueatur libr&aelig; E H, centrum grauitatis, quod e&longs;t <pb pagenum="157"/>ad D, remanet vltra priorem Directionis lineam; &amp; quia pondus non am&shy;<lb/>plius illi &aelig; que ponderat, grauitabit, &amp; quia libra c&ugrave;m affixa &longs;it ad A, nequit <lb/>deor&longs;um recta tendere, circumferretur circa A, trahente ip&longs;am grauitatis <lb/>centro, cum nihil ob&longs;it, donec iterum perpendiculum A D G, priori &longs;itui <lb/>A D M, congruat: hac enim ratione centrum grauitatis, quantum pote&longs;t, <lb/>iuxta naturam &longs;uam de&longs;cendet, <expan abbr="libra&qacute;">libraque</expan>; ad pri&longs;tinum &aelig;quilibrij B C, &longs;itum <lb/>re&longs;tituetur. </s>
6973 
6974 <s>Si autem deor&longs;um fuerit &longs;partum in &longs;ecunda figura textus, im&shy;<lb/>po&longs;ito pondere contrarium accidit, quia maior pars libr&aelig;, &amp; in qua cen&shy;<lb/>trum grauitatis e&longs;t, in tali motu de&longs;cendit: altera autem pars minor, ac l&aelig;&shy;<lb/>uior &longs;ur&longs;um tollitur. </s>
6975 
6976 <s>&amp; quia graue natura &longs;ua nequit a&longs;cendere, propterea <lb/>ablato pondere non reuertitur ad &aelig;quilibrium B C, cum centrum grauita&shy;<lb/>tis a&longs;cendere ne queat, quod tunc oporteret.</s></p><p type="main">
6977 
6978 <s>Sit libra N G, in &longs;ecunda figura, cuius perpendiculum, <expan abbr="&longs;imul&qacute;">&longs;imulque</expan>; directio&shy;<lb/>nis linea &longs;it K L M, qu&aelig; libram in prima po&longs;itione diuidit bifariam; impofi&shy;<lb/>to autem onere in N. N, trahetur ad O, &amp; G, ad R, &amp; K L, vbi K P. quare <lb/>maior e&longs;t O L, in quo <expan abbr="centr&utilde;">centrum</expan> grauitatis, &amp; propterea grauior qu&agrave;m &longs;it L R: <lb/>&longs;uperat enim O L, ip&longs;am L R, exce&longs;&longs;u dupl&aelig; P L, quod facil&egrave; apparet &longs;i po&shy;<lb/>natur tota O R, 10. &amp; dimidia O P, &amp; O R, 5. &amp; P L, ponatur 2. erit enim <lb/>tunc O L, 7. &amp; L R, 3. qu&aelig; hanc &longs;uperat 4. duplo &longs;cilicet ip&longs;ius P L, 2. qua&shy;<lb/>re ne&longs;cio cur Ari&longs;t. 
6979 
6980 dicat, ip&longs;am O L, &longs;uperare ip&longs;am L R, &longs;ol&ugrave;m quantitate <lb/>P L. <!-- KEEP S--></s>
6981 
6982 <s>Quapropter etiam &longs;i onus auferatur, nece&longs;&longs;e e&longs;t ibi libram manere, <lb/>quia maior, &amp; grauior ip&longs;ius pars deor&longs;um e&longs;t, nec pote&longs;t natura &longs;ua l&aelig;ui&shy;<lb/>tare, vel a&longs;cendere, vt oporteret, &longs;i ad pri&longs;tinum &longs;itum N G, re&longs;titui debe&shy;<lb/>ret. </s>
6983 
6984 <s>remanebit igitur in O R.</s></p><p type="main">
6985 
6986 <s>Ex his, qu&aelig;&longs;tionis &longs;olutionem, textus explicationem, ac re&longs;titutio&shy;<lb/>nem habeto.</s></p><p type="main">
6987 
6988 <s>Aduertendum quoad &longs;ecundam libram, ne &longs;imul cum 10. Bapti&longs;ta Bene&shy;<lb/>dicto in libro &longs;peculationum immerit&ograve; Ari&longs;t. 
6989 
6990 erroris arguamus: ip&longs;e enim, <lb/>quia libram hanc non agnouit, au&longs;us e&longs;t affirmare, Ari&longs;tot. hoc loco fal&longs;um <lb/>pror&longs;us dixi&longs;&longs;e, cum dixit libram &longs;patto infim&egrave; collocato, non redire ad <lb/>pri&longs;tinam po&longs;itionem.</s>
6991 
6992 </p><p type="head">
6993 
6994 <s><emph type="italics"/>QV&AElig;STIO TERTIA<emph.end type="italics"/></s></p><p type="head">
6995 
6996 <s><emph type="italics"/>De Vecte.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
6997 
6998 <s><arrow.to.target n="marg234"/></s></p><p type="margin">
6999 
7000 <s><margin.target id="marg234"/>244</s></p><p type="main">
7001 
7002 <s>Cvm textus tam gr&aelig;ci, qu&agrave;m latini mendis &longs;cateant, <expan abbr="neq;">neque</expan> hi textus <lb/>maioris &longs;int momenti, eos per paraphra&longs;im explicabo, in qua ta&shy;<lb/>men totus textus continebitur, <expan abbr="atq;">atque</expan> emendabitur. </s>
7003 
7004 <s>Cur exigu&aelig; <lb/>vires (quemadmodum &agrave; principio dictum e&longs;t) adhibito vecte, ma&shy;<lb/>iora mouent pondera, quam <expan abbr="ab&longs;q;">ab&longs;que</expan> vecte? </s>
7005 
7006 <s>contrarium enim videtur debere <lb/>fieri, nam mouenti additur grauitas vectis, &amp; ide&ograve; pondus augetur, erg&ograve; <lb/>difficilius ip&longs;um cum vecte, qu&agrave;m &longs;ine eo mouere deberet.</s></p><p type="main">
7007 
7008 <s>Vectis porr&ograve; e&longs;t in&longs;trumentum oblongum, quo ad &longs;ubleuandum graue <lb/>quodpiam vtuntur opifices, quod innititur cuidam fulcimento, quod gr&aelig;c&egrave; <lb/>hypomoclion dicitur: hypomoclion antem oncri leuando, quanrum &longs;ieri <pb pagenum="158"/>pote&longs;t proximum e&longs;&longs;e debet, vt vectis pars longior &longs;it ad partes potenti&aelig; <lb/>mouentis. </s>
7009 
7010 <s>vt plurimum ver&ograve; fulcimentum e&longs;t inter pondus, &amp; potentiam: <lb/>aliquando etiam e&longs;t ex altero vectis extremo, ita vt onus &longs;it inter fulturam, <lb/>&amp; potentiam; aliquando potentia e&longs;t inter vtrunque, vnde tres vectis &longs;pe&shy;<lb/>cies exi&longs;tunt. </s>
7011 
7012 <s>vt in &longs;ubiectis figuris apparet. </s>
7013 
7014 <s>In prima, vectis e&longs;t A B, fultu&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.158.1.tif"/><lb/>ra E, onus C. potentia autem &longs;eu vis, <lb/>&longs;eu aliud pondus <expan abbr="mou&etilde;s">mouens</expan> &longs;it vbi D. qu&aelig; <lb/>deor&longs;um in D, pr&aelig;mens eleuabit &longs;ur&shy;<lb/>&longs;um ex altera parte onus C. &amp; vectis <lb/>circa fulturam E, tanquam centrum <lb/>conuertetur. </s>
7015 
7016 <s>In altera figura pondus <lb/>e&longs;t inter fulturam, &amp; potentiam, ful&shy;<lb/>tura autem in altera extremitate, vt <lb/>patet in figura, hic autem potentia <lb/>non pr&aelig;mit deor&longs;um in D: &longs;ed &longs;ur&longs;um <lb/>vectem eleuando pondus C, attollitur. <lb/></s>
7017 
7018 <s>In tertia tandem figura potentia, e&longs;t <lb/>inter vtrunque, e&longs;t enim in D, ibique <lb/>&longs;ur&longs;um vrget. </s>
7019 
7020 <s>verum tamen e&longs;t hunc vectem artificibus e&longs;&longs;e inutilem, quip&shy;<lb/>pe qui nullo modo iuuet potentiam, im&ograve; ver&ograve; pondus ip&longs;um grauius reddit: <lb/><expan abbr="neq;">neque</expan> hoc genere in his Mechanicis indigemus.</s></p><p type="main">
7021 
7022 <s>Re&longs;pondet igitur dubitationi, dicens rationem huius incrementi poten&shy;<lb/>ti&aelig; motricis, quod fit a&longs;&longs;umpto vecte fort&egrave; inde oriri, quod vectis &longs;it qu&aelig;&shy;<lb/>dam libra, cuius alterum brachium &longs;it altero longius; in prima autem qu&aelig;&shy;<lb/>&longs;tione explicatum e&longs;t, cur libra maior, maiorem vim habeat, eam ad cir&shy;<lb/>culum reducendo; vectis autem fit libra, hypomoclion enim e&longs;t loco &longs;parti, <lb/>tam enim &longs;partum, quam hypomoclion veluti centra manent. </s>
7023 
7024 <s>quoniam ve&shy;<lb/>r&ograve; ab eodem pondere, c&ecedil;lerius, &longs;iue maiori vi mouetur linea, quant&ograve; lon&shy;<lb/>gior &agrave; centro fuerit, vt dictum e&longs;t de admiranda circuli natura; hinc fit, vt <lb/>cum du&aelig; &longs;int in vecte potenti&aelig;, &longs;iue duo pondera, mouens, &amp; motum, illud <lb/>facilius ac maiore vi moueat, &longs;iue vires ex vecte acquirat, quod longiorem <lb/>vectis partem pre&longs;&longs;erit. </s>
7025 
7026 <s>quemadmodum igitur pars vectis longior, qu&aelig; &longs;pe&shy;<lb/>ctabat ad mouentem potentiam, &longs;uperat minorem partem, in qua e&longs;t mo&shy;<lb/>tum; ita etiam maius e&longs;t pondus <expan abbr="mot&utilde;">motum</expan>, qu&agrave;m mouens. </s>
7027 
7028 <s>&longs;emper autem quan&shy;<lb/>to ab hypomoclio magis di&longs;tabit potentia, tant&ograve; facilius mouebit, cuius <lb/>cau&longs;a &longs;upra reddita e&longs;t, quoniam nimirum, qu&aelig; plus &agrave; centro elongatur ma&shy;<lb/>iorem de&longs;cribit circulum, qui magis ad lineam rectam accedit: quare ab <lb/>eadem potentia adhibito vecte, tant&ograve; facilius pars vectis mouens dimoue&shy;<lb/>bitur, quant&ograve; magis &agrave; fulcimento di&longs;tabit. </s>
7029 
7030 <s>Exempli gratia &longs;it in &longs;uperiori <lb/>prima figura vectis A B, pondus C, mouens D, hypomoclion E, in qua pr&aelig;&shy;<lb/>dicta poteris contemplari. </s>
7031 
7032 <s>vltima illa textus verba <emph type="italics"/>(Quod autem vbi D, mo&shy;<lb/>uens, vbi F, motum autem vbi C, pondus in G,)<emph.end type="italics"/> videntur &longs;uperuacanea, atque <lb/>mendos&egrave; addita.</s></p><p type="main">
7033 
7034 <s>In hac qu&aelig;&longs;tione re&longs;pexit Ari&longs;t. &longs;ol&ugrave;m ad primam vectis &longs;peciem. </s>
7035 
7036 <s>Illud <lb/>demum, quod dixit eandem habere rationem potentiam ad pondus, qu&agrave;m <lb/>partes vectis inuicem demon&longs;tratum e&longs;t po&longs;tea acuti&longs;&longs;im&egrave; ab Archimede <pb pagenum="159"/>propo&longs;itione 6. &amp; 7. de &aelig;queponderantibus: &amp; no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> alio quam&shy;<lb/>uis modo, &amp; vnica demon&longs;tratione &agrave; Guido Vbaldo in &longs;uis Mechanicis pro&shy;<lb/>po&longs;itione 1. de Vecte, qu&aelig; e&longs;t huiu&longs;modi; Potentia &longs;u&longs;tinens pondus vecti <lb/>appen&longs;um, eandem ad ip&longs;um pondus proportionem habet, quam vectis di&shy;<lb/>&longs;tantia inter fulcimentum, ac ponderis &longs;u&longs;pen&longs;ionem, ad di&longs;tantiam, &agrave; fulci&shy;<lb/>mento ad potentiam interiectam. </s>
7037 
7038 <s>quod de omni vecte ab eo demon&longs;tratur, <lb/>cuius propo&longs;itionis &longs;en&longs;us e&longs;t hic; in &longs;uperiori prima figura &longs;i pars vectis <lb/>E B, fuerit, v.g. <!-- REMOVE S-->qua drupla partis A E; etiam pondus C, erit quadruplo ma&shy;<lb/>ius pondere, &longs;eu vi in D, qu&aelig; ip &longs;um C, ope vectis &longs;u&longs;tinet. </s>
7039 
7040 
7041 
7042 <s>quod etiam trans&shy;<lb/>ferre debes ad &longs;ecundam figuram.</s></p><p type="head">
7043 
7044 <s><emph type="italics"/>QV&AElig;STIO QVARTA<emph.end type="italics"/></s></p><p type="head">
7045 
7046 <s><emph type="italics"/>De Remo.<emph.end type="italics"/></s></p><p type="main">
7047 
7048 <s><arrow.to.target n="marg235"/></s></p><p type="margin">
7049 
7050 <s><margin.target id="marg235"/>245</s></p><p type="main">
7051 
7052 <s>EI, qui &longs;uperiora intellexerit &longs;atis clara videtur. </s>
7053 
7054 <s>Illud tamen non <lb/>omittendum, &longs;cilicet dicendum potius Remum e&longs;&longs;e vectem &longs;ecundi <lb/>generis, qu&agrave;m primi, quod fort&egrave; Ari&longs;t. 
7055 
7056 non animaduertit, nec Pic&shy;<lb/>colomineus, nam mare e&longs;t hypomoclion, re&longs;pectu enim nauis non <lb/>mouetur, &longs;ed manet, &longs;calmus autem &longs;imul cum tota naui e&longs;t pondus motum; <lb/>ver&egrave; enim nauis ip&longs;a mouetur. </s>
7057 
7058 <s>mouens e&longs;t ip&longs;e remex. </s>
7059 
7060 <s>Reliqua in textu <lb/>&longs;unt clara.</s></p><p type="head">
7061 
7062 <s><emph type="italics"/>QV&AElig;STIO QVINTA<emph.end type="italics"/></s></p><p type="head">
7063 
7064 <s><emph type="italics"/>De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7065 
7066 <s><arrow.to.target n="marg236"/></s></p><p type="margin">
7067 
7068 <s><margin.target id="marg236"/>246</s></p><p type="main">
7069 
7070 <s>Qvemadmodum in pr&aelig;cedenti qu&aelig;&longs;tione Ari&longs;t. 
7071 
7072 vectem &longs;ecundi ge&shy;<lb/>neris ad &longs;olutionem non adhibuit, vt par erat, &amp; propterea ob&longs;cu&shy;<lb/>rior eua&longs;it, ita etiam in pr&aelig;&longs;enti, qu&ecedil;&longs;tionem ad ve ctem primi ge&shy;<lb/>neris reducit, qu&aelig; ad alterum reducend&agrave; erat: <expan abbr="atq;">atque</expan> hinc ob&longs;curi&shy;<lb/>tas, atque prolixitas &longs;olutionis manauit. </s>
7073 
7074 <s>E&longs;t enim propri&egrave; Temo, &longs;iue gu&shy;<lb/>bernaculum nauis, vectis &longs;ecundi generis, vt mox explicabo, e&longs;t enim temo <lb/><figure place="text" xlink:href="figures-la/009.01.159.1.tif"/><lb/>in&longs;trumentum in extrema nanis par&shy;<lb/>te, &longs;eu puppi affixum, vt in figura pr&ccedil;&shy;<lb/>&longs;enti vides tabellam, in qua B C D, <lb/>cuius manubrium A B, intra nauim <lb/>recipitur, qu&aelig; tabella, &longs;eu temo in <lb/>duobus cardinibus, vbi C, &amp; D, cir&shy;<lb/>cumuertitur &agrave; Nauis gubernatore, <lb/>manubrium vbi A, tractante; ex qua <lb/>conuer&longs;ione nauigium, qu&ograve; vult ip&longs;e <lb/>gubernator facil&egrave; dirigit, ip&longs;umque <lb/>nauigium huc illuc quamuis ade&ograve; magnum ip&longs;e &longs;olus impellit, &amp; agitat. </s>
7075 
7076 <s>e&longs;t <lb/>enim temo vectis, cuius auxilio vires mirum in modum augentur, nam to&shy;<lb/>ta A B, e&longs;t ip&longs;a Vectis longitudo, cuius hypomoclion e&longs;t mare, cui contra&shy;<pb pagenum="160"/>nititur tabella B E; onus autem e&longs;t puppis, quod onus pr&aelig;&longs;ertim in cardini&shy;<lb/>bus C D, mouenti re&longs;i&longs;tit, &amp; quod pr&aelig;cipu&egrave; mouere gubernator intendit. <lb/></s>
7077 
7078 <s>cum igitur motum onus &longs;it intra vectis extrema, hypomoclion in extremo <lb/>ad B E, vbi in motu temonis tabella mare vrget, quod minim&egrave; cedit, <expan abbr="ip&longs;a&qacute;">ip&longs;aque</expan>; <lb/>in hoc motu fer&egrave; maneat, &amp; fiat qua&longs;i centrum, circa quod totus temo cir&shy;<lb/>cumducitur, patet temonem e&longs;&longs;e vectem &longs;ecund&aelig; &longs;peciei, vt dicebam. </s>
7079 
7080 <s>quod <lb/>etiam hinc patere pote&longs;t, quia temo e&longs;t veluti remus, cuius &longs;calmus &longs;int car&shy;<lb/>dines C, D. &longs;icut ergo remus e&longs;t vectis &longs;ecundi generis, cuius pondus e&longs;t <lb/>&longs;ealmus, &amp; mare hypomoclion; ita temo erit vectis eiu&longs;dem generis, cuius <lb/>pondus erit vbi cardines, fultura ver&ograve; mare.</s></p><p type="main">
7081 
7082 <s>Qu&aelig;rit igitur Ari&longs;t. 
7083 
7084 vnde nam tantas vires paruus nauis temo guberna&shy;<lb/>tori &longs;uggerat, <expan abbr="re&longs;pondet&qacute;">re&longs;pondetque</expan>; propterea id contingere, quod temo vectis na&shy;<lb/>turam obtineat, cuius inquit onus e&longs;t mare, melius autem, vt dixi, dixi&longs;&longs;et <lb/>onus e&longs;&longs;e nauim, mare autem hypomoclion, mouens autem e&longs;t gubernator. <lb/></s>
7085 
7086 <s>Differunt autem remus, &amp; temo, quamuis <expan abbr="vterq;">vterque</expan> &longs;it vectis, quoniam remus <lb/>&longs;ecundum latitudinem nauis, &longs;eu ad latera nauis mari obnititur. </s>
7087 
7088 <s>temo au&shy;<lb/>tem in directum fer&egrave; nauigij con&longs;titutus mare &longs;cindit. </s>
7089 
7090 <s>hinc fit, vt remus ad <lb/>nauem antror&longs;um rect&agrave; agitandam, gubernaculum ver&ograve; ad eam in latera, <lb/>&amp; obliqu&egrave; contor quendam idoneum &longs;it. </s>
7091 
7092 <s>quoniam enim mare e&longs;t hypomo&shy;<lb/>clion, fit vt dum gubernator mouet an&longs;am temonis in A, &longs;eu ad dextram, <lb/>&longs;eu ad &longs;ini&longs;tram &longs;ecum ad eandem partem trahat nauigium, quod temoni <lb/>e&longs;t connexum; ad <expan abbr="c&otilde;trariam">contrariam</expan> tamen partem trahit ei, &longs;ecundum quam mare <lb/>impingit. </s>
7093 
7094 <s><expan abbr="atq;">atque</expan> hoc pacto remus antror&longs;um, temo ver&ograve; obliqu&egrave; nauim agit.</s></p><p type="main">
7095 
7096 <s>Po&longs;th&aelig;c &longs;equuntur huiu&longs;modi verba <emph type="italics"/>(In extremo autem, &amp; non in medio <lb/>iacet, quoniam <expan abbr="mou&etilde;ti">mouenti</expan> facillimum est ab extremo motum mouere: prima enim pars <lb/>celerrim&egrave; fertur, quoniam quemadmodum in ijs, qu&oelig; feruntur in fine deficit latio, <lb/>&longs;ic ip&longs;ius continui in fine imbecili&longs;&longs;ima e&longs;t latio, imbecili&longs;&longs;ima autem ad <expan abbr="expell&etilde;dum">expellendum</expan> <lb/>est facilis, propter h&oelig;c igitur in puppi gubernaculum ponitur)<emph.end type="italics"/> quorum &longs;en&longs;us <lb/>videtur difficilis, <expan abbr="neq;">neque</expan> gr&aelig;cus textus excu&longs;andus e&longs;t, ben&egrave; enim tran&longs;lata <lb/>&longs;unt. </s>
7097 
7098 <s>Piccolomin&aelig;us quidem plura qu&agrave;m Ari&longs;t. 
7099 
7100 fatur, &longs;ed non clariora. </s>
7101 
7102 <s>dif&shy;<lb/>ficultas e&longs;t in verbis illis <emph type="italics"/>(Prima enim pars celerrim&egrave; fertur)<emph.end type="italics"/> &amp; in illis <emph type="italics"/>(Sic ip&shy;<lb/>&longs;ius continui in fine imbecili&longs;&longs;ima eft latio)<emph.end type="italics"/> videtur velle dicere, quod quando <lb/>continuum aliquod proiectum fertur per aera, pars ip&longs;ius anterior ea e&longs;t, <lb/>qu&aelig; pr&aelig; c&aelig;teris partibus principaliter mouetur, &amp; ad cuius motum reliqu&aelig; <lb/>po&longs;teriores tanquam &longs;ub&longs;e quentes moueantur; qua&longs;i dicat tota vis lationis <lb/>e&longs;t in anteriori parte: &longs;iue ip&longs;i impetus maior ine&longs;t: videmus enim proiecta, <lb/>quorum vna pars e&longs;t c&aelig;teris grauior, quia ei parti melius imprimitur mo&shy;<lb/>tus, eam etiam fieri anteriorem in latione, quamuis initio fuerit po&longs;terior. <lb/></s>
7103 
7104 <s>&longs;ic etiam quando graue fertur deor&longs;um, dicimus ip&longs;um ferri &longs;ecundum cen&shy;<lb/>trum grauitatis ip&longs;ius, <expan abbr="ibi&qacute;">ibique</expan>; maiorem vim grauitandi exi&longs;tere, &longs;ic in proie&shy;<lb/>ctis partem anteriorem dicere po&longs;&longs;umus e&longs;&longs;e, &longs;ecundum quam totum conti&shy;<lb/>nuum fertur: <expan abbr="ibi&qacute;">ibique</expan>; totum e&longs;&longs;e impetum lationis, &amp; propterea etiam maio&shy;<lb/>ri impetu, <expan abbr="atq;">atque</expan> celerrim&egrave; ferri: &amp; <expan abbr="con&longs;equ&etilde;ter">con&longs;equenter</expan> partem po&longs;teriorem, quam&shy;<lb/>uis priorem &aelig;qua velocitate con&longs;equatur, non tamen tanto impetu, cum ip&shy;<lb/>&longs;a ad alterius impetum moueatur, &amp; propterca latio ip&longs;ius e&longs;t admodum <lb/>imbecillis.</s></p><pb pagenum="161"/><p type="main">
7105 
7106 <s>Si quis &longs;agittam per aerem latam &agrave; &longs;uo motu vellet deflectere, eam faci&shy;<lb/>lius in po&longs;teriore parte &agrave; &longs;uo cur&longs;u deuiaret, qu&agrave;m in anteriore. </s>
7107 
7108 <s>hunc con&shy;<lb/>cinui corporis motum continuo proiectorum motui a&longs;&longs;imilat: quemadmo&shy;<lb/>dum enim motus proiectorum in fine debilior lente&longs;cit: &longs;ic totum conti&shy;<lb/>nuum in po&longs;trema parte &longs;egnius impellitur. </s>
7109 
7110 <s>Quia igitur nauis e&longs;t <expan abbr="c&otilde;tinuum">continuum</expan>, <lb/>quod vi remorum recta antror&longs;um fertur, &amp; propterea maiore vi prora, <lb/>qu&agrave;m puppis, facilius e&longs;t &agrave; &longs;uo directo cur&longs;u nauem deflectere, eam in pup&shy;<lb/>pi, qu&agrave;m in prora commouendo. </s>
7111 
7112 <s>hac igitur de cau&longs;a, gubernaculum puppi <lb/>affigitur. </s>
7113 
7114 <s>qu&aelig; quidem ratio, &amp; quantum valcat, &amp; an naui quadret, &amp; num <lb/>ben&egrave; &longs;it explicata, phy&longs;icorum e&longs;t iudicare.</s></p><p type="main">
7115 
7116 <s>Ego tamen aliam huius rationem video, quia nimirum &longs;i temo in priori <lb/>parte e&longs;&longs;et, quando &agrave; rectitudine ip&longs;ius nauis ad dextram, aut ad &longs;ini&longs;tram <lb/>e&longs;&longs;et inclinandus, tunc quia aqua in vnam tantum ipfius partem, &longs;eu faciem <lb/>tota impingeret, in eam &longs;cilicet, qu&aelig; antror&longs;um re&longs;piceret, eam aqua re&shy;<lb/>tror&longs;um &longs;imul cum tota naui auerteret, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; totam nauim inuerteret, ita <lb/>vt prora, cui adh&aelig;reret temo extrema fieret. </s>
7117 
7118 <s>impetus igitur aqu&aelig;, &amp; naui&shy;<lb/>gij temonati, cogit temonem e&longs;&longs;e po&longs;tremum non primum, nec medium. <lb/></s>
7119 
7120 <s><expan abbr="atq;">atque</expan> hinc oritur nece&longs;&longs;itas <expan abbr="e&utilde;">eum</expan> po&longs;teriori parti affigendi. </s>
7121 
7122 <s>&longs;ubdit po&longs;tea aliam <lb/>eiu&longs;dem rationem, quia nimirum parua motione facta in puppi multo ma&shy;<lb/>ius interuallum cogitur mutare prora; nam idem angulus, quo eius line&aelig; <lb/>&longs;unt longiores, e&ograve; maiorem &longs;ubten&longs;am &longs;ibi lineam re&longs;picit, quod facil&egrave; in <lb/><figure place="text" xlink:href="figures-la/009.01.161.1.tif"/><lb/>ad&longs;cripta figura intueri licet; in qua du&aelig; <lb/>line&aelig; A B, A C, continent angulum A, cui <lb/>angulo &longs;ubtenduntur tres line&aelig; parallel&aelig; <lb/>F G, D E, B C, quarum B C, maxima e&longs;t, <lb/>quia ibi maiores, &longs;iue remotiores &longs;unt ab <lb/>angulo A, du&aelig; rect&aelig; A B, A C, ip&longs;um con&shy;<lb/>tinentes, quod Geometric&egrave; per 4. 6. pro&shy;<lb/>bari pote&longs;t. </s>
7123 
7124 <s>&longs;ic etiam facta motione, vel <lb/>parua in puppi, tota nauis transfertur ad <lb/>alium &longs;itum, ita vt prora multum ali&ograve; transferatur, quod non accideret, &longs;i <lb/>eadem motio fieret ad medium nauigij. </s>
7125 
7126 <s>propterea igitur apti&longs;&longs;im&egrave; puppi <lb/>gubernaculum connectitur.</s></p><p type="main">
7127 
7128 <s><arrow.to.target n="marg237"/></s></p><p type="margin">
7129 
7130 <s><margin.target id="marg237"/>247</s></p><p type="main">
7131 
7132 <s>Ex ij&longs;dem etiam rationibus mathematicis patet, cur magis antror&longs;um <lb/>procedit nauigium, qu&agrave;m remi ip&longs;ius palmula retror&longs;um: eadem enim ma&shy;<lb/>gnitudo, ij&longs;dem mota viribus in aere plus, qu&agrave;m in aqua progreditur. <lb/></s>
7133 
7134 <s>Sit igitur A B, remus, G, ver&ograve; &longs;calmus. </s>
7135 
7136 <s>A, autem in nauigio &longs;it remi initium. <lb/></s>
7137 
7138 <s>B, ver&ograve; in mari palmula. </s>
7139 
7140 <s>&longs;i igitur A, vbi D, transferatur, per totum &longs;pa&shy;<lb/>tium A D, non permeabit tantumdem &longs;patij B, <expan abbr="v&longs;q;">v&longs;que</expan> ad E. <!-- KEEP S--></s>
7141 
7142 <s>B E, enim ponitur <lb/>&aelig;qualis ip&longs;i A D, &longs;ed minus interuallum propter re&longs;i&longs;tentiam aqu&aelig; ex &longs;up&shy;<lb/>po&longs;itione percurret, quale e&longs;t B F, quod minus e&longs;t qu&agrave;m A D, quare etiam li&shy;<lb/>nea B G, abbreuiabitur, <expan abbr="erit&qacute;">eritque</expan>; veluti F Y, qu&aelig; etiam erit minor ip&longs;a D G, <lb/>qu&aelig; facta e&longs;t D Y, propter duo &longs;indlia triangula D Y A, B Y F, &longs;imilia au&shy;<lb/>tem triangula &longs;unt ea, quorum anguli vnius &longs;unt &aelig;quales angulis alterius, <lb/>quo po&longs;ito &longs;unt etiam latera vnius proportionalia lateribus alterius, vt pa&shy;<lb/>tet ex prima definitione 6. necnon ex quarta eiu&longs;dem demon&longs;tratione. </s>
7143 
7144 <s>h&aelig;c <pb pagenum="162"/><figure place="text" xlink:href="figures-la/009.01.162.1.tif"/><lb/>quidem duo triangula &longs;unt &longs;imi&shy;<lb/>lia, &amp; rect&egrave; concluditur F Y, mi&shy;<lb/>nus e&longs;&longs;e qu&agrave;m D Y, &longs;ed tamen <lb/>non videntur i&longs;ta propo&longs;itum <lb/>o&longs;tendere, quod erat, plus nauim <lb/>procedere, qu&agrave;m palmulam re&shy;<lb/>trocedere. </s>
7145 
7146 <s>Fateor quidem tex&shy;<lb/>tum hunc e&longs;&longs;e ob&longs;curi&longs;&longs;imum, <lb/><expan abbr="id&qacute;">idque</expan>; propterea fort&egrave; quia e&longs;t admodum corruptus, pr&aelig;&longs;ertim circa chara&shy;<lb/>cteres, qui corrigendi &longs;unt vti nos facimus. </s>
7147 
7148 <s>ne&longs;cio qua ratione Piccolomi&shy;<lb/>neus videatur &longs;ibi locum hunc explica&longs;&longs;e. </s>
7149 
7150 <s>For&longs;itan addenda &longs;unt nonnulla <lb/>hoc pacto; cum initio remigationis ponamus remum in &longs;itu A B, in fine ve&shy;<lb/>r&ograve; prim&aelig; impul&longs;ionis in D F, &longs;calmum ver&ograve; circa medium remi in G, pri&shy;<lb/>mo; vltimo erit etiam circa medium D F, vbi H, quare &longs;calmus tran&longs;latus <lb/>e&longs;t &agrave; G, ad H, <expan abbr="tota&qacute;">totaque</expan>; G H, perficit, quam deberet Ari&longs;tot. vt &longs;ibi con&longs;taret <lb/>probare e&longs;&longs;e maiorem ip&longs;a B F, quam palmula obiuit, &amp; con&longs;equenter pro&shy;<lb/>ba&longs;&longs;et nauigium plus proce&longs;&longs;i&longs;&longs;e, qu&agrave;m palmula rece&longs;&longs;erit: quod propo&longs;ue&shy;<lb/>rat. </s>
7151 
7152 
7153 
7154 <s>Verum hoc non demon&longs;trat; <expan abbr="neq;">neque</expan> ex pr&aelig;mi&longs;&longs;is deduci pote&longs;t. </s>
7155 
7156 <s>po&longs;tea <lb/>&longs;ubdit <emph type="italics"/>(Stans autem erit medium vbi e&longs;t G, in contrarium enim ip&longs;i, qu<foreign lang="greek">q</foreign>d in mari <lb/>e&longs;t, extremo B, procedit, vbi extremum in nauigio e&longs;t A, non procederet autcm <lb/>vbi est D, ni&longs;i commoueretur nauigi&ubreve;, &amp; e&ograve; transferretur vbi e&longs;t remi principium)<emph.end type="italics"/><lb/>vbi in textu mendos&egrave; legitur C, pro G.<!-- KEEP S--></s></p><p type="main">
7157 
7158 <s>Sen&longs;us porr&ograve; horum verborum e&longs;t hic; &longs;i remus cirea &longs;calmum G, verte&shy;<lb/>retur, &amp; tamen nauis ab eo non propelleretur, &longs;ed &longs;taret, tunc medium na&shy;<lb/>uis maneret vbi G, per motum enim remi impellitur in contrarias partes <lb/>ip&longs;i palmul&aelig; B, qu&aelig; e&longs;t in mari, quia &longs;equitur motum alterius extremi A, <lb/>manubrij &longs;cilicet remi, qui e&longs;t in naui: quod autem nauigium &agrave; remo mo&shy;<lb/>neatur, &longs;ignum e&longs;t, quia manubrium A, non procederet vbi e&longs;t D, ni&longs;i pari&shy;<lb/>ter cum remo nauigium illor&longs;um con&longs;equeretur. </s>
7159 
7160 <s>H&aelig;c quidem Ari&longs;t. 
7161 
7162 circa <lb/>motum nauigij imperfect&egrave; admodum ni&longs;i textus corruptionem cau&longs;etur, di&shy;<lb/>xi&longs;&longs;e videatur. </s>
7163 
7164 <s>Quapropter oper&aelig;pretium me facturum exi&longs;timo, &longs;i Petri <lb/>Nonij acuti&longs;&longs;imi Mathematici, &longs;ubtili&longs;&longs;imas, <expan abbr="&longs;citu&qacute;">&longs;cituque</expan>; digni&longs;&longs;imas in pr&aelig;&longs;ens <lb/>problema anuotationes hoc loco de&longs;crip&longs;ero, ex quibus perfect&egrave;, ac ma&shy;<lb/>thematic&egrave; toti huic qu&aelig;&longs;tioni fit &longs;atis, qu&aelig; &longs;ic &longs;e habent.</s></p><p type="head">
7165 
7166 <s><emph type="italics"/>In Problema Mechanicum Arist. 
7167 
7168 de motu Nauigij <lb/>ex remis, annotatio Petri Nonij.<emph.end type="italics"/></s></p><p type="main">
7169 
7170 <s>Cvm olim di&longs;cipulis no&longs;tris mechanicas Ari&longs;t. 
7171 
7172 qu&aelig;&longs;tiones interpre&shy;<lb/>taremur, nonnulla circa problema illud annotauimus, cur magis <lb/>procedat nauigium, quam remi palmula in contrarium. </s>
7173 
7174 <s>Ari&longs;tot. <lb/>enim ratiocinatio ob&longs;cura e&longs;t; quam nos tamen, vt aliquid lucis <lb/>haberet, ad hunc modum explicauimus; &amp; propter materi&aelig; &longs;imilitudinem <lb/>hi&longs;ce no&longs;tris libris de nauigandi ratione adiunximus. </s>
7175 
7176 
7177 
7178 <s>Supponit autem ip&longs;e <lb/>auctor remi palmulam retrocedere, quoties nauigium in anteriora progre&shy;<pb pagenum="163"/>ditur, <expan abbr="locum&qacute;">locumque</expan>; &longs;calmi, &longs;uper quo circulari motu remus vertitur, in medio <lb/>ip&longs;ius remi po&longs;itum e&longs;&longs;e, vt &longs;cilicet tantum di&longs;tet &agrave; manubrio, quantum &agrave; <lb/>palmula. </s>
7179 
7180 <s>Du&aelig; <expan abbr="itaq;">itaque</expan> rect&aelig; line&aelig; ponantur &aelig;quales A B, &amp; D E, qu&aelig; quidem <lb/>in C, puncto medio &longs;e inuicem &longs;ecent, &amp; connectantur A B, &amp; D E: remus <lb/>autem in initio vnius remigationis po&longs;itionem habeat rectam lineam A B, <lb/><expan abbr="&longs;it&qacute;">&longs;itque</expan>; A, manubrium; B, palmula; C, ver&ograve; &longs;ealmus. </s>
7181 
7182 <s>Cum igitur A, remi ca&shy;<lb/>put in fine ip&longs;ius remigationis e&ograve; tran&longs;latum fuerit D, non erit B, vbi E; &longs;i <lb/><figure place="text" xlink:href="figures-la/009.01.163.1.tif"/><lb/>enim ibi fuerit; remus igitur po&longs;itionem <lb/>habebit rectam lineam D E; &amp; quoniam <lb/>contrapo&longs;iti anguli, qui ad C, &aelig;quales &longs;unt, <lb/>&amp; duo latera A C, &amp; D C, trianguli A D C, <lb/>duobus lateribus B C, &amp; C E, trianguli B&shy;<lb/>E C, &aelig;qualia etiam &longs;unt: reliqui igitur an&shy;<lb/>guli, <expan abbr="atq;">atque</expan> ba&longs;es ip&longs;orum <expan abbr="tri&atilde;gulorum">triangulorum</expan> &aelig;qua&shy;<lb/>les erunt per 4. propo&longs;itionem primi libri <lb/>Euclidis, &amp; propterea tantum &longs;patium per&shy;<lb/>curret B, quantum A: &longs;calmus ver&ograve; C, im&shy;<lb/>motus omnin&ograve; erit: &amp; nauigium idcirc&ograve;, in <lb/>quo ip&longs;e &longs;calmus, immotum etiam erit con&shy;<lb/>tra hypothe&longs;im. </s>
7183 
7184 <s>&longs;upponitur enim in que&longs;tio&shy;<lb/>ne, quod nauigium illa remigatione in anteriora moueatur, remi ver&ograve; pal&shy;<lb/>mula retrocedat. </s>
7185 
7186 <s>Scalmus porr&ograve; quamquam circularis remi motus expers <lb/>&longs;it; motu tamen nauigij commouetur. </s>
7187 
7188 <s>Remus igitur po&longs;itionem habeat in <lb/>fine ip&longs;ius remigationis rectam lineam D Z, qu&aelig; quidem rectam A B, &longs;ecec <lb/>in T, inter B, &amp; C; rectam ver&ograve; B E, in Z. <!-- KEEP S--></s>
7189 
7190 <s>Et quoniam duo coalterni anguli <lb/>C A D, &amp; C B E, &aelig;quales <expan abbr="o&longs;t&etilde;&longs;i">o&longs;ten&longs;i</expan> &longs;unt, &amp; angulus A T D, contrapo&longs;ito B T Z, <lb/>&aelig;qualis e&longs;t: duo igitur triangula A T D, &amp; B Z T, &aelig;quiangula erunt per 32. <lb/>primi, &amp; communem &longs;ententiam. </s>
7191 
7192 <s>Similia <expan abbr="itaq;">itaque</expan> erunt ip&longs;a triangula, <expan abbr="late-ra&qacute;">late&shy;<lb/>raque</expan>; habebunt proportionalia per 4. 6. &longs;icut A T, ad B T, ita D A, ad B Z. <lb/><!-- KEEP S--></s>
7193 
7194 <s>Maior e&longs;t autem A T, qu&agrave;m B T: maior igitur D A, qu&agrave;m B Z, quod etiam <lb/>per <expan abbr="c&otilde;munem">communem</expan> <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> neglecta <expan abbr="triangulor&utilde;">triangulorum</expan> &longs;imilitudine concludi pote&longs;t.</s></p><p type="main">
7195 
7196 <s>Maius <expan abbr="itaq;">itaque</expan> &longs;patium decurrit manubrium, qu&agrave;m remi palmula, <expan abbr="atq;">atque</expan> illuc <lb/>tran&longs;uehetur nauigium, qu&ograve; remi capulus deportatus fuerit: nauigium igi&shy;<lb/>tur in diuer&longs;a procedens, plus &longs;patij, qu&agrave;m remi palmula tran&longs;mittet. </s>
7197 
7198 <s>Vti&shy;<lb/>mur aurem tralatione, <expan abbr="atq;">atque</expan> demon&longs;trationis figura Victoris Fau&longs;ti. </s>
7199 
7200 <s>Aduer&shy;<lb/>tendum e&longs;t tamen, quod cum remus po&longs;itionem habuerit D Z, remi palmu&shy;<lb/>la erit infra Z. <!-- KEEP S--></s>
7201 
7202 <s>Nam quoniam <expan abbr="tri&atilde;guli">trianguli</expan> A D C, duo latera A C, &amp; D C, &aelig;qua&shy;<lb/>lia po&longs;ita &longs;unc: duo igitur anguli, qui ad D, &amp; A, &aelig;quales erunt: angulus <lb/>igitur A D T, angulo D A T, maior erit: &amp; idcirc&ograve; latus A T, trianguli A&shy;<lb/>T D, latere D T, maius erit per 19. primi. </s>
7203 
7204 <s>A&aelig;qualis porr&ograve; o&longs;ten&longs;us e&longs;t an&shy;<lb/>guius B Z T, angulo A D T, pr&aelig;terea angulus D A T; angulo T B Z, &aelig;qua&shy;<lb/>lis: angulus igitur B Z T, angulo T B Z, maior erit, &amp; propterea latus B T, <lb/>trianguli B T Z, latere T Z, maius erit: tota igitur recta linea A B, tota <lb/>D Z, maior erit: &amp; idcirc&ograve; cum remus po&longs;itionem habuerit rectam lineam <lb/>D Z palmula erit vltra Z. <!-- KEEP S--></s>
7205 
7206 <s>E&longs;to igitur in K, &amp; connectantur rect&aelig; line&aelig; B D, <lb/>&amp; B K: &longs;patium igitur decur&longs;um ab ip&longs;a palmula non erit B Z, &longs;ed B K: quod <pb pagenum="164"/>quidem minus etiam o&longs;tendemus e&longs;&longs;e ip&longs;o D A. <!-- KEEP S--></s>
7207 
7208 <s>Nam quoniam duo latera <lb/>B D, &amp; D K, trianguli B D K, duobus lateribus B D, &amp; D E, <expan abbr="tri&atilde;guli">trianguli</expan> B E D, <lb/>&aelig;qualia &longs;unt, &longs;ed minor e&longs;t angulus B D K, angulo B D E: minorigitur erit <lb/>ba&longs;is B K, ba&longs;e B E, per 24. primi, quod demon&longs;trandum erat</s></p><p type="main">
7209 
7210 <s>Pr&aelig;terea, quod Ari&longs;t. 
7211 
7212 ratiocinando &longs;umit tantum &longs;patium conficere na&shy;<lb/>uigium, quantum remi manubrium, ambiguum e&longs;t. </s>
7213 
7214 <s>Nam remi manubrium <lb/>duabus fertur motionibus: vna propria, <expan abbr="circulari&qacute;">circularique</expan>; &longs;uper &longs;calmo: altera <lb/>ver&ograve;, qua vn&agrave; fertur cum ip&longs;o nauigio. </s>
7215 
7216 <s>&longs;patium igitur, quod omnin&ograve; decur&shy;<lb/>&longs;um e&longs;t &agrave; remi manubrio, eo quod &agrave; nauigio confectum e&longs;t, mains erit. </s>
7217 
7218 <s>At <lb/>&longs;i paria &longs;patia decur&longs;a e&longs;&longs;e intelligat &agrave; remi manubrio motu proprio, &amp; &agrave; <lb/>nauigio, <expan abbr="neq;">neque</expan> hoc difficultate caret. </s>
7219 
7220 <s>Nam nauiginm interdum maius &longs;pa&shy;<lb/>tium percurret, interdum minus, iuxta remigum vires, &amp; prout mari remi <lb/>palmula immer&longs;a fuerit: remi ver&ograve; manubrium tamet&longs;i ab exiguis viribus <lb/>moueatur haud minorem tamen ambitum de&longs;cribet, qu&agrave;m &longs;i &agrave; multo ma&shy;<lb/>iore virtute moueretur. </s>
7221 
7222 <s>Quapropter, vt huiu&longs;modi Ari&longs;t. &longs;ententiam exa&shy;<lb/>minaremus, Theoremata, qu&aelig; &longs;equuntur, demonftrauimus.</s></p><p type="head">
7223 
7224 <s><emph type="italics"/>PROPOSITIO PRIMA.<emph.end type="italics"/></s></p><p type="head">
7225 
7226 <s>Si Remiges nauigium mouere po&longs;&longs;unt, maius &longs;emper &longs;pa&shy;<lb/>tium remi manubrium percurrit, qu&agrave;m nauigium.</s></p><p type="main">
7227 
7228 <s>Sit enim remus A C, manubrium A, &longs;calmus B, qui propter nauigij <lb/>motum &longs;patium percurrat &agrave; B, in D, in quo loco ip&longs;eremus A C, &longs;i&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.164.1.tif"/><lb/>tum rectitudinis habeat E F. <!-- KEEP S--></s>
7229 
7230 <s>Spatium <lb/>itaque, quod A, conficit, curna linea <lb/>&longs;it A E, cui recta linea re&longs;pondeat A Z, in re&shy;<lb/>ctam E F, perpendieularis. </s>
7231 
7232 <s>Nauigium ver&ograve; <lb/>idem &longs;patium conficiet, quod &longs;ealmus B: aio <lb/>igitur ip&longs;am A Z, rectam lineam, recta B D, <lb/>maiorem e&longs;&longs;e. </s>
7233 
7234 <s>&longs;ecet enim recta A C, rectam <lb/>E F, in G: &aelig;quiangula &longs;unt igitur bina trian&shy;<lb/>gula A G Z, &amp; B G D, quapropter &longs;icut A G, <lb/>ad B G, &longs;ie A Z, ad B D, per. </s>
7235 
7236 <s>4. 6. libri Eucli&shy;<lb/>dis: maior e&longs;t autem A G, ipfa B G, &amp; maior <lb/>igitur erit A Z, quam B D. &amp; proinde maius <lb/>&longs;patium remi manubrium percurrit, quam <lb/>nauigium, quod demon&longs;trandum erat.</s></p><p type="main">
7237 
7238 <s>Quod &longs;i &agrave; puncto B, rectam lineam vtrinque <lb/>ducamus H K, ad remi men&longs;uram, rectos facientem angulos cum B D, <expan abbr="re-ctam&qacute;">re&shy;<lb/>ctamque</expan>; A Z, &longs;ecantem in I, manife&longs;t&egrave; intelligemus ip&longs;am rectam A Z, con&shy;<lb/>&longs;tare ex A I, &amp; I Z, quarum prior re&longs;pondet curu&aelig; A H, qu&aelig; motu proprio <lb/>manubrij de&longs;cripta e&longs;t; po&longs;terior ver&ograve; &aelig;qualis e&longs;t rect&aelig; B D, qu&aelig; motu na&shy;<lb/>uigij decur&longs;a e&longs;t.</s></p><pb pagenum="165"/><p type="head">
7239 
7240 <s><emph type="italics"/>PROPOSITIO SECVNDA.<emph.end type="italics"/></s></p><p type="head">
7241 
7242 <s>Si remi manubrium motu proprio, &amp; nauigium, &aelig;qualia <lb/>&longs;patia pertran&longs;ierint, fieri non poterit, vt palmula mo&shy;<lb/>ueatur: &longs;ed veluti centrum immota manebit.</s></p><p type="main">
7243 
7244 <s>Esto iterum remus A C, manubrium A, &longs;calmus B: tantum autem &longs;pa&shy;<lb/>tium conficiat nauigium; quantum motu proprio A. Dico, quod C, <lb/>remi palmula immota manebit. </s>
7245 
7246 <s>Nam &longs;i a loco &longs;uo dimota fuerit: <lb/>&longs;patium igitur permeet C D, ad po&longs;teriora: quo quidem decur&longs;o, <lb/>remus A C, po&longs;itionem rectitudmis habeat F D, &longs;calmus <expan abbr="itaq;">itaque</expan> B, tran&longs;latus <lb/>erit in G. <!-- KEEP S--></s>
7247 
7248 <s>Excitetur autem &agrave; puncto B, in <expan abbr="vtramq;">vtramque</expan> partem linea E B R, ad <lb/><figure place="text" xlink:href="figures-la/009.01.165.1.tif"/><lb/>rectos angulos &longs;uper B G, &amp; &agrave; <expan abbr="p&utilde;cto">puncto</expan> A, recta A H, <lb/>&longs;uper D F: itemque &agrave; puncto E, recta C E, &longs;uper <lb/>E R; ip&longs;arum ver&ograve; rectarum linearum E R, &amp; <lb/>A H, &longs;ectio &longs;it in K, &longs;ed C F., &amp; D F, &longs;it in Z, &amp; quo&shy;<lb/>niam A K, id &longs;patium e&longs;t, quod motu proprio re&shy;<lb/>mi manubrium permeauit, curuilineo enim re&shy;<lb/>&longs;pondeat A R, recta autem B G, id &longs;patium e&longs;t, <lb/>quod nauigium confecit: ip&longs;&aelig; igitur rect&aelig; line&aelig; <lb/>H K, &amp; B G, &aelig;quales erunt. </s>
7249 
7250 <s>Atqui in duobus &aelig;qui&shy;<lb/>angulis triangulis E B C, &amp; B A K, vel per 26. <lb/>propo&longs;itionem primi Euclidis, vel 4. 6. &aelig;quales <lb/>e&longs;&longs;e concludes A K, &amp; E C, rectas lineas: quapro&shy;<lb/>pter &aelig;qualis erit E C, rect&aelig; B G, per communem <lb/>&longs;ententiam: eidem autem B G, &aelig;qualis e&longs;t E Z, <lb/>in parallelogrammo, per 34. propo&longs;itionem ip&shy;<lb/>&longs;ius primi libri: &aelig;qualis igitur erit recta E Z, re&shy;<lb/>ct&aelig; E C, pars toti, quod e&longs;t impo&longs;&longs;ibile. </s>
7251 
7252 <s>Et pro&shy;<lb/>pterea immota manebit palmula C, quod erat &agrave; <lb/>nobis o&longs;tendendum.</s></p><p type="head">
7253 
7254 <s><emph type="italics"/>PROPOSITIO TERTIA.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7255 
7256 <s>Si remi manubrium motu proprio duplum confecerit &longs;pa&shy;<lb/>tium, qu&agrave;m nauigium, tantum prouehetur ea remiga&shy;<lb/>tione nauigium, quantum palmula retroce&longs;&longs;erit.</s></p><p type="main">
7257 
7258 <s>Remus enim incipiente motu po&longs;itionem habeat A C, de&longs;inente <lb/>ver&ograve; rectitudinis &longs;itum F G. &longs;calmus igitur B, propter nauigij <lb/>motum, &longs;patium con&longs;iciet B D. <!-- KEEP S--></s>
7259 
7260 <s>Excitetur &agrave; puncto B, in <expan abbr="vtramq;">vtramque</expan> <lb/>partem perpendicularis E Z, in quam veniant a punctis A, &amp; C, <lb/>ad rectos angulos rect&aelig; line&aelig; A E, &amp; C Z: &longs;patium autem A E, &agrave; manubrio <pb pagenum="166"/><figure place="text" xlink:href="figures-la/009.01.166.1.tif"/><lb/>decur&longs;um motu proprio &longs;patij B D, duplum <lb/>&longs;it: recta ver&ograve; linea C H, curu&aelig; re&longs;pondeat <lb/>C G, qu&aelig; &agrave; remi palmula de&longs;cripta e&longs;t. </s>
7261 
7262 <s>Di&shy;<lb/>co ip&longs;as rectas lineas B D, &amp; C H, &aelig;quales <lb/>e&longs;&longs;e. </s>
7263 
7264 <s>Nam in duobus triangulis B A E, &amp; <lb/>C B Z, du&aelig; rect&aelig; line&aelig; A E, &amp; C Z, &aelig;qua&shy;<lb/>les &longs;unt. </s>
7265 
7266 <s>In parallelogrammo autem B H, <lb/>du&aelig; B D, &amp; H Z, &aelig;quales, atqui recta A E, <lb/>dupla e&longs;t rect&aelig; B D, per hypothe&longs;im; dupla <lb/>e&longs;t igitur, &amp; C Z, rect&aelig; H Z, quapropter <lb/>C H, &amp; H Z, &aelig;quales erunt, Du&aelig; igitur <lb/>C H, &amp; B D, &aelig;quales per communem &longs;en&shy;<lb/>tentiam.</s></p><p type="main">
7267 
7268 <s>Et quia nauigium tantum &longs;patium de&shy;<lb/>currit &longs;emper, quantum &longs;calmus: &longs;i igitur <lb/>remi manubrium motu proprio duplum <lb/>confecerit &longs;patium, qu&agrave;m nauigium, tan&shy;<lb/>tum prouehetur nauigium, quantum pal&shy;<lb/>mula retroce&longs;&longs;erit, quod demon&longs;trandum <lb/>erat.</s></p><p type="head">
7269 
7270 <s><emph type="italics"/>PROPOSITIO QVARTA.<emph.end type="italics"/></s></p><p type="head">
7271 
7272 <s>Si nauigium minus &longs;patium decurrat, qu&agrave;m remi manu&shy;<lb/>brium, &longs;ed &longs;upra dimidium, magis prouehetur, qu&agrave;m pal&shy;<lb/>mula retrocedat; &longs;i ver&ograve; citra dimidium, minus.</s></p><p type="main">
7273 
7274 <s>In de&longs;cripta enim figura ponatur B D, minor quam A E, &longs;ed eius dimi&shy;<lb/>dio maior. </s>
7275 
7276 <s>Dico, quod ip&longs;a B D, maior e&longs;t qu&agrave;m C H. <!-- KEEP S--></s>
7277 
7278 <s>Nam B D, &amp; <lb/>H Z, &aelig;quales &longs;unt: Ad h&aelig;c A E, &amp; C Z, &aelig;quales &longs;unt rect&aelig; line&aelig;; ma&shy;<lb/>ior igitur erit H Z, dimidio ip&longs;ius A E: quapropter reliqua C H, mi&shy;<lb/>nor dimidio erit eiu&longs;dem A E, &amp; minor igitur erit C H, qu&agrave;m B D. <!-- KEEP S--></s>
7279 
7280 <s>Spa&shy;<lb/>tium autem B D, id e&longs;t, quod nauigium conficit, &longs;patium ver&ograve; C H, remi <lb/>palmula in contrarium decurrit; idcirc&ograve; prior pars Theorematis vera e&longs;t. <lb/></s>
7281 
7282 <s>Po&longs;terior autem &longs;imiliter o&longs;tendetur. </s>
7283 
7284 <s>&longs;i enim B D, minor e&longs;t dimidio ip&longs;ius <lb/>A E: minor igitur erit, &amp; H Z, dimidio eiu&longs;dem A E; &amp; quoniam A E, &amp; <lb/>C Z, &aelig;quales &longs;unt: reliqua igitur C H, dimidio eiu&longs;dem A E, maior erit: &amp; <lb/>proinde minor erit B D, qu&agrave;m C H. <!-- KEEP S--></s>
7285 
7286 <s>Nauigium igitur minus &longs;patium de&shy;<lb/>curret in anteriora, quam remi palmula in contrarium, quod demon&longs;tran&shy;<lb/>dum &longs;u&longs;cepimus.</s></p><p type="head">
7287 
7288 <s><emph type="italics"/>Corollarium.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7289 
7290 <s>Ex hac, &amp; pr&aelig;cedenti infertur, quod &longs;i remi manubrium motu proprio <lb/>maius &longs;patium decurrat, qu&agrave;m nauigium, &longs;iue id &longs;it duplum, &longs;iue mi&shy;<pb pagenum="167"/>nus duplo, &longs;iue maius duplo, &longs;patium, quod nauigium interim decurrit ad <lb/>anteriora, &amp; quod palmula remi in contrarium &longs;imul iuncta, ei quod ip&longs;um <lb/>remi manubrium motu proprio conficit, &aelig;qualia erunt. </s>
7291 
7292 <s>&longs;emper enim B D, <lb/>&aelig;qualis e&longs;t H Z: tota ver&ograve; C Z, qu&aelig; &aelig;qualis e&longs;t A E, ex &longs;uis partibus C H, <lb/>&amp; H Z, con&longs;tabit.</s></p><p type="head">
7293 
7294 <s><emph type="italics"/>Propo&longs;itionis conuer&longs;io.<emph.end type="italics"/></s></p><p type="head">
7295 
7296 <s>Si nauigium longius progrediatur, qu&agrave;m remi palmula re&shy;<lb/>trocedat, &longs;patium conficiet plu&longs;quam dimidium eius, <lb/>quod motu proprio remi manubrium decurrit: <lb/>&longs;i minus, citra dimidium.</s></p><p type="head">
7297 
7298 <s><emph type="italics"/>Huius demonctratio ex &longs;upradictis facil&egrave; colligi poterit.<emph.end type="italics"/></s></p><p type="head">
7299 
7300 <s><emph type="italics"/>PROPOSITIO QVINTA.<emph.end type="italics"/></s></p><p type="head">
7301 
7302 <s>Si celerius feratur nauigium, qu&agrave;m remi manubrium, mo&shy;<lb/>uebitur palmula in vlteriora, <expan abbr="nil&qacute;">nilque</expan>; vnquam retroce&shy;<lb/>det, <expan abbr="id&qacute;">idque</expan>; &longs;patium decurret, quo nauigij motus <lb/>motum manubrij &longs;uperat.</s></p><p type="main">
7303 
7304 <s>Habeat enim remus incipiente motu po&longs;itionem A C: de&longs;inente <lb/><figure place="text" xlink:href="figures-la/009.01.167.1.tif"/><lb/>ver&ograve; <expan abbr="&longs;it&utilde;">&longs;itum</expan> rectitudinis F G. &longs;cal&shy;<lb/>mus igitur B, propter nauigij <lb/>motum tran&longs;latus, erit in D, &longs;it <lb/><expan abbr="itaq;">itaque</expan> &longs;patium B D, maius qu&agrave;m A H, &agrave; re&shy;<lb/>mi manubrio motu proprio decur&longs;um: &longs;ic <lb/>enim celerius dicetur ferri <expan abbr="nauigi&utilde;">nauigium</expan>, qu&agrave;m <lb/>manubrium. </s>
7305 
7306 <s>Dico, qu&ograve;d palmula C, in <lb/>vlteriora mouebitur. </s>
7307 
7308 <s>Nam cum &longs;calmus <lb/>B, prouectus fuerit in D: tran&longs;lata erit ip&shy;<lb/>fa palmula C, vbi G, in rectitudinis &longs;itu, <lb/><expan abbr="&longs;patium&qacute;">&longs;patiumque</expan>; conficiet C G, curuilineum, cui <lb/>re&longs;pondet C K: mouebitur igitur palmula <lb/>in vlteriora. </s>
7309 
7310 <s>Nihil autem vnquam retro&shy;<lb/>cedere, o&longs;tendetur in hunc modum. </s>
7311 
7312 <s>eadem <lb/>enim celeritate mouentur A, in H, &amp; C, <lb/>ver&longs;us I, circa &longs;calmum. </s>
7313 
7314 <s>Atqui per hypo&shy;<lb/>the&longs;im celerius fertur nauigium, quam A. <lb/>in H, celerius igitur ip&longs;um nauigium fer&shy;<lb/>tur, qu&agrave;m C, ver&longs;us I. &longs;ed mouetur idem <pb pagenum="168"/>C. ip&longs;a nauigij celeritate ver&longs;us K; celerius igitur ferretur C, ad K, quam <lb/>ad I, quapropter nihil vnquam retrocedet ip&longs;um C, im&ograve; ver&ograve; in vlteriora <lb/>progredietur, <expan abbr="&longs;patium&qacute;">&longs;patiumque</expan>; decurret C K, quod quidem relinquitur detracto <lb/>I C, ex I K. &longs;i enim remi palmula tota ip&longs;a nauigij celeritate moueretur, vl&shy;<lb/>tra K, progrederetur, cum B, perueniret ad D: &longs;ed retrahitur interim, pro&shy;<lb/>pter eum motum, qui fit circa B. <!-- KEEP S--></s>
7315 
7316 <s>Sic igitur palmul&aelig; celeritate, qu&aelig; &agrave; mo&shy;<lb/>tu nauigij prouenit retardata, decur&longs;um &longs;patium erit C K. <!-- KEEP S--></s>
7317 
7318 <s>Videtur autem <lb/>&longs;olo remorum impul&longs;u hoc fieri non po&longs;&longs;e, &longs;ed alia in&longs;uper virtute impel&shy;<lb/>lente opus e&longs;&longs;e, vt venti, vel aqu&aelig;.</s></p><p type="main">
7319 
7320 <s>Ex his Theorematis liquet, inquit Nonius, qu&agrave;m incerta interroget Ari&shy;<lb/>&longs;toteles, &amp; qu&agrave;m in&longs;cit&egrave; re&longs;pondeat. </s>
7321 
7322 <s>Nam non continu&ograve; &longs;i nauigium in an&shy;<lb/>teriora mouetur, remi palmula retroceder; neque etiam &longs;i retrocedat, mi&shy;<lb/>nus &longs;pat&igrave;um tran&longs;mittit in contrarium, qu&agrave;m nauigium progrediatur. </s>
7323 
7324 <s>De&shy;<lb/>mon&longs;trant hoc &longs;ecunda, &amp; tertia propo&longs;itio. </s>
7325 
7326 <s>Remi ver&ograve; manubrium motu <lb/>proprio, qui circa &longs;calmum fit, &amp; vn&agrave; cum nauigij motu maius &longs;patium con&shy;<lb/>ficit qu&agrave;m nauigium. </s>
7327 
7328 <s>&longs;olo autem proprio motu, &longs;i contingat tantum &longs;pa&shy;<lb/>tium conficere, quantum nauigium, fieri non poterit, vt palmula mouea&shy;<lb/>tur. </s>
7329 
7330 <s>fru&longs;tra igitur conatur in vniuer&longs;um demon&longs;tr are remi manubrium ma&shy;<lb/>ius &longs;patium decurrere, qu&agrave;m palmulam in contrarium. </s>
7331 
7332 <s>Pr&aelig;terea quando <lb/>nauigium <expan abbr="l&otilde;gius">longius</expan> progreditur, qu&agrave;m remi palmula regrediatur, minus &longs;pa&shy;<lb/>tium decurrit, quam manubrium: igitur hon &aelig;quale. </s>
7333 
7334 <s>Et proinde con&longs;tat <lb/>neque veritatem in propo&longs;ito, neque demon&longs;trationem in ijs, qu&aelig; conge&shy;<lb/>rit, reperiri.</s></p><p type="main">
7335 
7336 <s>Hucu&longs;que Petrus Nonius:</s></p><p type="main">
7337 
7338 <s>Reliqua huius textus vtinam quemadmodum &longs;unt clara, ita etiam vera <lb/>e&longs;&longs;ent: &longs;ed quia qu&aelig; modo dixit de remo, eadem temoni applicat propte&shy;<lb/>rea ij&longs;dem etiam obnoxia &longs;unt difficultatibus.</s></p><p type="head">
7339 
7340 <s><emph type="italics"/>QV&AElig;STIO SEXTA<emph.end type="italics"/></s></p><p type="head">
7341 
7342 <s><emph type="italics"/>De Antenna.<emph.end type="italics"/></s></p><p type="main">
7343 
7344 <s><arrow.to.target n="marg238"/></s></p><p type="margin">
7345 
7346 <s><margin.target id="marg238"/>248</s></p><p type="main">
7347 
7348 <s>Qv&aelig;rit cur quanto Antenna &longs;ublimior fuerit, ij&longs;dem velis, &amp; vento <lb/>eodem celerius ferantur nauigia. </s>
7349 
7350 <s>Re&longs;pondet inde id prouenire, <lb/>quia malus, &longs;iue arbor nauis in huiu&longs;modi ventorum impul&longs;u ve&shy;<lb/>ctis euadit, cuius auxilio idem ventus, qui mouens e&longs;t, maiorem <lb/>vim acquirit, quanto longior fuerit pars vectis, qu&aelig; inter hypomoclion, &amp; <lb/>vim mouentem intercipitur: quando autem altior fuerit antenna, tunc ea <lb/>vectis pars longior euadit, &amp; propterea accidit, vt vires ventorum augean&shy;<lb/>tur. </s>
7351 
7352 <s>&longs;ed i&longs;ta melius in figura in&longs;piciamus. </s>
7353 
7354 <s>&longs;it nauis A B, cuius arbor C D E, <lb/>antenna F C G, velum F G H, vectis e&longs;t arbor, cuius fultura e&longs;t in E, extre&shy;<lb/>mo mali in fundo nauis, onus autem in D, vbi malus exit &egrave; carina. </s>
7355 
7356 <s>mouens <lb/>potentia e&longs;t ventus, qui mouet in antenna F C G. quanto igitur &longs;ublimior <lb/>e&longs;t antenna, tanto longior euadit vectis E C, <expan abbr="tanto&qacute;">tantoque</expan>; maiores fiunt venti <lb/>vires. </s>
7357 
7358 <s>dixi autem onus e&longs;&longs;e in D, quia &longs;i nauis vento ob&longs;i&longs;teret, ip&longs;a inuerte&shy;<lb/>retur hac ratione, vt puppis A, eleuata, prora B, demergeretur, manente <pb pagenum="169"/><figure place="text" xlink:href="figures-la/009.01.169.1.tif"/><lb/>veluti centro parte E. quia ve&shy;<lb/>r&ograve; ob maris liquiditatem na&shy;<lb/>uis minim&egrave; obfi&longs;tit, &longs;ed facil&egrave; <lb/>cedens &agrave; ventis vrgetur, hinc <lb/>fit, vt merit&ograve; dixerim pondus <lb/>nauis e&longs;&longs;e ad D, fulcimentum <lb/>ver&ograve; ad E.<!-- KEEP S--></s></p><p type="main">
7359 
7360 <s>Qu&aelig;&longs;tio &longs;eptima, &amp; &longs;atis pec <lb/>&longs;e clara e&longs;t; <expan abbr="neq;">neque</expan> Mathemati&shy;<lb/>ci e&longs;t eam exponere.</s></p><p type="head">
7361 
7362 <s><emph type="italics"/>QV&AElig;STIO OCTAVA<emph.end type="italics"/></s></p><p type="head">
7363 
7364 <s><emph type="italics"/>De Rota.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7365 
7366 <s>Cur ex figurarum genere qu&aelig;cun que rotund&aelig; &longs;unt, &amp; cir&shy;<lb/>culares facilius mouentur?</s></p><p type="main">
7367 
7368 <s><arrow.to.target n="marg239"/></s></p><p type="margin">
7369 
7370 <s><margin.target id="marg239"/>249</s></p><p type="main">
7371 
7372 <s>Tribus autem modis circulum rotari contingit; aut enim &longs;ecun&shy;<lb/>dum ap&longs;idem, &longs;iue curuaturam centro &longs;imul moto, quemadmo&shy;<lb/>dum plau&longs;trorum rot&aelig; vertuntur: aut circa manentem axem, <lb/>tanquam centrum veluti rotul&aelig; ill&aelig;, ex quibus trochlea compo&shy;<lb/>nitur; vel quibus ad puteos vtimur, qu&aelig; quidem rect&aelig; ad horizontem &longs;o&shy;<lb/>lent con&longs;titui. </s>
7373 
7374 <s>aut quem ad modum rota figuli, qu&aelig; pariter circa <expan abbr="man&etilde;s">manens</expan> cen&shy;<lb/>trum gyratur, &longs;ed qua&longs;i pro&longs;trata horizonti &aelig;quidi&longs;tans collocata e&longs;t. </s>
7375 
7376 <s>Qu&aelig; <lb/>igitur primo modo mouentur, fort&egrave; facilius quam figur&aelig; rectiline&aelig;, vt &longs;unt <lb/>triangulares, quadrat&aelig;, pentagon&aelig;, &amp;c. </s>
7377 
7378 <s>mouentur, quia circulares figur&aelig; <lb/>parua &longs;ui parte, &amp; qua&longs;i in puncto planum, &longs;eu pauimentum contingunt, vn&shy;<lb/>de fit, vt <expan abbr="neq;">neque</expan> offen&longs;ent, <expan abbr="neq;">neque</expan> impingant; cuius cau&longs;a e&longs;t, quia &agrave; terra &longs;emo&shy;<lb/>tus e&longs;t angulus, ide&longs;t tali angulo planum contingunt, vt ab eo &longs;tatim rot&aelig; <lb/>curuatura &agrave; terra eleuari incipiat, &amp; propterea parum terr&aelig; h&aelig;reat: in fi&shy;<lb/>guris ver&ograve; rectilineis, in quadrata. </s>
7379 
7380 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;ecus accidit, quia ab angulo ad an&shy;<lb/>gulum linea recta tenditur, vnde in ip&longs;ius volutatione po&longs;t contactum vnius <lb/>anguli tota recta linea &longs;equens, plano adaptabitur, &amp; non &longs;emouebitur &longs;ta&shy;<lb/>tim in altum, &amp; ide&ograve; multum offen&longs;abit, &amp; impinget, <expan abbr="tarde&qacute;">tardeque</expan>; idcirc&ograve; mo&shy;<lb/>uebitur. </s>
7381 
7382 
7383 
7384 
7385 
7386 <s>Pr&aelig;terea circulares etiam, &longs;i cui obulam fiunt corpori, illud &longs;imi&shy;<lb/>liter &longs;ecundum pu&longs;illum tan gunt: rectiline&aelig; ver&ograve; figur&aelig;, rectitudine &longs;ua <lb/>plani multum contingerent. </s>
7387 
7388 <s>Ad h&aelig;c motor mouens huiu&longs;inodi rotas, eas <lb/>mouet, qu&ograve; nutant: nam quando rota erecta e&longs;t &longs;uper pauimentum, dia&shy;<lb/>meter ip&longs;ius, qu&aelig; &agrave; contactu pauimenti ad angulos rectos, ad &longs;upremum <pb pagenum="170"/>rot&aelig; perducitur totum rot&aelig; pondus in duas &aelig;quas partes diuidit, ita vt ta&shy;<lb/>le pondus in &aelig;quilibrio con&longs;tituatur, cum ex vna parte tantum &longs;it, quantum <lb/>ex altera; ex quo fit, vt vel exigua vis ip&longs;am impellere valeat: quando enim <lb/>duo &aelig;qualia pondera &longs;unt in &aelig;quilibrio, quelibet vis pote&longs;t ea ab &aelig;quilibrio <lb/>dimouere. </s>
7389 
7390 <s>quando po&longs;tea rota e&longs;t in motu, vel cum primum ei motus fuerit <lb/>&agrave; motore inditus, &longs;emper nutat ad partes illas, ad quas primum fuit incita&shy;<lb/>ta per impre&longs;&longs;am motionem, quapropter nullo negotio ad ea&longs;dem partes, <lb/>&longs;eu antror&longs;um mouetur; qu&ograve; enim <expan abbr="vnumquodq;">vnumquodque</expan> vergit, illuc facillim&egrave; fer&shy;<lb/>tur: quemadmodum &egrave; contrario difficillimum e&longs;t in contrariam nutus &longs;ui <lb/>partem vnumquodque pellere. </s>
7391 
7392 <s>Huc etiam pertinet, quod nonnulli dicunt, <lb/>circuli nimirum periph&aelig;riam perenni ver&longs;ari motu, <expan abbr="atq;">atque</expan> hinc facilius mo&shy;<lb/>ueri. </s>
7393 
7394 <s>&longs;icuti etiam dicunt, quod manentia propterea manent, quia contrani&shy;<lb/>tuntur, &amp; ob&longs;i&longs;tunt mouenti: quod fort&egrave; dicebant propter maximam circu&shy;<lb/>li ad motum aptitudinem. </s>
7395 
7396 <s>&amp; quia &longs;icut diameter ad diametrum, ita maio&shy;<lb/>ris circuli periph&aelig;ria ad minoris periph&aelig;riam (vt po&longs;tea o&longs;tendam) &amp; quia <lb/>quo <expan abbr="l&otilde;gior">longior</expan> diameter e&longs;t, e&ograve; facilius, vt initio probaui, mouetur, fit vt etiam <lb/>periph&aelig;ria maioris facilius, qu&agrave;m minoris moueatur, &longs;iue dixeris, quod an&shy;<lb/>gulus maioris circuli ad angulum minoris nutum quendam habet; &amp; quia <lb/>facilius mouetur angulus maioris, qu&agrave;m minoris, fit, vt maior rota adhi&shy;<lb/>beatur ad minorem mouendam: &amp; quia intra maiorem infinit&aelig; circa idem <lb/>centrum concipi po&longs;&longs;unt, hinc fit, vt rot&aelig; maiores facilius moueantur, &amp; <lb/>mot&aelig; moueant c&aelig;teras intra &longs;e contentas. </s>
7397 
7398 <s>quod dictum e&longs;t de nutu anguli <lb/>maioris circuli ad angulum minoris ex appo&longs;ita figura facil&egrave; patebit, vbi <lb/><figure place="text" xlink:href="figures-la/009.01.170.1.tif"/><lb/>pro minore angulo intelligendus e&longs;t arcus C B, <lb/>pro maiore autem arcus D E, quorum <expan abbr="vterq;">vterque</expan> vo&shy;<lb/>catur angulus, quoniam angulo A, qui e&longs;t in cen&shy;<lb/>tro opponuntur. </s>
7399 
7400 <s>Atque h&aelig;c &longs;ufficiant deijs, qu&aelig; <lb/>primo modo moueutur.</s></p><p type="main">
7401 
7402 <s>Nunc ad ea, qu&aelig; reliquis duobus modis cieri <lb/>&longs;olent, qu&aelig; &longs;cilicet non mouentur &longs;ecundum ap&longs;i&shy;<lb/>dem, &longs;ed aut iuxta planitiem, ide&longs;t, qu&aelig; &aelig;quidi&shy;<lb/>&longs;tanter pauimento collo <expan abbr="c&atilde;tur">cantur</expan>, vt rot&aelig; figulorum, <lb/>aut qu&aelig; in loco &agrave; terra eleuato, vt troclearum or&shy;<lb/>biculi. </s>
7403 
7404 <s>rot&aelig; h&aelig; facilius ip&longs;&aelig;, &amp; ea etiam, qu&aelig; ip&longs;is annectuntur commouen&shy;<lb/>tur, quam &longs;i rectilinea figura con&longs;tarent; non quia parua &longs;ui portione vel <lb/>tangant planum, vel offen&longs;ent, &longs;ed ob aliam inclinationem, de qua initio <lb/>huius operis ante qu&aelig;&longs;tiones dictum e&longs;t, vbi diximus circulum duas incli&shy;<lb/>nationes ad motum obtinere, &longs;ecundum quas &agrave; motore mouetur; vna e&longs;t, <lb/>quam diximus naturalem, qua &longs;olet cieri &longs;ecundum periph&aelig;riam, motor <lb/>enim &longs;emper mouet circulum in periph&aelig;ria, &amp; &longs;ecundum hanc inclinatio&shy;<lb/>nem extremum diametri rect&agrave;, non circulariter moueretur: hanc inclina&shy;<lb/>tionem fort&egrave; habet &agrave; materia grauitante, &amp; in ip&longs;o circulo con&longs;tituta in <lb/>&aelig;quilibrio: qu&aelig; autem in &aelig;quilibrio, facillim&egrave; cedunt; &amp; qui talia mouent, <lb/>qua&longs;i prius mota mouent, &amp; ide&ograve; facillim&egrave;. </s>
7405 
7406 <s>Secundum igitur inclinatio&shy;<lb/>nem hanc, qu&aelig; in obliquum e&longs;t, ide&longs;t, qu&aelig; &longs;ecundum circunferentiam &longs;it, <lb/>ip&longs;am rotam mouens facillim&egrave; mouet. </s>
7407 
7408 <s>altera latio e&longs;t, &longs;ecundum quam cir&shy;<pb pagenum="171"/>culus &agrave; &longs;eip&longs;o &longs;ecundum diametrum mouetur, ide&longs;t circa &longs;uum centrum re&shy;<lb/>trahit continu&ograve; extrema diametri; ne recta &longs;ecundum naturalem lationem <lb/>ferantur, &longs;ed in orbem circulariter circa centrum gyrentur. </s>
7409 
7410 <s>h&aelig;c Ari&longs;t. <!-- KEEP S--></s>
7411 
7412 <s>Re&shy;<lb/>&longs;tat vt &longs;atisfaciam promi&longs;&longs;is.</s></p><p type="main">
7413 
7414 <s>Dictum e&longs;t ab Ari&longs;t. 
7415 
7416 in textu <emph type="italics"/>(Sicut diameter ad diametrum, ita maior circu&shy;<lb/>lus ad maiorem)<emph.end type="italics"/> qu&aelig; verba intelligenda e&longs;&longs;e non de circulis, &longs;ed de periph&aelig;&shy;<lb/>rijs, vti expo&longs;ui, manife&longs;tum e&longs;t ex 11. propo&longs;it. </s>
7417 
7418 <s>5. Pappi Alexandrini, qu&aelig; <lb/>talis e&longs;t: Circulorum circunferenti&aelig; inter &longs;e &longs;unt vt diametri. </s>
7419 
7420 <s>quam etiam <lb/>Pater Clauius demon&longs;trat propo&longs;. </s>
7421 
7422 <s>2. lib. 
7423 
7424 8. &amp; propo&longs;. </s>
7425 
7426 <s>1. lib. 
7427 
7428 4. Geom. <!-- REMOVE S-->pract. <lb/><!-- REMOVE S-->&longs;i autem de ip&longs;is circulis intelligerentur fal&longs;a e&longs;&longs;ent, non enim e&longs;t circulus <lb/>ad circulum, vt diameter ad diametrum; &longs;ed circuli &longs;unt inter &longs;e, quemad&shy;<lb/>modum &agrave; diametris ip&longs;orum quadrata per &longs;ecundam 12. Elem. 
7429 
7430 quadrata <lb/>autem &longs;unt inter &longs;e in duplicata ratione laterum per 20. 6. <expan abbr="eiusq;">eiusque</expan> corolla&shy;<lb/>rium; hoc e&longs;t &longs;i fiat, vt latus maioris quadrati ad latus minoris, ita latus mi&shy;<lb/>noris ad aliam tertiam lineam, erit quadratum maius ad minus, vt latus <lb/>ip&longs;ius ad tertiam illam lineam; non autem vt ad latus minoris. </s>
7431 
7432 
7433 
7434 
7435 
7436 <s>cum ergo <lb/>circulus &longs;it ad circulum, vt quadratum diametri ad quadratum diametri, <lb/>&amp; quadrata non <expan abbr="habe&atilde;t">habeant</expan> rationem laterum, &longs;eu diametrorum pr&aelig;dictorum, <lb/>&longs;ed illorum duplicatam, <expan abbr="neq;">neque</expan> circuli inuicem illam habere poterunt.</s></p><p type="main">
7437 
7438 <s>Illud demum non ignorandum, quod Guidus Vbaldus propo&longs;it. </s>
7439 
7440 <s>1. de Tro&shy;<lb/>chlea, demon&longs;trat, quod nimirum potentia &longs;u&longs;tinens pondus per rotulam, <lb/>cui funis &longs;upern&aelig; fuerit circumductus, qualis ea e&longs;t, qua ad hauriendam ex <lb/>puteis aquam vtimur, talis inquam potentia e&longs;t &aelig;qualis ponderi; cuius ra&shy;<lb/>tio e&longs;t, quia tunc trochlea fit vectis, cuius fulcimentum e&longs;t in medio vectis, <lb/>pondus ver&ograve;, &amp; potentia in extremitatibus &longs;unt, &amp; &aelig;quidi&longs;tant ab hypomo&shy;<lb/>clio, &amp; propterea cum &longs;it eadem proportio ponderis ad potentiam, qu&aelig; di&shy;<lb/>&longs;tanti&aelig; ad di&longs;tantiam, vt &longs;upra qu&ecedil;&longs;t. </s>
7441 
7442 <s>3. probatum e&longs;t ex Archimede, &amp; Gui&shy;<lb/>do Vbaldo, di&longs;tanti&aelig; autem &longs;int &aelig;quales, erunt etiam pondus, &amp; potentia <lb/>&aelig;qualia, ide&longs;t, &longs;i pondus e&longs;&longs;et vnius libr&aelig;, &longs;u&longs;tineretur &agrave; tanta vi, <expan abbr="qu&atilde;ta">quanta</expan> opus <lb/>e&longs;t ad libram vnam &longs;u&longs;tinendam, &amp; non amplius. </s>
7443 
7444 <s>vt autem clar&egrave; appareat <lb/>vectis in trochlea, &amp; hypomoclion, &amp; &aelig;quales di&longs;tanti&aelig;, &longs;it figura, in qua <lb/><figure place="text" xlink:href="figures-la/009.01.171.1.tif"/><lb/>pondus D, ductario funi D C B E, alligatum. </s>
7445 
7446 <s>poten&shy;<lb/>tia <expan abbr="&longs;u&longs;tin&etilde;s">&longs;u&longs;tinens</expan> E. axis autem erit diameter rotul&aelig; B A C, <lb/>nam potentia premit rotulam in B, &amp; pondus in C, &amp; <lb/>cum rotula &longs;u&longs;tineatur in A, &agrave; &longs;u&longs;pen&longs;orio F A. erit <lb/>punctum A, hypomoclion, quia in motu vectis eua&shy;<lb/>dit centrum, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; punctum manens. </s>
7447 
7448 <s>&aelig;quales autem <lb/>di&longs;tanti&aelig; <expan abbr="vtrinq;">vtrinque</expan> ab hypomoclio &longs;unt B A, A C, &longs;unt <lb/>enim ex centro eodem. </s>
7449 
7450 <s>ex quibus manife&longs;tum e&longs;t hu&shy;<lb/>iu&longs;modi rotulam nullam vim mouenti addere, &longs;ed &longs;o&shy;<lb/>lum illud pr&aelig;&longs;tat, vt omne tollat impedimentum, <lb/>quemadmodum ait Ari&longs;t. 
7451 
7452 manife&longs;tum etiam e&longs;t ma&shy;<lb/>iorem vim quamlibet, quam &longs;it ea, qu&aelig; &longs;u&longs;tinet, po&longs;&longs;e <lb/>idem pondus &longs;ur&longs;um mouere. </s>
7453 
7454 <s>h&aelig;c &amp; pr&aelig;&longs;enti loco, &amp; <lb/>&longs;equentibus lucem afferre po&longs;&longs;unt.</s></p><pb pagenum="172"/><p type="head">
7455 
7456 <s><emph type="italics"/>QV&AElig;STIO NONA<emph.end type="italics"/></s></p><p type="head">
7457 
7458 <s><emph type="italics"/>De Trochleis, &amp; Scytalis.<emph.end type="italics"/></s></p><p type="main">
7459 
7460 <s><arrow.to.target n="marg240"/></s></p><p type="margin">
7461 
7462 <s><margin.target id="marg240"/>250</s></p><p type="main">
7463 
7464 <s><emph type="italics"/>Cvr ea, qu&aelig; per maiores circulos tollantur, &amp; trahuntur facilius, &amp; ci&shy;<lb/>tius mouentur? </s>
7465 
7466 <s>veluti per maiores trochleas, qu&agrave;m per minores, &amp; &longs;cy&shy;<lb/>talas &longs;imiliter? </s>
7467 
7468 <s>An quanto maior fuerit illa, qu&aelig; &agrave; centro e&longs;t, in &aelig;quali <lb/>temporis &longs;patio maius &longs;patium conficit? </s>
7469 
7470 <s>quamobrem &aelig;qual&igrave; inexi&longs;tente <lb/>onere, idem faciet, &longs;icuti diximus maiores libras minoribus exactiores e&longs;&longs;e; &longs;par&shy;<lb/>tum enim in illis centrum e&longs;t: partes ver&ograve; libr&aelig; vtrinque &agrave; &longs;parto &longs;unt veluti line&aelig; <lb/>ex centro)<emph.end type="italics"/> Cum textus huius qu&aelig;&longs;tionis fatis clarus &longs;it, pr&aelig;&longs;ertim &longs;i prius <lb/>legantur, qu&aelig; dicta &longs;unt de libra in prima qu&aelig;&longs;t. </s>
7471 
7472 <s>&amp; qu&aelig; de rota, &amp; trochlea <lb/>in proxima pr&aelig;cedenti, &agrave; paraphra&longs;i ip&longs;ius &longs;uper&longs;edebo. </s>
7473 
7474 <s>Illud tamen, quod <lb/>magis nece&longs;&longs;arium e&longs;t, non omittam, vt &longs;cilicet difficultatibus quibu&longs;dam <lb/>occurram. </s>
7475 
7476 <s>Et primo, quod Ari&longs;t. 
7477 
7478 ait, ea qu&aelig; per maiores circulos veluti <lb/>trochleas, &longs;eu rotulas trahuntur, facilius trahi, qu&agrave;m ea, qu&aelig; per minores, <lb/>non videtur ex omni parte verom. </s>
7479 
7480 <s>nam &longs;icuti in <expan abbr="pr&aelig;ced&etilde;ti">pr&aelig;cedenti</expan> qn&aelig;&longs;tione o&longs;ten&shy;<lb/>&longs;um e&longs;t ex Guido Vbaldo, trochlea &longs;implex, &longs;iue rotula illa &longs;triata, cui funis <lb/>&longs;upern&egrave; inditur, vt in &longs;uperiori figura; nullas addit vires potenti&aelig;, quia re&shy;<lb/>ducitur ad vectem, cuius fultura &longs;it in medio ip&longs;ius. </s>
7481 
7482 <s>&longs;iue igitur rotula illa <lb/>magna fuerit, &longs;iue parua, &longs;emper in talem vectem re&longs;oluetur, &amp; propterea, <lb/>vt etiam experientia con&longs;tat eodem labore aquam hauriunt, &longs;iue rotula illa <lb/>magna fuerit, &longs;ine parua. </s>
7483 
7484 <s>nec minus vera videtur re&longs;pon&longs;io, cum ait <emph type="italics"/>(An quia <lb/>quanto maior fuerit illa, qu&aelig; &agrave; centro e&longs;t, in &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> maius mouetur (patium)<emph.end type="italics"/><lb/>qu&aelig; quidem vera &longs;unt, &longs;i intelligantur hoc modo, nimirum, quod quando <lb/>plures <expan abbr="circul&longs;conc&etilde;trici">circul&longs;concentrici</expan>, <expan abbr="atq;">atque</expan> inuicem connexi fuerint, ita vt vans &longs;ine alijs <lb/>moueri nequeat, tunc quanto maior fuerit diameter, &amp; con&longs;equenter cir&shy;<lb/>cunferentia, tanto velocius mouebitur. </s>
7485 
7486 <s>&longs;i autem intelligantur de duobus <lb/>circulis ab inuicem &longs;eparatis, quorum vnus <expan abbr="ab&longs;q;">ab&longs;que</expan> altero moueri pote&longs;t, vt &longs;ie <lb/>quando vtimur modo rotula magna, modo parua ad aquam hauriendam <lb/>non videntur vera, in quo &longs;en&longs;u manife&longs;t&egrave; loquitur Ari&longs;t. <!-- KEEP S--></s>
7487 
7488 <s>Quapropter vt &longs;in&shy;<lb/>cer&egrave; loquar, nunc ne&longs;cio, qua ratione Ari&longs;t ab errore excu&longs;are valeam, alijs <lb/>fort&egrave; occurret.</s></p><p type="main">
7489 
7490 <s>Secundo loco videndum quid &longs;int &longs;cyntal&aelig;. </s>
7491 
7492 <s>Vt autem con&longs;tat ex &longs;equenti <lb/>qu&aelig;&longs;tione 11. &longs;cyntala erat in&longs;trumentum quoddam vectorium, quod ro&shy;<lb/>tas, &longs;icut currus, aliter tamen factas, habebat, porr&ograve; <foreign lang="greek">sxutalh\,</foreign> ide&longs;t &longs;cytala <lb/>inter alia &longs;ignificat <expan abbr="bacul&utilde;">baculum</expan>, &longs;iue hgnum oblongum, ac teres, qualia ea &longs;unt, <lb/>quibus vtimur in &longs;ucculis, vulg&ograve; Na&longs;pe; &amp; in axe in peritrochio, vt videre <lb/>e&longs;t apud <expan abbr="Guid&utilde;">Guidum</expan> Vbaldum. </s>
7493 
7494 <s>hinc factum e&longs;t, vt apud Lac&aelig;demonios &longs;cytala <lb/>&longs;ignificaret quoddam genus epi&longs;tol&aelig;, quam &longs;cytalem laconicam dicebant, <lb/>quia in charta in&longs;tar zon&aelig; oblonga, &amp; circa &longs;cytalam, hoc e&longs;t circa bacillum <lb/>quendam &longs;piratim circumuoluta exarabatur; ita vt yer&longs;us &longs;criptur&aelig; &longs;ecun&shy;<lb/>dum &longs;urculi longitudinem ducerentur, ex quo &longs;iebat, vt per iuncturas mem&shy;<lb/>bran&aelig;, liter&aelig;, ac verba procederent, membranam hanc ex &longs;cytala reuolu&shy;<lb/>tam, &amp; aliter complicatam Imperatori mittebant, re&longs;olutio autem mem&shy;<pb pagenum="173"/>bran&aelig; literas truncas, atque mutilas reddebat; cum partim continerentur <lb/>citra iuncturas, partim vltra: e&aelig;qu&egrave; partes, qu&aelig; &longs;imul fuerant &longs;cript&aelig;, &amp; <lb/>continuat&aelig;, po&longs;t re&longs;olutionem erant ab innicem valde di&longs;&longs;it&aelig;. </s>
7495 
7496 <s>quapropter <lb/>Imperator commenti totius con&longs;cius, eandem membranam &longs;cytali alteri <lb/>priori omnin&ograve; &longs;imili, <expan abbr="&aelig;quali&qacute;">&aelig;qualique</expan>; eodem modo, quo prius circumponebat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <lb/>iunctur&aelig; priores redibant, qu&aelig; literas, ac verba mutila, &amp; imperfecta in <lb/>integrum re&longs;tituebant, vt facil&egrave; legi po&longs;&longs;ent. </s>
7497 
7498 <s>hoc illi vtebantur &longs;ecreto, cum <lb/>literas ad Imperatores &longs;uos mi&longs;&longs;as, ho&longs;tibus occultas e&longs;&longs;e volebant.</s></p><p type="main">
7499 
7500 <s>Ex quibus conijcere licet &longs;cytalam fui&longs;&longs;e lignum oblongum, &amp; teres, &longs;iue <lb/>vt Geometr&aelig; dicunt, Cylindrum; in cuius tamen extremitatibus e&longs;&longs;ent <lb/>margines duo aliquantulum prominentes, ceu bin&aelig; rot&aelig;, cum ip&longs;o tamen <lb/>continu&aelig;, &amp; connex&aelig;, vt cum ip&longs;o &longs;imul conuoluerentur; non tamen tan&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.173.1.tif"/><lb/>quam circa axem. </s>
7501 
7502 <s>cuius hanc accipe fi&shy;<lb/>guram. </s>
7503 
7504 <s>Qu&aelig;rit igitur Ari&longs;t. 
7505 
7506 cur huiu&longs;&shy;<lb/>modi &longs;cytal&aelig; facilius moueantur, quo <lb/>maiores ip&longs;arum &longs;unt rot&aelig;. </s>
7507 
7508 <s>Cui qu&aelig;&shy;<lb/>&longs;tioni &longs;imul, ij&longs;demque verbis, quibus <lb/>qu&aelig;&longs;tioni de maioribus rotulis re&longs;pondet, &longs;ed non &longs;atisfacit ob eandem ra&shy;<lb/>tionem, quam ibi attuli. </s>
7509 
7510 <s>Crediderim tamen maiores &longs;cytalas, &amp; maiores <lb/>curruum rotas, &amp; alia id generis, qu&aelig; volutantur, ita vt motu progre&longs;&longs;iuo <lb/>mutent locum, facilius moueri, &longs;ed ob aliam cau&longs;am, quia nimirum maio&shy;<lb/>res rot&aelig; minus &longs;i quid obuiam fiat, offen&longs;ant, quia &longs;ua magnitudine quem&shy;<lb/>libet obicem facil&egrave; &longs;uperare po&longs;&longs;unt; cuius cau&longs;a e&longs;t angulus <expan abbr="acuti&longs;&longs;im&utilde;s">acuti&longs;&longs;imuns</expan>, <lb/>quem cum terra facit; at ver&ograve; exigu&aelig; rot&aelig;, &longs;i cui maiori ob&longs;taculo obuia&shy;<lb/>rint, ip&longs;um nequeunt &longs;uperare, aut &longs;upera&longs;cendere, quia angulum cum ter&shy;<lb/>ra faciunt in&longs;to maiorem, vnde facil&egrave; ip&longs;orum cur&longs;us inhibetur, <expan abbr="ip&longs;&aelig;&qacute;">ip&longs;&aelig;que</expan>; pro&shy;<lb/>pterea pr&aelig; maioribus tardiores euadunt. </s>
7511 
7512 <s>Atque h&aelig;c in hanc qu&aelig;&longs;tionem <lb/>dicta &longs;ufficiant.</s></p><p type="head">
7513 
7514 <s><emph type="italics"/>QV&AElig;STIO DECIMA<emph.end type="italics"/></s></p><p type="head">
7515 
7516 <s><emph type="italics"/>De libra vacua, &amp; alijs &longs;imilibus.<emph.end type="italics"/></s></p><p type="main">
7517 
7518 <s><arrow.to.target n="marg241"/></s></p><p type="margin">
7519 
7520 <s><margin.target id="marg241"/>251</s></p><p type="main">
7521 
7522 <s>Cvr libr&aelig;, qu&aelig; omni incumbente pondere &longs;unt vacu&aelig; ab impo&longs;ito <lb/>pondere facilius mouentur, qu&agrave;m &longs;i quopiam inexi&longs;tente pondere <lb/>aliud rur&longs;us onus &longs;uperaddatur. </s>
7523 
7524 <s>&longs;imiliter etiam rota, &amp; huiu&longs;modi <lb/>quippiam, quod grauius quidem e&longs;t, difficilius commouetur qu&agrave;m <lb/>l&aelig;ue, v. <!-- REMOVE S-->g. <!-- REMOVE S-->rota ferrea difficilius, qu&agrave;m lignea. </s>
7525 
7526 
7527 
7528 
7529 
7530 <s>&longs;imiliter qu&aelig; maiora &longs;unt, <lb/>etiam &longs;i ex eadem materia con&longs;tent difficilius mouentur qu&agrave;m minora, vt <lb/>rota maior ferrea, qu&agrave;m minor etiam ferrea. </s>
7531 
7532 <s>Habet h&aelig;c qu&aelig;&longs;tio tres par&shy;<lb/>tes, quibus Ari&longs;t. 
7533 
7534 re&longs;pondet dicens, quod graue e&longs;t &aelig;gr&egrave; moneri non &longs;olum <lb/>contra nutum &longs;uum, idc&longs;t &longs;ur&longs;um, &longs;ed etiam in obliquum, &longs;eu ad latera, quia <lb/>grauia deor&longs;um <expan abbr="nut&atilde;t">nutant</expan>, non &longs;ur&longs;um, nec in tran&longs;uer&longs;um: ideo libr&aelig; cum one&shy;<lb/>re, quia &longs;unt grauiores, &amp; rota ferrea qu&agrave;m lignea, &amp; ferrea ctiam maior, <lb/>qu&agrave;m minor grauior e&longs;t, ide&ograve; difficilius agitatur.</s></p><p type="main">
7535 
7536 <s>Contra quam re&longs;pon&longs;ionem &longs;ic fort&egrave; obijcies; in pr&aelig;cedenti enim qu&aelig;&shy;<pb pagenum="174"/>&longs;tione dictum e&longs;t ab Ari&longs;t. 
7537 
7538 maiores trochleas, &amp; &longs;cytalas, minoribus facilius <lb/>commoueri, hic autem dicit maiorem rotam difficilius qu&agrave;m minorem mo&shy;<lb/>ueri. </s>
7539 
7540 <s>Hanc obiectionem Piccolomineus di&longs;&longs;imula&longs;&longs;e videtur, cui ego, inge&shy;<lb/>nu&egrave; fateor, me &longs;atisfacere ne&longs;cire, vt enim in pr&aelig;cedenti annotaui, nulla <lb/>mihi ratio Ari&longs;t. 
7541 
7542 excu&longs;andi occurrit, alijs fort&egrave; occurret. </s>
7543 
7544 <s>In pr&aelig;&longs;enti au&shy;<lb/>tem ben&egrave; quidem re&longs;pondet, &longs;ed tamen intimam rei cau&longs;am non attingit.</s></p><p type="main">
7545 
7546 <s>Sciendum igitur e&longs;t id, quod Guidus Vbaldus in tractatu de libra pluri&shy;<lb/>bus demon&longs;trauit: quod &longs;i quoduis graue &longs;u&longs;pendatur pror&longs;us in <expan abbr="c&etilde;tro">centro</expan> gra&shy;<lb/>uitatis, ita vt in perfecto &longs;it &aelig;quilibrio, tunc &longs;iue magnum, &longs;iue paruum, <lb/>&longs;iue graue, grauiu&longs;u&egrave; fuerit, &agrave; quauis exigua vi poterit ab &aelig;quilibrio dimo&shy;<lb/>ueri. </s>
7547 
7548 <s>cur ergo in libris, &amp; rotis grauioribus, aut maioribus <expan abbr="experi&etilde;tia">experientia</expan> con&shy;<lb/>trarium o&longs;tendit? </s>
7549 
7550 <s>ratio e&longs;t, quia h&aelig;c omnia communiter non collocantur, <lb/>ita vt circa centrum &longs;uum, quod etiam centrum grauitatis e&longs;t, conuerti <lb/>po&longs;&longs;int: verum aptantur circa axem, &amp; quidem iu&longs;to maiorem, laxiu&longs;que <lb/>circa ip&longs;um conuertuntur, vnde fit, vt ip&longs;a ob in&longs;itam grauitatem premant <lb/>axem in &longs;uperiori parte, vnde quando ab aliquo gyrantur, non propri&egrave; gy&shy;<lb/>rant, &longs;ed in &longs;uperiori axis parte h&aelig;rentes ip&longs;um atterunt; ex qua attritione <lb/>fit, vt retardentur, <expan abbr="id&qacute;">idque</expan>; e&ograve; magis, quo graniora magis premunt; h&aelig;rent, <lb/><expan abbr="difficilius&qacute;">difficiliusque</expan>; propterea raptantur potius, qu&agrave;m gyrentur.</s></p><p type="main">
7551 
7552 <s>Ex his, &amp; textus, &amp; ratio Ari&longs;totelis &longs;atis clara redduntur.</s></p><p type="head">
7553 
7554 <s><emph type="italics"/>QV&AElig;STIO VNDECIMA<emph.end type="italics"/></s></p><p type="head">
7555 
7556 <s><emph type="italics"/>De Scytala, &amp; Curru.<emph.end type="italics"/></s></p><p type="main">
7557 
7558 <s><arrow.to.target n="marg242"/></s></p><p type="margin">
7559 
7560 <s><margin.target id="marg242"/>252</s></p><p type="main">
7561 
7562 <s>Cvr &longs;uper &longs;cytalas facilius portantur onera qu&agrave;m &longs;uper currus, cum <lb/>tamen currus magnas habeant rotas, &longs;cytal&aelig; ver&ograve; pu&longs;illas?</s></p><p type="main">
7563 
7564 <s>Quidnam &longs;cytala e&longs;&longs;et explicatum e&longs;t in 9. qu&aelig;&longs;t. </s>
7565 
7566 <s>Quo autem <lb/>modo per &longs;cytalas onera <expan abbr="port&etilde;tur">portentur</expan>, &longs;ic, accipe: exi&longs;timo binas &longs;cy&shy;<lb/>talas inuicem &aelig;quidi&longs;tantes, &amp; aliquantulum &longs;emotas inuicem &longs;ic di&longs;poni, <lb/>vt efficiant in&longs;trumentum vectorium currus in&longs;tar, &amp; fort&egrave; veteres vteban&shy;<lb/>tur his &longs;cytalis eo modo, quo nunc architectores vtuntur duobus illis lignis <lb/>longis, ac rotundis, qu&aelig; vulg&ograve; dicuntur Ruccioli.</s></p><p type="main">
7567 
7568 <s>Re&longs;pondet igitur id accidere, quia rot&aelig; &longs;cytalarum &longs;imul &longs;unt cum &longs;uo <lb/>axe coinpact&aelig;, ita vt &longs;imul cum ip&longs;o rotentur: rot&aelig; autem curruum, quia <lb/>&longs;eiunct&aelig; &longs;unt ab earum axe, ita vt &longs;ine illius rotatione ip&longs;&aelig; voluantur, fit vt <lb/>ill&aelig; firmius incedant, nechuc, <expan abbr="illuc&qacute;">illucque</expan>; nutent, veluti rot&aelig; plan&longs;tri: <expan abbr="neq;">neque</expan> ill&aelig; <lb/>ad ip&longs;um axem offen&longs;ent, quemadmodum i&longs;t&aelig;. </s>
7569 
7570 <s>addit aliam rationem, quia <lb/>currus nimia oneris grauitate premens rotas ip&longs;as fer&egrave; &longs;i&longs;tit, quod &longs;cytalis <lb/>non accidit, cum rot&aelig; ip&longs;arum vnum, &amp; idem cum &longs;uo &longs;int axe. </s>
7571 
7572 <s>qu&aelig; ratio <lb/>quantum valeat, ne&longs;cio, nam quamuis rot&aelig; &longs;cytalarum non premantur ab <lb/>axe, premitur tamen axis ip&longs;arum ab onere, &agrave; quo &longs;imiliter &longs;i&longs;ti debe&shy;<lb/>rent &longs;cytal&aelig;.</s></p><p type="main">
7573 
7574 <s>Crediderim ego facilius portari magna onera per &longs;cytalas, propter ip&longs;a&shy;<lb/>rum firmitatem, currus enim <expan abbr="ip&longs;orumq;">ip&longs;orumque</expan> rot&aelig; &longs;unt mult&ograve; debiliores, neque <lb/>maioribus oneribus &longs;ufficiunt. </s>
7575 
7576 <s>Concludit po&longs;tea qu&aelig;&longs;tionem dicens, quia <pb pagenum="175"/>igitur &longs;cytal&aelig; ab ip&longs;o onere non ita premuntur quin moueri melius po&longs;&longs;int <lb/>qu&agrave;m currus, im&ograve; ab ip&longs;o onere iam commoto, ip&longs;&aelig; quoque incitentur, &amp; <lb/>pr&aelig;terea &agrave; potentia per planum infern&egrave;, ben&egrave; &longs;ub&longs;tratum, &amp; complanatum <lb/>trahantur, fit, vt qua&longs;i in duobus locis ip&longs;arum rot&aelig; impellantur ab onere <lb/>&longs;upra, &amp; &agrave; potentia infra; &longs;icque facilius quam currus ingentia pr&aelig;&longs;ertim <lb/>onera vehunt.</s></p><p type="head">
7577 
7578 <s><emph type="italics"/>De Funda.<emph.end type="italics"/></s></p><p type="head">
7579 
7580 <s><emph type="italics"/>QV&AElig;STIO DVODECIMA.<emph.end type="italics"/></s></p><p type="head">
7581 
7582 <s>Non videtur declaratione indigere.</s></p><p type="head">
7583 
7584 <s><emph type="italics"/>QV&AElig;STIO DECIMATERTIA<emph.end type="italics"/></s></p><p type="head">
7585 
7586 <s><emph type="italics"/>De Iugo, &amp; Succula.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7587 
7588 <s><arrow.to.target n="marg243"/></s></p><p type="margin">
7589 
7590 <s><margin.target id="marg243"/>253</s></p><p type="main">
7591 
7592 <s>Declarandum prius quid &longs;it hoc loco iugum: e&longs;t igitur iugum li&shy;<lb/>gnum illud cylindricum, quod vulg&ograve; dicitur Subbio. </s>
7593 
7594 <s>quorum bi&shy;<lb/>na ponuntur in ea machina textoria, quam vulg&ograve; dicunt Telaio, <lb/>qua&longs;i telarium, eo quod in ip&longs;a tel&aelig; texantur. </s>
7595 
7596 <s>alteri autem iugo <lb/>conuoluitur &longs;tamen: alteri ver&ograve; contexta iam tela &longs;ubinde cum opus e&longs;t cir&shy;<lb/>cumponitur: qu&aelig; duo textores faciunt ip&longs;a iuga conuertendo. </s>
7597 
7598 <s>qu&aelig; vt faci&shy;<lb/>lius conuertant, iugis vtrinque in&longs;erunt per bina foramina binos collopes. <lb/></s>
7599 
7600 <s>qui collopes &longs;unt duo ligna oblonga &longs;atis gracilia vnius vln&aelig; fer&egrave; in longi&shy;<lb/>tudinem; quibus <expan abbr="appr&aelig;h&etilde;&longs;is">appr&aelig;hen&longs;is</expan>, <expan abbr="motis&qacute;">motisque</expan>; iugum facil&egrave; ver&longs;atur. </s>
7601 
7602 <s>quanto autem <lb/>collopes &longs;unt longiores, facilius iugum circumagitur. </s>
7603 
7604 <s>cuius cau&longs;a e&longs;t, quia <lb/>collops ad vectem reducitur, cuius fultura e&longs;t circa medium iugi, pondus <lb/>ver&ograve; e&longs;t extima iugi &longs;uperficies &egrave; qua tel&aelig;, aut &longs;taminis pondus pendet: in <lb/>altera ver&ograve; extremitate collopis, qu&aelig; extra iugum multum prominet, e&longs;t <lb/>potentia: ibi enim textoris manus premit, vel trahit. </s>
7605 
7606 <s>quando erg&ograve; longior <lb/>e&longs;t collops, ea pars, qu&aelig; e&longs;t inter fulturam, &amp; vim, augetur; altera non mu&shy;<lb/>tata; quia &longs;emper inter fulturam, &longs;eu centrum iugi, &amp; vltimam iugi &longs;uper&shy;<lb/>ficiem continetur; quanto autem illa hanc &longs;uperar, tantum virium po&shy;<lb/>tenti&aelig; addi.</s></p><p type="main">
7607 
7608 <s>Secund&ograve;, videndum quid &longs;it &longs;uccula: hanc vulg&ograve; Na&longs;pa appellant, ni fal&shy;<lb/>lor &agrave; verbo gr&aelig;co <foreign lang="greek">a)gaspa/w,</foreign> oriunda, quod &longs;ur&longs;um extrahere &longs;ignificat. </s>
7609 
7610 <s>cum <lb/>quo, &amp; voce, &amp; &longs;ignificatione conuenit; e&longs;t enim in&longs;trumentum, quo &longs;&aelig;pius <lb/>architectores in extrahendis &longs;ur&longs;um ruderibus effo&longs;&longs;is vtuntur. </s>
7611 
7612 <s>e&longs;t autem <lb/>compago qu&aelig;dam cylindrica non admodum longa, cuiex vna parte poti&longs;&shy;<lb/>&longs;imum prominent plures collopes non mobiles, vt in iugo, verum &longs;tabiles, <lb/>ac cum ip&longs;a &longs;uccula compacti, quibus manu appr&aelig;hen&longs;is &longs;uccula &longs;upra bi&shy;<lb/>nos polos ver&longs;atur, <expan abbr="ei&qacute;">eique</expan>; interim ductarius funis circumuoluitur, &longs;ecumque <lb/>&longs;ur&longs;um pondus educit. </s>
7613 
7614 <s>cuius imaginem <expan abbr="qualcmcunq;">qualcmcunque</expan> in&longs;pice. </s>
7615 
7616 <s>qu&aelig;rit igitur, <lb/>cur quanto gracilius fucrit corpus &longs;uccul&aelig; A B, tanto facilius vertitur. <lb/></s>
7617 
7618 <s>Ratio e&longs;t, quia collops, quemadmodum etiam iugum, reducitur ad vectem, <pb pagenum="176"/><figure place="text" xlink:href="figures-la/009.01.176.1.tif"/><lb/>cuius hypomoclion e&longs;t in medio <lb/>&longs;uccul&aelig;, &longs;iue in axe ip&longs;ius &longs;uccul&aelig;; <lb/>potentia ver&ograve; e&longs;t in &longs;ummitatibus <lb/>collopum, vt in C, E, F, D, pon&shy;<lb/>dus ver&ograve; e&longs;t vbi funis ductarius <lb/>cum onere pendet &egrave; &longs;uccula in &longs;u&shy;<lb/>perficie nimirum, vt vbi L, quare <lb/>pars vectis inter axim, &amp; &longs;uperfi&shy;<lb/>ciem &longs;uccul&aelig; eadem e&longs;t, qu&aelig; inter <lb/>hypomoclium, &amp; pondus. </s>
7619 
7620 <s>quanto <lb/>igitur &longs;uccul&aelig; corpus gracilius fuerit, tanto h&aelig;c pars minuetur; &amp; con&longs;e&shy;<lb/>quenter altera inter hypomoclium, &amp; potentiam productior euadet: eaque <lb/>propter facilius &agrave; motore ver&longs;abitur.</s></p><p type="head">
7621 
7622 <s><emph type="italics"/>De ligno ad genu fracto.<emph.end type="italics"/></s></p><p type="head">
7623 
7624 <s><emph type="italics"/>QV&AElig;STIO DECIMAQVARTA.<emph.end type="italics"/></s></p><p type="head">
7625 
7626 <s>Satis per&longs;e clara videtur.</s></p><p type="head">
7627 
7628 <s><emph type="italics"/>QV&AElig;STIO DECIMAQVINTA<emph.end type="italics"/></s></p><p type="head">
7629 
7630 <s><emph type="italics"/>De Vmbilicis.<emph.end type="italics"/></s></p><p type="main">
7631 
7632 <s><arrow.to.target n="marg244"/></s></p><p type="margin">
7633 
7634 <s><margin.target id="marg244"/>254</s></p><p type="main">
7635 
7636 <s>Notandum prim&ograve;, qu&aelig; Gr&aelig;cis <foreign lang="greek">*krexai,</foreign> ide&longs;t Croc&aelig; dicuntur, Latinis <lb/>Vmbilicos appellari; de his enim loquitur Cic. <!-- REMOVE S-->2. de Oratore, vbi <lb/>&longs;ic, non audeo dicere de talibus viris, &longs;ed tamen ita narrare &longs;ole&shy;<lb/>bat Sceuola, conchas, eos, &amp; vmbilicos ad Caietam, &amp; ad Lucri&shy;<lb/>num legere con&longs;ueui&longs;&longs;e. </s>
7637 
7638 
7639 
7640 <s>hos autem vmbilicos exponunt Grammatici e&longs;&longs;e <lb/>lapillos paruos, acrotundos, polito&longs;que, de quibus etiam Ari&longs;t. 
7641 
7642 loquitur. <lb/></s>
7643 
7644 <s>Quare decipitur Piccolomineus dum negat, nos harum crocarum latinum <lb/>nomen habere. </s>
7645 
7646 <s>C&aelig;ter&ugrave;m, &amp; qu&aelig;&longs;tio, &amp; re&longs;pon&longs;io, ex &longs;uperioribus &longs;atis <lb/>per&longs;picua e&longs;&longs;e videntur.</s></p><p type="head">
7647 
7648 <s><emph type="italics"/>QV&AElig;STIO DECIM ASEXTA<emph.end type="italics"/></s></p><p type="head">
7649 
7650 <s><emph type="italics"/>De ligno oblongo.<emph.end type="italics"/></s></p><p type="main">
7651 
7652 <s><arrow.to.target n="marg245"/></s></p><p type="margin">
7653 
7654 <s><margin.target id="marg245"/>255</s></p><p type="main">
7655 
7656 <s>Ex appo&longs;ita figura totus huius problematis textus, alioquin &longs;atis cla&shy;<lb/>rus patebit. </s>
7657 
7658 <s>&longs;int duo ligna oblonga, vnum altero longius, &amp; cra&longs;&longs;ius. <lb/></s>
7659 
7660 <s>in eleuatione maioris, fulcimentum e&longs;t in B, vbi manus altera fer&egrave; <lb/>manens appr&aelig;hendit; in C, ver&ograve;, vbi altera manus mouens premit <lb/>e&longs;t potentia, &longs;iue maius onus. </s>
7661 
7662 <s>in A, ver&ograve; onus ip&longs;ius ligni, deor&longs;um tendens <lb/>premit, quod nunc e&longs;t in&longs;tar potenti&aelig; motricis, quare A, &amp; C, &longs;unt &longs;ibi in&shy;<lb/>uicem, &amp; potenti&aelig;, &amp; pondera. </s>
7663 
7664 <s>In minori autem ligno, onus ligni in D, <pb pagenum="177"/><figure place="text" xlink:href="figures-la/009.01.177.1.tif"/><lb/>fultura manus in E, potentia alterius ma&shy;<lb/>nus in F. iam inquir Ari&longs;t. 
7665 
7666 maius lignum <lb/>A B C, magis flectitur, quamuis cra&longs;&longs;ius <lb/>&longs;it, qu&agrave;m lignum D E F, quod e&longs;t tenuuius, <lb/>&longs;ed mult&ograve; breuius; quia in maiori onus <lb/>ip&longs;ius ligni, quod circa A, deor&longs;um pre&shy;<lb/>mit <expan abbr="l&otilde;gius">longius</expan> di&longs;tat ab hypomoclio B, qu&agrave;m <lb/>in minori ligno. </s>
7667 
7668 <s>Ex quo &longs;equitur iuxta <lb/>ip&longs;ius principia, vt onus A, facilius lignum mouere, aut inflectere <lb/>po&longs;&longs;it.</s></p><p type="main">
7669 
7670 <s>C&aelig;ter&ugrave;m exi&longs;timo, quod &longs;i maioris ligni longitudo ad eiu&longs;dem <lb/>cra&longs;&longs;itiem haberet <expan abbr="e&atilde;dem">eandem</expan> proportionem, qu&agrave;m minoris longitudo ad eiu&longs;&shy;<lb/>dem cra&longs;&longs;itiem, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <expan abbr="vtrumq;">vtrumque</expan> e&longs;&longs;et ab hypomoclio in eadem ratione diui&shy;<lb/>&longs;um, fore, vt <expan abbr="vtrunq;">vtrunque</expan> eodem modo inflecteretur, quia haberent pondera <lb/>eandem rationem ad di&longs;tantias ab hypomoclio, oportet igitur vt &longs;int non <lb/>analoga, &longs;ed aloga, vt eis pr&aelig;&longs;ens problema Ari&longs;totelis vn&agrave; cum eiu&longs;dem <lb/>&longs;olutione competat.</s></p><p type="head">
7671 
7672 <s><emph type="italics"/>QV&AElig;STIO XVII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7673 
7674 <s><emph type="italics"/>De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7675 
7676 <s><arrow.to.target n="marg246"/></s></p><p type="margin">
7677 
7678 <s><margin.target id="marg246"/>256</s></p><p type="main">
7679 
7680 <s>Cvr paruo cuneo magna finduntur onera, &amp; corporum moles, <expan abbr="adeoq;">adeoque</expan> <lb/>valida fit impre&longs;&longs;io? </s>
7681 
7682 <s>fort&egrave;, quia cuneus duobus vectibus &longs;ibi inui&shy;<lb/>cem oppo&longs;itis con&longs;tat; quorum vterque, &amp; potentiam mouentem, <lb/>&amp; hypomoclion, &amp; <expan abbr="p&otilde;dus">pondus</expan> habet. </s>
7683 
7684 <s>hypomoclion autem illud ip&longs;um <lb/>e&longs;&longs;e ait, quod cuneo diuellitur; hoc autem dicit Ari&longs;tot. quia non agnouit <lb/>alium, pr&aelig;ter primi generis vectem, vt &longs;upra etiam dixi.</s>
7685 
7686 </p><p type="main">
7687 
7688 <s>Verum &longs;atius e&longs;t cum Guido Vbaldo reducere cuneum ad duos &longs;ecundi <lb/>generis vectes, quorum fultura &longs;it in cunei apice extremo, pondus ver&ograve; in&shy;<lb/>tra vectem, ea nimirum pars ligni, que &agrave; cuneo vrgetur, ac diuellitur. </s>
7689 
7690 <s>cuneo <lb/>pr&aelig;terea vires adduntur ex valida mallei percu&longs;&longs;ione; malleus autem ip&longs;e <lb/>magna vi percutit, quia motus mouet, &longs;eu quia mouens malleum, mouet <lb/>ip&longs;um etiam dum e&longs;t in ip&longs;a latione, vnde ip&longs;a lationis celeritate malleus <lb/>fit valentior: <expan abbr="hoc&qacute;">hocque</expan>; modo paruos cunci vectes maiores con&longs;equuntur vires, <lb/><figure place="text" xlink:href="figures-la/009.01.177.2.tif"/><lb/>qu&agrave;m ip&longs;a vectium magnitudo po&longs;tulet. <lb/></s>
7691 
7692 <s>&longs;it cuneus A B C. lignum autem &longs;cinden&shy;<lb/>dum D E F G, <expan abbr="vectes&qacute;">vectesque</expan> duo &longs;int A C, &amp; <lb/>B C, quorum commune hypomoclion e&longs;t <lb/>in C, onus autem vectis B C, e&longs;t pars li&shy;<lb/>gni G, h&aelig;c enim ip&longs;i contranititur, <expan abbr="atq;">atque</expan> <lb/>ab eo expellitur. </s>
7693 
7694 <s>potentia ver&ograve; mouens <lb/>vectem e&longs;t in malleo, dum &longs;uperius latus <lb/>cunei A B, percutit. </s>
7695 
7696 <s>alter huic auer&longs;us <lb/>vectis e&longs;t latus A C, cuius fultura e&longs;t C, <lb/>cadem cum priori, onus propul&longs;atum D, <pb pagenum="178"/>potentia cum altero communis e&longs;t in latere A B, &agrave; malleo valid&egrave; percu&longs;&longs;o. <lb/></s>
7697 
7698 <s>cunei igitur virtus partim ex vectibus, partim ex percu&longs;&longs;ione con&longs;tat.</s></p><p type="head">
7699 
7700 <s><emph type="italics"/>QV&AElig;STIO XVIII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7701 
7702 <s><emph type="italics"/>De Trochlea.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7703 
7704 <s><arrow.to.target n="marg247"/></s></p><p type="margin">
7705 
7706 <s><margin.target id="marg247"/>257</s></p><p type="main">
7707 
7708 <s>Hvius qu&aelig;&longs;tionis &longs;en&longs;us, ac verba optim&egrave; intelligentur ex &longs;equen&shy;<lb/>tibus. </s>
7709 
7710 <s>Trochlea, vt patet ex &longs;uperioribus Ari&longs;t. 
7711 
7712 e&longs;t orbiculus in <lb/>periph&aelig;ria &longs;triatus, vna cum toto loculumento, cui in&longs;eritur: <lb/>cuius imaginem ad 8. qu&aelig;&longs;t. </s>
7713 
7714 <s>exhibui. </s>
7715 
7716 <s>Apud Architectores ver&ograve; <lb/>trochlea con&longs;tat &longs;altem ex duobus pr&aelig;dictis loculamentis, in quibus &longs;unt <lb/>orbiculi; &amp; vnus orbiculus e&longs;t &longs;upern&egrave; collocatus, alter ver&ograve; infern&egrave;, vt pa&shy;<lb/>tebit in &longs;equenti figuratione: quod <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> nunc vulg&ograve; dicitur Taglia, <lb/>&agrave; nonnullis dicitur etiam Rechamo. </s>
7717 
7718 <s>Auxilio huius in&longs;trumenti machinato&shy;<lb/>res parua vi attollunt ingentia pondera. </s>
7719 
7720 <s>communiter autem con&longs;tat ex plu&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.178.1.tif"/><lb/>ribus orbiculis, qui partim &longs;uperiori loculamento, <lb/>partim infetiori inditi &longs;unt, per quos orbiculos cer&shy;<lb/>ta lege circumductus e&longs;t ductarius funis, qui deinde <lb/>in &longs;ui po&longs;trema parte &agrave; potentia tractus omnes illos <lb/>orbiculos, per quos tran&longs;it circumuoluens inferius <lb/>loculamentum, cui appen&longs;um e&longs;t pondus, vn&agrave; cum <lb/>ponderc attollit. </s>
7721 
7722 <s>figuram &longs;implicis trochle&aelig;, con&shy;<lb/>&longs;tantis &longs;cilicet ex duobus tantum orbiculis, facilita&shy;<lb/>tis cau&longs;a exhibebo, in hac enim melius apparebit, <lb/>qua ratione trochlea ad vectem reducatur. </s>
7723 
7724 <s>vnde, &amp; <lb/>Ari&longs;t. &longs;en&longs;um, quamuis ob&longs;curi&longs;&longs;imum, ac proinde <lb/>problematis &longs;olutionem optim&egrave; percipere licebit. <lb/></s>
7725 
7726 <s>Sit igitur orbiculus &longs;uperior A, qui in pegmate I K&shy;<lb/>L D, voluatur circa axem G, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; pegma i&longs;tud &longs;upe&shy;<lb/>rius fixum, &amp; immobile &agrave; clauo H, pendens. </s>
7727 
7728 <s>Infe&shy;<lb/>rior orbiculus B, in loculamento O P Q R, circa <lb/>axem B, conuoluatur: &longs;itque funis ductarius circa <lb/>hos orbiculos hoc modo circumductus. </s>
7729 
7730 <s>primo ca&shy;<lb/>put funis religetur clauo D, in &longs;uperiori pegmate <lb/>infixo, hinc demi&longs;&longs;us &longs;ubtus inferiorem rotulam per <lb/>ip&longs;ius &longs;triam de&longs;cendat per puncta L S, a&longs;cendatque <lb/>po&longs;tea per M E N, ad &longs;uperiorem rotulam, &longs;upra <lb/>quam a&longs;cendat per punctum T, <expan abbr="de&longs;cendat&qacute;">de&longs;cendatque</expan>; ad V, &amp; <lb/>inde demittatur ad <expan abbr="pot&etilde;tiam">potentiam</expan> F. am &longs;i quepiam po&shy;<lb/>tentia in F, traxerit funem F V, deor&longs;um, interim <lb/>partes T, N, E, M, &longs;ur&longs;um attrahentur, &amp; locula&shy;<lb/>mentum inferius &longs;imul cum appen&longs;o pondere eleua&shy;<lb/>bitur, manente tamen interim fune prope D, vbi <lb/>clauo D, e&longs;t religatus, &amp; immobilis. </s>
7731 
7732 <s>&longs;ed vbinam hic <lb/>vectis? </s>
7733 
7734 <s>con&longs;idera diametrum M L, inferioris orbiculi, h&aelig;c enim ea e&longs;t, qu&aelig; <pb pagenum="179"/>vectem gerit. </s>
7735 
7736 <s>huius enim extrema L M, &agrave; fune tanguntur, &amp; ab eius medio <lb/>B, onus pender, &amp; grauitat; &amp; quia funis in M, &longs;ur&longs;um trahitur, <expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; ex <lb/>parte illa &longs;ur&longs;um eieuat diametrum L M, erit potentia mouens, &amp; eleuans <lb/>in M. pondus ver&ograve; intra vectem ad B, medium vectis; quare fulcimentum <lb/>erit in reliquo extremo L, vbi funis &longs;u&longs;tinet loculamentum, &amp; vbi diameter, <lb/>&longs;eu vectis innititur. </s>
7737 
7738 <s>quare diameter h&aelig;c e&longs;t vectis &longs;ecundi generis expo&longs;iti. <lb/></s>
7739 
7740 <s>aduerte pr&aelig;terea vectem hunc e&longs;&longs;e mobilem, &longs;imul cum <expan abbr="fulcim&etilde;to">fulcimento</expan>, quia dum <lb/>ex parte M, &longs;ur&longs;um tollitur &longs;imul cum toto orbiculo, ac loculamento, &longs;ub&shy;<lb/>&longs;equitur etiam alterum extremum L, quod fune fulcitur, &amp; in ip&longs;o fune &longs;ur&shy;<lb/>&longs;um ver&longs;us D, a&longs;cendit; &amp; hoc modo inferius tignum cum onere tandem ad&shy;<lb/>&longs;uperius tignum &longs;ublatum erit. </s>
7741 
7742 <s>hinc verum dixi&longs;&longs;e Ari&longs;t. 
7743 
7744 con&longs;tat, trochleam <lb/>&longs;cilicet idem e&longs;&longs;e, ac vectem. </s>
7745 
7746 <s>quod tamen de &longs;olo inferiori orbiculo intelli&shy;<lb/>gi debet, &longs;uperior enim rotula quamuis vectis fiat, non tamen vires vllas <lb/>potenti&aelig; tribuit, cum eius hypomoclion &longs;it in medio, quemadmodum &longs;upra <lb/>ad 8. qu&aelig;&longs;t. </s>
7747 
7748 <s>expo&longs;ui. </s>
7749 
7750 <s>Inferior igitur ille e&longs;t, qui mouenti maximo e&longs;t adiu&shy;<lb/>mento. </s>
7751 
7752 <s>quod &longs;i &longs;cire aueas quantum iuuet, re&longs;pondeo ip&longs;um vires potenti&aelig; <lb/>duplicare; adeo vt &longs;i quatuor. </s>
7753 
7754 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->homines erant nece&longs;&longs;arij ad pondus tol&shy;<lb/>lendum, auxilio huius &longs;implicis trochle&aelig; duo tantum &longs;ufficiant. </s>
7755 
7756 
7757 
7758 
7759 
7760 <s>quod &longs;i ad&shy;<lb/>dantur duo alij orbiculi, vnus &longs;uperior, alter inferior, rur&longs;us vires duplica&shy;<lb/>buntur, <expan abbr="erit&qacute;">eritque</expan>; vnus <expan abbr="t&atilde;tum">tantum</expan> homo nece&longs;&longs;arius. </s>
7761 
7762 <s>quod &longs;i plures ali&aelig; rotul&aelig; tam <lb/>&longs;upern&egrave;, qu&agrave;m infern&egrave; addantur, vt&longs;olet in maioribus trochleis, quas ve&shy;<lb/>teres Poly&longs;pa&longs;tos, ide&longs;t multum trahentes dixerunt, augebuntur vires in in&shy;<lb/>finitum. </s>
7763 
7764 <s>quod dixi de virium duplicatione con&longs;tat ex 6. &amp; 7. propo&longs;itione <lb/>Archimedis de Aequip. <!-- KEEP S--></s>
7765 
7766 <s>quia enim in vecte no&longs;tro L M, dupla e&longs;t proportio <lb/>inter L M, &amp; L B, eadem etiam proportio erit inter pondus, &amp; potentiam, <lb/>quare pondus C, duplum erit potenti&aelig; in M, hoc e&longs;t &agrave; minore potentia &longs;ibi <lb/>&longs;ubdupla &longs;u&longs;tinebitur: &amp; &agrave; quauis adhuc <expan abbr="quantumcunq;">quantumcunque</expan> maiore eleuabitur.</s></p><p type="main">
7767 
7768 <s>Qui plura de trochlea de&longs;iderat, adeat Guidi Vbaldi, Mechanica, cuius <lb/>auxilio fateor me verum &longs;en&longs;um harum Mechanicarum Ari&longs;t. &amp; pr&aelig;&longs;ertim <lb/>huius loci enuclea&longs;&longs;e. </s>
7769 
7770 <s>qu&aelig; &longs;i cum Piccolominei expo&longs;itione contuleris, vide&shy;<lb/>bis eum nequaquam cognoui&longs;&longs;e, vbi nam vectis in trochlea lateret, eumque <lb/>tam &longs;uperiorem, qu&agrave;m inferiorem <expan abbr="rotul&atilde;">rotulam</expan> &aelig;qu&egrave; vectem facere; in quo etiam <lb/>Io. <!-- REMOVE S-->Bapti&longs;ta Benedictus pariter erra&longs;&longs;e videtur in &longs;uis &longs;peculationibus, cum <lb/>inferiores tantummodo vice vectium fungantur, vt probatum e&longs;t.</s>
7771 
7772 </p><p type="main">
7773 
7774 <s><expan abbr="Atq;">Atque</expan> ex his &longs;atis mihi videtur textus, ac &longs;en&longs;us Ari&longs;t. 
7775 
7776 illu&longs;trari.</s></p><p type="head">
7777 
7778 <s><emph type="italics"/>QV&AElig;STIO XVIIII.<emph.end type="italics"/></s></p><p type="head">
7779 
7780 <s><emph type="italics"/>De Securi.<emph.end type="italics"/></s></p><p type="main">
7781 
7782 <s><arrow.to.target n="marg248"/></s></p><p type="margin">
7783 
7784 <s><margin.target id="marg248"/>258</s></p><p type="main">
7785 
7786 <s>Pattim ex &longs;e, partim ex dictis in 17. qu&aelig;&longs;t. </s>
7787 
7788 <s>&longs;atis clara e&longs;t. </s>
7789 
7790 <s>placet au&shy;<lb/>tem his, qu&aelig; de cuneo, &amp; &longs;ecuri dicta &longs;unt, nonnulla ex Guido Vbal&shy;<lb/>do loco corollarij adijcere, videlicet. </s>
7791 
7792 <s>Ad huiu&longs;modi facultatis in&shy;<lb/>&longs;trumentum ca <expan abbr="quoq;">quoque</expan> omnia commod&egrave; referri po&longs;&longs;unt, qu&aelig; percu&longs;&shy;<lb/>&longs;ione, &longs;iue impul&longs;u incidunt, diuidunt, perforant, <expan abbr="huiu&longs;modi&qacute;">huiu&longs;modique</expan>; alia obeunt <lb/>munera; vt en&longs;es, gladij, mucrones, &longs;ecures, terebr&aelig;, &amp; &longs;imilia: &longs;erra <expan abbr="quoq;">quoque</expan> <lb/>ad hoc reducitur, dentes enim percutiunt, <expan abbr="cunei&qacute;">cuneique</expan>; in&longs;tar exi&longs;tunt.</s></p><pb pagenum="180"/><p type="head">
7793 
7794 <s><emph type="italics"/>Additio de veteri Securi, &amp; Bipenne.<emph.end type="italics"/></s></p><p type="main">
7795 
7796 <s>Libet etiam huic tractationi de &longs;ecuri nonnulla addere, qu&aelig; olim oc&shy;<lb/>ca&longs;ione ex Proclo accepta in tenebris diu delite&longs;centia in lucem re&shy;<lb/>&longs;tituimus, &longs;unt autem h&aelig;c. </s>
7797 
7798 <s>Prim&ograve;, antiqu&aelig; &longs;ecuris, necnon bipen&shy;<lb/>nis figuram re&longs;tituam. </s>
7799 
7800 <s>Secund&ograve;, o&longs;tendam angulum &longs;ecuris, qui <lb/>curuilineus e&longs;t, &aelig;qualem e&longs;&longs;e angulo trianguli &aelig;quilateri, qui rectilineus e&longs;t. <lb/></s>
7801 
7802 <s>Proclus igitur in comm. <!-- REMOVE S-->23. primi Euclidis, &longs;ic ait: o&longs;ten&longs;um fuit ab anti&shy;<lb/>quis, &longs;cilicet Geometris, quod angulus figur&aelig; illius, qu&aelig; &longs;ecuri &longs;imilis e&longs;t, <lb/>&aelig;qualis e&longs;t angulo rectilineo, quippe qui duabus tertijs anguli recti &aelig;qualis <lb/>e&longs;t. </s>
7803 
7804 
7805 
7806 <s>hanc anguli &longs;ecuris affectionem, cum nec ille, nec alij, quod &longs;ciam de&shy;<lb/>mon&longs;trent, ego paul&ograve; po&longs;t demon&longs;trabo. </s>
7807 
7808 <s>deinde &longs;ubdit; fit autem huiu&longs;mo&shy;<lb/>di &longs;ecuralis figura, qu&aelig; pelecoides vocatur duobus circulis per centra &longs;e <lb/>mutu&ograve; &longs;ecantibus. </s>
7809 
7810 <s>h&aelig;c Proclus. <!-- KEEP S--></s>
7811 
7812 <s>Ex his autem po&longs;tremis verbis de&longs;criptio&shy;<lb/>nem antiqu&aelig; &longs;ecuris, &longs;ic puto eruendam. </s>
7813 
7814 <s>Ducatur primo recta A C, qu&aelig; <lb/><figure place="text" xlink:href="figures-la/009.01.180.1.tif"/><lb/>erit in&longs;tar manubrij &longs;ecuris. </s>
7815 
7816 <s>de&shy;<lb/>inde ex centro C, interuallo. </s>
7817 
7818 <s>v. <!-- REMOVE S-->g. <lb/>C B, de&longs;cribatur circulus B F; &longs;i&shy;<lb/>militer eodem interuallo B D, ex <lb/>centro D, de&longs;cribatur circulus <lb/>B E; tandem ex B, centro, atque <lb/>eodem interuallo ducatur alius <lb/>circulus D E F C, qui priores duos &longs;ecabit in punctis E F. <expan abbr="c&otilde;&longs;ideremus">con&longs;ideremus</expan> iam, <lb/>reliquis circulorum partibus ommi&longs;&longs;is, curuilineam figuram B E F, quam <lb/>e&longs;&longs;e veteris &longs;ecuris formam ex <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan> Proclinon e&longs;t dubitandum, cum cir&shy;<lb/>culis &longs;e mutu&ograve; per centra &longs;ecantibus con&longs;tituatur, vt vult ip&longs;e, &amp; pr&aelig;terea <lb/>habeat angulos E F, tantos, quantos ip&longs;e tradit, vt mox patebit; linea au&shy;<lb/>tem A B C, &longs;ecuris manubrium refert.</s>
7819 
7820 </p><p type="main">
7821 
7822 <s>Quod autem tam angulus E, qu&agrave;m angulus F, &longs;int &aelig;quales duabus tertijs <lb/>vnius angulirecti, &longs;iue quod idem e&longs;t angulo trianguli &aelig;quilateri, manife&shy;<lb/>ftum erithoc modo. </s>
7823 
7824 <s>De&longs;cribatur iterum &longs;ecuralis figura pr&aelig;dicto modo, <lb/>&longs;<expan abbr="itq;">itque</expan> ea A B C. ducantur pr&aelig;terea ad &longs;ingulos angulos tres rect&aelig; A B, B C, <lb/>C A, qu&aelig; con&longs;tituunt trianguium &aelig;quilaterum A B C, tria enim ip&longs;ius late&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.180.2.tif"/><lb/>ra &longs;ubtendunt tres arcus &aelig;quales A B, B C, C A, <lb/>&longs;unt enim tres &longs;extantes &aelig;qualium circulorum, <lb/>ut facil&egrave; colligi pote&longs;t ex 15. 4. ex quo etiam &longs;e&shy;<lb/>quitur tres ilias circulorum portiones, quas re&shy;<lb/>ct&egrave; cum &longs;uis arcubus con&longs;tituunt e&longs;&longs;e inuicem <lb/>&aelig;quales, &amp; limiles portiones nimirum A B E, <lb/>B C D, C A F. hinc pr&ecedil;terea &longs;equitur angulos ip&shy;<lb/>&longs;arum e&longs;&longs;e inuicem &aelig;quales, angulos, v.g. <!-- REMOVE S-->A B E, <lb/>C B D, mixtos e&longs;&longs;e &aelig;quales, quod facil&egrave; e&longs;t per imaginatiam &longs;uperpo&longs;itio&shy;<lb/>nem demon&longs;trare. </s>
7825 
7826 
7827 
7828 <s>cum igitur pr&aelig;dicti duo anguli &longs;int &aelig;quales, &longs;itque intet <lb/>eos medius alius angulus E B C, qui pariter mixtus e&longs;t, &longs;i ip&longs;e addatur tanl <lb/>angulo C B D, qu&agrave;m angulo A B E, inuicem &aelig;qualibus, erunt duo anguli <pb pagenum="181"/>A B C, rectilineus, &amp; E B D, curuilineus &aelig;quales. </s>
7829 
7830 <s>ille autem e&longs;t angulus <lb/>&aelig;quilateri, qui &aelig;qualis e&longs;t duabus tertijs vnius recti ex corollario 32. primi. <lb/></s>
7831 
7832 <s>hic ver&ograve; e&longs;t angulus &longs;ecuris. </s>
7833 
7834 <s>e&longs;t igitur angulus &longs;ecuris &aelig;qualis duabus ter&shy;<lb/>tijs vnius recti, vt ait Proclus, quod demon&longs;trandum erat. </s>
7835 
7836 <s>quod etiam ma&shy;<lb/>nife &longs;tum &longs;ignum e&longs;t &longs;ecuris figuram a me re&longs;titutam e&longs;&longs;e illam veterem, de <lb/>qua idem Proclus loquitur.</s></p><p type="main">
7837 
7838 <s>Re&longs;tat, vt de antiqu&aelig; bipennis etiam figura di&longs;&longs;eramus; qu&aelig; nihil aliud <lb/>erat, qu&agrave;m duplex &longs;ecuris, &longs;iue &longs;ecuris anceps, qualis e&longs;t pr&aelig;&longs;ens figura, vt <lb/><figure place="text" xlink:href="figures-la/009.01.181.1.tif"/><lb/>propterea etiam &longs;&aelig;pius <expan abbr="bip&etilde;nis">bipennis</expan> ip&shy;<lb/>&longs;a &longs;ecuris appelletur. </s>
7839 
7840 <s>dicitur enim <lb/>bipennis, qua&longs;i binis pinnis, qu&aelig; &longs;e&shy;<lb/>cures erant, con&longs;tet, vt &amp; Gr&aelig;cis <lb/><foreign lang="greek">dixteros</foreign> dicebatur. </s>
7841 
7842 <s>te&longs;te etiam No&shy;<lb/>nio, illud bipenne e&longs;t, quod <expan abbr="vtrinq;">vtrinque</expan> <lb/>acutum e&longs;t. </s>
7843 
7844 <s>collegi autem <expan abbr="vtcunq;">vtcunque</expan> <lb/>hanc bipennis figuram ex Simmi&aelig; <lb/>peruetufti poet&aelig; gr&aelig;ci <expan abbr="epigr&atilde;mate">epigrammate</expan>, quod Simmi&aelig; &longs;ecuris appellattur. </s>
7845 
7846 <s>quod <lb/>epigramma carminibus loco linearum con&longs;tat, qu&aelig; in &longs;ecuris formam con&shy;<lb/>&longs;tituta &longs;unt.</s></p><p type="main">
7847 
7848 <s>Sciendum namque e&longs;t Simmiam, poeticam hanc &longs;ecurim concinna&longs;&longs;e in <lb/>gratiam Epei illius, qui equum Troianum ligneum fuerat architectatus, vt <lb/>e&longs;t apud Virg. <!-- KEEP S--></s>
7849 
7850 <s>Et ip&longs;e doli fabricator Epeus. <!-- KEEP S--></s>
7851 
7852 <s>qui cum &longs;oluendi voti cau&longs;a <lb/>vellet &longs;ecurim, &longs;iue bipennem, qua in equi Durij molitione v&longs;us fuerat, Mi&shy;<lb/>neru&aelig; De&aelig;, quod &longs;ibi in eo opere faciendo auxilio fui&longs;&longs;et, dedicare, <expan abbr="eam&qacute;">eamque</expan>; <lb/>vt Ari&longs;t. 
7853 
7854 in libello de admirandis audit. </s>
7855 
7856 <s>num. </s>
7857 
7858 <s>104. narrat, in templo gr&aelig;&shy;<lb/>c&aelig; Mineru&aelig;, quod erat in Gargaria Itali&aelig; Regione prop&egrave; Metapontum, <lb/>&longs;u&longs;pendere, a pr&aelig;fato Simmia qu&aelig;&longs;iuit, vt epigrammate aliquo dedicatio&shy;<lb/>nem hanc &longs;uam complecteretur. </s>
7859 
7860 <s>qui vt illi morem gereret ingenio&longs;&aelig; illius <lb/>bipennis dedicationem, vt melius imitaretur, &longs;ecuri hac carminum com&shy;<lb/>plexus e&longs;t. </s>
7861 
7862 <s>qu&aelig; dedicatio, &longs;iue epigramma, quod adhuc extat, deinceps &longs;e&shy;<lb/>curis Simmi&aelig; vocitata e&longs;t; ex qua figura bipennis illius, equi Durij fabrica&shy;<lb/>tricis nobis adhuc magna cum voluptate innotuit. </s>
7863 
7864 <s>Porr&ograve; gratum, <expan abbr="atq;">atque</expan> ad <lb/>ea, qu&aelig; diximus intelligenda vtile Lectori fore arbitrati &longs;umus, ip&longs;am Sim&shy;<lb/>mi&aelig; bipennem ex operibus Theocriti, quibus addi &longs;olet, huc referre; quam <lb/>P. <!-- REMOVE S-->Ricardus E&longs;ius de no&longs;tra Societate lingu&aelig; gr&aelig;c&aelig; periti&longs;&longs;imus, in hunc <lb/>modum tran&longs;tulit. </s>
7865 
7866 
7867 
7868 <s>hoc autem ordine legenda e&longs;t: lectio &agrave; manubrio <lb/>incipiat, deinde legatur carmen; forti&longs;&longs;im&aelig; De&aelig;, quod &longs;ub&longs;e&shy;<lb/>quatur; dedit Epeus, &amp; &longs;ic in orbem lectio, <expan abbr="v&longs;q;">v&longs;que</expan> ad me&shy;<lb/>dium circumducatur. </s>
7869 
7870 <s>h&aelig;c &longs;unt, qu&aelig; pr&aelig;&longs;ertim <lb/>in gratiam eorum, qui &longs;uaui&longs;&longs;imo an&shy;<lb/>tiquitatis &longs;tudio tenentur, la&shy;<lb/>tere nolui.</s></p><pb pagenum="182"/><p type="head">
7871 
7872 <s><emph type="italics"/>Simmi&aelig; Rhodij <lb/>Bipennis.<emph.end type="italics"/></s></p><figure place="text" xlink:href="figures-la/009.01.182.1.tif"/><pb pagenum="183"/><p type="head">
7873 
7874 <s><emph type="italics"/>QV&AElig;STIO XX.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7875 
7876 <s><emph type="italics"/>De Statera.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7877 
7878 <s><arrow.to.target n="marg249"/></s></p><p type="margin">
7879 
7880 <s><margin.target id="marg249"/>259</s></p><p type="main">
7881 
7882 <s>Antequam ad textus explicationem accedamus, con&longs;ultius e&longs;&longs;e iu&shy;<lb/>dico veteris &longs;tater&aelig; figuram, atque de&longs;criptionem pr&aelig;mittere, <lb/>qu&agrave;m ex hoc Ari&longs;t. 
7883 
7884 loco, magna mihi licuit cum delectatione col&shy;<lb/>ligere: quod etiam antiquitatis &longs;tudio&longs;is pergratum fore non du&shy;<lb/>bito: <expan abbr="atq;">atque</expan> hinc etiam ineptas, <expan abbr="atq;">atque</expan> ad&longs;cititias textus huius figuras tanquam <lb/>adulterinas reijcere; <expan abbr="in&qacute;">inque</expan>; earum locum veras re&longs;tituere licebit. </s>
7885 
7886 <s>erat igitur <lb/><figure place="text" xlink:href="figures-la/009.01.183.1.tif"/><lb/>&longs;tatera, quantum ex Ari&longs;t. 
7887 
7888 conijcio <lb/>primum ha&longs;ta oblonga, qualis e&longs;t in <lb/>pr&aelig;&longs;enti figura A B, ex cuius altero <lb/>extremo B, pendebat appendicu&shy;<lb/>lum, quod propri&egrave; &aelig;quipondium <lb/>dicitur: ex altera ver&ograve; extremitate <lb/>A, lanx vna pendebat; in qua carnes, ali&aelig;u&egrave; merces ponderabantur: in me&shy;<lb/>dia <expan abbr="deniq;">denique</expan> ha&longs;ta paribus interuallis plures trutin&aelig;, ex quibus &longs;ingulis modo <lb/>hac, modo illa, prout pondus emptoris po&longs;tulabat &longs;u&longs;pendebatur, <expan abbr="atq;">atque</expan> in&shy;<lb/>terim tantum mercis lanci imponebatur, donec &aelig;quipondio pr&aelig;pondera&shy;<lb/>ret in &aelig;quilibrio. </s>
7889 
7890 <s>&longs;ingul&aelig; autem trutin&aelig; ad aliquod determinatum pondus <lb/>trutinandum, erant con&longs;titut&aelig;, v. <!-- REMOVE S-->g. <!-- REMOVE S-->vna ad &longs;ex libras, altera ad octo, &amp;c. <lb/></s>
7891 
7892 
7893 
7894 
7895 
7896 <s>quam diui&longs;ionem, ac fabricam &longs;tater&aelig; non e&longs;t difficil&egrave; exhibere, cum ex Ar&shy;<lb/>chimede propo&longs;. </s>
7897 
7898 <s>6. &amp; 7. de &aelig;quip. </s>
7899 
7900 <s>eadem &longs;it proportio inter pondus mer&shy;<lb/>cis, &amp; pondus &aelig;quipondij, qu&aelig; e&longs;t permutatim inter di&longs;tantias vtrinque ab <lb/>a&longs;&longs;umpta trutina, qu&aelig; in trutinando hypomoclij vicem gerit: nam &longs;tatera <lb/>reducitur ad vectem; pondus erit &aelig;quipondium; &amp; merces in lance erit po&shy;<lb/>tentia mouens: &longs;unt autem in tota &longs;tater&aelig; ha&longs;ta trutin&aelig; plures, hoc enim <lb/>modo tota fit vniformis quoad pondus. </s>
7901 
7902 <s>&aelig;quipondium pr&aelig;terea debet ha&shy;<lb/>bere tantum pondus, quantum e&longs;t in nuda lance, vt &longs;ic tota &longs;tatera &longs;it per &longs;e <lb/>&longs;ola &aelig;quilibrabilis: &amp; pr&aelig;terea debet habere pondus &longs;tatum, a c legitimum, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->vnius libr&aelig;, aut duarum, aut trium, prout magis <expan abbr="trutin&atilde;d&aelig;">trutinand&aelig;</expan> merci ido&shy;<lb/>neum erit, &amp; hoc erit proprium &aelig;quipondij pondus. </s>
7903 
7904 
7905 
7906 
7907 
7908 <s>vt autem ex &longs;ingulis <lb/>trutinis &longs;ingula pondera ponderentur. </s>
7909 
7910 <s>&longs;ingulis nota aliqua &longs;culpenda e&longs;t, vt <lb/>facil&egrave; mercatores merces ponderent, quod hac ratione fieri pote&longs;t. </s>
7911 
7912 <s>pona&shy;<lb/>mus &aelig;quipondium e&longs;&longs;e 12. librarum. </s>
7913 
7914 <s>dico, quod trutina C, dabit in lance <lb/>pondus mercis 12. librarum, &longs;i ex ea fiat &aelig;quilibrium, e&longs;t enim vt A C, ad <lb/>C B, ita permutatim &aelig;quipondium 12. ad mercem; &longs;ed A C, ip&longs;i C B, e&longs;t <lb/>&aelig;qualis, erg&ograve; etiam &aelig;quipondium 12. erit merci &aelig;quale, hoc e&longs;t vtrunque <lb/>erit, 12. librarum.</s></p><p type="main">
7915 
7916 <s>Similiter &longs;i &longs;ieret a quilibrium ex trutina D, e&longs;&longs;et vt A D, 3. ad B D, 9. <lb/>ita 12. ad 36. tandem trutina E, &aelig;quilibrante, e&longs;&longs;et vt A E, 9. ad E B, 3. ita <lb/>12. ad 4. Si igitur trutina C, notetur 12. numero, trutina D, num. </s>
7917 
7918 <s>36. tru&shy;<lb/>tina E, num. </s>
7919 
7920 <s>4. &amp; idem de c&aelig;teris: &longs;tatim facil&egrave; erit quodlibet pondus per <lb/>huiu&longs;modi &longs;tateram exhibere. </s>
7921 
7922 <s>Vnde videas contrario ab illis modo in no&shy;<pb pagenum="184"/>&longs;tris &longs;tateris &aelig;quipondium totam ha&longs;tam percurrere; in illis ver&ograve; manent&egrave; <lb/>&aelig;quipondio trutinam quodammodo per ha&longs;tam moueri.</s></p><p type="main">
7923 
7924 <s>His pr&aelig;mi&longs;&longs;is ad textus paraphra&longs;im veniamus.</s></p><p type="main">
7925 
7926 <s>Cur &longs;tatera, qua carnes ponderantur, paruo appendiculo magna truti&shy;<lb/>nat onera, cum alioquin tota &longs;tatera nihil aliud &longs;it, qu&agrave;m dimidiata libra, <lb/>vbi enim onus mercis imponitur vna lanx pendet, quam vnicam &longs;tatera ha&shy;<lb/>bet; in altera autem parte, vbi libra habet alteram lancem, &longs;tatera nullam <lb/>habet, &longs;ed &longs;ola &longs;ine lance e&longs;t. </s>
7927 
7928 <s>Cau&longs;a igitur e&longs;t, quia &longs;tatera &longs;imul, &amp; libra e&longs;t, <lb/>&amp; vectis. </s>
7929 
7930 <s>libra e&longs;t, quia &longs;partorum, &longs;iue trutinarum qu&aelig;libet fit veluti cen&shy;<lb/>trum libr&aelig;, <expan abbr="in&qacute;">inque</expan>; altera parte e&longs;t lanx; in altera ver&ograve; loco lancis ip&longs;um &aelig;qui&shy;<lb/>pondium, quod libr&aelig; incumbit, <expan abbr="fungitur&qacute;">fungiturque</expan>; vice alterius lancis, cui &longs;it onus <lb/>impo&longs;itum; manife&longs;tum enim e&longs;t, quod &aelig;quipondium &longs;tater&aelig; tantumdem <lb/>trahit oneris, quantum e&longs;t illud, quod in altera lance e&longs;t. </s>
7931 
7932 <s>eapropter &longs;tatera <lb/>quodammodo tot libras in &longs;e continet, quot trutinas: quarum vna qu&aelig;que <lb/>cum &longs;it intra appendiculum, &amp; lancem, apta e&longs;t e&longs;&longs;e medium, &longs;eu centrum <lb/>&longs;tater&aelig;, <expan abbr="atq;">atque</expan> adeo etiam libr&aelig;; qu&aelig; vnam quidem lancem habeat ex vna <lb/>parte, ex altera ver&ograve; pro lance &aelig;quipondium. </s>
7933 
7934 <s>&longs;tatera ver&ograve; dicitur, quate&shy;<lb/>nus ex vna parte habet non lancem, &longs;ed perpendiculum. </s>
7935 
7936 <s>&longs;ed hoc nihil e&longs;t <lb/>aliud qu&agrave;m e&longs;&longs;e plures in vna libras; Cur autem &longs;parta, qu&aelig; lanci, &longs;iue ap&shy;<lb/>pen&longs;o oneri proximiora &longs;unt, maiora &longs;ubleuent onera, cau&longs;a e&longs;t vectis natu&shy;<lb/>ra, qu&aelig; &longs;tater&aelig; ine&longs;t. </s>
7937 
7938 <s>e&longs;t enim &longs;tatera vectis, quamuis quodammodo inuer&shy;<lb/>fus, e&longs;t enim ip&longs;ius fulcimentum trutina ip&longs;a &longs;upern&egrave; collocata, pondus ve&shy;<lb/>r&ograve; leuandum e&longs;t ip&longs;a merx, potentia ver&ograve; appendiculum. </s>
7939 
7940 <s>quant&ograve; autem pro&shy;<lb/>ductior fuerit pars vectis &agrave; fulcimento ad potentiam, tanto facilius poten&shy;<lb/>tia mouet, vt in pr&aelig;&longs;entia accidit. </s>
7941 
7942 <s>mouet autem <expan abbr="v&longs;q;">v&longs;que</expan> ad &aelig;quilibrium; <expan abbr="hoc&qacute;">hocque</expan>; <lb/>modo pars illa productior &longs;tater&aelig;, qu&aelig; vergit ad &aelig;quipondium, facit, vt <lb/>onus &longs;tater&aelig; impo&longs;itum facil&egrave; trutinetur.</s></p><p type="head">
7943 
7944 <s><emph type="italics"/>QV&AElig;STIO XXI.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7945 
7946 <s><emph type="italics"/>De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7947 
7948 <s><arrow.to.target n="marg250"/></s></p><p type="margin">
7949 
7950 <s><margin.target id="marg250"/>260</s></p><p type="main">
7951 
7952 <s>Cvr Medici facilius dentes extrahunt dentiforcipis onere adiecto, <lb/>qu&agrave;m &longs;i &longs;ola manu vtantur? </s>
7953 
7954 <s>fort&egrave;, quia ex manu facilius dens ela&shy;<lb/>bitur propter &longs;ui ip&longs;ius lubricitatem, qu&agrave;m ex forcipe. </s>
7955 
7956 <s>Vel etiam, <lb/>quia digiti propter carnis mollitiem cedentem nequeunt dentem <lb/>firmiter circumplecti; &longs;errum ver&ograve;, cum vndique durum &aelig;que &longs;it, nec ce&shy;<lb/>dens, melius dentem compr&ccedil;hendit. </s>
7957 
7958 <s>Aut tandem, quia forceps h&aelig;c duos <lb/>in &longs;e continet contrarios vectes; quorum, vnum tantum e&longs;t hypomoclion, <lb/><figure place="text" xlink:href="figures-la/009.01.184.1.tif"/><lb/>corum &longs;cilicet connexio; Virtute igitur <lb/>vectis arctius dentem per&longs;tringunt, <expan abbr="atq;">atque</expan> <lb/>ade&ograve; obtinent, <expan abbr="atq;">atque</expan> hinc etiam facilius <lb/>commouent. </s>
7959 
7960 <s>&longs;it dentiforcip is figura, ex&shy;<lb/>po&longs;ita, cuius alterum extremum, vbi &longs;unt <lb/>A, B, e&longs;t illud, quod binis &longs;emicirculis <lb/>concurrentibus dentem arct&egrave; <expan abbr="c&otilde;&longs;tringit">con&longs;tringit</expan>, <pb pagenum="185"/>&amp; commouet. </s>
7961 
7962 <s>Vectis vnus e&longs;t A G D, alter B G C, communis fultura e&longs;t G, <lb/>vbi e&longs;t ip&longs;orum decu&longs;&longs;ata connexio; dens loco ponderis e&longs;t; vtroque igitur <lb/>C, &amp; D, tanquam manubrijs vectium dentem Medici compr&aelig;hendentes ip&shy;<lb/>&longs;um facil&egrave; commouent: quando autem commotus fuerit, facilius manu, <lb/>qu&agrave;m in&longs;trumento extrahitur.</s></p><p type="head">
7963 
7964 <s><emph type="italics"/>QV&AElig;STIO XXII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
7965 
7966 <s><emph type="italics"/>De Instrumento Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
7967 
7968 <s><arrow.to.target n="marg251"/></s></p><p type="margin">
7969 
7970 <s><margin.target id="marg251"/>261</s></p><p type="main">
7971 
7972 <s>Tempore Ari&longs;t. 
7973 
7974 vt colligitur ex hac qu&aelig;&longs;tione, ad frangendas nu&shy;<lb/>ces peculiare in&longs;trumentum ligneum adhibeant, quod erat in&longs;tar <lb/>forcipis, ita tamen concinnatum, vt non ad &longs;cindendum, nec ad <lb/>extrahendum, &longs;ed ad frangendum per <expan abbr="c&otilde;pre&longs;&longs;ionem">compre&longs;&longs;ionem</expan> e&longs;&longs;et aptum. <lb/></s>
7975 
7976 <s>cuius hanc qualemcum que figuram in&longs;pice. </s>
7977 
7978 <s>cuius latus inferius A D, fort&egrave; <lb/>alicui fulcimento in plano horizontis, fixum h&aelig;rebat: alterum ver&ograve; A C, <lb/>manu tractabatur, vt &longs;ic expedit&aelig; nucium plurima quantitas breui po&longs;&longs;et <lb/>confringi. </s>
7979 
7980 <s>Credibile e&longs;t nucifragam hanc ad capita F E, habui&longs;&longs;e aliquod <lb/>impedimentum, ne omnin&ograve; con&longs;tringeretur, vt nuces <expan abbr="franger&etilde;tur">frangerentur</expan> quidem, <lb/>non autem comminuerentur. </s>
7981 
7982 <s>Cur igitur nuces <expan abbr="ab&longs;q;">ab&longs;que</expan> ictu facil&egrave; confringun&shy;<lb/>tur hi&longs;ce in&longs;trumentis, qu&aelig; ad eum fiunt v&longs;um? </s>
7983 
7984 <s>contrarium <expan abbr="namq;">namque</expan> accidere <lb/>deberet, vtentes enim pr&aelig;dictis in&longs;trumentis, omnibus illis viribus de&longs;ti&shy;<lb/>tuuntur, quas motio, ac violentia percu&longs;&longs;ionis afferre &longs;olent. </s>
7985 
7986 <s>pr&aelig;terea cur <lb/>ligneo vtuntur, ac proinde leui? </s>
7987 
7988 <s>non ne aptius e&longs;&longs;et durum, <expan abbr="atq;">atque</expan> pondero&shy;<lb/>&longs;um veluti ferreum?</s></p><p type="main">
7989 
7990 <s>His re&longs;pondendum e&longs;t, nucifragum i&longs;tud in&longs;trumentum reduci ad binos <lb/>vectes, quemadmodum etiam dentiforcipem. </s>
7991 
7992 <s>nuxigitur hoc modo duplici <lb/>vecte comprimitur. </s>
7993 
7994 <s>vecte autem facil&egrave; onera qu&aelig;libet <expan abbr="obui&atilde;tia">obuiantia</expan> diuelluntur. <lb/></s>
7995 
7996 <s>qui duo vectes vnicum habent hypomoclion ip&longs;am &longs;cilicet connexionem <lb/><figure place="text" xlink:href="figures-la/009.01.185.1.tif"/><lb/>A. vectes &longs;unt bin&aelig; in&longs;trumenti ha&longs;t&aelig;, F A D, <lb/>E A C. <expan abbr="dilat&atilde;do">dilatando</expan> igitur extrema C D, deducun&shy;<lb/>tur etiam alia extrema F, E, &amp; impo&longs;ita nuce in <lb/>hiatu K, qu&aelig;uis potentia con&longs;tringendo C, D, <lb/>con&longs;tringet &longs;imul F, E, <expan abbr="ip&longs;am&qacute;">ip&longs;amque</expan>; nucem confrin&shy;<lb/>get. </s>
7997 
7998 <s>quod igitur cum percu&longs;&longs;ione feci&longs;&longs;et pon&shy;<lb/>dus mallei, id valentiori vectium virtute efficiunt F A D, E A C. quanto au&shy;<lb/>tem locus nucis K, propinquior fuerit hypomoclio A, tanto celerius <lb/>confringitur, quia partes vectium A C, A D, tunc &agrave; centro <lb/>A, productiores fiunt, ide&longs;t mult&ograve; maiores fiunt, <lb/>qu&agrave;m &longs;int di&longs;tanti&aelig; inter nucem, &amp; cen&shy;<lb/>trum A, quod maxim&egrave; poten&shy;<lb/>tiam iuuat.</s></p><p type="main">
7999 
8000 <s>Ex quibus pr&aelig;&longs;enti qu&aelig;&longs;tioni &longs;atisfactum videtur.</s></p><pb pagenum="186"/><p type="head">
8001 
8002 <s><emph type="italics"/>QV&AElig;STIO XXIII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8003 
8004 <s><emph type="italics"/>De Rhombo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
8005 
8006 <s><arrow.to.target n="marg252"/></s></p><p type="margin">
8007 
8008 <s><margin.target id="marg252"/>262</s></p><p type="main">
8009 
8010 <s>Rhombus ex definitione 23. primi Elem. 
8011 
8012 e&longs;t figura &aelig;quilatera qui&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.186.1.tif"/><lb/>dem, &longs;ed non &aelig;quiangula, habet enim <lb/>binos oppo&longs;itos angulos acutos, &amp; alies <lb/>binos oppo&longs;itos obtu&longs;os, talis e&longs;t pr&aelig;&shy;<lb/>&longs;ens figura A B D C. <!-- KEEP S--></s>
8013 
8014 <s>In pr&aelig;&longs;enti porr&ograve; qu&aelig;&longs;tione <lb/>&longs;upponitur punctum A, quod e&longs;t vnum extremum <lb/>in rhombo moueri &longs;uper latus A B, ver&longs;us B, &amp; &longs;i&shy;<lb/>militer interim &aelig;qua velocitate moueri alterum <lb/>extremum B, &longs;uper idem latus A B_{2} ver&longs;us A, &amp; in&shy;<lb/>terim dum h&aelig;c duo puncta hoc modo &longs;ibi obuiam <lb/>procedunt, moueri latus totum A B, eadem ve&shy;<lb/>locitate, ver&longs;us latus C D, ita vt &longs;emper ip&longs;i C D, <lb/>&aelig;quidi&longs;ter, <expan abbr="de&longs;cendat&qacute;">de&longs;cendatque</expan>; per latera A C, B D, quo&shy;<lb/>u&longs;que ip&longs;i C D, congruat.</s></p><p type="main">
8015 
8016 <s>Horum igitur trium motuum quemadmodum <lb/>&aelig;qu&aelig; &longs;unt celeritates, ita etiam &longs;patia, quibus peraguntur, nam puncta duo <lb/>mouentur in latere A B, ip&longs;um ver&ograve; A B, mouetur in lateribus A C, &amp; B D, <lb/>qu&aelig; cum priori A B, &longs;unt &aelig;qualia.</s></p><p type="main">
8017 
8018 <s>Aduertendum pr&aelig;terea, quod hac ratione duo puncta A, &amp; B, duabus la&shy;<lb/>tionibus mouebuntur, &longs;i quidem proprio motu <expan abbr="mou&etilde;tur">mouentur</expan> in ip&longs;o latere A B, <lb/>&amp; quia latus A B, per quod ip&longs;a incedunt eodem tempore mouetur ver&longs;us <lb/>C D, &longs;equitur, quod etiam ip&longs;a hoc eodem motu ferantur. </s>
8019 
8020 <s>erit igitur ip&longs;o&shy;<lb/>rum motus ex his duobus mixtus; &amp; quidem ip&longs;ius A, latio erit per longio&shy;<lb/>rem diametrum A D; ip&longs;ius ver&ograve; B, per breuiorem B C. <!-- KEEP S--></s>
8021 
8022 <s>Quare cum pun&shy;<lb/>ctum A, peruenerit ad D, etiam punctum B, eadem c&ecedil;leritate acce&longs;&longs;erit ad <lb/>C. maius autem e&longs;t &longs;patium A D, quod confecit A, quam &longs;patium B C, con&shy;<lb/>fectum a C. <!-- KEEP S--></s>
8023 
8024 <s>Qu&aelig;rit igitur prim&ograve;, cur c&ugrave;m A, &amp; B, mota fmt &aelig;quali celeri&shy;<lb/>rate in vtra que latione, vnum tamen maiorem lineam, qu&agrave;m alterum per&shy;<lb/>tran&longs;iuit? </s>
8025 
8026 <s>Qu&aelig;rit &longs;ecund&ograve;, cur punctum B, confecit lineam B C, qu&aelig; mi&shy;<lb/>nor e&longs;t quam ip&longs;um latus A C, quod in &longs;uo motu conficit latus A B, quando <lb/>ad D C, acce&longs;&longs;it. </s>
8027 
8028 <s>&amp; tamen B, duplici fertur latione; A B, ver&ograve; vnica; vtrun&shy;<lb/>que autem in &aelig;quali velocitate? </s>
8029 
8030 <s>Quod autem punctus A, motu illo de&longs;eri&shy;<lb/>bat lineam A D, punctus ver&ograve; B. lineam B C, manife&longs;tum erit hoc modo. </s>
8031 
8032 <s>&longs;it <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->punctum A, motu proprio delatum, <expan abbr="v&longs;q;">v&longs;que</expan> ad punctum E, medium late&shy;<lb/>ris A B, erit interim totum latus A B, tran&longs;latum vbi e&longs;t F G, hoc e&longs;t, ad &longs;ui <lb/>itineris dimidium, quia horum motus ponuntur &aelig;quales: hoc autem motu <lb/>ip&longs;um punctum A, erit nece&longs;&longs;ari&ograve; in K, hoc e&longs;t in linea A D, vt dicebamus. <lb/></s>
8033 
8034 
8035 
8036 
8037 
8038 <s>Similiter in fine <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> motus, A, erit in B, proprio motu, &longs;ed alieno in D, <lb/>extremo &longs;cilicet line&aelig; A D. &longs;imili ratione o&longs;tendi pote&longs;t de ip&longs;o B, qui cum <lb/>&aelig;qua velocitate moueatur, ac punctum A, quando A erit in E; B, pariter <lb/>illi occurret in E, proprio motu: &longs;ed alieno &agrave; latere B A, proueniente erit <pb pagenum="187"/>in K, vbi etiam ob alterum motum erit A: erit igitur B, in linea B C, vt vo&shy;<lb/>lebamus. </s>
8039 
8040 <s>&agrave; quo po&longs;tea di&longs;cedens ver&longs;us C, motu pariter compo&longs;ito &longs;i&longs;titur <lb/>tandem in C, extremo line&aelig; pariter B C. eodem ergo tempore duo rhombi <lb/>extrema puncta &aelig;qu&egrave; velocia, &longs;ecundum <expan abbr="vtramq;">vtramque</expan> lationem mota, interual&shy;<lb/>la nequaquam &aelig;qualia confecerunt, &longs;ed A, maius, nimirum A D; B, ver&ograve; <lb/>minus nimirum B C.<!-- KEEP S--></s></p><p type="main">
8041 
8042 <s>Ex quibus etiam &longs;ecund&aelig; qu&aelig;&longs;tionis explicatio, &amp; dubitandi ratio pate&shy;<lb/>bit: nam cum in rhombo duo &longs;int obtu&longs;i anguli B, &amp; C, &amp; duo acuti A, &amp; D, <lb/>punctus ille, qui ab obtu&longs;o angulo B, recedit, fertur duabus lationibus inui&shy;<lb/>cem fer&egrave; contrarijs, propria enim tendit &longs;ur&longs;um ad A, aliena ver&ograve; deor&longs;um <lb/>trahitur ver&longs;us D; cau&longs;a huius contrarietatis &longs;unt line&aelig; D B, B A, obtu&longs;um <lb/>angulum continentes, qu&aelig; &agrave; pr&aelig;dicto angulo in contrarias partes &longs;eparan&shy;<lb/>tur: per has autem lineas fiunt pr&aelig;dicti motus, vnde ip&longs;i quoque contrarij <lb/>&longs;int nece&longs;&longs;e e&longs;t: &amp; propterea &longs;e mutu&ograve; impediunt: <expan abbr="atq;">atque</expan> hinc nece&longs;&longs;e e&longs;t pun&shy;<lb/>ctum B, motu compofito hinc inhibito minus interuallum B C, pertran&longs;ire. <lb/></s>
8043 
8044 <s>At ver&ograve; punctum A, quia ab acuto angulo de&longs;cendit, <expan abbr="vtraq;">vtraque</expan> latione fertur <lb/>deor&longs;um, qu&aelig; lationes &longs;e mutu&ograve; iuuant, <expan abbr="faciunt&qacute;">faciuntque</expan>; vt A, maius, quamuis eo&shy;<lb/>dem tempore, &amp; eadem celeritate peragret &longs;patium A D. nam punctum A, <lb/>&longs;ua &longs;pont&egrave; <expan abbr="de&longs;c&etilde;dit">de&longs;cendit</expan> per latus A B, &amp; ab ip&longs;o latere A B, quod fertur ad C D, <lb/>pariter deor&longs;um vehitur. </s>
8045 
8046 <s>nihil igitur mirum fit, &longs;i A, maius <expan abbr="interuall&utilde;">interuallum</expan> A D, <lb/>quam B C, percurrat. </s>
8047 
8048 <s>cau&longs;a ver&ograve; huius motuum concordi&aelig; e&longs;t angulus acu&shy;<lb/>tus A, ob quem latera rhombi magis inuicem approximantur, redduntque <lb/>longiorem A D, qu&agrave;m B C: &egrave; contrari&ograve; autem, quo obtu&longs;iores &longs;unt anguli <lb/>B, C, minorem faciunt ip&longs;am B C, latera enim &longs;emper magis ad rectam li&shy;<lb/>neam accedunt; donec tandem omni angulo euane&longs;cente in directum con&shy;<lb/>&longs;tituantur; quo ca&longs;u congruerent cum linea A D, <expan abbr="rhombus&qacute;">rhombusque</expan>; ip&longs;e amplius <lb/>nullus e&longs;&longs;et.</s></p><p type="main">
8049 
8050 <s>Ex his igitur &longs;equitur, quod punctum A, ab angulo A, acuto di&longs;cedens, <lb/>duobus feratur motibus &longs;imilibus ad eandem partem tendentibus, &amp; qu&ograve; <lb/>acutiores &longs;unt anguli, e&ograve; magis tendent ad eandem partem; &amp; melius &longs;e <lb/>mutu&ograve; inuabunt. </s>
8051 
8052 <s>B, autem vice ver&longs;a, quoniam quanto obtu&longs;ior e&longs;t angulus <lb/>B, tanto magis latera illius diuaricantur; du&aelig; etiam motiones, quibus B, <lb/>progreditur in diuer&longs;as partes tendent; fiunt enim per illa latera; &amp; tanto <lb/>etiam magis &longs;ibi contrari&aelig; erunt; <expan abbr="magis&qacute;">magisque</expan>; &longs;ibi mutu&ograve; impedimento erunt. <lb/></s>
8053 
8054 <s>&amp; propterea punctum B, minus interuallum, quale e&longs;t B C, percurret, quan&shy;<lb/>do A, maius A D, percurrit.</s></p><p type="main">
8055 
8056 <s>Ad &longs;ecundam ver&ograve; qu&aelig;&longs;tionis partem, re&longs;pondeo con&longs;iderandum e&longs;&longs;e <lb/>latus B A, moueri vnico motu ad D C, quare &agrave; nullo impedi&shy;<lb/>tur, vnde nihil mirum videri debet, qu&ograve;d ip&longs;um vnica <lb/>latione maius conficiat &longs;pacium qu&agrave;m B, quod <lb/>quamuis duplici pellatur motu, vnus <lb/>tamen ab altero inhibetur.</s></p><pb pagenum="188"/><p type="head">
8057 
8058 <s><emph type="italics"/>QV&AElig;STIO XXIIII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8059 
8060 <s><emph type="italics"/>De duobus circulis.<emph.end type="italics"/></s></p><p type="main">
8061 
8062 <s><arrow.to.target n="marg253"/></s></p><p type="margin">
8063 
8064 <s><margin.target id="marg253"/>263</s></p><p type="main">
8065 
8066 <s>Vnde e&longs;t, quod &longs;i duo circuli, vnus altero maior, cirea idem cen&shy;<lb/>trum po&longs;iti, volutentur, ita vt etiam centrum feratur, eo &longs;cilicet <lb/>modo, quo plau&longs;trorum rot&aelig; &longs;olent, &longs;ecundum &aelig;qualem lineam <lb/>conuoluuntur, &longs;iue &aelig;quale &longs;patium conficiunt: &longs;i ver&ograve; &longs;eor&longs;um <lb/>&longs;eparati quilibet eodem modo volutetur, non &aelig;quale <expan abbr="&longs;pati&utilde;">&longs;patium</expan> pertran&longs;ibunt, <lb/>&longs;ed maior maiorem lineam, qu&agrave;m minor; <expan abbr="id&qacute;">idque</expan>; ea proportione, quam inui&shy;<lb/>cem eorum circunferenti&aelig; obtinent, cum in hac veluti rot&aelig; conuolutione, <lb/>circunferentia tota &longs;ucce&longs;&longs;iu&egrave; decur&longs;o &longs;patio adaptetur, ita vt tanta &longs;it de&shy;<lb/>cur&longs;a linea, quanta e&longs;t rot&aelig; circunferentia? </s>
8067 
8068 <s>Quin etiam eodem exi&longs;tente <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> centro, aliquando confectum &longs;patium ab <expan abbr="vtroq;">vtroque</expan> tantum e&longs;t, quan&shy;<lb/>tum minor circulus &longs;olus, &longs;ecundum &longs;uam periph&aelig;riam reuolutus perfeci&longs;&shy;<lb/>&longs;et; <expan abbr="quando&qacute;">quandoque</expan>; ver&ograve; quantum maior &longs;olus ab&longs;olui&longs;&longs;et. </s>
8069 
8070 <s>Quod autem maior <lb/>&longs;olus in &longs;ua reuolutione maiorem lineam de&longs;cribat, manife&longs;tum e&longs;t hinc, <lb/>quia &longs;en&longs;u patet maiorem circunferentiam in maiori circulo &longs;ubtendere <lb/>angulum, qui fit &agrave; diametris in centro; minorem ver&ograve; circunferentiam <lb/>&longs;ubtendere eundem angulum in minori orbe, vt etiam in 8. qu&aelig;&longs;t. </s>
8071 
8072 <s><expan abbr="dict&utilde;">dictum</expan> e&longs;t: <lb/>eandem igitur, vt proxim&egrave; dixi habebunt etiam proportionem ill&aelig; line&aelig;, <lb/>qu&aelig; &agrave; &longs;ingulis &longs;eor&longs;um orbibus reuolutis de&longs;ignabuntur. </s>
8073 
8074 <s>Quod pr&aelig;terea &longs;e&shy;<lb/>cundum &aelig;qualem conuoluuntur, quando circa idem po&longs;iti fuerint centrum, <lb/>manife&longs;tum e&longs;t, ita tamen, vt aliquando amb&aelig; &aelig;quales &longs;int ei, &longs;ecundum <lb/>quam &longs;olus maior conuolueretur; aliquando ver&ograve; &longs;ecundum quam minor. <lb/><figure place="text" xlink:href="figures-la/009.01.188.1.tif"/><lb/>&longs;it enim circulus maior quidem vbi <lb/>D F C, minor ver&ograve; vbi E G B, <expan abbr="vtriq;">vtrique</expan> <lb/>autem centrum A, linea, &longs;ecundum <lb/>quam quadrans F C, maioris per &longs;e <lb/>rotaretur, &longs;it F L. linea ver&ograve;, &longs;ecun&shy;<lb/>dum quam <expan abbr="quadr&atilde;s">quadrans</expan> G B, minoris &longs;e&shy;<lb/>iuncti &agrave; maiori, volutaretur &longs;it G K, <lb/>qu&aelig; &aelig;qualis e&longs;t dicto quadranti G B, <lb/>&longs;icut etiam F I, &aelig;qualis e&longs;t quadran&shy;<lb/>ti F C. &longs;i quis igitur impellat mino&shy;<lb/>rem orbem mouens &longs;imul commune <lb/>centrum A, cui maior e&longs;t circumpo&shy;<lb/>&longs;itus, donec diameter A B, perpendicularis &longs;it line&aelig; G K, in puncto K. tunc <lb/>pariter diameter maioris A C, erit perpendicularis line&aelig; F L, in puncto L. <lb/><!-- KEEP S--></s>
8075 
8076 <s>G K, autem, &amp; F L, nece&longs;&longs;ari&ograve; erunt &aelig;quales per 34. primi, &aelig;quales igitur <lb/>lineas hoc modo peragrarunt in&aelig;quales circunferenti&aelig;, &longs;iue quadrantes <lb/>G B, F C. &longs;i autem quadrantes hoc pr&aelig;&longs;tant, manife&longs;tum e&longs;t, quod &amp; toti <lb/>ambitus idem efficiunt, quare quando tota periph&aelig;ria G B E G, fuerit re&shy;<lb/>uoluta etiam tota F C D F, &longs;uum orbem <expan abbr="complet&utilde;">completum</expan> habebit. </s>
8077 
8078 <s>&longs;imiliter &longs;i ma&shy;<lb/>iorem quis mouerit, cui minor &longs;it annexus eodem exi&longs;tente centro, &longs;imul ac <pb pagenum="189"/>diameter A C, erit perpendicularis ad F I, in puncto I, erit etiam A B, per&shy;<lb/>pendicularis ip&longs;i G M, in M; &longs;unt autem G M, &amp; F I, &aelig;quales, quare quan&shy;<lb/>do F C, quadrans maioris pertran&longs;iuerit rectam F C, etiam C B, quadrans <lb/>minoris tran&longs;actam habebit illi parem G M. hoc autem accidit nulla inter&shy;<lb/>cedente mora in vllo ip&longs;orum: quando enim mouetur maior, nihil ce&longs;&longs;at <lb/>minor: &amp; quando minor agitur, maior nunquam quie&longs;cit. </s>
8079 
8080 <s>quod &longs;i hoc acci&shy;<lb/>dit quart&aelig; parti circulorum, idem, &amp; totis accidit periph&aelig;rijs. </s>
8081 
8082 <s>vbi in&longs;uper <lb/>illud etiam mirum, centrum nimirum ip&longs;orum eadem celeritate motum, <lb/>ac vnica &longs;emper exi&longs;tenti latione, modo maius, modo minus &longs;patium per&shy;<lb/>ficere; idem ver&ograve; eadem velocitate latum, &aelig;quale &longs;emper deberet interual&shy;<lb/>lum tran&longs;ilire. </s>
8083 
8084 <s>&amp; tamen in pr&aelig;&longs;entia vtrouis modo moueas eadem pernici&shy;<lb/>tate, mod&ograve; maius, mod&ograve; minus &longs;patium pertran&longs;ibit.</s></p><p type="main">
8085 
8086 <s>Huius qu&aelig;&longs;tionis enodand&aelig; cau&longs;a, &longs;upponendum prim&ograve; e&longs;t, quod eadem, <lb/>&longs;eu &aelig;qualis potentia, hanc quidem magnitudinem tardius, illam ver&ograve; citius <lb/>mouere pote&longs;t. </s>
8087 
8088 <s>&longs;i enim fuerit quippiam, quod &agrave; &longs;eip&longs;o moueri minim&egrave; ap&shy;<lb/>tum &longs;it; &amp; aliud, quod &agrave; &longs;e ip&longs;o moueri aptum &longs;it; qui hoc &longs;imul cum illo <lb/>coniunctum mouerit, tardius mouebit, qu&agrave;m &longs;i ip&longs;um &longs;olum moueret. </s>
8089 
8090 <s>&amp; &longs;i <lb/>quid moueatur, quod aptum &longs;it ex &longs;e moueri, verumtamen in eo motu nihil <lb/>ex &longs;e moueatur, perinde e&longs;t, ac &longs;i minim&egrave; aptum &longs;it ad motum, &amp; proinde <lb/>tardius mouebitur; nec fieri poterit, vt plu&longs;quam mouens moueatur, cum <lb/>nihil innata motione vtatur. </s>
8091 
8092 <s>Si quis igitur minorem circulum, quem mo&shy;<lb/>do B, appello, mouerit &longs;upra &longs;uam circunferentiam, cui annexus &longs;it maior, <lb/>quem modo appello A, &longs;ic quidem maior mouebitur, non autem ex &longs;e, &longs;ed <lb/>&longs;olum quatenus &agrave; minori feretur, vnde tantum pertran&longs;ibit de recta F L, <lb/>quantum &agrave; minori fuerit impul&longs;us; tantum autem e&longs;t impul&longs;us, quantum <lb/>minor e&longs;t motus; quare &aelig;qualem cum illo viam confecit. </s>
8093 
8094 <s>&longs;i igitur minor fe&shy;<lb/>cit pedalem G K, maior confecit etiam pedalem F L, quia maior nihil de <lb/>proprio motu addidit, &longs;ed &longs;olum motione minoris e&longs;t tran&longs;latus. </s>
8095 
8096 <s>&longs;imiliter <lb/>&longs;i quis rotet maiorem &longs;upra &longs;uam circunferentiam annexo minori, tantum <lb/>minor mouebitur, quantum &agrave; maiori deportabitur, quia nihil ex &longs;e impel&shy;<lb/>litur. </s>
8097 
8098 <s>Verum &longs;i &longs;eor&longs;um ambo ex &longs;e &longs;ecundum &longs;uos ambitus moueantur, &longs;iue <lb/>cit&ograve;, &longs;iue tard&egrave;, eadem etiam velocitate perficiant integram &longs;u&aelig; periph&aelig;&shy;<lb/>ri&aelig; volutationem, maior maius, minor ver&ograve; minus conficiet &longs;patium.</s></p><p type="main">
8099 
8100 <s>Sed fort&egrave; augebitur difficultas con&longs;ideranti, quod pr&aelig;dicti circuli &longs;unz <lb/>circa idem centrum, &amp; circa illud mouentur. </s>
8101 
8102 <s>moueri autem circulum cir&shy;<lb/>ca &longs;uum centrum, e&longs;t moueri &longs;ecundum &longs;uum naturalem motum, ad quem <lb/>circuli ex &longs;e &longs;unt apti. </s>
8103 
8104 <s>&longs;i ver&ograve; vnus moueretur circa &longs;uum centrum, alter ve&shy;<lb/>r&ograve; non, vt quando alter alteri non e&longs;t circa idem centrum compactus, &amp; ab <lb/>altero mouetur, vbi manife&longs;t&egrave; apparet, quod fertur omnin&ograve; ab illo, &amp; in il&shy;<lb/>la latione non circumuertitur circa proprium centrum, quare tunc minim&egrave; <lb/>mirum e&longs;t, &longs;i <expan abbr="neq;">neque</expan> plus, <expan abbr="neq;">neque</expan> minus &longs;patium conficiat, qu&agrave;m ab altero de&shy;<lb/>portetur, cui quoquo modo adiacet, aut appen&longs;us e&longs;t extra illius centrum.</s></p><p type="main">
8105 
8106 <s>Huic obiectioni <expan abbr="re&longs;pond&etilde;dum">re&longs;pondendum</expan> e&longs;t, quod quamuis pr&aelig;dicti orbes &longs;int con&shy;<lb/>centrici, nihilominus non mouentur ambo &longs;uamet motione, &longs;ed ille, qui ab <lb/>alio fertur mouetur &longs;ecundum motionem illam, tanquam &longs;i nullam ad eam <lb/>haberet aptitudinem; quamuis enim po&longs;lit moueri circa centrum illud A, <pb pagenum="190"/>propria natura, in pr&aelig;&longs;enti tamen ca&longs;u minim&egrave; vtitur illa aptitudine; &amp; <lb/>propterea motus debet moueri, quantum mouens, nec plus, nec minus.</s></p><p type="main">
8107 
8108 <s>Qu&ograve;d autem &longs;pectat ad id, quod initio dicebatur de eodem centro, &amp; de <lb/>mouente eadem velocitate, &amp; de &aelig;quali ab in&aelig;qualibus orbibus pertran&longs;i&shy;<lb/>ta linea, &longs;ubeft huic dubitationi paralogi&longs;mus: quamuis enim &longs;it idem am&shy;<lb/>borum centrum, e&longs;t tamen vnius centrum per &longs;e in motione, alteri ver&ograve; per <lb/>accidens, veluti per accidens e&longs;t eundem virum e&longs;&longs;e mu&longs;icum, &amp; album. </s>
8109 
8110 <s>ille <lb/>enim circulus, qui mouet alterum, obtinet illud centrum per &longs;e, &amp; ex natu&shy;<lb/>ra &longs;ua; alter ver&ograve;, qui mouetur, habet illud idem per accidens, quia non <lb/>vtitur illo tanquam centro. </s>
8111 
8112 <s>non igitur circa idem &longs;impliciter centrum fit <lb/>horum motus, &longs;ed alio modo vnus, alio modo alter, vnde &amp; reliquis dubi&shy;<lb/>tationibus facil&egrave; &longs;atisfiet.</s></p><p type="head">
8113 
8114 <s><emph type="italics"/>QV&AElig;STIO XXV.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8115 
8116 <s><emph type="italics"/>De Lecto<emph.end type="italics"/></s></p><p type="main">
8117 
8118 <s><arrow.to.target n="marg254"/></s></p><p type="margin">
8119 
8120 <s><margin.target id="marg254"/>264</s></p><p type="main">
8121 
8122 <s>Cvr lectulorum &longs;pondas faciunt &longs;ecundum duplam proportionem, <lb/>hoc e&longs;t longiorem &longs;pondam duplo longiorem, qu&agrave;m &longs;it altera: il&shy;<lb/>lam enim &longs;ex pedum, vel paul&ograve; plus, hanc ver&ograve; trium? </s>
8123 
8124 <s>pr&aelig;terea <lb/>cur re&longs;tes, quibus culcitr&aelig; &longs;u&longs;tinentur non extendunt per diame&shy;<lb/>trum, &longs;ed per tran&longs;uer&longs;um?</s></p><p type="main">
8125 
8126 <s>Ad primum re&longs;pondetur ide&ograve; facere &longs;pondas in dup la ratione, vt &longs;int hu&shy;<lb/>mano corpori proportionat&aelig;, &longs;ic enim lecti longitudinem habebunt qua&shy;<lb/>tuor cubitorum, latitudinem ver&ograve; duorum, in tali enim &longs;patio commo&shy;<lb/>d&egrave; cubamus.</s></p><p type="main">
8127 
8128 <s>Ad &longs;ecundum ver&ograve; dicendum extendi illos funes non per diametrum, &longs;ed <lb/>ex oppo&longs;ito, quia hoc modo ligna ip&longs;ius lecti minus di&longs;trahuntur: facil&egrave; <lb/>enim ex natura &longs;ua ligna h&aelig;c ab inuicem &longs;ecundum longum &longs;eparantur; ar&shy;<lb/>ctius autem ductis funibus per tran&longs;uer&longs;um, qu&agrave;m per diametrum inuicem <lb/>con&longs;tringuntur: pr&aelig;terea, quia &longs;ic etiam funes minus laborant, cum &longs;int eo&shy;<lb/>rum ductus breuiores; &amp; quia debent &longs;u&longs;tinere onus ftragulorum, <expan abbr="atq;">atque</expan> cul&shy;<lb/>c&igrave;trarum, &longs;ic cert&egrave; ex hoc onere minus laborabunt &longs;i tran&longs;uer&longs;im, qu&agrave;m &longs;i <lb/>diametraliter &longs;ubtendantur.</s></p><p type="main">
8129 
8130 <s>Tertia demum ratio e&longs;t, quia hac ratione minus re&longs;tium ab&longs;umitur, qu&aelig; <lb/><figure place="text" xlink:href="figures-la/009.01.190.1.tif"/><lb/>vt ben&egrave; intelligatur, de&longs;eriba&shy;<lb/>tur lectuli figura A F G K, &amp; <lb/>bifariam diuidatur latus F G, <lb/>in B. &amp; quia tota F G, dupla <lb/>e&longs;t ip&longs;ius A F, erit dimidium <lb/>F B, &aelig;quale ip&longs;i A F. &amp; propte&shy;<lb/>rea tot erunt foramina, quibus <lb/>funes immittuntur in F B, quot <lb/>in A F. <expan abbr="ext&etilde;dunt">extendunt</expan> autem funem <lb/>hoc modo incipiunt ab A, &amp; <lb/>ducunt ad B, po&longs;tea per C, re&shy;<pb pagenum="191"/>nertuntur ad D; hinc flectunt per H, v&longs;que ad E, &amp; per G, angulum iterum <lb/>de&longs;cendunt ad M, &agrave; quo recta tendunt in F, hinc per 2. deducunt ad 3. &agrave; quo <lb/>foramine, per foramen 4. reflexum faciunt ad 5. &agrave; quo iterum per B, de&longs;cen&shy;<lb/>dunt ad angulum K, <expan abbr="ibi&qacute;">ibique</expan>; alterum funis extremum de&longs;init: <expan abbr="hoc&qacute;">hocque</expan>; modo duo <lb/>anguli A, &amp; K, re&longs;tis habent capita, &amp; re&longs;tes exten&longs;&aelig; &longs;unt non diametrali&shy;<lb/>ter, &longs;ed tran&longs;uer&longs;im.</s></p><p type="main">
8131 
8132 <s>Notandum autem, quod re&longs;tes &aelig;quales &longs;unt cum &longs;uis curuaturis. </s>
8133 
8134 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->re&shy;<lb/>&longs;tis A B, cum &longs;ua curuatura B C, &aelig;qualis e&longs;t re&longs;ti C D, vn&agrave; cum eius curua&shy;<lb/>tura D H, &amp; ali&aelig; eodem modo &longs;e habent, quia eadem demon&longs;tratio omni&shy;<lb/>bus accommodari pote&longs;t: quia enim figura A B G M, parallelogrammum <lb/>e&longs;t, &aelig;qualia enim &longs;unt latera B G, A M, &amp; quot foramina &longs;unt in vno, tot <lb/>etiam &longs;unt in altero, <expan abbr="ea&qacute;">eaque</expan>; inuicem &aelig;quidi&longs;tant, &longs;equitur omnes re&longs;tes e&longs;&longs;e <lb/>parallelas, &amp; &aelig;quales, per 33, primi. </s>
8135 
8136 
8137 
8138 
8139 
8140 <s>ex qua etiam &longs;cquitur pr&aelig;dictas cu&shy;<lb/>ruaturas, B C, D H, E G, e&longs;&longs;e &aelig;quales. </s>
8141 
8142 <s>quare manife&longs;tum e&longs;t in dimidio le&shy;<lb/>ctulo tot e&longs;&longs;e re&longs;tes &aelig;quales re&longs;ti A B, quot &longs;unt foramina in dimidio latere <lb/>B G, vel in dimidio F B, hoc e&longs;t e&longs;&longs;e quatuor. </s>
8143 
8144 <s>porr&ograve; oportet quantitatem <lb/>harum omnium re&longs;tium per&longs;crutari, vt eam cum quantitate re&longs;tium diame&shy;<lb/>traliter exten&longs;arum conferamus, quod geometric&egrave; hoc modo a&longs;&longs;eque mur: <lb/>triangulum enim B G K, rectangulum e&longs;t, erg&ograve; per 47. primi, quadrata la&shy;<lb/>terum B G, G K, &aelig;qualia &longs;unt quadrato line&aelig; B K: latus B G, e&longs;t trium pe&shy;<lb/>dum, quemadmodum etiam latus G K quadratus autem numerus ternarij <lb/>e&longs;t 9. ergo duo quadrati numeri 9. &longs;iue 18. &aelig;quales &longs;unt quadrato line&aelig; B K, <lb/>erg&ograve; linea B K, e&longs;t radix quadrata numeri 18. qu&aelig; radix non pote&longs;t exact&egrave; <lb/>in numeris repr&aelig;&longs;entari, e&longs;t enim, vt aiunt, radix &longs;urda. </s>
8145 
8146 <s>verumtamen per <lb/>radicum extractionem, <expan abbr="atq;">atque</expan> approximationem ea poni pote&longs;t e&longs;&longs;e 41/4. ide&longs;t <lb/>quatuor pedum cum vna quarta. </s>
8147 
8148 <s>cum igitur in toto lecto &longs;int huiu&longs;modi <lb/>octo re&longs;tes, erit omnium &longs;umma pedum 34. fer&egrave;. </s>
8149 
8150 <s>&longs;i autem &longs;eeundum diame&shy;<lb/>trum extendantur re&longs;tes, vti factum e&longs;t in lectulo A B C D, neutiquam re&shy;<lb/>&longs;tes omnes &longs;imul &longs;uperiori quantitati ad&aelig;quabuntur, &longs;ed illam long&egrave; &longs;upe&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.191.1.tif"/><lb/>rabunt. </s>
8151 
8152 <s>Sit igitur lectus A B&shy;<lb/>C D, in quo diametraliter du&shy;<lb/>ct&aelig; &longs;int re&longs;tes B D, E H, &amp; re&shy;<lb/>liqu&aelig;, vt in figura. </s>
8153 
8154 <s>har&ucirc; quan&shy;<lb/>titas &longs;i per 47. primi, &amp; per ra&shy;<lb/>dicis quadrat&aelig; extractionem <lb/>inueniatur, erit &longs;umma earum <lb/>pedum quadraginta cum dimi&shy;<lb/>dio; qu&aelig; quantitas pr&aelig;cedenti <lb/>maior e&longs;t &longs;ex pedibus cum di&shy;<lb/>midio.</s></p><p type="main">
8155 
8156 <s><expan abbr="Atq;">Atque</expan> hic e&longs;t &longs;en&longs;us Ari&longs;t. 
8157 
8158 quamuis tex. <!-- REMOVE S-->ip&longs;ius propter nimiam tam in gr&aelig;&shy;<lb/>cis, qu&agrave;m in latinis codicibus corruptionem, totus re&longs;titui nequiuerit.</s>
8159 
8160 </p><pb pagenum="192"/><p type="head">
8161 
8162 <s><emph type="italics"/>QV&AElig;STIO XXVI.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8163 
8164 <s><emph type="italics"/>De ligno humeris gestato.<emph.end type="italics"/></s></p><p type="main">
8165 
8166 <s><arrow.to.target n="marg255"/></s></p><p type="margin">
8167 
8168 <s><margin.target id="marg255"/>265</s></p><p type="main">
8169 
8170 <s>Cvr difficilius e&longs;t <expan abbr="l&otilde;ga">longa</expan> ligna ab extremo &longs;uper humeros ferre, qu&agrave;m <lb/>&longs;ecundum medium, c&ugrave;m tamen <expan abbr="vtroq;">vtroque</expan> modo &longs;it &longs;emper idem pon&shy;<lb/>dus? </s>
8171 
8172 <s>An quia dum fertur lignum &longs;uper humeros ab altero extre&shy;<lb/>mo, alterum extremum vibratur, &amp; agitatur, qu&aelig; agitario ip&longs;ius <lb/>lationem impedit? </s>
8173 
8174 <s>An quia licet nihil inflectatur ob agitationem, <expan abbr="neq;">neque</expan> ma&shy;<lb/>gnam habeat longitudinem, difficilius tamen ab extremo fertur, quoniam <lb/>facilius ex medio eleuatur, qu&agrave;m ab extremo, &amp; quia latio e&longs;t qua&longs;i qu&aelig;&shy;<lb/>dam continua eleuatio, propterea etiam difficilius &longs;ic portatur? </s>
8175 
8176 <s>cau&longs;a au&shy;<lb/>tem cur facilius ex medio eleuetur e&longs;t, quia hoc modo totum lignum fit ve&shy;<lb/>ctis, cuius hypomoclion e&longs;t in medio, vbi is, qui eleuat, tenet aut fert: ex&shy;<lb/>trema autem &longs;ibi mutu&ograve; <expan abbr="&aelig;queponder&atilde;t">&aelig;queponderant</expan>, ita vt <expan abbr="ab&longs;q;">ab&longs;que</expan> vllo alio auxilio, &acirc; tan&shy;<lb/>ta vi, quantum e&longs;t totum ligni pondus &longs;u&longs;tineatur; quod &longs;i ab extremo ele&shy;<lb/>uetur non &longs;ufficit amplius pr&aelig;dicta vis, &longs;ed opus erit maiori, quia non &longs;o&shy;<lb/>lum oportebit illud eleuare, &longs;ed pr&aelig;terea etiam illud in &aelig;quihbrio con&longs;ti&shy;<lb/>tuere, &amp; con&longs;eruare. </s>
8177 
8178 <s>pondus enim totius ligni vergit fer&egrave; ad alteram ligni <lb/>medietatem, qu&aelig; ab hypomoclio productior cuadit, quapropter ad onus <lb/>i&longs;tud &aelig;quilibrandum, opus e&longs;t alia potentia in altero extremo. </s>
8179 
8180 <s>&longs;it lignum <lb/><figure place="text" xlink:href="figures-la/009.01.192.1.tif"/><lb/>A B, &longs;u&longs;pen&longs;um ex medio C. <lb/>hoc modo lignum ponderi&shy;<lb/>bus libratum &longs;uis manet in <lb/>&aelig;quilibrio, pote&longs;tque &agrave; &longs;ola <lb/>potentia illud eleuante etiam deferri: quia A, &amp; B, extrema &longs;e mutu&ograve; &longs;u&longs;ti&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.192.2.tif"/><lb/>nent. </s>
8181 
8182 <s>quod &longs;i non ex medio eleuaretur, <lb/>&longs;ed ab extremo, vt in &longs;ecunda figura, <lb/>eleuans potentia ex C, &aelig;qualis oportet, <lb/>vt &longs;it pr&aelig;cedenti; &longs;ed pr&aelig;terea opus e&longs;t <lb/>alia vi, qu&aelig; in B, &aelig;quiponderet alteri <lb/>extremo A, quod magis grauitat, quo ab C, longius fuerit; &amp; hoc modo in <lb/>&aelig;quilibrio con&longs;titutum, &amp; con&longs;eruatum poterit non &longs;olum eleuari, &longs;ed <lb/>etiam circumferri.</s></p><p type="head">
8183 
8184 <s><emph type="italics"/>QV&AElig;STIO XXVII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8185 
8186 <s><emph type="italics"/>De Gestatis &longs;uper humerum.<emph.end type="italics"/></s></p><p type="main">
8187 
8188 <s><arrow.to.target n="marg256"/></s></p><p type="margin">
8189 
8190 <s><margin.target id="marg256"/>266</s></p><p type="main">
8191 
8192 <s>Cvr &longs;i vald&egrave; procerum &longs;uerit idem pondus difficilius &longs;uper humeros <lb/>ge&longs;tatur, etiam &longs;i ex medio illud feratur, qu&agrave;m &longs;i breuius &longs;it? </s>
8193 
8194 <s>quod <lb/>enim dudum dictum e&longs;t cau&longs;a non e&longs;t, &longs;ed vibratio, &amp; &longs;uccu&longs;&longs;atio <lb/>ligni nunc e&longs;t: quando enim ab humero productius fuerit, magis <lb/>vibrantur extrema, quam ob rem contingit portantem difficilius ge&longs;tare. <lb/></s>
8195 
8196 <s>vibrationis autem cau&longs;a e&longs;t, quoniam ab eadem vi moueute magis extrema <pb pagenum="193"/>huc illuc transferuntur, quanto procerius fuerit lignum, quia tunc maior <lb/>fit di&longs;tanti&agrave; &agrave; centro, &longs;eu hypomoclio, quod modo e&longs;t humerus ip&longs;e. </s>
8197 
8198 <s>&longs;it vt <lb/>in prima pr&aelig;cedentis qu&aelig;&longs;tionis figura, humerus vbi A. di&longs;tanti&aelig; autem ab <lb/>ip&longs;o centro &longs;unt A B, A C, quod autem maior di&longs;tantia; faciliorem reddat <lb/>motum o&longs;ten&longs;um e&longs;t initio huius operis.</s></p><p type="head">
8199 
8200 <s><emph type="italics"/>QV&AElig;STIO XXVIII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8201 
8202 <s><emph type="italics"/>De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
8203 
8204 <s><arrow.to.target n="marg257"/></s></p><p type="margin">
8205 
8206 <s><margin.target id="marg257"/>267</s></p><p type="main">
8207 
8208 <s>In&longs;trumentum i&longs;tud, quod gr&aelig;ca voce Leonicus interpres Celonia vo&shy;<lb/>cat, latinis dicitur Tolleno, &agrave; tollendo; quod etiam manife&longs;tum e&longs;t <lb/>ex Fe&longs;to, qui ait, Tolleno e&longs;t genus machin&aelig;, quo hauritur aqua in al&shy;<lb/>teram partem pr&aelig;grauante pondere; qu&aelig; tollenonis de&longs;criptio om&shy;<lb/>nin&ograve; machin&aelig; pr&aelig;&longs;entis qu&aelig;&longs;tionis competit. </s>
8209 
8210 <s>Hi&longs;pani Telonam fort&egrave; a tol&shy;<lb/>lenone nuncupant. </s>
8211 
8212 <s>E&longs;t autem tolleno <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> hauriend&aelig; &egrave; puteo aqu&aelig; <lb/>idoneum, quo ru&longs;tici pa&longs;&longs;im vtuntur: <expan abbr="id&qacute;">idque</expan>; iuxta puteos &longs;tabile, ac firmum <lb/>con&longs;truunt, quale &agrave; figura &longs;equenti refertur. </s>
8213 
8214 <s>vbi puteus F, tolleno con&longs;tat <lb/><figure place="text" xlink:href="figures-la/009.01.193.1.tif"/><lb/>erecto tigno D C, &amp; tran&longs;&shy;<lb/>uer&longs;a ha&longs;ta A C B, vn&agrave; cum <lb/>fune B E, &amp; hydria E. ap&shy;<lb/>ponitur pr&aelig;terea onus &longs;a&shy;<lb/>tis graue ad <expan abbr="part&etilde;">partem</expan> A, quale <lb/>e&longs;t G. ha&longs;ta porr&ograve; A B, ve&shy;<lb/>luti vectis circa <expan abbr="p&utilde;ctum">punctum</expan> C, <lb/>tanquam hypomoclion, <lb/><expan abbr="&longs;us&qacute;">&longs;usque</expan>; <expan abbr="de&qacute;">deque</expan>; agitur, &agrave; poten&shy;<lb/>tia funem B E, trahente. <lb/></s>
8215 
8216 <s>&longs;ed iam textus exponatur.</s></p><p type="main">
8217 
8218 <s>Cur iuxta puteos tolle&shy;<lb/>nones faciunt eo, quo vi&shy;<lb/>&longs;untur modo, ligno enim <lb/>tran&longs;uer&longs;o A B, adiungunt <lb/>onus plumbi G, cum alio&shy;<lb/>quin vas ip&longs;um E, &amp; vacuum, &amp; plenum pondus habeat: cur inquam, vt fa&shy;<lb/>cilius moueant tollenonem, tollenonis oneri onus addunt G? </s>
8219 
8220 <s>An quoniam <lb/>c&ugrave;m opus hauriendi diuidatur in duo, in intingendi nimirum, &amp; &longs;ur&longs;um tra&shy;<lb/>hendi tempora: accidit quidem <expan abbr="ab&longs;q;">ab&longs;que</expan> plumbi onere facilius intingere, quia <lb/>tunc vas e&longs;t vacuum: at ver&ograve; &longs;ur&longs;um vas deinde plenum trahere, laborio&shy;<lb/>&longs;ius erit. </s>
8221 
8222 <s>&longs;i ver&ograve; addatur onus G, tunc quidem paul&ograve; difficilius intingemus, <lb/>&longs;ed tamen vas plenum po&longs;tea mult&ograve; facilius, quod opus, &amp; labor e&longs;t, &longs;ur&longs;um <lb/>educemus: oper&aelig;pretium igitur e&longs;t, onus illud plumbi, aut lapidis adiun&shy;<lb/>gere in extremo A, quia &longs;ic pondus illud tanquam qu&aelig;dam potentia vecte <lb/>A B, vtens &longs;ur&longs;um hydriam plenam rapiet, <expan abbr="hac&qacute;">hacque</expan>; ratione nos labore leua&shy;<lb/>bit, <expan abbr="totum&qacute;">totumque</expan>; hauriendi opus demi&longs;&longs;ione, <expan abbr="atq;">atque</expan> eleuatione <expan abbr="con&longs;t&atilde;s">con&longs;tans</expan>, alleuabit,</s></p><pb pagenum="194"/><p type="head">
8223 
8224 <s><emph type="italics"/>QV&AElig;STIO XXVIIII.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8225 
8226 <s><emph type="italics"/>De onere phalanga gestato.<emph.end type="italics"/></s></p><p type="main">
8227 
8228 <s><arrow.to.target n="marg258"/></s></p><p type="margin">
8229 
8230 <s><margin.target id="marg258"/>268</s></p><p type="main">
8231 
8232 <s>Cvr quando &longs;uper ligno, aut huiu&longs;modi quopiam duo portauerint <lb/>homines &aelig;quale pondus, non &longs;imiliter grauantur, ni&longs;i quando pon&shy;<lb/>dus in medio eorum fuerit; &longs;ed magis ille premitur, cui onus vici&shy;<lb/>nius fuerit? </s>
8233 
8234 <s>An quia lignum illud vectis efficitur, cuius hypomo&shy;<lb/>clion e&longs;t vbi pondus ge&longs;tatum &longs;u&longs;penditur; ge&longs;tantium autem oneri proxi&shy;<lb/>mior gerit vicem illius, quod vecte mouetur, remotior ver&ograve; e&longs;t potentia <lb/>vecte mouens. </s>
8235 
8236 <s>quanto igitur plus di&longs;tat ab hypomoclio, &longs;eu ge&longs;tato ponde&shy;<lb/>re, tanto facilius mouet, hoc e&longs;t, alterum magis deor&longs;um premit, contra&shy;<lb/>nitente nimirum ge&longs;tato onere <expan abbr="t&atilde;quam">tanquam</expan> hypomoclio. </s>
8237 
8238 <s>&longs;i autem in medio fue&shy;<lb/>rit pondus, nihilo magis alter ge&longs;tantium fit id, quod vecte mouetur, qu&agrave;m <lb/>alter; <expan abbr="neq;">neque</expan> magis mouet: &longs;ed eodem modo alter alteri fit pondus.</s></p><p type="main">
8239 
8240 <s>C&aelig;terum &longs;ciendum huiu&longs;modi lignum, quo tran&longs;uer&longs;o onera <expan abbr="deport&atilde;tur">deportantur</expan> <lb/>dici &agrave; latinis phalangam, vnde etiam verbum phalangare deducitur, quod <lb/>huiu&longs;modi ge&longs;tationem &longs;ignificat; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; Vitruuio v&longs;itatum, &amp; Afranio, qui <lb/>ait, capream vnam &longs;emilaceram quaterni &longs;imul phalangabant.</s></p><p type="head">
8241 
8242 <s><emph type="italics"/>QV&AElig;STIO XXX.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
8243 
8244 <s><emph type="italics"/>De &longs;urgente &agrave; &longs;e&szlig;ione.<emph.end type="italics"/></s></p><p type="main">
8245 
8246 <s><arrow.to.target n="marg259"/></s></p><p type="margin">
8247 
8248 <s><margin.target id="marg259"/>269</s></p><p type="main">
8249 
8250 <s>Cvm &longs;edemus, pr&aelig;cipu&egrave; &longs;i commod&egrave; &longs;edeamus, &longs;olemus duos angu&shy;<lb/>los rectos facere, vnum quidem, quem facit thorax cum femore; <lb/>alterum quem facit femur cum crure, vt in figura thorax &longs;it A B, <lb/><figure place="text" xlink:href="figures-la/009.01.194.1.tif"/><lb/>femur B C, crus C D, anguli duo recti &longs;unt B, <lb/>&amp; C. <!-- KEEP S--></s>
8251 
8252 <s>Qu&aelig;rit igitur, cur quando &longs;urgere volumus angu&shy;<lb/>los ho&longs;ce rectos in acutos commutamus, nam crus re&shy;<lb/>trahimus &longs;ub femur ad acutum angulum, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad po&longs;itio&shy;<lb/>nem C F. <expan abbr="fit&qacute;">fitque</expan>; acutus angulus B C F. &longs;imiliter thoracem <lb/>femori aptamus ad acutum angulum E B C, alioquin &longs;ur&shy;<lb/>gere non valemus? </s>
8253 
8254 
8255 
8256 
8257 
8258 <s>An quia id, quod &aelig;quale e&longs;t, quietis <lb/><expan abbr="vbiq;">vbique</expan> e&longs;t cau&longs;a, rectus autem angulus e&longs;t angulus &aelig;quali&shy;<lb/>tatis, <expan abbr="atq;">atque</expan> &longs;tationis? </s>
8259 
8260 <s><expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> enim angulis rectis con&shy;<lb/>&longs;tant, vt quadratum, vt cubus, quieti, ac &longs;tationi &longs;unt <lb/>idonea, vt propterea Pytagorei dicerent terram e&longs;&longs;e cubicam, propten ip&shy;<lb/>&longs;ius immobilitatem. </s>
8261 
8262 <s>e&longs;t autem angulus rectus, angulus &aelig;qualitatis, quia <lb/>omnes anguli recti &longs;unt inuicem &aelig;quales, vel quia linea illa, qu&aelig; angulum <lb/>rectum facit e&longs;t perpendicularis alteri line&aelig;, cui incumbit, <expan abbr="&aelig;qualiter&qacute;">&aelig;qualiterque</expan>; in <lb/><expan abbr="vtramq;">vtramque</expan> partem inclinata e&longs;t: quapropter fit, vt qu&aelig;cunque con&longs;tituta &longs;int <lb/>&longs;uper &longs;uperficiem terr&aelig; ad angulos rectos non cadant, &longs;ed racta maneant. <lb/></s>
8263 
8264 <s>pariter <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ad angulos rectos pauimento incumbunt, non &longs;olum, quia <lb/>cum illo faciant angulos rectos, &longs;ed etiam, quia &longs;imul faciunt cum &longs;uperficie <pb pagenum="195"/>terr&aelig; perpendiculum. </s>
8265 
8266 <s>An quia qui &longs;urgit fit rectus; rectus autem manens, <lb/>oporter, vt &longs;it &longs;uperficiei terr&aelig; perpendicularis. </s>
8267 
8268 <s>debet igitur e&longs;&longs;e &longs;ecundum <lb/>eandem rectitudinem, ide&longs;t caput &longs;upra thoracem, thorax ver&ograve; &longs;upra femo&shy;<lb/>ra, femora ver&ograve; &longs;upra crura in eadem rectitudine, qu&aelig; horizonti perpendi&shy;<lb/>culariter in&longs;i&longs;tat: quando autem &longs;edemus thorax, &amp; crura, non &longs;unt in ea&shy;<lb/>dem linea horizonti perpendiculariter erecta, quapropter nece&longs;&longs;e e&longs;t pedes <lb/>retrahere, caput autem reclinare, vt &longs;ic in eadem recta linea horizonti per&shy;<lb/>pendiculariter con&longs;tituantur, <expan abbr="hoc&qacute;">hocque</expan>; modo a&longs;&longs;urgere erit po&longs;&longs;ibile.</s></p><p type="main">
8269 
8270 <s><arrow.to.target n="marg260"/></s></p><p type="margin">
8271 
8272 <s><margin.target id="marg260"/>270</s></p><p type="main">
8273 
8274 <s>Reliqu&aelig; qu&aelig;&longs;tiones ad Phy&longs;icum &longs;pectant. </s>
8275 
8276 <s>In 33. aperit propriam &longs;en&shy;<lb/>tentiam de motu proiectorum.</s></p><p type="main">
8277 
8278 <s>In 35. &amp; vltima de vortice quamuis vide atur mathematicam &longs;apere, e&longs;t <lb/>tamen phy&longs;ica. </s>
8279 
8280 <s>Eius autem re&longs;olutiones tres ab Ari&longs;t. 
8281 
8282 allatas, fal&longs;as e&longs;&longs;e <lb/>&longs;u&longs;picor; experientia enim docet, quod &longs;i quippiam ponatur &longs;upra rotam <lb/>figuli, id non ad centrum, &longs;ed extra rotam proijcitur. </s>
8283 
8284 <s>&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip &longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer&shy;<lb/>gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, qu&aelig; in ip&longs;a &longs;unt, &longs;imul cum <lb/>illa ad centrum per plures conuolutiones deducantur. </s>
8285 
8286 <s>C&aelig;terum &longs;i quis ve&shy;<lb/>lit Mechanicam facultatem &longs;eri&ograve; aggredi, nequaquam paucis his ab Ari&longs;t. <lb/>traditis, <expan abbr="eis&qacute;">eisque</expan>; leui brachio pertractatis, contentus &longs;it: ver&ugrave;m Archimedem <lb/>de Aqu&aelig;ponderantibus, Commandinum, ac Lucam Valerium de centro <lb/>grauitatis &longs;olidorum, ac tandem Guidi Vbaldi Mechanica adeat, vbi hu&shy;<lb/>ius &longs;cienti&aelig; admiranda plurima, <expan abbr="ea&qacute;">eaque</expan>; firmi&longs;&longs;im&egrave; demon&longs;trata reperiet.</s></p></chap><chap><p type="head">
8287 
8288 <s><emph type="italics"/>IN LIBELLVM DE MVNDO<lb/>AD ALEXANDRVM.<emph.end type="italics"/></s></p><p type="main">
8289 
8290 <s>Cvm plures libellum hunc Ari&longs;t. 
8291 
8292 attribuant, cogor loca ip&longs;ius ma&shy;<lb/>thematica ex in&longs;tituto exponere.</s></p><p type="main">
8293 
8294 <s><arrow.to.target n="marg261"/></s></p><p type="margin">
8295 
8296 <s><margin.target id="marg261"/>271</s></p><p type="main">
8297 
8298 <s>In 2. cap. 
8299 
8300 recen&longs;et Planetarum ordinem, iuxta antiqui&longs;&longs;imorum <lb/>A&longs;tronomorum traditiones, qui ob paucas, <expan abbr="eas&qacute;">easque</expan>; imperfectas ob&shy;<lb/>&longs;eruationes muita ignorarunt, <expan abbr="atq;">atque</expan> in multis, &amp; pr&aelig;cipu&egrave; in ordine Plane&shy;<lb/>tarum &longs;tatuendo, fal&longs;i &longs;unt: A&longs;tronomi enim po&longs;teriores, &amp; maxim&egrave; Ptol&aelig;&shy;<lb/>meus, vn&agrave; cum recentioribus no&longs;tri &longs;eculi alium ordinem exactioribus ob&shy;<lb/>&longs;eruationibus, <expan abbr="atq;">atque</expan> demon&longs;trationibus a&longs;trucntes vetu&longs;ti&longs;&longs;imorum illorum <lb/>errores patefecerunt. </s>
8301 
8302 <s>E&longs;t autem verus ordo, vt Luna &longs;it omnium terris pro&shy;<lb/>xima, deinde Mercurius, t&ugrave;m Venus, po&longs;tea Sol, Mars, Iupiter, <expan abbr="Saturnus&qacute;">Saturnusque</expan>; <lb/>&agrave; terris alti&longs;&longs;imus, quos omnes &longs;tellarum affixarum &longs;ph&aelig;ra, qu&aelig; etiam fir&shy;<lb/>mamentum dicitur, complectitur. </s>
8303 
8304 <s>non me latet huius no&longs;tri &longs;eculi di&shy;<lb/>ligenti&longs;&longs;imos a&longs;tronomos nouam mundani &longs;y&longs;tematis hy&shy;<lb/>pothe&longs;im inducere; &longs;ed ea pr&aelig;dicto Planctarum <lb/>ordini parum, aut nihil repugnat.</s></p><pb pagenum="196"/><p type="head">
8305 
8306 <s><emph type="italics"/>De&aelig;stu Maris.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
8307 
8308 <s><arrow.to.target n="marg262"/></s></p><p type="margin">
8309 
8310 <s><margin.target id="marg262"/>272</s></p><p type="main">
8311 
8312 <s>In 3. cap. <emph type="italics"/>(Aiunt etiam multos &aelig;stus vndarumqu&eacute; &longs;ublationes fiatis quibu&longs;&shy;<lb/>dam temporibus cum Luna circumag:)<emph.end type="italics"/> Perpaucis maris fluxum, &amp; reflu&shy;<lb/>xum attingit, qui quia ex motu pr&aelig;cipu&egrave; Lun&aelig; pender, non videtur <lb/>alienum hoc loco eum fu&longs;ius explicare, <expan abbr="atq;">atque</expan> nonnullis difficultatibus <lb/>occurrere, quibus recentiores nonnulli nimis implicautur. </s>
8313 
8314 <s>Ae&longs;tus maris <lb/>e&longs;t qu&aelig;dam maris ebullitio, ob quam vt &longs;olet in ebullientibus aquis, mare <lb/>intume&longs;cit: fiunt autem in toto mundo duobus tantum in locis ex hoc &aelig;&longs;tu <lb/>tumores duo, quorum vnus &longs;emper direct&egrave; Lun&aelig; &longs;ubiacet, alter ver&ograve; in <lb/>auer&longs;a terr&aelig; parte, &longs;iue huic antipoda, &amp; diametraliter oppo&longs;ita.</s></p><p type="main">
8315 
8316 <s>Ex his Marium tumoribus fit vt aqu&oelig;, qu&aelig; natur&aelig; &longs;ua decliuiora petunt, <lb/>qua&longs;i exundantes ad littora flaant. </s>
8317 
8318 <s>atque hic aquarum cur&longs;us fluxus maris <lb/>appellatur. </s>
8319 
8320 <s>decre&longs;cente deinde maris &aelig;&longs;tu, &amp; tumore ex rece&longs;&longs;u Lun&aelig;, aqu&aelig; <lb/>iterum ad medium mare refluunt: <expan abbr="atq;">atque</expan> hic maris refluxus dicitur. </s>
8321 
8322 <s>Cum au&shy;<lb/>tem in toto die &longs;int 24. hor&aelig; &amp; &longs;emper &longs;int &longs;imul in mundo duo &aelig;&longs;tus, &amp; tu&shy;<lb/>mores, fit vt &longs;int pariter &longs;emper in mundo duo fluxus, qui tumores illos co&shy;<lb/>mitantur; necnon duo refluxus, qui eo&longs;dem &longs;ub&longs;equantur; hinc fit vt <expan abbr="vni-cuiq;">vni&shy;<lb/>cuique</expan> illorum &longs;ex her&aelig; <expan abbr="conueni&atilde;t">conueniant</expan>, &longs;ex fluxui, &longs;ex refluxui, qui &longs;ub Luna fiunt; <lb/>&longs;ex ver&ograve; fluxui, &amp; &longs;ex tandem refluxui Lun&aelig; auer&longs;is, qu&aelig; totam Lun&aelig; circa <lb/>mundum periodum 25. horarum expleant. </s>
8323 
8324 <s>Cau&longs;am autem cur mare hoc <lb/>modo &longs;tatis horis, paul&ograve; tamen &longs;erius ob Lun&aelig; tardiorem ortum &longs;emper <lb/>cre&longs;cat, &amp; decre&longs;cat antiqui omnes in Lunam retulerunt, vt primus omnium <lb/>Ari&longs;t. 
8325 
8326 hoc loco, deinde Strabo, Pomponius Mela, Plinius, Solinus, &amp; alij <lb/>plures idem &longs;en&longs;erunt. </s>
8327 
8328 <s>Lunam &longs;cilicet eam habere vim in mare, vt pars il&shy;<lb/>la, qu&aelig; Lun&aelig; &longs;irbiacet, &longs;iue quam Luna radijs ferit, &aelig;ftuet, &amp; turgeat; non <lb/>aliter pars maris huic antipoda, &amp; auer&longs;a, quamuis tota terr&aelig; moles inter <lb/><figure place="text" xlink:href="figures-la/009.01.196.1.tif"/><lb/>ip&longs;am, &amp; Lunam interpona&shy;<lb/>tur, &aelig;&longs;tuat, fluxumque, ac re&shy;<lb/>fluxum quamuis priori mi&shy;<lb/>norem, efficit. </s>
8329 
8330 <s>qu&aelig; omnia <lb/>melius in figura cernentur; <lb/>vbi infra Lunam vides tumo&shy;<lb/>rem A, ex quo fluxus deriua&shy;<lb/>tur. </s>
8331 
8332 <s>&amp; in parte huic auer&longs;a <lb/>tumorem B, ex quo alter flu&shy;<lb/>xus deriuatur. </s>
8333 
8334 <s>&amp; quia in alijs <lb/>duobus mundi lateribus non <lb/><expan abbr="fi&utilde;t">fiunt</expan> huin&longs;modi tumores, im&ograve; <lb/>mare ob refrigerationem <lb/>&longs;ub&longs;idet, ibi fiunt duo reflu&shy;<lb/>xus C, &amp; D, ita vt &longs;emper &longs;int <lb/>in mari pr&aelig;&longs;ertim Oceano <lb/>quatuor pr&aelig;dicti effectus, qui <lb/>&longs;imul, vt ait hic Ari&longs;t. &amp; ex&shy;<pb pagenum="197"/>perientia te&longs;tatur, &longs;imul cum Luna circa mundum circumaguntur. </s>
8335 
8336 <s>hoe e&longs;t <lb/>&longs;i Luna, qu&aelig; modo e&longs;t in &longs;uperiori parte meridionali, venerit ad locum E, <lb/>occidentalem, eam fluxus A, &longs;uble quitur, <expan abbr="vergit&qacute;">vergitque</expan>; tumorem &longs;uum ad occi&shy;<lb/>dentem E, vnde, &amp; fluxus B, promouebitur ad orientem, ita vt punctum F, <lb/>orientalem a&longs;piciat.</s></p><p type="main">
8337 
8338 <s>Alij pr&aelig;terea duo refluxus eadem proportione promoti erunt, vbi prius <lb/>erant fluxus: qu&aelig; <expan abbr="con&longs;equ&etilde;tia">con&longs;equentia</expan> ad Lunam perpetua, manife&longs;tum e&longs;t, fignum, <lb/>ho&longs;ce fluxus, acrefluxus non aliunde qu&agrave;m &agrave; Luna manare. </s>
8339 
8340 <s>quod adhuc ma&shy;<lb/>nife&longs;tius erit, &longs;i con&longs;ideremus, quod quanto tardius quotidie Luna oritur, <lb/>tanto etiam maris &aelig;&longs;tus tardius incipit. </s>
8341 
8342 <s>Porr&ograve; vt appareat hanc e&longs;&longs;e vete&shy;<lb/>rum &longs;ententiam libet hic attexere qu&aelig;dam ex lib. 
8343 
8344 3. Strabonis, qu&aelig; ip&longs;e ex <lb/>Po&longs;&longs;idonio acceperat. </s>
8345 
8346 <s>&longs;ic. </s>
8347 
8348 <s>Oceani ver&ograve; motum ait, &longs;cilicet Po&longs;&longs;idonius, &longs;y&shy;<lb/>deris &longs;ubire circuitum, quendam quidem diurnum, quendam men&longs;truum, <lb/>quendam annuum, vt Lun&aelig; etiam contingit. </s>
8349 
8350 <s>quo etiam tempore i&longs;ta &longs;uper <lb/>horizontem a&longs;cenderit, mare terram a&longs;cendere incipit, &longs;en&longs;u te&longs;te, <expan abbr="quou&longs;q;">quou&longs;que</expan> <lb/>ad c&oelig;li medium Luna con&longs;cenderit. </s>
8351 
8352 <s>Vbi ver&ograve; declinare &longs;ydus ip&longs;um c&oelig;&shy;<lb/>perit, &longs;en&longs;im rur&longs;us &agrave; terra pelagus ad medium mare reuertitur, donec ad <lb/>occidentis painctum Luna de&longs;cenderit. </s>
8353 
8354 <s>deinde tanto eadem incon&longs;tantia <lb/>tempore manet, quanto Luna ad iplum occa&longs;um coniungitur, &amp; adhuc tan&shy;<lb/>to magis, quanto &longs;ub terram mota, &longs;ignnm ab horizonte di&longs;tet. </s>
8355 
8356 <s>po&longs;tea rur&shy;<lb/>&longs;us mare a&longs;cendere, quou&longs;que &longs;ub teliurem in medio c&oelig;li &longs;it Luna, deinde <lb/>mare &agrave; littore regredi quoad iterum Luna in orientem procedat, ac &longs;upra <lb/>horizontem eleuetur, con&longs;i&longs;ere ver&ograve; v&longs;que quo fignum &longs;upra terram eleue&shy;<lb/>tur, &amp; rur&longs;us terras mare a&longs;cendere. </s>
8357 
8358 <s>Hanc diurnam e&longs;&longs;e circuitionem a&longs;&longs;e&shy;<lb/>rit Po&longs;&longs;idonius, men&longs;truam ver&ograve;, &amp;c. </s>
8359 
8360 <s>vbi pergit explicare, qua ratione, ma&shy;<lb/>ria etiam alijs motibus men&longs;trno. </s>
8361 
8362 <s>&longs;cilicet, &amp; annuo cieantur, iuxta Lun&aelig; <lb/>periodos men&longs;truam, &amp; annuam. </s>
8363 
8364 <s>Eadem omnin&ograve; habet Plinius, &amp; alij ve&shy;<lb/>teres omnes, quos tu con&longs;ulere poteris vnde mirum videri debeat, cur re&shy;<lb/>centiores plurimi, <expan abbr="neq;">neque</expan> veterum auctoritate, <expan abbr="neq;">neque</expan> ratione, aut experientia <lb/>nixi, hanc maris affectionem, &agrave; Luna effici negarint.</s></p><p type="main">
8365 
8366 <s>Verum ip&longs;i duabus poti&longs;&longs;imum rationibus id negant.</s></p><p type="main">
8367 
8368 <s>Prima e&longs;t, quod vario admodum tempore, &amp; modo in diuer&longs;is fiant ma&shy;<lb/>ribus, &amp; in nonnullis nihil horum &aelig;&longs;tuum appareat.</s></p><p type="main">
8369 
8370 <s>Huic re&longs;pondendum e&longs;t, id ex varia marium di&longs;pofitione, tum eriam va&shy;<lb/>rio fitu, quo Lunam a&longs;piciunt prouenire. </s>
8371 
8372 <s>hoc modo videmus vario tempo&shy;<lb/>re, &amp; modo, in toto orbe effici dies, ac noctes, &aelig;&longs;tatem, &amp; hyemem; &amp; ta&shy;<lb/>men certum e&longs;t Solem i&longs;ta omnia efficere. </s>
8373 
8374 <s>Sed melius etiam huic dubita&shy;<lb/>tioni occurremus certa quadam, <expan abbr="atq;">atque</expan> omnin&ograve; explorata experientia ex ar&shy;<lb/>te Nautica de&longs;umpta. </s>
8375 
8376 <s>libri enim nautici ab&longs;que vlla dubitatione Luu&aelig; h&aelig;c <lb/>cmnia ver&egrave; a&longs;cribunt, dum qua&longs;dam regulas tradunt, eastamen pro varijs <lb/>maribus varias, quibus per &aelig;tatem Lun&aelig;, &amp; &longs;itum ip&longs;ius &longs;upra horizonteni <lb/>illius maris cert&ograve; certius horam fluxus; &amp; refluxus, im&ograve; eorum etiam ma&shy;<lb/>gnitudinem pr&aelig;uo&longs;cunt, ac pr&aelig;dicunt. </s>
8377 
8378 <s>huiu&longs;modi librum vidiego Parm&aelig;, <lb/>manu &longs;criptum, auctore Augu&longs;tino C&aelig;&longs;areo, quem ille olim Sereni&longs;s. <!-- REMOVE S-->Duci <lb/>Octauio dono dederat. </s>
8379 
8380 
8381 
8382 <s>quod &longs;i hi &aelig;&longs;tus &agrave; Luna minim&egrave; penderent, nulla ra&shy;<lb/>tione regul&aelig; ill&aelig; effici potui&longs;&longs;ent, quibus per &aelig;tatem ipfius, ac &longs;itum &longs;upra <lb/>horizontem eos pr&aelig;dicere tuto valerent.</s></p><pb pagenum="198"/><p type="main">
8383 
8384 <s>Secunda ver&ograve; ratio, qu&aelig; maxim&egrave; eos torquet e&longs;t quanam ratione &agrave; Luna <lb/>effici po&longs;&longs;it &longs;ecundus refluxus B, prim&ograve; oppo&longs;itus, cum tota terr&aelig; moles in&shy;<lb/>teriecta ob&longs;tare videatur.</s></p><p type="main">
8385 
8386 <s>Verum huic difficultati optim&egrave; ex opticis &longs;atisfacere po&longs;&longs;umus, fi dixe&shy;<lb/>rimus, &aelig;&longs;tum illum effici quidem &agrave; Luna, &amp; Sole, &longs;ed tamen per lumen ex <lb/>&longs;yderibus ad partem illam auer&longs;am reflexum; quod vt melius explicetur, &amp; <lb/>confirmetur. </s>
8387 
8388 <s>Illud prim&ograve; &longs;ciendum non &longs;olam Lunam, verumetiam Solem <lb/>ad&aelig;&longs;tum maris ciendum concurrere, quamuis primas in hoc Lun&aelig; conce&shy;<lb/>dat; experientia enim con&longs;tat maiorem fieri fluxum, quando Sol, &amp; Luna <lb/>&longs;imul &longs;unt coniuncta, vt in nouilunio accidit, quia lumina, &amp; eorum virtu&shy;<lb/>tes vnit&aelig; fortius eandem maris partem directis radijs percellunt. </s>
8389 
8390 <s>&longs;imiliter <lb/>maior fit, quando luminaria &longs;unt oppo&longs;ita, vt in plenilunio contingit, quia <lb/>tunc radij vnius directi, a&longs;&longs;ociantur cum reflexis alterius radijs, <expan abbr="hoc&qacute;">hocque</expan>; mo&shy;<lb/>do duplicati ea&longs;dem terr&aelig; partes, &amp; direct&egrave;, &amp; reflex&egrave; feriunt, vt melius in <lb/>&longs;equenti figura patebit.</s></p><p type="main">
8391 
8392 <s>Secund&ograve; pr&aelig;mittendum e&longs;t, lumen Solis, &amp; Lun&aelig; reflecti ex den&longs;is, ac per&shy;<lb/>politis corporibns, vti &longs;unt omnia &longs;ydera.</s></p><p type="main">
8393 
8394 <s>Terti&ograve;, ex opticis a&longs;&longs;umendum, &longs;i corpora plurima &longs;ph&aelig;rica lumen re&shy;<lb/>flectentia fuerinuin circulari ambitu con&longs;tituta, quemadmodum &longs;unt &longs;tell&aelig; <lb/>affix&aelig; in ambitu firmamenti collocat&aelig;, reflectere <expan abbr="plurim&utilde;">plurimum</expan> lumen ad vnum, <lb/>&amp; idem punctum, quod &longs;it inter lumen, &amp; ambitum illum; quod a&longs;&longs;umptum <lb/>manife&longs;tum e&longs;t ex Iride, vbi ex plurimis &longs;ph&aelig;ricis guttulis lumen Solis re&shy;<lb/>flectitur ad oculum; quamuis geometric&egrave;, &amp; quidem facil&egrave; &agrave; Per&longs;pectiuo <lb/>demon&longs;trari po&longs;&longs;it.</s></p><p type="main">
8395 
8396 <s>Quart&ograve;, ex opticis, dato corpore lumino&longs;o, &amp; &longs;ph&aelig;rico reflectente, &amp; <lb/>puncto quouis, ad quod po&longs;&longs;it reflecti lumen, pote&longs;t inueniri in &longs;ph&aelig;ra refle&shy;<lb/>ctente punctum reflexionis.</s></p><p type="main">
8397 
8398 <s>Quint&ograve;, quanto radij perpendiculariores incidunt, tanto maiorem <lb/>vim habere.</s></p><p type="main">
8399 
8400 <s>Sit erg&ograve; Sol, &amp; Luna &longs;imul, vt in figura <expan abbr="&longs;it&qacute;">&longs;itque</expan>; octau&aelig; &longs;ph&aelig;r&aelig; portio A B C, <lb/>cum innumeris in ea affixis &longs;yderibus. </s>
8401 
8402 <s>e&longs;&longs;e autem totum c&oelig;lum &longs;tellis pen&egrave; <lb/>infinitis, ac con&longs;tipatis refertum &longs;en&longs;ui palam fit, adhibito nouo illo, ac mi&shy;<lb/>rabili Tele&longs;copij inuento.</s></p><p type="main">
8403 
8404 <s>Iam, vt patet ex 39.5. Alhazeni, ex &longs;ingulis &longs;tellis Solis, ac Lun&aelig; lumen <lb/>reflecti pote&longs;t (ni&longs;i quid ob&longs;tet) ad partem terr&aelig; D, luminaribus auer&longs;am, <lb/>vt quarto loco &longs;uppo&longs;ui. </s>
8405 
8406 <s>&amp; pr&aelig;terea ex &longs;tellis circa B, po&longs;itis radij Solis re&shy;<lb/>percuti po&longs;&longs;unt ad eandem terr&aelig; partem D, perpendiculares, qui pr&aelig; c&aelig;te&shy;<lb/>ris maximam vim obtinent. </s>
8407 
8408 <s>quemadmodum line&aelig; in figura reflex&aelig; <expan abbr="vtcunq;">vtcunque</expan> <lb/>o&longs;tendunt, ide&ograve; a&longs;&longs;erendum e&longs;t eos, &aelig;&longs;tum D, excitare pr&aelig;cipu&egrave; po&longs;&longs;e, <expan abbr="neq;">neque</expan> <lb/>terr&aelig; quantitas Solis luci obe&longs;t, cum con&longs;tet vmbram terr&aelig; parum &longs;upra <lb/>Lun&aelig; c&oelig;lum produci. </s>
8409 
8410 <s>pote&longs;t tamen Lun&aelig; e&longs;&longs;e impedimento quoad hos ra&shy;<lb/>dios perpendiculares; &longs;ed tamen alios minus perpendiculares, &longs;eu parum <lb/>obliquos nullo modo impedire pote&longs;t, quo minus ad D, re&longs;iliant. </s>
8411 
8412 <s>qui quam&shy;<lb/>uis &longs;int minus qu&agrave;m perpendiculares efficaces, obtinent tamen non modi&shy;<lb/>cam vim. </s>
8413 
8414 <s>Ex &longs;tellis igitur circa A, &amp; C, reflecti pote&longs;t ex quarto fundamen&shy;<lb/>to lumen <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> luminaris ad D, quod &longs;atis e&longs;t efficax, c&ugrave;m fer&egrave; perpendi&shy;<pb pagenum="199"/><figure place="text" xlink:href="figures-la/009.01.199.1.tif"/><lb/>culariter terr&aelig; D, incidat. </s>
8415 
8416 <s>quamuis autem ex &longs;tellis F, E, lumen aliquod ad <lb/>D, tran&longs;mittatur, tamen cum obliqu&egrave; admodum illi accidat, nihil pen&egrave; ef&shy;<lb/>ficere valet. </s>
8417 
8418 <s>Verumenimuer&ograve; qui&longs;piam in hunc modum obijciet: hac ra&shy;<lb/>tione deberet fieri etiam &aelig;&longs;tus in terr&aelig; lateribus H, I, quando quidem etiam <lb/>illuc lumen ex quarto fundamento reflecti pote&longs;t.</s></p><p type="main">
8419 
8420 <s>Cui &longs;ic re&longs;pondendum, po&longs;&longs;e quidem aliquod lumen illuc re&longs;ilire, &longs;ed ta&shy;<lb/>men exiguum admodum, &amp; proinde nullius pen&egrave; roboris, quod experientia <lb/>de&longs;umpta ex illuminatione Lun&aelig; comprobari pote&longs;t; videmus enim, quod <lb/>quanto Luna magis Soli opponitur, &amp; proinde &longs;uam illuminationem magis <lb/>ver&longs;us terram obuertit, vt in plenilunio, tanto maiorem eam vim habere <lb/>&aelig;&longs;tus excitandi. </s>
8421 
8422 <s>multo ver&ograve; minorem, quando e&longs;t in a&longs;pectu Solis quadrato, <lb/>quia dimidiam tantum &longs;ui illuminationem nobis reflectit. </s>
8423 
8424 <s>Idem proportio&shy;<lb/>naliter de &longs;tellis dicendum, qu&aelig; enim luminari maxim&egrave; opponuntur, vt qu&aelig; <lb/>&longs;unt circa B, ill&aelig; totam illuminationem terr&aelig; o&longs;tendunt, vnde, &amp; efficacio&shy;<lb/>res &longs;unt. </s>
8425 
8426 <s>c&aelig;ter&aelig;, quo magis ab illis di&longs;tant minus de &longs;ua illuminatione ter&shy;<lb/>r&aelig;, &longs;eu mari <expan abbr="obuert&utilde;t">obuertunt</expan>, &amp; proinde minus efficiunt. </s>
8427 
8428 <s>vnde fit, vt quamuis non&shy;<lb/>nulli radij etiam perpendiculares ad terr&aelig; latera H, I, referri po&longs;&longs;int, tamen <lb/>quia pauciores &longs;unt, qu&agrave;m alibi, propterea nullam ibi &aelig;&longs;tus <expan abbr="prouoc&atilde;di">prouocandi</expan> vim <lb/>obtinent. </s>
8429 
8430 <s>&longs;ydera porr&ograve; illa, qu&aelig; &longs;upra Solem exi&longs;tunt, etiam &longs;i ip&longs;orum illu&shy;<pb pagenum="200"/>minatio tota ad terras vergat, tamen in lateribus terr&aelig; pr&aelig;dictis nihil ef&shy;<lb/>ficiunt, quia in illa vel obliqu&egrave; admodum radij incidunt, vel ea tantummo&shy;<lb/>do tangunt. </s>
8431 
8432 <s>Verum illuminatione &longs;ua ea&longs;dem maris partes, qu&aelig; &longs;unt ad G, <lb/>vn&agrave; cum Sole, ac Luna percellunt.</s></p><p type="main">
8433 
8434 <s>Ex quibus apparet duas tantum orbis terr&aelig; partes totis, ac plenis a&longs;tro&shy;<lb/>rum luminibus impeti, in quibus &longs;cilicet duo opoo&longs;iti &aelig;&longs;tus ebulliunt.</s></p><p type="main">
8435 
8436 <s>Idem po&longs;&longs;umus hoc modo confirmare, quia cum totum firmamentum &longs;it <lb/>innumeris pen&egrave; &longs;yderibus &longs;tipatum, loco concaui, ac &longs;ph&aelig;ri&ccedil;i &longs;peculi ha&shy;<lb/>beri pote&longs;t, &amp; proinde illius in&longs;tar amborum luminarium lumen reflectere; <lb/>qua ratione patet omnem fer&egrave; ad partes pr&aelig;dictas D, emitti reflexionem.</s></p><p type="main">
8437 
8438 <s>His rationibus manife&longs;tum e&longs;&longs;e patet pr&aelig;dictum &aelig;&longs;tus tumorem lumina&shy;<lb/>ribus auer&longs;um, <expan abbr="atq;">atque</expan> antipodum ex pr&aelig;dicta reflexione exurgere.</s></p><p type="main">
8439 
8440 <s>Po&longs;&longs;et etiam qui&longs;piam &longs;ic opponere, &longs;i illuc pr&aelig;dicta luminum reflexio <lb/>pertineret, non &longs;olum illam aquarum ebullitionem efficeret, verum etiam <lb/>lucem aliquam e&ograve;dem afferret, quod tamen &longs;en&longs;u minim&egrave; apparet. </s>
8441 
8442 <s>cui &longs;ic <lb/>re&longs;pondendum videtur, nece&longs;&longs;arium non e&longs;&longs;e, vt reflexio illa, qu&aelig; hoc modo <lb/>mare afficit tanta &longs;it, vt etiam illud luce &longs;olito maiori afficiat; quod <expan abbr="expe-ri&etilde;tia">expe&shy;<lb/>rientia</expan> con&longs;tat in alijs c&ecedil;li influxibus: qu&agrave;m &longs;&aelig;p&egrave; enim Luna nubilo&longs;o etiam <lb/>tempore, fluxum, ac re&longs;luxum priorem parit, cum tamen nullam tunc lu&shy;<lb/>cem nobis afferat? </s>
8443 
8444 <s>quamuis enim lumen &longs;tellarum &longs;uperficiem maris non <lb/>attingat, attingit tamen &longs;uperficiem vaporum, exhalationum, ac nubium, <lb/>qu&aelig; terram in &longs;ph&aelig;r&aelig; modum ambiunt, ac parum &agrave; terra <expan abbr="circumquaq;">circumquaque</expan> at&shy;<lb/>tolluntur: quem exhalationum ambitum deinde luminarium virtus facil&egrave; <lb/>penetrare pote&longs;t. </s>
8445 
8446 <s>Nullum pr&aelig;terea lumen apparet, quia lumen reflexum <lb/>pr&aelig;&longs;ertim ex conuexis corporibus, vt &longs;unt &longs;tell&aelig;, valde debile e&longs;t, quia <expan abbr="con-uex&utilde;">con&shy;<lb/>uexum</expan> illud reflectendo non vnit, &longs;ed di&longs;gregat, contra quam facit concauum.</s></p><p type="main">
8447 
8448 <s>Tandem qu&aelig;rere quis po&longs;&longs;et, cur &aelig;&longs;tus hic &longs;ecundus minor &longs;it priori. </s>
8449 
8450 <s>Cui <lb/>re&longs;pondendum, quia ille &agrave; directis radijs, hic ver&ograve; &agrave; reflexis progignitur: <lb/>radios autem reflexos debiliores e&longs;&longs;e directis optici docent, <expan abbr="atq;">atque</expan> experien&shy;<lb/>tia confirmat.</s></p><p type="main">
8451 
8452 <s>Porr&ograve; quando luminaria &longs;unt oppo&longs;ita, vt &longs;i Luna e&longs;&longs;et in B, Sol ver&ograve; in K, <lb/>tunc maximus fit <expan abbr="vterq;">vterque</expan> fluxus, quia radij directi <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> vniuntur cum ra&shy;<lb/>dijs reflexis alterius; ita vt <expan abbr="vterq;">vterque</expan> &aelig;&longs;tus fiat, &amp; per radium reflexum, &amp; per <lb/>directum &longs;imul, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&aelig;&longs;tus, qui Lun&aelig; &longs;ubiacet fit per radium Lun&aelig; directum, <lb/>&amp; quia Sol e&longs;t in oppo&longs;itione cum Luna, &longs;it vt ip&longs;ius radij reflectantur, &amp; <lb/>vniantur cum directis Lun&aelig; ad eundem tumorem excitandum. </s>
8453 
8454 
8455 
8456 
8457 
8458 <s>&longs;imiliter in&shy;<lb/>fra Solem direct&egrave; alius fit &agrave; directis ip&longs;ius radijs; &amp; quia Luna ei opponitur <lb/>lumen eius ad <expan abbr="v&longs;q;">v&longs;que</expan> &longs;ydera pertinens reuertitur, <expan abbr="vna&qacute;">vnaque</expan>; cum directa Solis lu&shy;<lb/>ce ad eundem efficiendum concurrit.</s></p><p type="main">
8459 
8460 <s>Exi&longs;tentibus demum lumidaribus circa quadratum a&longs;pectum, vt &longs;i Luna <lb/>e&longs;&longs;et in F, Sole exi&longs;tente in K. exiguus, ac pen&egrave; nullus fit fluxus, quia eorum <lb/>vires non &longs;unt vnit&aelig;, c&ugrave;m radij nec incidentes, nec reflexi vniantur im&ograve; vi&shy;<lb/>res corum &longs;eparat&aelig; inaria in contrarias partes di&longs;trahunt, vnde fit, vt neu&shy;<lb/>tro alteri concedente, apud neutrum victoria con&longs;tet.</s></p><p type="main">
8461 
8462 <s><expan abbr="Atq;">Atque</expan> h&aelig;c e&longs;t mea de &aelig;&longs;tu maris per reflexionem &longs;ententia. </s>
8463 
8464 <s>quam iamdiu <lb/>inuentam, <expan abbr="atq;">atque</expan> auditoribus meis &longs;&aelig;pius explicatam, reperi tandem non &longs;ine <pb pagenum="201"/>gaudio fui&longs;&longs;e etiam &longs;ubtili&longs;&longs;imi Scoti opinionem, quam ip&longs;e breuiter in pri&shy;<lb/>mum &longs;ent. </s>
8465 
8466 <s>de creatione mundi tantummodo &longs;ine vlla expo&longs;itione, <expan abbr="atq;">atque</expan> con&shy;<lb/>firmatione proponit. </s>
8467 
8468 <s>in eadem pror&longs;us &longs;ententia e&longs;t Rogerius Bachon inter <lb/>Opticos probati&longs;&longs;imus, cap. 
8469 
8470 5. de Speculis Mathematicis.<!-- KEEP S--></s></p><p type="main">
8471 
8472 <s>Aliorum demum opinationes, &longs;iue Angelo cuidam, &longs;iue virtuti totam <lb/>terram peruadenti hunc &aelig;&longs;tum a&longs;cribentium, non e&longs;t meum refellere, cum <lb/>non phy&longs;icum, &longs;ed mathematicum agere in&longs;tituerim.</s></p><p type="main">
8473 
8474 <s><arrow.to.target n="marg263"/></s></p><p type="margin">
8475 
8476 <s><margin.target id="marg263"/>273</s></p><p type="main">
8477 
8478 
8479 <s>Cap. 7. <emph type="italics"/>(Quod Imagunculas animatas e&longs;&longs;e, &amp;c.)<emph.end type="italics"/> huiu&longs;modi imagines, &amp; <lb/>&longs;tatuas, qu&aelig; &longs;pont&egrave; mouebantur Gr&aelig;ci appellarunt Automata, ide&longs;t &longs;pon&shy;<lb/>tanea, cuiu&longs;modi &longs;unt automata Heronis, Alexandrini, qu&aelig; adhuc extant.</s>
8480 </p></chap><chap><p type="head">
8481 
8482 <s><emph type="italics"/>IN LIBELLVM<lb/>De admirandis auditionibus.<emph.end type="italics"/></s></p><p type="main">
8483 
8484 <s><arrow.to.target n="marg264"/></s></p><p type="margin">
8485 
8486 <s><margin.target id="marg264"/>274</s></p><p type="main">
8487 
8488 <s>Nvmero 82. Qu&aelig; de illa in&longs;ula extra Herculis columnas &longs;ita narrat, <lb/>eam putant recentiores Geographi, &amp; quidem merit&ograve; nouo orbi <lb/>conuenire.</s></p><p type="main">
8489 
8490 <s><arrow.to.target n="marg265"/></s></p><p type="margin">
8491 
8492 <s><margin.target id="marg265"/>275</s></p><p type="main">
8493 
8494 <s>Numero 100. Qu&aelig; de I&longs;tro, &longs;iue Dannubio tradit, eum &longs;cilicet <lb/>e&longs;&longs;e bifidum, <expan abbr="altero&qacute;">alteroque</expan>; ramo in Pontum, altero ver&ograve; in Mediterraneum ex&shy;<lb/>onerari: &longs;unt contra omnes recentiores Geographos; apparet tamen eam <lb/>fui&longs;&longs;e veterum nonnullorum opinionem, quos <expan abbr="&longs;e&qacute;uutus">&longs;equutus</expan> Ari&longs;t. 
8495 
8496 deceptus e&longs;t, <lb/>&agrave; quibus etiam mult&ograve; po&longs;t fal&longs;i &longs;unt Diodorus, Pomponius, &amp; Solinus, qui <lb/>I&longs;trum I&longs;tri&aelig; Prouinc&igrave;&aelig; fluuium faciunt, quem ex I&longs;tro Germani&aelig; veluti ra&shy;<lb/>mum contra omnem veritatem deriuant. </s>
8497 
8498 <s>Ver&ugrave;m hoc illis-condonandum <lb/>pr&aelig;&longs;ertim antiquioribus, cum tunc temporis Geographia parum e&longs;&longs;et <lb/>exculta.</s></p><p type="main">
8499 
8500 <s>Primus Strabo hanc fal&longs;itatem libro 1. redarguit, &amp; po&longs;t ip&longs;um Plinius <lb/>I&longs;trum i&longs;tum fabulo&longs;um appellat.</s></p></chap><chap><p type="head">
8501 
8502 <s><emph type="italics"/>IN LIBELLVM<lb/>De lineis in&longs;ecabilibus, &longs;iue indiuiduis.<emph.end type="italics"/></s></p><p type="main">
8503 
8504 <s><arrow.to.target n="marg266"/></s></p><p type="margin">
8505 
8506 <s><margin.target id="marg266"/>276</s></p><p type="main">
8507 
8508 <s>Di&longs;putat libellus hic &longs;an&egrave; acuti&longs;&longs;imus, Vtrum quantitas con&longs;tet ex <lb/>indiui&longs;ibilibus, quam qu&ecedil;&longs;tionem recentiores agitant in Phy&longs;icis <lb/>tractatione de Quantitate; <expan abbr="atq;">atque</expan> hinc nonnulla &longs;umunt argumen&shy;<lb/>ta: plura &longs;umpturi ni&longs;i operis ob&longs;curitas, &amp; mathematicarum, <lb/>ignoratio hactenus ob&longs;titi&longs;&longs;et.</s></p><p type="main">
8509 
8510 <s>Sciendum igitur primo loco, nos po&longs;&longs;e duo indiui&longs;ibilium genera in quan&shy;<lb/>titate concipere. </s>
8511 
8512 <s>primum eorum, qu&aelig; ver&egrave; indiuidua &longs;unt, <expan abbr="nullas&qacute;">nullasque</expan>; habent <lb/>partes, &longs;iue nullo modo &longs;unt quanta; cuiu&longs;inodi e&longs;t <expan abbr="punct&utilde;">punctum</expan> mathematicum.</s></p><p type="main">
8513 
8514 <s>Alterum quorumdam indiui&longs;ibilium quidem, &longs;ed tamen quantorum cu&shy;<lb/>iu&longs;modi e&longs;&longs;ent, qu&aelig;dam ade&ograve; minim&aelig; line&aelig;, qu&aelig; omnem effugiant diui&longs;io&shy;<lb/>nem: ex quibus antiqui opinabantur lineas totales, ac diniduas componi. <lb/></s>
8515 
8516 <s>atque de hec &longs;ecundo indiuiduorum, quantorum genere videtur opu&longs;culum <pb pagenum="202"/>i&longs;tud di&longs;&longs;erere. </s>
8517 
8518 <s>&amp; quia partim rationibus phy&longs;icis, partim geometricis vti&shy;<lb/>tur, ide&ograve; nec omnin&ograve; phy&longs;icus nec omnin&ograve; mathematicus e&longs;t. </s>
8519 
8520 <s>Ego igitur, <lb/>qu&aelig; mathematica &longs;unt, exi &longs;tituto exponere aggrediar.</s></p><p type="main">
8521 
8522 <s>Ad intelligentiam igitur huius operis nece&longs;&longs;arium e&longs;t noui&longs;&longs;e, qu&aelig; nam <lb/>&longs;int quantitates commen&longs;urabiles, &amp; qu&aelig; in commen&longs;urabiles. </s>
8523 
8524 <s>qu&aelig; prima, <lb/>&amp; &longs;ecunda definitione 10. Elem. 
8525 
8526 explicantur; <expan abbr="ego&qacute;">egoque</expan>; eas primo Priorum oc&shy;<lb/>ca&longs;ione a&longs;ymetri&aelig; diametri cum co&longs;ta &longs;atis expo&longs;ui: vtrumuis locum vide&shy;<lb/>ris pr&aelig;&longs;enti nece&longs;&longs;itati con&longs;ultum erit.</s></p><p type="main">
8527 
8528 <s><arrow.to.target n="marg267"/></s></p><p type="margin">
8529 
8530 <s><margin.target id="marg267"/>277</s></p><p type="main">
8531 
8532 <s>Primus locus Mathematicus e&longs;t hic <emph type="italics"/>(Po&longs;trem&ograve; ex ijs, qu&aelig; tradunt Mathe&shy;<lb/>maticis imbuti di&longs;ciplinis, quiuis lineam aliquam in&longs;ecabilem e&longs;&longs;e concedet. </s>
8533 
8534 <s>nam <lb/>&longs;i, vt aiunt, ill&aelig; commen&longs;urabiles &longs;unt line&aelig;, qu&aelig; eadem men&longs;ura dimetiri queunt, <lb/>&amp; nihil impedit, quin omnes commen&longs;urabiles reip&longs;a dimetiantur, extabit profe&shy;<lb/>ct&ograve; longitudo aliqua, qua omnes commen&longs;urabuntur; qu&aelig; nece&longs;&longs;ario erit indiuidua, <lb/>nam &longs;i dicatur e&longs;&longs;e diuidua, huius <expan abbr="quoq;">quoque</expan> men&longs;ur&aelig; partes, men&longs;aram aliquam com&shy;<lb/>munem habebunt, partes enim toti commen&longs;urabiles &longs;unt ita, vt portio partis il&shy;<lb/>lius, qu&aelig; dimidium totius fuerat, efficiatur dupla alterius; quoniam autem hoc <lb/>fieri nequit, atoma debet e&longs;&longs;e men&longs;ura h&aelig;c communis.<emph.end type="italics"/></s></p><p type="main">
8535 
8536 <s><emph type="italics"/>Eodem modo, &amp; qu&aelig; &longs;imul ab ip&longs;a men&longs;ura commen&longs;urat&aelig;, tanquam omnes ex <lb/>ea men&longs;ura compo&longs;it&aelig; &longs;unt line&aelig;, veluti ex atomis conflantur.<emph.end type="italics"/></s></p><p type="main">
8537 
8538 <s>Affert rationem quandam ex Mathematicis, qua nonnulli probabant ex&shy;<lb/>tare lineas atomas, ex quibus c&aelig;ter&aelig; line&aelig; tanquam partibus con&longs;tarent: <lb/>ac proinde negabant lineas e&longs;&longs;e in infinitum diuiduas, &longs;eu quamlibet lineam <lb/>&longs;ecari po&longs;&longs;e, &longs;ed a&longs;&longs;erebant <expan abbr="diuid&etilde;do">diuidendo</expan>, tandem ad indiuiduas <expan abbr="deueniend&utilde;">deueniendum</expan> e&longs;&longs;e.</s></p><p type="main">
8539 
8540 <s>Pr&aelig;mi&longs;&longs;a igitur, vt monui commen&longs;urabilium, &amp; incommen&longs;urabilium <lb/>linearum cognitione in hunc modum, &amp; textum Ari&longs;tot. &amp; rationem ip&longs;o&shy;<lb/>rum exponam.</s>
8541 
8542 </p><p type="main">
8543 
8544 <s>Mathematici o&longs;tendunt extare lineas commen&longs;urabiles, qu&aelig; &longs;cilicet ea&shy;<lb/>dem communi men&longs;ura men&longs;urantur: at nihil impedit quin omnes <expan abbr="c&otilde;men-&longs;urabiles">commen&shy;<lb/>&longs;urabiles</expan> re ip&longs;a men&longs;urentur, debet erg&ograve; extare vna aliqua longitudo, qua <lb/>omnes commen&longs;urabiles dimetiamur. </s>
8545 
8546 <s>hanc autem uece&longs;&longs;e e&longs;t e&longs;&longs;e atomam, <lb/>nam &longs;i diuidua &longs;tatuatur, poterit &longs;emper &longs;ecari, &amp; &longs;ub&longs;ecari bifariam, qua&shy;<lb/>re cum partes huiu&longs;modi &longs;int toti commen&longs;urabiles, &longs;equetur aliam exi&longs;tere <lb/>men&longs;uram, qua omnes h&aelig; partes, &amp; proinde tota linea commen&longs;urentur. <lb/></s>
8547 
8548 <s>Ver&ugrave;m hoc fieri nequit, nam hoc pacto non e&longs;&longs;et vna tantum longitudo om&shy;<lb/>nium commen&longs;urabilium linearum communis men&longs;ura, ver&ugrave;m plures, &amp; <lb/>plures in infinitum, quod e&longs;t contra Mathematicorum placita. </s>
8549 
8550 <s>dicendum, <lb/>itaque, communem illam omnium men&longs;uram e&longs;&longs;e omnis diui&longs;ionis exper&shy;<lb/>tem; &amp; propterea etiam lineas omnes commen&longs;urabiles ex atomis lineis <lb/>componi, qu&aelig; nimirum pr&aelig;dict&aelig; communi men&longs;ur&aelig; &aelig;quales &longs;int. </s>
8551 
8552 <s><expan abbr="atq;">atque</expan> h&aelig;c <lb/>e&longs;t illarum prima argumentatio.</s></p><p type="main">
8553 
8554 <s><arrow.to.target n="marg268"/></s></p><p type="margin">
8555 
8556 <s><margin.target id="marg268"/>278</s></p><p type="main">
8557 
8558 <s>Secundus locus <emph type="italics"/>(Idem etiam contingit in figuris planis, qu&aelig; &agrave; lineis rationa&shy;<lb/>libus procreantur: nam omnes huiu&longs;modi figur&aelig; erunt etiam inuicem commen&longs;ura&shy;<lb/>biles, quare <expan abbr="&emacr;adem">enadem</expan> ratione, qua in lineis proxim&egrave; v&longs;i &longs;umus, &longs;equetur earum com&shy;<lb/>munem men&longs;uram e&longs;&longs;e pariter indiuiduam.<emph.end type="italics"/></s></p><p type="main">
8559 
8560 <s>Sciendum e&longs;t omnes lineas <expan abbr="c&otilde;men&longs;urabiles">commen&longs;urabiles</expan> longitudine, e&longs;&longs;e etiam com&shy;<lb/>men&longs;urabiles (vt aiunt Geometr&aelig;) potentia, ide&longs;t &longs;ecundum quadrata ea&shy;<pb pagenum="203"/>rum, &longs;iue dicas quadrata <expan abbr="quoq;">quoque</expan> earum e&longs;&longs;e commen&longs;urabilia, v. <!-- REMOVE S-->g. <!-- REMOVE S-->linea dua&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.203.1.tif"/><lb/>rum vnciarum, &amp; linea trium vnciarum &longs;unt <lb/>commen&longs;urabiles longitudine, &amp; potentia, <lb/>quia potentia line&aelig; duarum vnciarum, &longs;iue <lb/><expan abbr="quadrat&utilde;">quadratum</expan>, e&longs;t quatuor vnciarum &longs;uperficia&shy;<lb/>lium: &amp; quadratum line&aelig; trium vnciarum, <lb/>e&longs;t nouem vnciarum quadratarum, vt patet <lb/>in figuris, quorum quadratorum communis <lb/>men&longs;ura e&longs;t vncia vna quadrata. </s>
8561 
8562 
8563 
8564 
8565 
8566 <s>atque hanc <lb/>illi nullo modo diuidi po&longs;&longs;e contendebant.</s></p><p type="main">
8567 
8568 <s><arrow.to.target n="marg269"/></s></p><p type="margin">
8569 
8570 <s><margin.target id="marg269"/>279</s></p><p type="main">
8571 
8572 <s>Tertius locus <emph type="italics"/>(Pr&aelig;terea &longs;i quis communem &longs;tatam, ac determinatam men&longs;u&shy;<lb/>ram &longs;aciat diuiduam, non erit amplius in rerum natura linea vlla rationalis, aut <lb/>irrationalis, re&longs;pectu expo&longs;it&aelig;, ac determinat&aelig; line&aelig;; neque aliarum vlla erit, de <lb/>quibus modo dictum e&longs;t, veluti quam Apotomen vocant ex duobus nominibus. </s>
8573 
8574 <s>Ve&shy;<lb/>r&ugrave;m neque &longs;ecundum &longs;e aliquam definitam naturam habebunt, &longs;ed collat&aelig; &longs;ibi ip&longs;is <lb/>tam rationales, qu&agrave;m irrationales erunt omnes.<emph.end type="italics"/></s></p><p type="main">
8575 
8576 <s>H&aelig;c e&longs;t alia eorumdem ratio ad idem comprobandum: quam, vt ben&egrave; <lb/>percipiamus, nonnulla prius ex definitionibus 10. Elem. 
8577 
8578 &longs;unt explicanda: <lb/>vt qu&aelig; nam &longs;int line&aelig; rationales, qu&aelig; irrationales, qu&aelig; ex binis nomini&shy;<lb/>bus, qu&aelig; Apotom&aelig;.</s></p><p type="main">
8579 
8580 <s>Propo&longs;ita igitur linea quapiam, v. <!-- REMOVE S-->g. <!-- REMOVE S-->trium palmorum qualis e&longs;t linea A, <lb/>po&longs;&longs;unt inueniri quamplurim&aelig; line&aelig;, quarum ali&aelig; &longs;int illi longitudine com&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.203.2.tif"/><lb/>men&longs;urabiles, &longs;iue qu&aelig; cum expo&longs;ita A, ha&shy;<lb/>beant communem men&longs;uram. </s>
8581 
8582 
8583 
8584 
8585 
8586 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->linea B, <lb/><expan abbr="quinq;">quinque</expan> palmorum e&longs;t commen&longs;urabilis line&aelig; <lb/>A, quia vtramque communis men&longs;ura vnius <lb/>palmi metitur: ali&aelig; ver&ograve; &longs;int eidem A, lon&shy;<lb/>gitudine incommen&longs;urabiles, qualis e&longs;&longs;et diameter C D, quadrati line&aelig; A, <lb/>qu&aelig; e&longs;t cum latere A, incommen&longs;urabilis ex vltima 10.</s>
8587 
8588 
8589 
8590 </p><figure place="text" xlink:href="figures-la/009.01.203.3.tif"/><p type="main">
8591 
8592 <s>C&aelig;terum lineam prim&ograve; expo&longs;itam, vt e&longs;t in pr&aelig;&shy;<lb/>&longs;entia A, quod e&longs;&longs;et not&aelig; quantitatis, Gr&aelig;ci appella&shy;<lb/>runt <foreign lang="greek">Ph/thg,</foreign> ide&longs;t rationalem, quemadmodum Latini <lb/>eam appellant.</s></p><p type="main">
8593 
8594 <s>Linearum autem longitudine <expan abbr="incomm&etilde;&longs;urabilium">incommen&longs;urabilium</expan> <lb/>cum expo&longs;ita rationali A, ali&aelig; &longs;unt, qu&aelig; tamen &longs;unt <lb/>commen&longs;urabiles eidem potentia, ide&longs;t con&longs;tituunt <lb/>quadrata, qu&aelig; &longs;unt commen&longs;urabilia quadrato ra&shy;<lb/>tionali A, vt linea C D, cum &longs;it diameter quadrati li&shy;<lb/>ne&aelig; A, quadratum exhibet, quod e&longs;t duplum quadrati line&aelig; A, ex 47. primi, <lb/>quadratum autem line&aelig; A, e&longs;t nouem, igitur quadratum eius duplum erit <lb/>octodecim, quadratum &longs;cilicet line&aelig; C D. octodecim autem, &amp; nouem &longs;unt <lb/><expan abbr="c&otilde;men&longs;urabilia">commen&longs;urabilia</expan> communi vnitatis men&longs;ura, huiu&longs;modi line&aelig; dicuntur com&shy;<lb/>men&longs;urabiles poteutia tantum, potentia. </s>
8595 
8596 <s>n. </s>
8597 
8598 <s>line&aelig; dicuntur <expan abbr="quadrat&utilde;">quadratum</expan> illius.</s></p><p type="main">
8599 
8600 <s>Qu&aelig; igitur rationali propo&longs;it&aelig; &longs;unt commen&longs;urabiles aliquo modo, &longs;iue <lb/>longitudine, &amp; potentia (<expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> enim commen&longs;urabilis e&longs;t longitudine, <lb/>e&longs;t etiam potentia) &longs;iue potentia &longs;ol&ugrave;m, rationales ip&longs;&aelig; quoque dicuntur. <pb pagenum="204"/><figure place="text" xlink:href="figures-la/009.01.204.1.tif"/><lb/>Ali&aelig; ver&ograve; (quarum permult&aelig; in decimo reperiun&shy;<lb/>tur) qu&aelig; nec longitudine, nec potentia illi &longs;unt <lb/>commen&longs;urabiles, irrationales appellantur, qua&shy;<lb/>lis e&longs;&longs;et media proportionalis E F, inter duas A, <lb/>&amp; C D, in pr&aelig;&longs;enti figura ex 11. 10.</s></p><p type="main">
8601 
8602 <s>Sciendum pr&aelig;terea ex 37. 10. &amp; &longs;equentibus, <lb/>quod ex duabus lineis rationalibus re&longs;pectu rationalis expo&longs;it&aelig;. </s>
8603 
8604 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->A, com&shy;<lb/>men&longs;urabilibus inuicem tantum potentia, componitur linea, qu&aelig; cum ea&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.204.2.tif"/><lb/>dem expo&longs;ita e&longs;t irrationalis, <expan abbr="vocatur&qacute;">vocaturque</expan>; ex <lb/>duobus nominibus, &longs;iue Binomium, vt &longs;i ex <lb/>latere A, &amp; diametro C D, componatur li&shy;<lb/>nea A C D, erit irrationalis cum rationali <lb/>A, <expan abbr="dicetur&qacute;">diceturque</expan>; binomium. </s>
8605 
8606 
8607 
8608 
8609 
8610 <s>Amplius ex 74. 10. &amp; &longs;equentibus, &longs;i pr&aelig;dictum <lb/>minus nomen, &longs;iue minor linea A, detrahatur ex maiori nomine C D, vt re&shy;<lb/>linquatur B D linea, erit ip&longs;a reliqua B D, irrationalis, quam po&longs;tea appel&shy;<lb/>lant Apotomen, &longs;iue latin&egrave; Re&longs;iduum.</s></p><p type="main">
8611 
8612 <s>Po&longs;trem&ograve;, &amp; hoc non ignorandum ex 43. 10. lineam, &longs;iue <expan abbr="binomi&utilde;">binomium</expan> A C D, <lb/>non po&longs;&longs;e diuidi in alio puncto, pr&aelig;ter C, in duas lineas, qu&aelig; &longs;int rationales <lb/>expo&longs;it&aelig;, &amp; potentia tantum inuicem commen&longs;urabiles.</s></p><p type="main">
8613 
8614 <s>His pr&aelig;mi&longs;&longs;is textum, ac rationem illorum explicabo in hunc modum.</s></p><p type="main">
8615 
8616 <s>Si quis faciat diuiduam lineam illam, qu&aelig; e&longs;t communis <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> omnium <lb/>commen&longs;urabilium, &longs;equetur hoc ab&longs;urdum contra demon&longs;trationes 10. <lb/>quod nulla erit amplius linea rationalis, nec irrationalis, quia &longs;i communis <lb/>men&longs;ura diuidatur, tolletur ea de rerum natura; vnde non erit amplius in&shy;<lb/>ter lineas &longs;ymetria vlla, quare neque vll&aelig; erunt rationales, e&longs;&longs;e enim ratio&shy;<lb/>nale oritur ex commen&longs;urabilitate. </s>
8617 
8618 <s>quare <expan abbr="neq;">neque</expan> extabit illa rationalis expo&shy;<lb/>&longs;ita, ad quam c&aelig;ter&aelig; relat&aelig; dicuntur rationales, vel irrationales: quapro&shy;<lb/>pter etiam irrationales null&aelig; erunt, <expan abbr="neq;">neque</expan> vlla alia erit ex pr&aelig;dictis, veluti <lb/>nec irrationalis illa, quam vocant Apotomen ex Binomio, &longs;iue ex duobus <lb/>nominibus, de qua Euclides propo&longs;. </s>
8619 
8620 <s>74. 10. &amp; &longs;equentibus pertractat.</s></p><p type="main">
8621 
8622 <s>Notandum in ver&longs;u illo <emph type="italics"/>(Apotomen ex duobus nominibus compo&longs;itam)<emph.end type="italics"/> vni&shy;<lb/>ca voce illa <emph type="italics"/>(Compo&longs;itam)<emph.end type="italics"/> addita ab Interprete Iatino, qu&aelig; non extat in tex. <lb/><!-- REMOVE S-->gr&aelig;co, magnum Ari&longs;toteli imponi erratum, cum hac ratione dicat apoto&shy;<lb/>men ex duobus nominibus e&longs;&longs;e compo&longs;itam, quod fal&longs;i&longs;&longs;imum e&longs;t. </s>
8623 
8624 
8625 
8626 <s>Apotome <lb/>enim, vt &longs;upra dictum e&longs;t, ne dum ex duobus nominibus con&longs;tat, verum ip&shy;<lb/>&longs;a e&longs;t re&longs;iduum line&aelig; maioris, &longs;i minor ab ip&longs;a detrahatur. </s>
8627 
8628 <s>Verumenimuero <lb/>vox illa <emph type="italics"/>(Compo&longs;itam)<emph.end type="italics"/> in nullo codice reperitur, quare pro arbitrio, atque <lb/>ex Geometri&aelig; in&longs;citia addita, tolli debet, ne tant&aelig; in&longs;citi&aelig; Ari&longs;t. 
8629 
8630 ip&longs;e re&shy;<lb/>darguatur. </s>
8631 
8632 <s>h&aelig;c in hunc locum &longs;ufficiant.</s></p><p type="main">
8633 
8634 <s><arrow.to.target n="marg270"/></s></p><p type="margin">
8635 
8636 <s><margin.target id="marg270"/>280</s></p><p type="main">
8637 
8638 <s>Quartus locus <emph type="italics"/>(Quod ver&ograve; de commen&longs;urabilibus lineis po&longs;irem&ograve; dicunt, om&shy;<lb/>nes vua quadam, &amp; eadem men&longs;ura oportere men&longs;urari, fal&longs;um t&longs;i admodum, &amp; <lb/>nequaquam Mathematicorum &longs;uppo&longs;itionibus concordat. </s>
8639 
8640 <s>non enim ita &longs;upponunt <lb/>Geometr&aelig;, <expan abbr="neq;">neque</expan> vtile ip&longs;is i&longs;tud foret, im&ograve; potius aduer&longs;aretur, lineas omnes com&shy;<lb/>men&longs;urabiles e&longs;&longs;e, &amp; omnium commen&longs;urabilium linearam communem men&longs;uram<lb/>exi&longs;timare. </s>
8641 
8642 <s>quamobrem ridiculum e&longs;t eos, qui dicunt &longs;e demonstrare ex Geometra&shy;<lb/>rum decretis, &amp; ex quibus Mathematici docent in contentio&longs;am pariter, ac falla&shy;<emph.end type="italics"/><pb pagenum="205"/><emph type="italics"/>cem diuertere argumentationem, pr&aelig;&longs;ertim tam inualidam. </s>
8643 
8644 <s>nam multis modis im&shy;<lb/>hecillis e&longs;t eiu&longs;modi ratio, &amp; quouis modo licet euitare, ne aut inu&longs;itata dicere, aut <lb/>argui videamur.<emph.end type="italics"/></s></p><p type="main">
8645 
8646 <s>Refellit hoc loco &longs;uperiores rationes in tribus locis pr&aelig;mi&longs;&longs;is allatas, <lb/>quibus nonnulli probabant quantitatem ex indiuiduis con&longs;tare, &amp; proinde <lb/>concedenda e&longs;&longs;e qu&aelig;dam Quanta, omnin&ograve; atoma; &longs;ic igitur inquit. </s>
8647 
8648 <s>Quod <lb/>ver&ograve; de commen&longs;urabilibus lineis dicunt, omues videlicet vnica quadam, <lb/><expan abbr="eadem&qacute;">eademque</expan>; determinata men&longs;ura men&longs;urari oportere, fal&longs;um omnin&ograve; e&longs;t, &amp; <lb/>contra mathematicorum dogmata, non enim Geometr&aelig; hoc a&longs;&longs;erunt, c&ugrave;m <lb/>ip&longs;orum demon&longs;trationibus a duer&longs;etur; &longs;ed <expan abbr="tant&utilde;">tantum</expan> dicunt omnes lineas, qu&aelig; <lb/>ad inuicem &longs;unt commen&longs;urabiles, commen&longs;urari, vna <expan abbr="eadem&qacute;">eademque</expan>; men&longs;ura, <lb/><figure place="text" xlink:href="figures-la/009.01.205.1.tif"/><lb/>&longs;ed non tamen vnica, ide&longs;t non vnica, ac determi&shy;<lb/>nata. </s>
8649 
8650 <s>po&longs;&longs;unt enim e&longs;&longs;e plures <expan abbr="e&aelig;dem&qacute;">e&aelig;demque</expan>; men&longs;ur&aelig; <lb/>communes plurium quantitatum commen&longs;ura&shy;<lb/>bilium, vt pr&aelig;&longs;entium trium linearum 4. 6. 8. <lb/>communis <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> e&longs;t linea 2. binarius enim tres <lb/>numeros 4.6. &amp; 8. men&longs;urat. </s>
8651 
8652 <s>&amp; &longs;i linea 2. bifariam <lb/>&longs;ecetur, erit dimidium eius linea 1. qu&aelig; pariter <lb/>erit communis men&longs;ura trium pr&aelig;dictarum li&shy;<lb/>nearum, c&ucirc;m vnitas &longs;it omnium numerorum communis men&longs;ura. ben&egrave; ve&shy;<lb/>rum e&longs;t, quod Geometr&aelig;, quando &longs;impliciter loquuntur de huiu&longs;modi com&shy;<lb/>muni men&longs;ura, intelligunt de ea, qu&aelig; inter omnes e&longs;t maxima: vt in pr&aelig;di&shy;<lb/>ctis tribus lineis maxima earum communis men&longs;ura e&longs;t linea 2. <expan abbr="Atq;">Atque</expan> hec&longs;i&shy;<lb/>bi volunt Geometr&aelig;, ex quibus totus hic textus intelligi pote&longs;t.</s></p><p type="main">
8653 
8654 <s><arrow.to.target n="marg271"/></s></p><p type="margin">
8655 
8656 <s><margin.target id="marg271"/>281</s></p><p type="main">
8657 
8658 <s>Quintus locus <emph type="italics"/>(Ob rect&aelig; ver&ograve; line&aelig; motum in &longs;emicirculum, quam nece&longs;&longs;e e&longs;t <lb/>in rectum ita diuidere, vt infinit&aelig; circunferenti&aelig;, &amp; interualla totidem inuenian&shy;<lb/>tur)<emph.end type="italics"/> Interpres latinus &longs;ic vertit <emph type="italics"/>(Ob rect&aelig; ver&ograve; line&aelig; motum in &longs;emicirculum <lb/>diuiduas non credere, &amp;c.)<emph.end type="italics"/> vbi verba illa <emph type="italics"/>(Diuiduas non credere)<emph.end type="italics"/> pro arbittio, <lb/>ac &longs;ine ratione, im&ograve; contra rationem addidit: tum quia in Gr&aelig;co textu non <lb/>extant, tum quia &longs;en&longs;us totius &longs;ententi&aelig; is e&longs;t, vt potius debui&longs;&longs;et affirmati&shy;<lb/>u&egrave; dicere <emph type="italics"/>(Diuiduas credere)<emph.end type="italics"/> nam Ari&longs;toteles videtur &longs;ic <expan abbr="argum&etilde;tari">argumentari</expan>, quan&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.205.2.tif"/><lb/>do recta linea A B, vt in appo&longs;ita figura mo&shy;<lb/>uetur intrando in &longs;emicirculum C A D B, ita <lb/>vt prim&ograve; &longs;it in &longs;itu A B, &longs;ecund&ograve; in E F, terti&ograve; <lb/>in G H, &amp; &longs;imiliter in alijs omnibus &longs;emicir&shy;<lb/>culi locis, nece&longs;&longs;ari&ograve; accidit, vt infinit&aelig; peri&shy;<lb/>ph&ecedil;ri&aelig;, quales <expan abbr="s&utilde;t">sunt</expan> A B, E A B F, G E A B F H, <lb/>cadant inter infinitas partes line&aelig; ingredien&shy;<lb/>tis, vt &longs;unt A B, E F, G H, <expan abbr="atq;">atque</expan> tom tota recta <lb/>ingrediens, qu&agrave;m totus &longs;emicirculus, diuidatur in partes infinitas, ita vt <lb/>nulla pars line&aelig; rect&aelig;, <expan abbr="neq;">neque</expan> vlla &longs;emicirculi &longs;uper&longs;it, qu&aelig; &longs;e &longs;e mutu&ograve; non <lb/>diuidantur, erg&ograve; nihil tam in linea, qu&agrave;m in &longs;emicirculo remanet, quod non <lb/>&longs;ecetur: tota igitur linea recta, &amp; periph&aelig;ria illa diuidua e&longs;t, quam ob rem <lb/>nullo modo con&longs;tare pote&longs;t ex indiuiduis, ex quibus manife&longs;tum e&longs;t perpe&shy;<lb/>ram additamentum illud factum e&longs;&longs;e, &amp; &longs;imul ratio, &amp; textus Ari&longs;t. eadem <lb/>opera patefacta &longs;unt.</s></p><pb pagenum="206"/><p type="main">
8659 
8660 <s><arrow.to.target n="marg272"/></s></p><p type="margin">
8661 
8662 <s><margin.target id="marg272"/>282</s></p><p type="main">
8663 
8664 <s>Sextus locus <emph type="italics"/>(Rur&longs;us <expan abbr="quoq;">quoque</expan> facil&egrave; per&longs;uaderi pote&longs;t ex mota duorurm circulo&shy; <lb/>rum &aelig;qualium, nam qui&longs;quis borum moueatur, oportet per maiorem &longs;emicirculum <lb/>moueri, &amp; qu&aelig;cunque alia buiu&longs;modi constituta &longs;unt de lineis, fieri non po&longs;&longs;e, vt <lb/>talis vllus motus peragatur, quin prius omnibus, &amp; &longs;ingulis interiectis occurrat. <lb/></s>
8665 
8666 <s>Atque b&aelig;c Mathematicorum &longs;cita, mult&ograve; magis ab omnibus conce&longs;&longs;a &longs;unt, qu&agrave;m <lb/>illorum dicta.<emph.end type="italics"/></s></p><p type="main">
8667 
8668 <s>H&aelig;c e&longs;t alia ratio, qua probat totam circuli periph&aelig;riam e&longs;&longs;e diuiduam. <lb/><figure place="text" xlink:href="figures-la/009.01.206.1.tif"/><lb/>&longs;int enim duo circuli &aelig;quales primum in eo&shy;<lb/>dem loco, <expan abbr="vocentur&qacute;">vocenturque</expan>; A, &amp; B, deinde circu&shy;<lb/>lus B, moueatur, &amp; di&longs;cedat &agrave; circulo A, ma&shy;<lb/>nente; &longs;tatim <expan abbr="namq;">namque</expan> pars egre&longs;&longs;a E F G, erit <lb/>maior &longs;emicirculo, &amp; &longs;emper fiet maior, ac <lb/>maior. </s>
8669 
8670 <s><expan abbr="atq;">atque</expan> in tali motu omnes partes egre&shy;<lb/>dientis circuli &longs;ecantur ab omnibus partibus <lb/>circuli manentis. </s>
8671 
8672 <s>vnde patet nihil e&longs;&longs;e in eo&shy;<lb/>rum periph&aelig;rijs, quod non diuidatur. </s>
8673 
8674 <s>nul&shy;<lb/>lum igitur in eis e&longs;t indiuiduum. </s>
8675 
8676 <s>falluntur igitur aduer&longs;arij.</s></p><p type="main">
8677 
8678 <s><arrow.to.target n="marg273"/></s></p><p type="margin">
8679 
8680 <s><margin.target id="marg273"/>283</s></p><p type="main">
8681 
8682 <s>Septimus locus <emph type="italics"/>(Quamuis autem ex confutatis nuper rationibus appareat, ne&shy;<lb/>que probabile, neque nece&longs;&longs;arium e&longs;&longs;e lineas vllas indiuiduas extare, tamen ex ijs <lb/>etiam, qu&aelig; deinceps &longs;abiungam, mult&ograve; magis per&longs;picuum euadet. </s>
8683 
8684 <s>&amp; prim&ograve; quidem <lb/>per ea, qu&aelig; Mathematici demon&longs;trant, at que addi&longs;cenda proponunt, qu&aelig; mutare <lb/>non decet, ni&longs;t probabiliores rationes habeamus. </s>
8685 
8686 <s>Nam neque line&aelig;, neque rect&aelig; li&shy;<lb/>ne&aelig; definitio cum in&longs;ecabili linea con&longs;entit, vt qu&aelig; nec inter duo puncta exten&longs;a <lb/>&longs;it, nec medium vllam babeat.<emph.end type="italics"/></s></p><p type="main">
8687 
8688 <s>Idem, &longs;ed paul&ograve; mutatis verbis po&longs;tea repetit, qu&aelig; fort&egrave; ab aliquo per <lb/>errorem addita &longs;unt. </s>
8689 
8690 <s>Verumenimuer&ograve; maxim&egrave; con&longs;iderandum e&longs;t, quan&shy;<lb/>tum hoc loco Ari&longs;t. Mathematicis demon&longs;trationibus tribuat: quod dixe&shy;<lb/>rim propter recentiores quo&longs;dam, qui e&ograve; audaci&aelig; deuenerunt, vt Euclidis <lb/>firmi&longs;&longs;imas, <expan abbr="atq;">atque</expan> Ari&longs;tot. te&longs;timonio, <expan abbr="veterum&qacute;">veterumque</expan>; Philo&longs;ophorum omnium <lb/>comprobatas, negare non verentur Demon&longs;trationes.</s>
8691 
8692 </p><p type="main">
8693 
8694 <s>C&aelig;ter&ugrave;m Ari&longs;t. 
8695 
8696 iterum opinionem <expan abbr="a&longs;&longs;er&etilde;tium">a&longs;&longs;erentium</expan> lineas in&longs;ecabiles hoc mo&shy;<lb/>do confutat: nam &longs;i inquit, lineam illam, quam vocant in&longs;ecabilem, e&longs;t non <lb/>&longs;olum linea, &longs;ed etiam linea recta, illi conueniret rect&aelig; line&aelig; definitio, &longs;ed <lb/>nullo modo pote&longs;t ci conuenire, erg&ograve; tollend&aelig; &longs;unt de rerum natura huiu&longs;&shy;<lb/>modi line&aelig;. </s>
8697 
8698 <s>Porr&ograve; definitio line&aelig; e&longs;t, vt &longs;it longitudo latitudinis expers, &amp; <lb/>&longs;i recta &longs;it ex &aelig;quo &longs;ua interiacet puncta extrema, erg&ograve; ip&longs;a linea media erit <lb/>inter duo indiuidua extrema puncta; at ver&ograve; linea, quam ip&longs;i volunt e&longs;&longs;e <lb/>indiuiduum quoddam, qua ratione medium erit inter alia duo indiuidua? <lb/></s>
8699 
8700 <s>ip&longs;i enim <expan abbr="vid&etilde;tur">videntur</expan> velle i&longs;tam lineam non habere medium vllum, &longs;i enim con&shy;<lb/>cederent habere medium, iam po&longs;&longs;et in medio &longs;ecari, quod ipfi nequaquam <lb/>concederent: patet igitur definitionem line&aelig; minim&egrave; illi conuenire, &amp; pro&shy;<lb/>pterea <expan abbr="neq;">neque</expan> e&longs;&longs;e inter lineas enumerandam.</s></p><p type="main">
8701 
8702 <s><arrow.to.target n="marg274"/></s></p><p type="margin">
8703 
8704 <s><margin.target id="marg274"/>284</s></p><p type="main">
8705 
8706 <s>Octauus locus <emph type="italics"/>(Deinde omnes line&aelig; commen&longs;urabiles erunt: nam omnes ab in&shy;<lb/>diuiduis lineis dimetientur, qu&aelig;qu&eacute;; longitudine, qu&aelig;qu&eacute;; potentia &longs;unt commen&longs;urabi&shy;<lb/>les. </s>
8707 
8708 <s>indiuidu&aelig; autem line&aelig; &longs;ibi ip&longs;is commen&longs;urabiles &longs;unt longitudine, cum inter &longs;e <lb/>fiat &aelig;quales; quare potentia quoque, quod &longs;i hoc e&longs;t, diuiduum erit quadratum.<emph.end type="italics"/></s></p><pb pagenum="207"/><p type="main">
8709 
8710 <s>Pergit adhuc nouis rationibus aduer&longs;arios refellere, dicens, &longs;i extarent <lb/>huiu&longs;modi indiuidu&aelig; line&aelig;, &longs;equeretur omnes omnin&ograve; lineas e&longs;&longs;e commen&shy;<lb/>&longs;urabiles, quod e&longs;t contra demon&longs;trata in 10. Elem. 
8711 
8712 quia cum omnes line&aelig; <lb/><expan abbr="con&longs;t&etilde;t">con&longs;tent</expan> per ip&longs;os ex lineis atomis, i&longs;t&aelig; atom&aelig; e&longs;&longs;ent omnium linearum com&shy;<lb/>munes men&longs;ur&aelig;, vnde &amp; ill&aelig;, qu&aelig; dicuntur potentia tantum commen&longs;ura&shy;<lb/>biles, vt &longs;upra explicaui, erunt etiam commen&longs;urabiles longitudine. </s>
8713 
8714 <s>indiui&shy;<lb/>du&aelig; ver&ograve; ip&longs;&aelig;, cum &longs;int inuicem &aelig;quales, erunt ip&longs;&aelig; <expan abbr="quoq;">quoque</expan> commen&longs;urabi&shy;<lb/>les longitudine, quare &amp; potentia, omnes enim longitudine commen&longs;ura&shy;<lb/>biles, &longs;unt etiam potentia commen&longs;urabiles, ex 9. 10. vnde &longs;equitur qua&shy;<lb/>drata earum omnia e&longs;&longs;e <expan abbr="quoq;">quoque</expan> commen&longs;urabilia: <expan abbr="atq;">atque</expan> hinc con&longs;equitur, in&shy;<lb/>quit, ea e&longs;&longs;e <expan abbr="quoq;">quoque</expan> diuidua (quam con&longs;ecutionem probat infra num. </s>
8715 
8716 <s>290.) <lb/>vnde &longs;equeretur ip&longs;am <expan abbr="quoq;">quoque</expan> lineam latus quadrati po&longs;&longs;e diuidi, non igitur <lb/>ponenda erat indiuidua.</s></p><p type="main">
8717 
8718 <s><arrow.to.target n="marg275"/></s></p><p type="margin">
8719 
8720 <s><margin.target id="marg275"/>285</s></p><p type="main">
8721 
8722 <s>Nonus Iocus, cuius latinam interpretationem, cum admodum e&longs;&longs;et de&shy;<lb/>prauata ex gr&aelig;co textu, in hunc modum correxi <emph type="italics"/>(Pr&aelig;terea c&ugrave;m circa maio&shy;<lb/>rem lstitudinem facit applicata, &aelig;quale ei, quod ab indiuidua, &amp; pedali copulatis <lb/>circa bipedalem, minorem faciet latitudinem, qu&agrave;m &longs;it indiuidua: erit minus, quod <lb/>circa indiuiduam)<emph.end type="italics"/> ide&longs;t c&ugrave;m minor linea applicata cum maiore, latitudinem <lb/><figure place="text" xlink:href="figures-la/009.01.207.1.tif"/><lb/>faciat. </s>
8723 
8724 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->linea minor A B, applicata cum ma&shy;<lb/>iori B C, vt in figura, ita vt contineant figuram <lb/>A B C D. <!-- KEEP S--></s>
8725 
8726 
8727 
8728 
8729 
8730 <s>Minor A B, facit latitudinem figur&aelig;, <lb/>maior ver&ograve; B C, facit longitudinem. </s>
8731 
8732 <s>Iam cum <lb/>aduer&longs;arij velint extare huiu&longs;modi lineas ato&shy;<lb/>mas, con&longs;tituatur figura &longs;ub vna ex illis, qu&aelig; &longs;it v. <!-- REMOVE S-->g. <!-- REMOVE S-->A B, &amp; altera maiori, <lb/>qu&aelig; &longs;it pedalis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->B C, vt in pr&aelig;cedenti figura, &longs;umatur deinde linea bi&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.207.2.tif"/><lb/>pedalis E F, cui per 45. primi ap&shy;<lb/>plicetur &longs;patium E F G H, &aelig;quale <lb/>&longs;patio &longs;uperiori A B C D, nece&longs;&longs;a&shy;<lb/>ri&ograve; latitudo E H, huius &longs;ecund&aelig; fi&shy;<lb/>gur&aelig; minor erit qu&agrave;m latitudo il&shy;<lb/>lius, hoc e&longs;t minor, qu&agrave;m &longs;it indinidua A B, quod e&longs;t ab&longs;urdum. </s>
8733 
8734 
8735 
8736 
8737 
8738 
8739 
8740 
8741 
8742 <s>vel dicere <lb/>oportet <expan abbr="&longs;pati&utilde;">&longs;patium</expan> eirca indiuiduam A B, e&longs;&longs;e minus qu&agrave;m i&longs;tud po&longs;terius, quod <lb/>e&longs;t contra con&longs;tructionem, &amp; propterea pariter inconueniens, non igitur <lb/>huiu&longs;modi line&aelig; &longs;unt ponend&aelig;.</s></p><p type="main">
8743 
8744 <s><arrow.to.target n="marg276"/></s></p><p type="margin">
8745 
8746 <s><margin.target id="marg276"/>286</s></p><p type="main">
8747 
8748 <s>Decimus locus <emph type="italics"/>(Cum ex tribus datis lineis triangulus componatur, ex tribus <lb/><expan abbr="quoq;">quoque</expan> indiuiduis lineis componi poterit. </s>
8749 
8750 <s>in omni autem &aelig;quilatero perpendicularis <lb/>in mediam ba&longs;im mcidit, quare, &amp; in medium indiuidu&aelig;.<emph.end type="italics"/></s></p><p type="main">
8751 
8752 <s>Ex 22. primi Elem. 
8753 
8754 ex tribus datis lineis, quarum qu&aelig;libet du&aelig; &longs;int, re&shy;<lb/>liqua maiores pote&longs;t con&longs;titui triangulum: poterit igitur ex tribus indiui&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.207.3.tif"/><lb/>duis con&longs;titui <expan abbr="tri&atilde;gulum">triangulum</expan>, <expan abbr="illud&qacute;">illudque</expan>; &aelig;quilaterum, cum omnes in&shy;<lb/>diuidu&aelig; line&aelig; &longs;int &aelig;quales. </s>
8755 
8756 <s>&longs;it igitur ex eis triangulum A B C, <lb/>&longs;i igitur ab angulo A, ducatur perpendicularis A D, ad ba&longs;im <lb/>B C, eam bifariam &longs;ecabit ex &longs;cholio 26. primi, erit igitur li&shy;<lb/>nea B C, &longs;ecabilis, contra quam aduer&longs;arij opinantur.</s></p><p type="main">
8757 
8758 <s><arrow.to.target n="marg277"/></s></p><p type="margin">
8759 
8760 <s><margin.target id="marg277"/>287</s></p><p type="main">
8761 
8762 <s>Vndecimus locus <emph type="italics"/>(Si quadratum ex quatuor indiuiduis con&longs;tuatuatur diametro <lb/>protracta, &amp; perpendiculari ducta, quadrati co&longs;ta potentia <expan abbr="perp&etilde;dicularem">perpendicularem</expan>, diame-<emph.end type="italics"/><pb pagenum="208"/><emph type="italics"/>trumqu&eacute; mediam &aelig;quat: quare non erit minima. </s>
8763 
8764 <s>neque duplum erit &longs;patium &agrave; diame&shy;<lb/>tro con&longs;urgens illius, quod ab indiuidua procreatur: nans &aelig;quali ablato, reliquum <lb/>erit minus indiutdua, nam &longs;i &aelig;qualis, diameter quadruplum de&longs;criberet, &amp;c.)<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.208.1.tif"/><lb/>ide&longs;t &longs;i per 46 primi quadratum. </s>
8765 
8766 <s>v.g. <!-- REMOVE S-->A B C D, ex qua&shy;<lb/>tuor in&longs;ecabilibus componatur, cuius diametro B C, <lb/>perpendicularis A E, in&longs;i&longs;tat, erit per 47. primi qua&shy;<lb/>dratum line&aelig; A B, &aelig;quale quadratis <expan abbr="linear&utilde;">linearum</expan> A E, E B, <lb/>quare tam E B, qu&agrave;m A E, minores erunt ip&longs;a A B; <lb/>quare ip&longs;a non erit minima cum &longs;it indiuidua, quod e&longs;t <lb/>ab&longs;urdum. </s>
8767 
8768 
8769 
8770 <s>Pr&aelig;terea ex &longs;cholio 47. primi, quadratum <lb/>C B F G, diametri C B, duplum e&longs;t quadrati A B C D, <lb/>erg&ograve; diameter C B, maior qu&agrave;m A B. <!-- KEEP S--></s>
8771 
8772 <s>Auferatur igitur ab ip&longs;a, C B, &aelig;qua&shy;<lb/>lis ip&longs;i A B, qu&aelig; igitur reliqua erit, vel erit &aelig;qualis ip&longs;i A B, vel minor. </s>
8773 
8774 <s>non <lb/>&aelig;qualis, quia tunc diameter dupla e&longs;&longs;et lateris A B, &amp; quadratum diametri <lb/>quadruplum foret quadrati lateris A B. ex &longs;cholio 4. &longs;ecundi, quod ab&longs;ur&shy;<lb/>dum e&longs;t, repugnat enim 47. primi. </s>
8775 
8776 <s>nec minor, quia hoc modo exi&longs;teret linea <lb/>qu&aelig;dam minor minima, &longs;cilicet atoma, quod pariter e&longs;t inconueniens.</s></p><p type="main">
8777 
8778 <s><arrow.to.target n="marg278"/></s></p><p type="margin">
8779 
8780 <s><margin.target id="marg278"/>288</s></p><p type="main">
8781 
8782 <s>Duodecimus locus <emph type="italics"/>(Amplius &longs;i qu&aelig;uis linea pr&aelig;ter in&longs;ectilem in partes diui&shy; <lb/>di pote&longs;t, t&ugrave;m &aelig;quales, t&ugrave;m in&aelig;quales, &longs;eindatur linea in tria fru&longs;ta, qu&aelig; non con&shy;<lb/>&longs;tet ex tribus atomis, &longs;ed vniuer&longs;aliter ex imparibus numero atomis, &longs;ic diui&longs;a erit <lb/>linea indiuidua. </s>
8783 
8784 <s>&longs;imiliter autem &longs;i in duo diuidatur linea, qu&aelig; ex imparibus <expan abbr="c&otilde;&longs;tat">con&longs;tat</expan>)<emph.end type="italics"/><lb/>hoc e&longs;t detur linea qu&aelig;piam ab aduer&longs;ario ex lineis indiuiduis numer&ograve; im&shy;<lb/>paribus, con&longs;tans. </s>
8785 
8786 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->ex quinque; h&aelig;c diuidi pote&longs;t in tres &aelig;quas partes <lb/>per 10.6. Si igitur diuidatur in tria &aelig;qualia, nece&longs;&longs;ari&ograve; tres ex atomis illam <lb/>integrantibus erunt di&longs;&longs;ect&aelig;, nam tertia qu&aelig;libet pars continebit indiui&shy;<lb/>duam vnam cum duabus tertijs alterius partibus. </s>
8787 
8788 
8789 
8790 
8791 
8792 <s>idem accidet &longs;i bifariam <lb/>per 10. primi, &longs;ecetur qu&aelig;uis ex imparibus numero atomis conflata.</s></p><p type="main">
8793 
8794 <s><arrow.to.target n="marg279"/></s></p><p type="margin">
8795 
8796 <s><margin.target id="marg279"/>289</s></p><p type="main">
8797 
8798 <s>Decimustertius locus <emph type="italics"/>(Quod &longs;i bifariam quidem non omnis linea finditur, &longs;ed <lb/>qu&aelig; &longs;olum ex paribus conflata &longs;it. </s>
8799 
8800 <s>&longs;i iam in duas partes diui&longs;a, in <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> diuidi <lb/>pote&longs;t diuideretur, &longs;ic <expan abbr="quoq;">quoque</expan> in&longs;ectilis linea diuideretur, quando ex paribus compo&shy;<lb/>&longs;ita, per in&aelig;qualia &longs;cinderetur)<emph.end type="italics"/> ide&longs;t, quod &longs;i dixerit aduer&longs;arius, non omnem <lb/>lineam bifariam diuidi po&longs;&longs;e, &longs;ed eam &longs;ol&ugrave;m, qu&aelig; ex numero paribus atomis <lb/>con&longs;titerit: ea igitur diuidatur primo bifariam. </s>
8801 
8802 <s>deinde iterum diuidatur <lb/>quomodocunque, ide&longs;t &amp; bifariam, &amp; non bifariam, nam hoc etiam pacto <lb/>indiuidua diuidetur, quod e&longs;t inconueniens.</s></p><p type="main">
8803 
8804 <s><arrow.to.target n="marg280"/></s></p><p type="margin">
8805 
8806 <s><margin.target id="marg280"/>290</s></p><p type="main">
8807 
8808 <s>Decimusquartus locus <emph type="italics"/>(Amplius non e&longs;&longs;et cuiu&longs;uis line&aelig; quadratum: babe&shy;<lb/>ret enim longitudinem, &amp; latitudinem; <expan abbr="atq;">atque</expan> idcirc&ograve; diui&longs;ibile erit, cum illa quidem<lb/>aliquid, b&aelig;c autem aliquid aliud; quod &longs;i quadratum diuiduum e&longs;t, &amp; linea, vnde <lb/>procreatur, diuidua erit)<emph.end type="italics"/> po&longs;&longs;e &longs;uper quamuis datam lineam quadratum de&shy;<lb/>&longs;cribi patet ex 46. primi, quadratum igitur de&longs;criptum ab indiuidua, cum <lb/>&longs;it &longs;uperficies, latitudinem, ac longitudinem habebit, qu&aelig; diuer&longs;&aelig; &longs;unt di&shy;<lb/>men&longs;iones. </s>
8809 
8810 <s>poterit erg&ograve; &longs;ecundum <expan abbr="vtramq;">vtramque</expan> diuidi; ex qua diui&longs;ione nece&longs;&shy;<lb/>&longs;ari&ograve; latera ip&longs;ius, hoc e&longs;t line&aelig;, quas indiuiduas illi ponunt diuidentur, <lb/>quod e&longs;t inconueniens, non igitur indinidu&aelig; erunt.</s></p><p type="main">
8811 
8812 <s><arrow.to.target n="marg281"/></s></p><p type="margin">
8813 
8814 <s><margin.target id="marg281"/>291</s></p><p type="main">
8815 
8816 <s>Decimusquintus locus <emph type="italics"/>(Adbuc etiam, vt linea &longs;ic, &amp; &longs;uper&longs;icies, &amp; corpus <lb/>crit impartibile: vno quippe indiuiduo exi&longs;tente, c&aelig;tera <expan abbr="quoq;">quoque</expan> con&longs;equentur, quia<emph.end type="italics"/><pb pagenum="209"/><emph type="italics"/>vnum per aliud diuiditur, at corpus indiuiduum non e&longs;t, cum in &longs;e latitudinem, &amp; <lb/>profunditatem contineat: quare nec linea pote&longs;t e&longs;&longs;e atoma. </s>
8817 
8818 <s>corpus &longs;iquidem in &longs;u&shy;<lb/>per&longs;icies, &longs;uperficies ver&ograve; in lineas &longs;oluitur)<emph.end type="italics"/> hoc e&longs;t: pr&aelig;terea, quemadmodum <lb/>linea per aduer&longs;arium extat indiuidua, &longs;ic &amp; fuperficies ab eadem linea de&shy;<lb/>&longs;cripta erit atoma, &amp; corpus ab hac &longs;uperficie de&longs;criptum erit impartibile. <lb/></s>
8819 
8820 <s>Sciendum enim, quod ex motu puncti de&longs;cribitur linea: ex motu line&aelig; de&shy;<lb/>&longs;cribitur &longs;uperficies: ex motu tandem &longs;uperficiei corpus ortum habet, vt &longs;o&shy;<lb/>let in horum definitionibus explicari.</s></p><p type="main">
8821 
8822 <s>Si igitur horum vnum nemp&egrave; linea &longs;it atoma, &amp; reliqua, qu&aelig; ab ip&longs;a ma&shy;<lb/>nant erunt indiui&longs;a, quia corpus diuiditur per &longs;uperficiem, &amp; &longs;uperficies <lb/>per lineam, ide&longs;t ad diui&longs;ionem corporis nece&longs;&longs;e e&longs;t diuidi &longs;uperficiem, &amp; ad <lb/>&longs;uperficiei diui&longs;ionem diuidi lineam, qu&aelig; ip&longs;am terminat. </s>
8823 
8824 <s>At cum omne <lb/>corpus latitudinem, &amp; profunditatem habeat, nullum poterit extare cor&shy;<lb/>pus, quod diuidi nequeat; quare neque illud, quod ab atoma linea oriretur. <lb/></s>
8825 
8826 <s>Quare nec linea illa corporis procreatrix erit indiuidua; corpus &longs;iquidem <lb/>in &longs;uperficies, &amp; &longs;uperficies in lineas quodammodo re&longs;oluitur: &amp; ex diui&shy;<lb/>&longs;ione &longs;olidi &longs;uperficies &longs;ecari debet, &amp; demum &longs;uperficiei, &longs;ectionem line&aelig; <lb/>&longs;ectio &longs;ub&longs;equitur. </s>
8827 
8828 <s>Tollend&aelig; igitur &longs;unt de rerum natura line&aelig; atom&aelig;.</s></p><p type="main">
8829 
8830 <s><arrow.to.target n="marg282"/></s></p><p type="margin">
8831 
8832 <s><margin.target id="marg282"/>292</s></p><p type="main">
8833 
8834 <s>Decimus&longs;extus locus <emph type="italics"/>(Quin etiam orbis circunferentia rectam lineam pluri&shy;<lb/>bus tanget punctis, punctus enim contactus, quiqu&eacute; e&longs;t in circulo, quiqu&eacute; e&longs;t in recta, <lb/>&longs;e &longs;e mutu&ograve; tangunt. </s>
8835 
8836 <s>quod &longs;i hoc fieri nequit, <expan abbr="neq;">neque</expan> punctus punctum tangere valet: <lb/>quod &longs;i &longs;e tangere nequeunt, <expan abbr="neq;">neque</expan> linea punctis con&longs;tare pote&longs;t, nam neque punctum <lb/>tangere nece&longs;&longs;arium e&longs;t.<emph.end type="italics"/></s></p><p type="main">
8837 
8838 <s>In 2. 3. &amp; corollario eius demon&longs;tratur circuli peripheriam tangere re&shy;<lb/>ctam lineam in vnico puncto. </s>
8839 
8840 <s>iam &longs;i linea con&longs;taret ex punctis indiuiduis <lb/>tanquam partibus, po&longs;&longs;et circulus <expan abbr="t&atilde;gere">tangere</expan> rectam lineam in duobus punctis. <lb/><figure place="text" xlink:href="figures-la/009.01.209.1.tif"/><lb/>Sit circulus, cuius centrum A, tangens lineam <lb/>rectam B C, con&longs;tantem ex punctis, quorum vnus <lb/>&longs;it in extremo D, line&aelig; B D, alterum ver&ograve; in E, <lb/>principio line&aelig; E C, circulus A, tangere poterit <lb/>in F, termino communi vtriu&longs;que line&aelig;, hocque <lb/>modo tanget <expan abbr="vtrunq;">vtrunque</expan> punctum D, &amp; E, quod e&longs;t <lb/>impo&longs;&longs;ibile per 2. 3. &longs;equitur igitur <expan abbr="neq;">neque</expan> illa duo puncta D, E, &longs;e mutu&ograve; tan&shy;<lb/>gere, &amp; eadem ratione nulla alia <expan abbr="p&utilde;cta">puncta</expan> eiu&longs;dem line&aelig;, ex quibus manife&longs;tum <lb/>e&longs;t, impo&longs;&longs;ibile e&longs;&longs;e, lineam ex huiu&longs;modi punctis con&longs;tare po&longs;&longs;e.</s></p><p type="main">
8841 
8842 <s>Reliqua huius opu&longs;culi, quamuis Mathematica alicui videri po&longs;&longs;int, <lb/>non tamen &longs;unt, non enim linearibus indigent demon&longs;trationi&shy;<lb/>bus, <expan abbr="neq;">neque</expan> ex Geometri&aelig; principijs procedunt. </s>
8843 
8844 <s>ad Phy&longs;i&shy;<lb/>cum igitur pertinebunt, cuius e&longs;t di&longs;putare, num <lb/>indiuidua exi&longs;tant, &amp; quomodo in quanti&shy;<lb/>tate, <expan abbr="id&qacute;">idque</expan>; rationibus aliunde, qu&agrave;m <lb/>ex Geometria deductis.</s></p><pb pagenum="210"/><p type="head">
8845 
8846 <s><emph type="italics"/>In Librum de Propriet. <!-- REMOVE S-->Elementorum.<emph.end type="italics"/><!-- KEEP S--></s>
8847 
8848 </p><p type="main">
8849 
8850 <s>Libellum de cau&longs;is proprietatum Elementorum, quamuis nonnulla <lb/>mathematica loca contineat, tamen, quia cert&ograve; con&longs;tat ex ijs, <lb/>qu&aelig; in eo de Secta Arabum, de Sclauis, de Dalmatis, qui multis <lb/>po&longs;t Ari&longs;totelem &longs;&aelig;culis floruerunt, auctorem alium e&longs;&longs;e ab Ari&longs;to&shy;<lb/>tele con&longs;ult&ograve; &amp; merit&ograve; omi&longs;i.</s></p><p type="head">
8851 
8852 <s><emph type="italics"/>In Librum de Cau&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
8853 
8854 <s>Alterum de cau&longs;is libellum pariter pr&aelig;termi&longs;i, cum is vocibus Arabi&shy;<lb/>cam barbariem redolentibus &longs;cateat: phra&longs;is pr&aelig;terca, &amp; qu&ecedil;dam <lb/>de Deo dicta, plan&egrave; indicant authorem non e&longs;&longs;e Ari&longs;tctelem; &longs;ed potius <lb/>Arabem quempiam.</s></p></chap><pb pagenum="211"/><chap><p type="head">
8855 
8856 <s>EX LIBRO NONO<lb/>DE HIST. ANIMALIVM</s></p><p type="head">
8857 
8858 <s><emph type="italics"/>Araneorum industri&aelig;.<emph.end type="italics"/></s></p><p type="main">
8859 
8860 <s><arrow.to.target n="marg283"/></s></p><p type="margin">
8861 
8862 <s><margin.target id="marg283"/>293</s></p><p type="main">
8863 
8864 
8865 <s>Cap. 39. <emph type="italics"/>(Aranei &longs;tatim cum editi &longs;unt, fila mittunt, non ab intrin&longs;eco <lb/>tanquam excrementum, vt Democritus ait, &longs;ed ab extrin&longs;eco de &longs;uo cor&shy;<lb/>pore, veluti cortice; aut more eorum animalium, qu&aelig; &longs;uos villos iacu&shy;<lb/>lantur, vt hystricis)<emph.end type="italics"/> Cum olim in hunc locum incidi&longs;&longs;em, ince&longs;&longs;ic <lb/>animum meum illa cupido, vt &longs;cilicet cert&ograve; &longs;cirem, numiure, an iniuria <lb/>Ari&longs;t. Democritum hoc loco reijceret, Araneum fila ab intrin&longs;eco emitte&shy;<lb/>re a&longs;&longs;erentem: quapropter ad magi&longs;tram rerum experientiam confugi, ac&shy;<lb/>cepto manu bacillo Araneum quendam ex ijs, qui circulares telas, quas <lb/><expan abbr="n&otilde;nulli">nonnulli</expan>, &amp; quidem apt&egrave; labyrinthos appellant, ingenio <expan abbr="vtiq;">vtique</expan> mathematico <lb/>contexunt, lic adij, vt Araneus pro arbittio &longs;uper bacillum liber&egrave; inambu&shy;<lb/>laret, dum ip&longs;e interim curio&longs;ius illum ob&longs;eruarem, quanam videlicet ex <lb/>parte filum foras ederet; cum ecce tibi Araneus experienti mihi vltr&ograve; fa&shy;<lb/>uens &longs;e &longs;e ex baculo demi&longs;it, ita tamen, vt ex filo &longs;uo in aere &longs;u&longs;pen&longs;us re&shy;<lb/>maneret. </s>
8866 
8867 <s>cum primum ob&longs;eruo ip&longs;um inuer&longs;um, hoc e&longs;t capite deor&longs;um, &amp; <lb/>ventre &longs;ur&longs;um pendere. </s>
8868 
8869 <s>vt autem acutius cernerem, eum opac&aelig; cuidam rei <lb/>oppo&longs;ui, ne pr&aelig; nimia luce tenui&longs;&longs;imum aranei filum aciem oculorum effu&shy;<lb/>geret; quo facto in temperata luce illa, clari&longs;&longs;im&egrave; videbam filum ex &longs;ece&longs;&longs;u <lb/>aranei prodire. </s>
8870 
8871 <s><expan abbr="Araneum&qacute;">Araneumque</expan>; vno pede filum illud retinere, ne amplius exi&shy;<lb/>ret, <expan abbr="longius&qacute;">longiusque</expan>; fieret, qu&agrave;m &longs;uo con&longs;ilio par e&longs;&longs;et. </s>
8872 
8873 <s>coegi deinde ip&longs;um a&longs;cen&shy;<lb/>dere, &amp; de&longs;cendere &longs;&aelig;pius, donec cert&ograve; certius, mihi con&longs;titi&longs;&longs;et filum illud <lb/>non ab extrin&longs;eco, vt hoc loco Ari&longs;t. 
8874 
8875 affirmat, &longs;ed ab intrin&longs;eco quippe ex <lb/>&longs;ece&longs;&longs;u prodire, ac proinde veri&longs;&longs;imam e&longs;&longs;e quamuis ab Ari&longs;t. 
8876 
8877 reiectam De&shy;<lb/>mocriti &longs;ententiam. </s>
8878 
8879 <s>cum Ari&longs;t. 
8880 
8881 pariter errauit Vly&longs;&longs;es Aldobrandus in &longs;uo <lb/>de in&longs;ectis pulcherrimo, <expan abbr="atq;">atque</expan> docti&longs;&longs;imo Opere.</s></p><p type="main">
8882 
8883 <s>Verumenimuer&ograve; opportun&egrave; accidit, vt huius dubitationis &longs;olutio, aliam <lb/>mihi alterius qu&aelig;&longs;tionis, iam olim &longs;ummis votis expetitam afferret expli&shy;<lb/>cationem. </s>
8884 
8885 <s>ea e&longs;t huiu&longs;modi. </s>
8886 
8887 <s>&longs;&aelig;pius fueram expertus, Araneos quo&longs;dam e&longs;&shy;<lb/>&longs;e, qui ex vno loco ad alium omnin&ograve; &longs;ibi inacce&longs;&longs;ibilem, tran&longs;eant, &longs;iue quod <lb/>idem e&longs;t, ex eo loco, ad illum fila deducant, vt ex vna arbore ad aliam; <lb/>quamuis inter <expan abbr="vtramq;">vtramque</expan> aut aqu&aelig;, aut den&longs;il&longs;ima &longs;pineta, ac &longs;epes interpo&shy;<lb/>nantur. </s>
8888 
8889 <s>quod maxim&egrave; mane &aelig;quitantes experimur, dum nobis fila per vias <lb/>tran&longs;uer&longs;a, oculis, atque vultui obuiantia adh&aelig;rent. </s>
8890 
8891 <s>Qua ratione id Ara&shy;<lb/>neus perficeret, neminem, quiliteris manda&longs;&longs;et, reperi, ne ip&longs;um quidem. <lb/></s>
8892 
8893 <s>Vly&longs;&longs;em Aldobrandum, qui in hac eruditorum pal&aelig;&longs;tra, maiores no&longs;tros <lb/>omnes videtur &longs;upera&longs;&longs;e. </s>
8894 
8895 <s>Phy&longs;iologi &agrave; me hac de re interrogati, varij va&shy;<lb/>ria, nec con&longs;entientia refpondebant. </s>
8896 
8897 <s>Alij aiebant Araneum &longs;e demittere, <lb/>ac &longs;u&longs;pendere ex vna arbore, &amp; deinde ad aliam &agrave; vento perferri, at ego his <lb/>minim&egrave; a&longs;&longs;entiebar, quia m Araneo nullum e&longs;&longs;et naturale in&longs;trumentum, <pb pagenum="212"/>veluti velum, in quod ventus po&longs;&longs;itimpingere. </s>
8898 
8899 <s>Alij Araneum ex vna arbo&shy;<lb/>re de&longs;cendere, &amp; po&longs;tea alteram con&longs;cendere, interim emi&longs;&longs;um retro filum <lb/>raptando, ac deinde &longs;ur&longs;um attrahendo attollere, ac pr&aelig;tendere: &longs;ed ho&shy;<lb/>rum re&longs;pon&longs;ionum ob plurima impedimenta, qu&aelig; tenui&longs;&longs;imum filum &longs;&aelig;pius <lb/>&longs;cidi&longs;&longs;ent, &longs;ubridens refellebam. </s>
8900 
8901 <s>Alij ver&ograve; aiebant Araneum qualitate qua&shy;<lb/>dam pr&aelig;ditum e&longs;&longs;e, qua ip&longs;e per aera, non &longs;ecus, ac per aquam pi&longs;ces, &amp; <lb/>per aerem volucres, ambulare po&longs;&longs;et. </s>
8902 
8903 <s>Verum opinatio i&longs;ta, ne ri&longs;u quidem <lb/>digna videbatur. </s>
8904 
8905 <s>Huius igitur qu&aelig;&longs;iti &longs;olutionem, quam omnes ad hanc <lb/><expan abbr="v&longs;q;">v&longs;que</expan> diem latui&longs;&longs;e put&ograve;, <expan abbr="quam&qacute;">quamque</expan>; omnibus grati&longs;&longs;imam fore cognoui tibi lo&shy;<lb/>co auctarij initio promi&longs;&longs;i, nunc per&longs;oluam. </s>
8906 
8907 <s>accidit erg&ograve;, vt dicebam, vt <lb/>dum Araneus fug&aelig; cupidus ex bacillo in temperat&aelig; lucis loco, nimirum &egrave; <lb/>regione alicuius opaci penderet, vt cernerem ex filo illo, ex quo &longs;u&longs;pende&shy;<lb/>batur plura alia fila hinc inde alternatim prodire, quemadmodum ex alter&shy;<lb/>nis arundinum nodis folia ena&longs;ci &longs;olent. </s>
8908 
8909 <s>qu&aelig; fila, innata l&aelig;uitate, per ae&shy;<lb/>rem quoquo ver&longs;us ceu natantia diffundebantur. </s>
8910 
8911 <s>factum e&longs;t autem, vt eo&shy;<lb/>rum vnum quendam arboris cuiu&longs;dam ramum attingeret, <expan abbr="ei&qacute;">eique</expan>; &longs;tatim adh&aelig;&shy;<lb/>reret; quod illic&ograve; Araneus optim&egrave; per&longs;en&longs;it, quippe quod filum illud vi&longs;ce&shy;<lb/>ribus eius ex altero capite affigeretur, atque per filum illud, alijs ommi&longs;&longs;is, <lb/>&longs;ubit&ograve;, vti egregius funambulus accurrit, &longs;ed tamen pedibus &longs;ur&longs;um, dor &longs;o <lb/>autem deor&longs;um, non &longs;upra filum, &longs;ed infra ad ramum illum &longs;e contulit, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <lb/>me ho&longs;tem &longs;uum fuga &longs;&aelig;pius elu&longs;it. </s>
8912 
8913 <s>Ex qna repetita &longs;&aelig;pius ob&longs;eruatione lu&shy;<lb/>ce clarius comperi Araneum non &longs;implex filum, &longs;ed ramo&longs;um, ac multiplex <lb/>emittere, <expan abbr="atq;">atque</expan> aliquando ex &longs;ece&longs;&longs;u etiam ip&longs;o duo &longs;imul eijcere, <expan abbr="alter&utilde;">alterum</expan> quo <lb/><figure place="text" xlink:href="figures-la/009.01.212.1.tif"/><lb/>&longs;u&longs;pendatur, alterum <lb/>ver&ograve;, quod &longs;orte hac, <lb/><expan abbr="atq;">atque</expan> illac volitans, ali&shy;<lb/>cui rei occurrat, <expan abbr="atq;">atque</expan> <lb/>h&aelig;reat, per quod po&shy;<lb/>&longs;tea ip&longs;e incedens, ad <lb/>locum &longs;ibi prius inac&shy;<lb/>ce&longs;&longs;um, aditum parat. <lb/></s>
8914 
8915 <s>qua inre fures eos per&shy;<lb/>bell&egrave; imitatur, qui <lb/>&longs;chalas ex funibus con&shy;<lb/>textas, ac hamis fer&shy;<lb/>reis munitas, ad fene&shy;<lb/>&longs;tras proijciunt, vt per <lb/>cas ibi affixas con&longs;cen&shy;<lb/>dere queant. </s>
8916 
8917 <s>qu&aelig; om&shy;<lb/>nia ex appo&longs;ita figura <lb/>melius percipies, vbi <lb/>ex &longs;ini&longs;tra arbore pen&shy;<lb/>det Araneus A, ex filo <lb/>B A, ex quo tanquam <lb/>rami alia fila C G, D H, <lb/>E I, M O, F L, alter&shy;<pb pagenum="213"/>natim prodeunt, ac per aerem hinc inde volitant. </s>
8918 
8919 <s>Si erg&ograve; filum E I, dextr&aelig; <lb/>arbori occurrerit, <expan abbr="ei&qacute;">eique</expan>; h&aelig;&longs;erit, vt in figura, illic&ograve; Araneus huius rei con&shy;<lb/>&longs;cius per filum A E I, a&longs;cendit, <expan abbr="&longs;e&qacute;">&longs;eque</expan>; ad prius inacce&longs;&longs;am &longs;ibi dextram arbo&shy;<lb/>rem transfert; <expan abbr="atq;">atque</expan> deinde inter <expan abbr="vtramq;">vtramque</expan> ducto iam filo vno, pote&longs;t vltr&ograve;, <lb/><expan abbr="citro&qacute;">citroque</expan>; means, &longs;uam etiam circularem, ac labyrinthiacam telam in mu&longs;ca&shy;<lb/>rum capturam contexere; quales aliquando inter duas arbores admira&shy;<lb/>ri &longs;olemus.</s></p><p type="main">
8920 
8921 <s>Qu&aelig;res fort&egrave;, num Araneus filum intus tanquam in glomo, vel fpira con&shy;<lb/>uolutum contineat? </s>
8922 
8923 <s>dicam, quod non &longs;ine experientia conijcio, exi&longs;timo <lb/>Araneum non continere intra &longs;e filum vllum, verum humorem quendam <lb/>vi&longs;co&longs;um, qui in tenui&longs;&longs;ima fila &longs;it ductilis; quemadmodum videmus acci&shy;<lb/>dere gummi, qu&aelig; di&longs;rupta exhibet lentorem quendam, qui &longs;olo attritu ita <lb/>digitis h&aelig;ret, vt amoto &longs;en&longs;im digito, filum tenue, &amp; oblongum vald&egrave; de&shy;<lb/>ducatur, hoc inde conijcio, quia aliquando cum ventrem Araneorum &longs;ecui&longs;&shy;<lb/>&longs;em nullum intus filum, &longs;ed &longs;olus humor quidam lentus apparuit.</s></p><p type="main">
8924 
8925 <s>C&ugrave;m ex paruulis hi&longs;ce meis ob&longs;eruationibus circa animalculum i&longs;tud <lb/>vnum tam pr&aelig;clara cognoui&longs;&longs;em, qu&aelig; nullus ad hanc <expan abbr="v&longs;q;">v&longs;que</expan> diem, quod &longs;ciam <lb/>ob&longs;erua&longs;&longs;et; animaduerti lati&longs;&longs;imum patere campum ad animalium hi&longs;to&shy;<lb/>riam ampliandam, &longs;i ij, qui huic pulcherrim&aelig; cognitioni dant operam, non <lb/>ijs &longs;olum, qu&aelig; ab alijs per&longs;cripta &longs;unt contenti e&longs;&longs;ent, ver&ugrave;m etiam certi&longs;&shy;<lb/>&longs;imis, <expan abbr="atq;">atque</expan> explorati&longs;&longs;imis experientijs ea coniungerent.</s></p><p type="main">
8926 
8927 <s>Atque h&aelig;c de Araneo &longs;atis.</s></p></chap><chap><p type="head">
8928 
8929 <s><emph type="italics"/>De ince&longs;&longs;u animalium.<emph.end type="italics"/></s></p><p type="main">
8930 
8931 <s><arrow.to.target n="marg284"/></s></p><p type="margin">
8932 
8933 <s><margin.target id="marg284"/>294</s></p><p type="main">
8934 
8935 
8936 <s>Cap. 7. <emph type="italics"/>(Etenim habentia pedes, quoniam &longs;uper <expan abbr="vtrumq;">vtrumque</expan> oppo&longs;itorum cru&shy;<lb/>rum vici&longs;&longs;im &longs;tant, pondusqu&eacute; &longs;ustinent, nece&longs;&longs;e habent altero progredien&shy;<lb/>te, inflectere alterum; &aelig;qualia namque longitudine nata &longs;unt habere op&shy;<lb/>po&longs;ita membra. </s>
8937 
8938 
8939 <s>&amp; quod ponderi &longs;ub&longs;tat rectum e&longs;&longs;e oportet, vt perpen&shy;<lb/>diculum ad terram. </s>
8940 
8941 <s>quando autem progreditur, fit hypotenu&longs;a, valens manentem <lb/>magnitudinem, &amp; eam, qu&aelig; interiacet. </s>
8942 
8943 <s>quoniam autem &aelig;qualia &longs;unt membra, ne&shy;<lb/>ce&longs;&longs;e e&longs;t inflecti id, quod manet, aut in poplite, aut in conflexione)<emph.end type="italics"/> Vult probare <lb/>in gre&longs;&longs;u nece&longs;&longs;ariam e&longs;&longs;e aliquam flexionem membrorum. </s>
8944 
8945 <s>verum prius <lb/>&longs;ciendum, quod lineam hypotenu&longs;am, quemadmodum etiam Athen&aelig;us lib. <lb/><!-- REMOVE S-->10. te&longs;tatur, eam appellant geometr&aelig;, qu&aelig; in triangulo rectangulo recto <lb/>angulo &longs;ubtenditur, vnde &amp; denominata e&longs;t hypotenu&longs;a, ide&longs;t &longs;ubten&longs;a, vt <lb/><figure place="text" xlink:href="figures-la/009.01.213.1.tif"/><lb/>in triangulo A B C, cuius angulus B, rectus &longs;it, recta <lb/>A C, angulo recto B, &longs;ubten&longs;a, hypotenu&longs;a dicitur. <lb/></s>
8946 
8947 
8948 
8949 <s>Ari&longs;t. 
8950 
8951 igitur ait, quod antequam animal ambulare in&shy;<lb/>cipiat, dum &longs;cilicet manet, habet crura, qu&aelig; manent <lb/>recta, &longs;iue perpendicularia horizonti, cum autem in&shy;<lb/>cipit progredi nece&longs;&longs;e e&longs;t <expan abbr="vtr&utilde;q;">vtrunque</expan> crus inclinari ad ho&shy;<lb/>rizontem. </s>
8952 
8953 <s>nam primum crus in ingre&longs;lu prolatum fit <lb/>hypotenu&longs;a, quia &longs;cilicet &longs;ubtendit angulum rectum, <lb/>quem facit alterum crus adhuc quie&longs;cens, cum hori&shy;<pb pagenum="214"/>zonte; vt in &longs;uperiori triangulo, &longs;i concipiamus crura fui&longs;&longs;e duo latera A B, <lb/>A D, qu&aelig; manente animali, fui&longs;&longs;ent ambo &longs;imul in &longs;itu A B, perpendicula&shy;<lb/>ria horizonti; incipiens autem animal ambulare, proferat primo crus A D, <lb/>A D, fiet hypotenu&longs;a trianguli A B C, &amp; quia crus hoc A D, factum hypo&shy;<lb/>tenu&longs;a &aelig;quale e&longs;t alteri manenti A B, nequit totius ver&aelig; hypotenuf&aelig; A C, <lb/>officio fungi, qu&aelig; &aelig;quiualet toti A D, &amp; pr&aelig;terea interiacenti D C, vrea au&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.214.1.tif"/><lb/>tem hypotenu&longs;a debet e&longs;&longs;e maior, quia opponitun <lb/>maiori angulo nimirum recto B, quam latus A B, <lb/>quod angulo acuto C, opponitur per 19. primi, &amp; <lb/>propterea ni&longs;i alterum &longs;ub&longs;equens crus A B, incli&shy;<lb/>netur, vt in &longs;ecunda figura, non pote&longs;t hypotenu&longs;a <lb/>A D, terram attingere, <expan abbr="atq;">atque</expan> hac de cau&longs;a nece&longs;&longs;e <lb/>e&longs;t, vt initio gre&longs;&longs;us <expan abbr="vtrumq;">vtrumque</expan> crus, quod prius per&shy;<lb/>pendiculare erat, inclinetur; inclinato igitur crure <lb/>A B, antror&longs;um tunc prolatum crus A C, terram <lb/>contingit, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; factus e&longs;t primus gre&longs;&longs;us B C.<!-- KEEP S--></s></p><p type="main">
8954 
8955 <s><arrow.to.target n="marg285"/></s></p><p type="margin">
8956 
8957 <s><margin.target id="marg285"/>295</s></p><p type="main">
8958 
8959 <s>Eodem loco <emph type="italics"/>(Signum autem, quod hoc ita &longs;e habet illud est. </s>
8960 
8961 <s>&longs;i quis enim iuxta <lb/>parietem per terram ambulet, qu&aelig; de&longs;ignatur linea non e&longs;t recta, &longs;ed obtorta, quo&shy;<lb/>niam minorem quidem flectentis fieri de&longs;criptam nece&longs;&longs;e e&longs;t; &longs;tantis autem, &amp; ere&shy;<lb/>cti maiorem)<emph.end type="italics"/> Vt probet, quod animal in gradiendo modo attollitur, modo <lb/>deprimitur, &longs;ignum hoc affert, quia &longs;i quis &longs;ecus parietem per terram am&shy;<lb/>bulet, linea quam vertex capitis in pariete de&longs;ignat non e&longs;t recta, &longs;eb obtor&shy;<lb/>ta: qu&aelig; linea optim&egrave; de&longs;ignatur, &longs;i ambulantis vmbra in pariete apparens <lb/>&longs;imul, cum ip&longs;o in pariete ambulet; videmus enim vmbram illam modo al&shy;<lb/>tiorem fieri, modo breuiorem; quod &longs;ignum e&longs;t ambulantem modo incli&shy;<lb/>nari, quando &longs;cilicet crus alterum profert, &longs;eu crura dilatat; modo erigi, <lb/>cum crus &longs;ub&longs;equens pr&aelig;ce denti coniungit, tune enim incedens fit horizon&shy;<lb/>ti perpendicularis.</s></p><p type="main">
8962 
8963 <s><arrow.to.target n="marg286"/></s></p><p type="margin">
8964 
8965 <s><margin.target id="marg286"/>296</s></p><p type="main">
8966 
8967 <s>Eodem cap. <emph type="italics"/>(Quoniam autem fiat ad rectum, vel concidet recto minore effe&shy;<lb/>cto, vel non progredietur: &longs;i enim altero crure recto progreditur alterum, maius <lb/>erit cum &longs;it &aelig;quale: hoc <expan abbr="nanq;">nanque</expan> poterit, &amp; id, quod quie&longs;cit, &amp; ip&longs;am hypotenu&shy;<lb/>&longs;am, nece&longs;&longs;e igitur e&longs;t, &amp; inflectere id, quod procurrit, &amp; inflexum &longs;imul alterum <lb/>extendere, membra enim triangulorum &aelig;quilaterorum efficiuntur, <expan abbr="caput&qacute;">caputque</expan>, fit infe&shy;<lb/>rius, vbi perpendiculum fuerit, in quo firmatum e&longs;t)<emph.end type="italics"/> H&aelig;c &longs;unt fer&egrave; eadem cum <lb/>ijs, qu&aelig; in primo huius capitis loco dicta &longs;unt. </s>
8968 
8969 <s>proinde ea cum duabus illis <lb/>triangulorum figuris repetenda &longs;unt, vt breuius qu&aelig; nunc re&longs;tant explicen&shy;<lb/>tur. </s>
8970 
8971 <s>quoniam igitur animal antequam gradiatur, maxim&egrave; homo, &longs;tat hori&shy;<lb/>zonti perpendicularis, nece&longs;&longs;e e&longs;t ad progrediendum, vt fiat aliqua mem&shy;<lb/>brorum inflexio, &longs;i enim homo &longs;ine vlla &longs;ui corporis flexura inclinet &longs;e ad <lb/>horizontem, ita vt cum horizonte faciat ex anteriori parte. </s>
8972 
8973 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->angulum <lb/>recto minorem, &longs;iue acutum, vel concidet, vel non poterit progredi; &longs;i enim <lb/>alterum crus pr&aelig;mitteretur, altero manente perpendiculari, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; progre&shy;<lb/>deretur qui&longs;piam, &longs;equeretur crus prolatum, quale e&longs;t A D, iu priori trian&shy;<lb/>gulo, debere fieri maius altero crure A B, manente, quia fieret tota hypo&shy;<lb/>tenu&longs;a A C, &longs;ie enim terram attingeret; at non pote&longs;t fieri illo maius, quia <lb/>e&longs;t illi &aelig;quale, erg&ograve; hac ratione ince&longs;&longs;us fieri nequit. </s>
8974 
8975 
8976 
8977 
8978 
8979 <s>nece&longs;&longs;e igitur refle&shy;<pb pagenum="215"/>ctere <expan abbr="vtrumq;">vtrumque</expan> crus non &longs;olum ad horixontem, &longs;ed etiam circa aliquam cor&shy;<lb/>poris flexuram, vel nodum, vt circa genu, aut alia. </s>
8980 
8981 <s>crura enim in gre&longs;&longs;u fiunt <lb/>latera &longs;uperiora trianguli i&longs;o&longs;celis, vt in &longs;ecunda figura patuit, cuius ba&longs;is <lb/>e&longs;t pa&longs;&longs;us. </s>
8982 
8983 <s>&amp; tunc caput ambulantis fit inferius, qu&agrave;m antequam gradere&shy;<lb/><figure place="text" xlink:href="figures-la/009.01.215.1.tif"/><lb/>tur; quia tunc ambo crura erant horizonti perpen&shy;<lb/>dicularia. </s>
8984 
8985 <s>quando autem caput fuerit in linea <expan abbr="per-p&etilde;diculari">per&shy;<lb/>pendiculari</expan> trianguli i&longs;o&longs;celis, tunc erit inferius qu&agrave;m <lb/>alibi, vt in pr&ecedil;&longs;enti figura, linea <expan abbr="perp&etilde;dicularis">perpendicularis</expan> trian&shy;<lb/>guli huius i&longs;o&longs;celis e&longs;t linea A E, quia ba&longs;i B C, per&shy;<lb/>pendicularis incidit; quando igitur caput ambulan&shy;<lb/>tis. </s>
8986 
8987 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->D, fuerit in hac linea, <expan abbr="t&utilde;c">tunc</expan> erit inferius qu&agrave;m <lb/>in quauis alia gre&longs;&longs;us parte: quia tunc crura A B, <lb/>A C, &longs;unt maxim&egrave; diuaricata, &amp; proinde angulus A, <lb/>&amp; &longs;imul punctum D, maxim&egrave; demi&longs;&longs;a.</s>
8988 
8989 
8990 
8991 </p></chap><chap><p type="head">
8992 
8993 <s><emph type="italics"/>De motu animalium.<emph.end type="italics"/></s></p><p type="main">
8994 
8995 <s><arrow.to.target n="marg287"/></s></p><p type="margin">
8996 
8997 <s><margin.target id="marg287"/>297</s></p><p type="main">
8998 
8999 
9000 <s>Cap. 1. <emph type="italics"/>(Primum quidem in animalibus: oportet enim &longs;i moueatur aliqua <lb/>particularum quie&longs;cere ahquam, &amp; propter hoc, &amp; flexus animalibus <lb/>in&longs;unt: tanquam enim centro vtuntur flex: bus &amp; fit tota pars, in qua <lb/>e&longs;t flexus &amp; vna, &amp; du&aelig;; &amp; recta, &amp; flexa, qu&aelig; permutatur potentia, <lb/>&amp; actu, propter flexum. </s>
9001 
9002 
9003 <s>cum autem flectitur, &amp; mouetur, hoc quidem &longs;ignum mo-<emph.end type="italics"/><lb/><figure place="text" xlink:href="figures-la/009.01.215.2.tif"/><lb/><emph type="italics"/>etur, illud autem manet in flexibus, quemadmodum <expan abbr="vtiq;">vtique</expan> &longs;i dia&shy;<lb/>metri, qu&aelig; quidem A D, maneat, qu&aelig; cutem B, moueatur, &amp; <lb/>fiat A C, &longs;ed hic quidem videtur, &longs;ecundum omnem modum in&shy;<lb/>diui&longs;ibile e&longs;&longs;e centrum. </s>
9004 
9005 <s>etenim moueri, vt aiunt, fingunt in ip&longs;is, <lb/>non enim mouetur mathematicorum aliquid.<emph.end type="italics"/></s></p><p type="main">
9006 
9007 <s>Intendit probare nece&longs;&longs;e e&longs;&longs;e ad motum animalium, vt <lb/>vna pars quie&longs;cat, dum altera mouetur. </s>
9008 
9009 <s>propter hoc enim inquit flexus ani&shy;<lb/>malibus in&longs;unt, vbi in gr&aelig;co pro voce flexus legitur <foreign lang="greek">xampth,</foreign> quod &longs;ignifi&shy;<lb/>cat nodum, articulum, &amp; <expan abbr="deniq;">denique</expan> locum ip&longs;um, vbi fit membri flexura, tan&shy;<lb/>quam enim centro quodam vtuntur flexibus, ide&longs;t nodis, &longs;eu iunctur&aelig; &longs;unt <lb/>in motu membrorum in&longs;tar centri. </s>
9010 
9011 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->nodus cubiti fit centrum, cum bra&shy;<lb/>chij parte, qu&aelig; e&longs;t inter humerum, &amp; cubitum manente, reliquum brachij <lb/>circumducimus; &longs;ic manente genu tanquam centro, crus huc illud agita&shy;<lb/>mus, &amp; fit tota pars. </s>
9012 
9013 
9014 
9015 
9016 
9017 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->totum brachium, in quo e&longs;t cubiti iunctura, &amp; vna <lb/>tota pars, quando manet rectum; &amp; du&aelig; <expan abbr="qu&atilde;do">quando</expan> in flexura cubiti brachium <lb/>infle ctitur; &amp; fit tota h&aelig;c longitudo recta prius, po&longs;tea flexa: qu&aelig; propter <lb/>flexuram modo vna e&longs;t actu, &longs;ed du&aelig; potentia. </s>
9018 
9019 
9020 
9021 
9022 
9023 <s>modo du&aelig; in actu, &longs;ed vna in <lb/>potentia. </s>
9024 
9025 <s>cum autem flectitur, &amp; mouetur brachium, vnum quidem fignum, <lb/>&longs;iue punctum, quod e&longs;t extremum partis manentis, manet; alterum ver&ograve; &longs;i&shy;<lb/>gnum, &longs;iue punctum, quod e&longs;t extremum partis mot&aelig; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; alteri &longs;igno con&shy;<lb/>tiguum mouetur &longs;imul cum tota parte mota. </s>
9026 
9027 <s>quemadmodum, &longs;i diametri <lb/>&longs;uperioris figur&aelig;, pars D A, maneat, pars autem A B, moueatur ad A C, <lb/>erit huius flexur&aelig; centrum A, quod vt extremum line&aelig; D A, manentis, ma&shy;<pb pagenum="216"/>net: vt ver&ograve; extremum mot&aelig; A B, mouetur. </s>
9028 
9029 <s>quamuis in mathematicis h&aelig;c <lb/>quidem duorum centrorum di&longs;tinctio nulla &longs;it, quia centrum mathemati&shy;<lb/>cum omnin&ograve; indiuiduum e&longs;t: neque in mathematicis e&longs;t propri&egrave; motus, <lb/>quamuis enim aliquando Mathematici dicant, &longs;i linea, vel &longs;i punctum mo&shy;<lb/>ueretur, vel moueatur, &amp; &longs;imilia, huiu&longs;modi tamen motus &longs;unt rebus ma&shy;<lb/>thematicis extrin&longs;eci, nec quatenus hoc modo mouentur con&longs;iderantur: <lb/>patet igitur, qua ratione Ari&longs;tot. partem manentem in motu nece&longs;&longs;ariam <lb/>e&longs;&longs;e velit.</s>
9030 
9031 </p><p type="main">
9032 
9033 <s><arrow.to.target n="marg288"/></s></p><p type="margin">
9034 
9035 <s><margin.target id="marg288"/>298 a</s></p><p type="main">
9036 
9037 
9038 <s>Cap. 5. <emph type="italics"/>(Quemadmodum autem &longs;pontanea mouentur paruo motu facto)<emph.end type="italics"/> Spon&shy;<lb/>tanea i&longs;ta erant machin&aelig;, qu&aelig; &agrave; &longs;eip&longs;is mouebantur, quas Gr&aelig;ci automata <lb/>dixerunt, cuin&longs;modi &longs;unt Automata Heronis Alexandrini, qu&aelig; adhuc <expan abbr="ext&atilde;t">extant</expan>.</s>
9039 </p><p type="main">
9040 
9041 
9042 <s>Cap. 8. E&longs;t ibi quoddam triangulum cum elementis more geometrarum <lb/>depictum, vnde locus ille videri po&longs;&longs;it mathematicus, verumtamen nullo <lb/>modo geometri&aelig; auxilio indiget.</s>
9043 </p></chap><chap><p type="head">
9044 
9045 <s><emph type="italics"/>De generatione animalium.<emph.end type="italics"/></s></p><p type="main">
9046 
9047 <s><arrow.to.target n="marg289"/></s></p><p type="margin">
9048 
9049 <s><margin.target id="marg289"/>298.b</s></p><p type="main">
9050 
9051 <s>Lib. 2. cap. 
9052 
9053 1. <emph type="italics"/>(Sitqu&eacute; perinde ac admirabilia illa &longs;pontanea)<emph.end type="italics"/> Intelligit ma&shy;<lb/>chinas illas miro artificio confictas, qu&aelig; &agrave; &longs;e ip&longs;is intrin&longs;eco prin&shy;<lb/>cipio mouebantur, quas Gr&aelig;ci veteres Automata, ide&longs;t &longs;pontanea, <lb/>vel &longs;pontina, vt vertit Interpres vocabant, cuiu&longs;modi &longs;unt Auto&shy;<lb/>mata Heronis Alexandrini, qu&aelig; adhuc extant gr&aelig;ca, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; ab Abbate Gua&shy;<lb/>&longs;tallen&longs;i in Italicum &longs;unt conuer&longs;a. </s>
9054 
9055 <s>Automata hodie &longs;unt Horologia, qu&aelig; ex <lb/>multis dentatis rotis Germani con&longs;truunt.</s></p><p type="main">
9056 
9057 <s><arrow.to.target n="marg290"/></s></p><p type="margin">
9058 
9059 <s><margin.target id="marg290"/>299</s></p><p type="main">
9060 
9061 <s>Lib. 2. cap. 
9062 
9063 4. <emph type="italics"/>(Nam &amp; triangula figura duobus rectis &aelig;quale &longs;emper habet)<emph.end type="italics"/><lb/>vide qu&aelig; de hac re &longs;crip&longs;i lib. 
9064 
9065 1. Priorum, &longs;ecto 3. cap. 
9066 
9067 1.<!-- KEEP S--></s></p><p type="main">
9068 
9069 <s><arrow.to.target n="marg291"/></s></p><p type="margin">
9070 
9071 <s><margin.target id="marg291"/>300</s></p><p type="main">
9072 
9073 <s>Ibidem <emph type="italics"/>(Et diametrum incommen&longs;urabilem e&longs;&longs;e cum co&longs;t a &longs;empiternum e&longs;t: at&shy;<lb/>tamen cau&longs;a eorum aliqua &amp; demon&longs;tratio e&longs;t.<emph.end type="italics"/></s></p><p type="main">
9074 
9075 <s>Qu&aelig;libro 1. Priorum, &longs;ecto 1. cap. 
9076 
9077 23. de hac re annotata &longs;unt, abund&egrave; <lb/>huic etiam loco &longs;atisfaciunt.</s></p></chap><chap><p type="head">
9078 
9079 <s><emph type="italics"/>In Ethica, &longs;eu Moralia ad Nicomachum.<emph.end type="italics"/></s></p><p type="main">
9080 
9081 <s><arrow.to.target n="marg292"/></s></p><p type="margin">
9082 
9083 <s><margin.target id="marg292"/>301</s></p><p type="main">
9084 
9085 <s>Lib. 1. cap. 
9086 
9087 7. <emph type="italics"/>(Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/><expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic ver&ograve; cum ve&shy;<lb/>ritatis &longs;peculator &longs;it, quid, &amp; qualis &longs;it, indagat)<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/>confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/><figure place="text" xlink:href="figures-la/009.01.216.1.tif"/><lb/>qu&aelig; nihil aliud e&longs;t qu&agrave;m angulus rectus, qu&aelig; vulg&ograve; <lb/>&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re&shy;<lb/>ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; norm&aelig;, aut amu&longs;&longs;is du&shy;<lb/>ctu &longs;ua ip&longs;i opera ad angulos rectos, ide&longs;t quadrata, <lb/>conficiunt. </s>
9088 
9089 <s>Geometra ver&ograve; con&longs;iderat eundem an&shy;<lb/>gulum, quatenus fit &agrave; linea &longs;uper lineam aliam per&shy;<lb/>pendiculariter in&longs;i&longs;tente, vt e&longs;t in definit. </s>
9090 
9091 <s>10. primi, <pb pagenum="217"/>vt in figura, vbi linea A B, in&longs;i&longs;tens alteri D C, perpendiculariter, ide&longs;t ita <lb/>vt faciat angulos hinc inde &aelig;qualis A B D, A B C, pr&aelig;dictos inquam duos <lb/>angulos con&longs;iderat e. </s>
9092 
9093 <s>&longs;e rectos. </s>
9094 
9095 <s>contemplatur pr&aelig;terea Geometra omnes <lb/>angulos rectos e&longs;&longs;e inter &longs;e &aelig;quales, vt in 12. axiomate primi Elem. 
9096 
9097 ponitur, <lb/>&amp; &longs;imilia plura alia, quorum con&longs;iderationem Faber omnin&ograve; negligit.</s></p><p type="main">
9098 
9099 <s><arrow.to.target n="marg293"/></s></p><p type="margin">
9100 
9101 <s><margin.target id="marg293"/>302</s></p><p type="main">
9102 
9103 <s>Libro 2. capite 6. <emph type="italics"/>(Id quod &longs;ecundum Arithmeticam rationem medium e&longs;t)<emph.end type="italics"/><lb/>Arithmetica ratio, fiue proportio ea e&longs;t, cuius termini cre&longs;cunt per &aelig;qua&shy;<lb/>les exce&longs;&longs;us, vt 2. 6. 10. 14. horum enim terminorum exce&longs;&longs;us &aelig;quales &longs;unt, <lb/>cum &longs;int omnes quaternarij. </s>
9104 
9105 <s>&longs;imiliter inter hos terminos 3. 6. 9. 12. e&longs;t arith&shy;<lb/>metica analogia, c&ugrave;m omnes ternario numero &longs;uperent pr&aelig;cedentes, &amp; &agrave; <lb/>&longs;equentibus &longs;uperentur. </s>
9106 
9107 <s>Porr&ograve; apud Mathematicos tria &longs;unt genera pro&shy;<lb/>portionum, &longs;iue medietatum, Arithmetica quam modo &longs;uppo&longs;ui; Geome&shy;<lb/>trica, &amp; Harmonica, quas inferius oblata occa&longs;ione opportunius explicabo.</s></p><figure place="text" xlink:href="figures-la/009.01.217.1.tif"/><p type="main">
9108 
9109 <s><arrow.to.target n="marg294"/></s></p><p type="margin">
9110 
9111 <s><margin.target id="marg294"/>303</s></p><p type="main">
9112 
9113 <s>Lib. 2. cap. 
9114 
9115 9. <emph type="italics"/>(Vt circuli medium deprehendere non <lb/>cuiu&longs;libet, &longs;ed <expan abbr="&longs;ci&etilde;tis">&longs;cientis</expan> &longs;olummodo e&longs;t)<emph.end type="italics"/> Reperire medium, <lb/>&longs;iue centrum dati circuli docet Euclides propo&longs;itio&shy;<lb/>ne prima 3. hoc modo. </s>
9116 
9117 <s>in datocirculo ducatur vt&shy;<lb/>cunque recta B C, qu&aelig; per 10. primi diuidatur bifa&shy;<lb/>riam in F, &amp; per F, ducatur <expan abbr="perp&etilde;dicularis">perpendicularis</expan> A E F D, <lb/>qu&aelig; &longs;ecetur bifariam in E, <expan abbr="erit&qacute;">eritque</expan>; punctum E, non &longs;o&shy;<lb/>lum ip&longs;ius line&aelig; medium; &longs;ed etiam totius circuli <lb/>centrum, quemadm odum ibi demon&longs;trat Euclides.<!-- KEEP S--></s></p><p type="main">
9118 
9119 <s><arrow.to.target n="marg295"/></s></p><p type="margin">
9120 
9121 <s><margin.target id="marg295"/>304</s></p><p type="main">
9122 
9123 <s>Lib. 3. cap. 
9124 
9125 3. <emph type="italics"/>(De &aelig;ternis autem nemo con&longs;ultat, vt <lb/>de mundo, aut diametro, &amp; latere, quod nulla inter &longs;e <lb/>&aelig;quabilitate conueniant)<emph.end type="italics"/> Qua ratione diameter, &amp; latus eiu&longs;dem quadrati <lb/>nulia &aelig;quabilitate, ide&longs;t nulla communi men&longs;ura inter &longs;e conueniant, fus&egrave; <lb/>explicatum e&longs;t libro Priorum, &longs;ecto 1. cap. 
9126 
9127 23.</s></p><p type="main">
9128 
9129 <s><arrow.to.target n="marg296"/></s></p><p type="margin">
9130 
9131 <s><margin.target id="marg296"/>305</s></p><p type="main">
9132 
9133 <s>Eodem cap. <emph type="italics"/>(Qui enim con&longs;ultat qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, <lb/>quemadmodum de&longs;ignationes)<emph.end type="italics"/> Per de&longs;ignationes Ari&longs;t. 
9134 
9135 intelligere geometri&shy;<lb/>cas demon&longs;trationes &longs;&aelig;pius dictum e&longs;t in logicis textibus, quod pariter ex <lb/>hoc loco confirmatur. </s>
9136 
9137 <s>quando autem ait <emph type="italics"/>(Re&longs;olutre pr&aelig;dicto modo, quemad&shy;<lb/>modum de&longs;ignationes)<emph.end type="italics"/> innuit re&longs;olutionem geometricam, de qua abund&egrave; di&shy;<lb/>ctum e&longs;t in explicatione tituli librorum Re&longs;olutoriorum; quam expo&longs;ui, ni&shy;<lb/>hil aliud e&longs;&longs;e, quam medij inqui&longs;itionem ad id, quod propo&longs;itum fuerit de&shy;</s></p><p type="main">
9138 
9139 <s><arrow.to.target n="marg297"/><lb/>mon&longs;trandum. </s>
9140 
9141 <s>veram autem, <expan abbr="atq;">atque</expan> germanam fui&longs;&longs;e huiu&longs;modi explicatio&shy;<lb/>nem, hoc loco Ari&longs;t. 
9142 
9143 ip &longs;e confirmat, cum hanc re&longs;olutionem dicat e&longs;&longs;e &longs;imi&shy;<lb/>lem con&longs;ultationi, &longs;iue inqui&longs;itioni mediorum ad finem in rebus practicis <lb/>con&longs;equendum; ip &longs;a ver&ograve; e&longs;t inqui&longs;itio mediorum ad id, quod in rebus &longs;pe&shy;<lb/>culatiuis propo&longs;itum e&longs;t, demon&longs;trandum. </s>
9144 
9145 <s>con&longs;ultatio igitur e&longs;t in rebus <lb/>practicis, quod in &longs;peculatiuis e&longs;t re&longs;olutio.<lb/><arrow.to.target n="marg298"/></s></p><p type="margin">
9146 
9147 <s><margin.target id="marg297"/>306</s></p><p type="margin">
9148 
9149 <s><margin.target id="marg298"/>307</s></p><p type="main">
9150 
9151 <s>Lib. 5. cap. 
9152 
9153 3. <emph type="italics"/>(Quod en m proportione con&longs;tat, id non tam vnitario numero, <lb/>qu&agrave;m numero in vniuer&longs;um proprium e&longs;t)<emph.end type="italics"/> Per vnitarium numerum intelligitur <lb/>numerus ex vnitatibus ab&longs;tractis con&longs;litus, ide&longs;t, cuius vnitates non &longs;int res <lb/>phy&longs;ic&aelig;, &longs;ed &agrave; naturalibus ab&longs;tract&aelig;, qualis con&longs;iderat Arithmeticus: omni <lb/>tamen numero &longs;iue ab&longs;tracto, &longs;iue non, connenit proportiones &longs;u&longs;cipere, <lb/>id e&longs;t &amp; numero, &amp; rebus numeratis.</s></p><pb pagenum="218"/><p type="main">
9154 
9155 <s><arrow.to.target n="marg299"/></s></p><p type="margin">
9156 
9157 <s><margin.target id="marg299"/>308</s></p><p type="main">
9158 
9159 <s>Ibidem <emph type="italics"/>(Nim proportio &aelig;qualitas e&longs;t rationum)<emph.end type="italics"/> Per proportionem hoc lo&shy;<lb/>co intelligenda e&longs;t illa, quam nunc appellant proportionalitatem, qu&aelig; e&longs;t <lb/>duarum rationum, &longs;eu proportionum &longs;imilitudo, &longs;iue &aelig;qualitas, vt manife&shy;<lb/>&longs;tum e&longs;t ex 4. definit. </s>
9160 
9161 <s>5. Elem. 
9162 
9163 v. <!-- REMOVE S-->g. <!-- REMOVE S-->cum &longs;it eadem ratio 9. ad 6. qu&aelig; e&longs;t 6. ad <lb/>4. propterea h&aelig;c rationum &longs;imilitudo, vel &aelig;qualitas dicitur ip&longs;a proportio, <lb/>&longs;eu di&longs;tinctionis gratia Proportionalitas.<!-- KEEP S--></s>
9164 
9165 
9166 
9167 </p><p type="main">
9168 
9169 <s><arrow.to.target n="marg300"/></s></p><p type="margin">
9170 
9171 <s><margin.target id="marg300"/>309</s></p><p type="main">
9172 
9173 <s>Ibidem <emph type="italics"/>(In quatuorqu&eacute; minimis reperitur, di&longs;iunctam &longs;an&egrave; in quatuor con&longs;istere <lb/>per&longs;picuum e&longs;t: &longs;ed &amp; continentem nibilominus, vno enim h&aelig;c perinde, ae duobus <lb/>vtitur, bi&longs;que id accipit in bunc modum, qualis primi re&longs;pectus e&longs;t ad &longs;ecundum, <lb/>talis &longs;ecundi ad tertium; bis enim bic, &longs;ecundum dictum e&longs;t, quare &longs;i &longs;ecundum bis <lb/>po&longs;itum &longs;it, quatuor erunt ea, qu&aelig; con&longs;tant proportione)<emph.end type="italics"/> Qu&aelig; hic ab Ari&longs;tot. di&shy;<lb/>cuntur de&longs;umpta &longs;unt, partim ex definit. </s>
9174 
9175 
9176 
9177 <s>6. 5. partim ex 9. definit. </s>
9178 
9179 <s>eiu&longs;dem. <lb/></s>
9180 
9181 <s>breuiter autem &longs;ic &longs;e habent. </s>
9182 
9183 <s>Ad con&longs;tituendam proportionalitatem ne&shy;<lb/>ce&longs;&longs;arij &longs;unt omnin&ograve; quatuor termini, quod quidem primum per&longs;picuum <lb/>e&longs;t in ea proportionalitate, quam Difiunctam vocant, qu&aelig; e&longs;t huiu&longs;modi, <lb/>vt 9. ad 6. ita 3. ad 2. deinde <expan abbr="ver&utilde;">verum</expan> e&longs;t etiam in ea, quam continuam dicunt, <lb/>qu&aelig; talis e&longs;t, vt 9. ad 6. ita 6. ad 4. qu&aelig; in tribus quidem terminis 9. 6. 4. <lb/>con&longs;i&longs;tit, &longs;ed tamen, qnia medius 6. <expan abbr="vtrumq;">vtrumque</expan> re&longs;picit extremum, ide&ograve; vices <lb/>duorum gerit, ac proinde e&longs;t, ac &longs;i hoc modo termini di&longs;ponantur 9. 6. 6. 4. <lb/>vbi 6. bis ponitur, <expan abbr="&longs;unt&qacute;">&longs;untque</expan>; quatuor huius etiam proportionalitatis termini. <lb/></s>
9184 
9185 <s>hinc Ari&longs;t. 
9186 
9187 textum &longs;atis intelligere poteris.</s></p><p type="main">
9188 
9189 <s><arrow.to.target n="marg301"/></s></p><p type="margin">
9190 
9191 <s><margin.target id="marg301"/>310</s></p><p type="main">
9192 
9193 <s>Eodem cap. <emph type="italics"/>(Sicut igitur primus terminus &longs;e babebit ad &longs;ecundum, ita tertius <lb/>ad quartum; igitur etiam alterna vice, &longs;icut primus ad tertium, ita &longs;ecundus ad <lb/>quartum. </s>
9194 
9195 <s>quare etiam totum ad totum, quod di&longs;tributio binatim copulat. </s>
9196 
9197 <s>qu&aelig; &longs;i <lb/>etiam ita compo&longs;ita fuerint, iust&egrave; copulat)<emph.end type="italics"/> Accipit Ari&longs;t. 
9198 
9199 illum argumentandi <lb/>modum, quem Geometr&aelig; alternam rationem vocant, <expan abbr="qu&agrave;m&qacute;">qu&agrave;mque</expan>; definit. </s>
9200 
9201 <s>12. <lb/>5. exponunt, vt eam rebus ip&longs;is accommodet, <expan abbr="atq;">atque</expan> in praxim deducat; e&longs;t <lb/>autem huiu&longs;modi, &longs;int primum quatuor termini proportionales, ide&longs;t, vt <lb/>primus ad &longs;ecundum, ita tertius ad quartum. </s>
9202 
9203 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->vt 9. ad 6. ita 3. ad 2. <lb/>valet con&longs;equentia h&aelig;c, erg&ograve; etiam alternatim erit, vt primus ad tertium, <lb/>ita &longs;ecundus ad quartum, v. <!-- REMOVE S-->g. <!-- REMOVE S-->in allato exemplo, ita erit 9. ad 3. vt 6. ad 2. <lb/>quam &longs;equelam e&longs;&longs;e validam probat deinde Euclides propo&longs;it. </s>
9204 
9205 
9206 
9207 
9208 
9209 
9210 
9211 
9212 
9213 <s>16. 5. hinc <lb/>aliam deducit con&longs;equentiam, quam Euclides propo&longs;it. </s>
9214 
9215 <s>12. 5. demon&longs;trat, <lb/>dum ait, quare etiam totum ad totum erit. </s>
9216 
9217 <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->quia conclu&longs;um e&longs;t ita e&longs;&longs;e <lb/>9. ad 3. quemadmodum 6. ad 2. ita etiam erit totum ad totum, ide&longs;t ita <lb/>etiam erunt antecedentes termini &longs;imul ad con&longs;equentes &longs;imul, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ita erit <lb/>etiam totum 15. quod e&longs;t totum ex antecedentibus terminis 9. &amp; 6. ad to&shy;<lb/>tum 5. conflatum ex con&longs;equentibus terminis 3. &amp; 2. In &longs;umma igitur &longs;i fue&shy;<lb/>rit vt 9. ad 3. ita 6. ad 2. ita etiam erit 15. ad 5. quod verum e&longs;&longs;e apparet in <lb/>his numeris, cum tam 9. ad 3. qu&agrave; 6. ad 2. &amp; 15. ad 5. habeant triplam <lb/>proportionem.</s>
9218 
9219 
9220 
9221 
9222 
9223 
9224 
9225 </p><p type="main">
9226 
9227 <s>Horum exemplum in rebus practicis &longs;it hoc: &longs;it vt Plato ad Proclum, ita <lb/>mille aurei ad quingentos aureos, erg&ograve; alternatim ita erit Plato ad 1000. <lb/>aureos, &longs;icuti Proclus ad 500. quare ita etiam totum erit ad totum, &longs;cilicet <lb/>Plato, &amp; Proclus &longs;imul ad 1000. &amp; 500. &longs;imul, qu&aelig; duo tota, di&longs;tributio mo&shy;<lb/>ralis, ac practica diuidit, &amp; binatim copulat, hoc modo dicens, vt Plato ad <pb pagenum="219"/>Proclum, ita 1000. ad 500, &amp; po&longs;tea, vt Plato ad 1000. ita Proclus ad 500. <lb/>iuxta <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> merita, &amp; quidem i&longs;ta e&longs;t huiu&longs;modi moralis di&longs;tributio, cum <lb/>modis argumentandi ab Euclide comprobatis, nitatur.</s></p><p type="main">
9228 
9229 <s><arrow.to.target n="marg302"/></s></p><p type="margin">
9230 
9231 <s><margin.target id="marg302"/>311</s></p><p type="main">
9232 
9233 <s>Ibidem <emph type="italics"/>(Hanc ver&ograve; proportionalitatem Mathematici Geometricam vocant: <lb/>propterea quod in Geometrica euenit, vt eandem totum ad totum rationem habeat, <lb/>quam habet alterutrum, ad alterutrum)<emph.end type="italics"/> ide&longs;t, hanc duarum Geometricarum <lb/>rationum &longs;imilitudinem Mathematici proportionalitatem Geometricam <lb/>appellant, propterea quod in hac duarum rationum geometricarum &longs;imili&shy;<lb/>tudine accidit, vt &longs;it totum ad totum, quemadmodum etiam partes toto&shy;<lb/>rum, vt &longs;upra explicatum e&longs;t; quod non accidit in duarum proportionum <lb/>arithmeticarum &longs;imilitudine; &longs;i enim ponamus has duas rationes arithme&shy;<lb/>ticas &longs;imiles, vt 10. ad 8. ita 6. ad 4. qu&aelig; &longs;unt &longs;imiles, propter &longs;imiles exce&longs;&shy;<lb/>&longs;us primorum, &amp; &longs;ecundorum terminorum, cum <expan abbr="vbiq;">vbique</expan> exce&longs;&longs;us &longs;it binarij. <lb/></s>
9234 
9235 <s>non erit tamen totum 16. ad totum 12. in eadem ratione cum diui&longs;is ter&shy;<lb/>minis, cum ibi &longs;it exce&longs;&longs;us binarij, hic ver&ograve; quaternarij. </s>
9236 
9237 <s>h&aelig;c videtur e&longs;&longs;e <lb/>Ari&longs;t. 
9238 
9239 ratio; quam adhuc melius declara&longs;&longs;e libet. </s>
9240 
9241 <s>Geometrica igitur pro&shy;<lb/>portionalitas ita dicta e&longs;t, quia qu&aelig;libet proportio pote&longs;t in materia Geo&shy;<lb/>metrica, lineis, &longs;uperficiebus, &amp; corporibus continuari in quatuor termi&shy;<lb/>nis, ita vt proportionalitas, &longs;eu &longs;imilitudo rationum exurgat, quod in nu&shy;<lb/>meris fieri &longs;emper nequit, cum plures fint proportiones, qu&aelig; numeris ex&shy;<lb/>primi nequeunt, vt &longs;unt e&aelig;, quas irrationales appellant, cuiu&longs;modi e&longs;t inter <lb/>diametrum, &amp; co&longs;tam eiu&longs;dem quadrati, cuius nec proportio, nec propor&shy;<lb/>tionalitas in numeris reperiri pote&longs;t, qu&aelig; tamen in lineis, &longs;uperficiebus, ac <lb/>corporibus e&longs;&longs;e po&longs;&longs;unt: e&longs;t enim vt diameter vnius quadrati ad latus eiu&longs;&shy;<lb/>dem, ita idem latus ad aliam lineam inuentam per 11. 6. vel vt diameter ad <lb/>co&longs;tam, ita qu&aelig;libet alia linea ad aliam inuentam, per 12. 6. omnis igitur <lb/>proportionalitas rebus Geometricis ine&longs;&longs;e pote&longs;t; non autem numeris, in <lb/>quibus &longs;olum po&longs;&longs;unt e&longs;&longs;e rationes rationales, &longs;eu <expan abbr="rer&utilde;">rerum</expan> commen&longs;urabilium; <lb/>latius igitur patet Geometrica h&aelig;c &longs;imilitudo, qu&agrave;m Arithmetica, c&ugrave;m <lb/>Geometrica complectatur tam rationales, qu&agrave;m irrationales. </s>
9242 
9243 <s>merit&ograve; igi&shy;<lb/>tur talis proportionalitas appellari debuit &agrave; rebus Geometricis, in quibus <lb/>&longs;emper reperitur, non autem ab Arithmeticis, cum quibus &longs;&aelig;pius reperiri <lb/>nequit. </s>
9244 
9245 <s>Vide Campanum in e