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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Biancani, Giuseppe</author> <title>Aristotelis loca mathematica</title> <date>1615</date> <place>Bologna</place> <translator/> <lang>la</lang> <cvs_file>bianc_locam_009_la_1615</cvs_file> <cvs_version/> <locator>009.xml</locator> </info> <text> <front> <pb xlink:href="009/01/001.jpg"/> <section> <p type="head"> <s id="s.000001">ARISTOTELIS <lb/>LOCA MATHEMATICA <lb/> Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/> & explicata.</s> </p> <p type="head"> <s id="s.000002"><emph type="italics"/>Aristotelicæ videlicet expo&longs;itionis complementum <lb/> hactenus de&longs;ideratum.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000003">Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/> <expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s> </p> <p type="head"> <s id="s.000004"><emph type="italics"/>Authore IOSEPHO BLANCANO Bononien&longs;i è 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"> <s id="s.000005">Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum <lb/>PETRVM FRANCISCVM MALASPINAM <lb/> Aedificiorum Marchionem, apud Cæ&longs;. <!-- REMOVE S-->Maie&longs;tatem <lb/> pro Sereni&longs;s. <!-- REMOVE S-->Parmen&longs;ium Duce Legatum.</s> </p> <p type="head"> <s id="s.000006">BONONIÆ M. <!-- REMOVE S-->D C. <!-- KEEP S--><!-- REMOVE S-->X V.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000007">Apud Bartholomæum Cochium. <!-- KEEP S--></s> <s id="s.000008">Superiorum permi&longs;&longs;u.</s> </p> <p type="head"> <s id="s.000009">Sumptibus Hieronymi Tamburini.</s> </p> <pb xlink:href="009/01/002.jpg"/> <pb pagenum="3" xlink:href="009/01/003.jpg"/> </section> <section> <p type="head"> <s id="s.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO <lb/>PETRO FRANCISCO <lb/>MALASPINAE <lb/> ÆDIFICIORVM MARCHIONI.</s> </p> <p type="main"> <s id="s.000011"><emph type="italics"/>En tandem Illustriß. <!-- REMOVE S-->Marchio opus no­<lb/> strum de Locis Mathematicis apud Ari­<lb/> stotelem, vnà cum Tractatione de natura <lb/> &longs;cientiarum Mathematicarum, necnon <lb/> Clarorum <expan abbr="Mathematicorũ">Mathematicorum</expan> Chronologia; <lb/> quod tibi Mecœnati meo munificenti&longs;simo iure meritò <lb/> dicare, ac &longs;ub clarißimi tui nominis patrocinio in lucem <lb/> dare con&longs;titui. </s> <s id="s.000012">primùm quidem, vt mei perpetui erga te <lb/> amoris, & ob&longs;eruantiæ hoc vnum &longs;altem specimen exta­<lb/> ret: tùm vt idoneum, æquumque propo&longs;itæ rei iudicem <lb/> nanci&longs;cerer. </s> <s id="s.000013">cùm enim ad iu&longs;tum <expan abbr="arbitrũ">arbitrum</expan> duo potißimùm <lb/> requirantur, rerum &longs;cilicet cognitio, atque prudentia, quem <lb/> te rei, de qua agitur peritiorem, quemuè prudentiorem <lb/> inuenire potuerim? </s> <s id="s.000014">tu enim cùm Phy&longs;iologiæ, ac Mathe­<lb/> maticarum omnium Encyclopædiam mirum in modum<emph.end type="italics"/> <pb pagenum="4" xlink:href="009/01/004.jpg"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/> per&longs;ua&longs;i&longs;ti, vt Archimedis, & Apollonij admirandis, ac <lb/> &longs;ubtilißimis Demon&longs;trationibus detinearis. </s> <s id="s.000015">Quanta por­<lb/> rò in rebus agendis prudentia valeas, toti penè Europæ <lb/> innotuit, cùm pro no&longs;tris Sereniß. <!-- REMOVE S-->Ducibus, non &longs;olùm ad <lb/> omnes ferè Italiæ, atque Germaniæ Principes, verùm etiam <lb/> ad Cæ&longs;aream Maie&longs;tatem rebus fœliciter ge&longs;tis Legatus <lb/> decimùm extiteris; ac demùm à Sereniß. <!-- REMOVE S-->Duce Ranutio <lb/> inter primarios de Rep. <!-- KEEP S--></s> <s id="s.000016">Con&longs;iliorum Authores ad&longs;citus <lb/> fueris. </s> <s id="s.000017">Cæterùm in Clarorum Mathematicorum Chro­<lb/> nologia perlegenda, &longs;æpißimè tibi nobilißimi æquè, ac do­<lb/> ctißimi Viri, tui omnino per&longs;imiles occurrent, quod tibi <lb/> nonni&longs;i gratißimum accidere po&longs;&longs;e arbitror. </s> <s id="s.000018">Complectere <lb/> igitur ea benignitate, atque clementia, qua &longs;oles no&longs;tra stu­<lb/> dia promouere, mea hæc quantulacumque munu&longs;cula. <lb/> </s> <s id="s.000019">quæ &longs;i tibi accepta e&longs;&longs;e intellexero, iam tandem ma­<lb/> ximorum munerum loco habenda e&longs;&longs;e cen&longs;e­<lb/> bo. </s> <s id="s.000020">incolumem tibi, ac fœlicem D. Opt. <lb/> <!-- REMOVE S-->Max. <!-- REMOVE S-->longæuitatem tueatur. <lb/> </s> <s id="s.000021">Vale.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000022"><emph type="italics"/>Parmæ Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/> <!-- KEEP S--></s> </p> </section> <pb pagenum="5" xlink:href="009/01/005.jpg"/> <section> <p type="head"> <s id="s.000023">Liber de &longs;e ip&longs;o.</s> </p> <p type="head"> <s id="s.000024"><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"> <s id="s.000025">Ego Iordanus Ca&longs;&longs;ini Præpo&longs;itus Prouincialis Prouinciæ Venetæ Societatis <lb/> Ie&longs;u, ex auctoritate Adm. <!-- REMOVE S-->Reuer. <!-- REMOVE S-->P. no&longs;tro Præpo&longs;iti Generalis P. <!-- REMOVE S-->Claudij <lb/> Aquæuiuæ, 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, & explicata, à deputatis Patribus recognitum, & ap­<lb/> probatum typis mandari po&longs;&longs;it. </s> <s id="s.000026">Parmæ die 15. Ianuarij 1615.</s> </p> <p type="main"> <s id="s.000027"><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/><!-- REMOVE S--><lb/> Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s> <s id="s.000028">& Reuerendi&longs;s. <!-- REMOVE S-->Archiepi&longs;c. <!-- REMOVE S-->Bonon.</s> </p> <p type="main"> <s id="s.000029">Imprimatur</s> <s id="s.000030">Fr. <!-- REMOVE S-->Hieronymus Onuphrius pro Reuerendi&longs;s. <!-- REMOVE S-->P. <!-- REMOVE S-->Inqui&longs;itore Bonon.</s> </p> </section> <pb pagenum="6" xlink:href="009/01/006.jpg"/> <section> <p type="head"> <s id="s.000031">LECTORI.</s> </p> <p type="main"> <s id="s.000032">Qvod pri&longs;cis olim temporibus (humani&longs;&longs;ime Lector) &longs;um­<lb/> mi duo Philo&longs;ophi, Philippus Mendeus, ac Theon Smyr­<lb/> næus in Platonis Dialogis egregiè perfecerunt, vt videli­<lb/> cet quæ pa&longs;&longs;im &longs;ummus hic Philo&longs;ophus de Mathemati­<lb/> cis &longs;cripta reliquit, eadem ip&longs;a ab illis &longs;electa, & 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 quæ de Mathematicis re­<lb/> bus in vniuer&longs;is eiu&longs;dem monumentis &longs;par&longs;a leguntur, eadem in vnum <lb/> à me collecta, & explicata ijs Philo&longs;ophiæ &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;ophiæ curriculum <lb/> aggrediuntur. </s> <s id="s.000033">Vt autem huius operis nece&longs;&longs;itas, <expan abbr="variæ&qacute;">variæque</expan>; vtilitates pla­<lb/> nius cogno&longs;cantur operæpretium erit initio illius cau&longs;as exponere; quæ <lb/> me poti&longs;&longs;imum ad illud con&longs;cribendum compulerunt, quarum</s> </p> <p type="main"> <s id="s.000034">Prima &longs;it, quod hæc Ari&longs;t. loca Mathematica, quæ quidem ferè 408. <lb/> numerantur, pe&longs;&longs;imè latinis literis con&longs;ignata &longs;unt v&longs;que adeò, vt Ari­<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;æpi&longs;&longs;imè compellant.</s> </p> <p type="main"> <s id="s.000035">Secunda, quòd plurima huiu&longs;modi loca à 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, & Mechanicæ quæ&longs;tiones, quamuis <lb/> enim Picolomineus in eas paraphra&longs;im ediderit, loca tamen earum dif­<lb/> ficiliora non &longs;atis illu&longs;trauit. </s> <s id="s.000036">Vt autem dixi 408. in vniuer&longs;um loca mi­<lb/> nimùm numerantur, quibus illud Platonis in&longs;criptum e&longs;t <foreign lang="greek">agaiome/trhtos <lb/> udei/s eisi/to</foreign>; & in quibus Mathematicæ di&longs;ciplinæ rudes, & imperiti, quem <lb/> &longs;equuntur ducem Ari&longs;t. eum &longs;æpe de&longs;erere non &longs;ine turpi dedecoris no­<lb/> ta coguntur; quo fit vt exempla illa Mathematica lucem rebus aliquan­<lb/> do allatura, tenebras cimmerijs, vt aiunt vmbris cra&longs;&longs;iores ij&longs;dem <lb/> obducant.</s> </p> <p type="main"> <s id="s.000037">Tertia, quia Græci eorumdem locorum commentatores breuiter, & <lb/> ob&longs;curè admodum ea, quæ ad Mathematicum &longs;pectant, attingunt, hoc <lb/> enim ab ip&longs;is <expan abbr="certũ">certum</expan> ponitur, Lectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/> Philo &longs;ophorum, Mathematicis imbutum; at verò no&longs;tra ætate magna <lb/> cum Philo&longs;ophiæ iactura, quamplurimi earumdem di&longs;ciplinarum de&longs;ti­<lb/> tuti præ&longs;idijs, ne Græcorum quidem Interpretum explanationes, ne­<lb/> dum Ari&longs;t. ob&longs;curè dicta intelligunt.</s> </p> <pb pagenum="7" xlink:href="009/01/007.jpg"/> <p type="main"> <s id="s.000038">Quarta. </s> <s id="s.000039">Adde, quod etiam &longs;i quis leuiter &longs;it erudito illo Mathemati­<lb/> corum puluere con&longs;per&longs;us, adeò tamen peruer&longs;a e&longs;t eorumdem Græco­<lb/> rum in Latinum tran&longs;latio, <expan abbr="tanta&qacute;">tantaque</expan>; figurarum, quæ nece&longs;&longs;ariæ erant <lb/> confu&longs;io, & deprauatio, vt nec abeo, qui &longs;it Mathematicarum &longs;cientia <lb/> excultus, &longs;ine magno labore percipi po&longs;&longs;int. </s> <s id="s.000040">Quin etiam figuræ illæ, quæ <lb/> omnino nece&longs;&longs;ariæ &longs;unt ob Scriptorum, & Typographorum in&longs;citiam, <lb/> aut inertiam pluribus in locis de&longs;iderantur. </s> <s id="s.000041">Latini verò multo minus, <lb/> quàm Græci Mathematicæ periti, qua ratione eadem loca pertractaue­<lb/> rint, facilius e&longs;t conijcere, quàm vt dici oporteat.</s> </p> <p type="main"> <s id="s.000042">Quinta. </s> <s id="s.000043">Ex his omnibus in aliud incommodum, vel maximum Phi­<lb/> lo&longs;ophi quidam incidebant; aut enim horum locorum expo&longs;itionem ta­<lb/> citi declinabant: aut eam minime nece&longs;&longs;ariam ad Ari&longs;t. percipiendam <lb/> &longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;­<lb/> &longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s> <s id="s.000044">Eorum verò nonnulli eorumdem <lb/> locorum expo&longs;itionem audacter nimis aggrediebantur, <expan abbr="atq;">atque</expan> hinc pueri­<lb/> les illæ, ac ridiculæ expo&longs;itiones pa&longs;&longs;im auditæ, cuiu&longs;modi e&longs;t illa, quan­<lb/> do Ari&longs;toteles ait, quod illi frequenti&longs;&longs;imum e&longs;t, omnis triangulus ha­<lb/> bet tres; nihil aliud &longs;ignificari volunt, quàm omnem triangulum habe­<lb/> re tres angulos. </s> <s id="s.000045">quod &longs;i dicat, omnis triangulus habet tres æquales duo­<lb/> bus rectis: hic hærent, hinc anguntur: <expan abbr="cumq;">cumque</expan> ex his angu&longs;tijs, ac tricis <lb/> &longs;e minimè expedire valeant, aurea verba illa, quibus ingentes &longs;apientiæ <lb/> the&longs;auri continentur, alto &longs;ilentij velo contegere Mathematicarum eos <lb/> cogit in&longs;citia: vnde illud, quod Græcæ linguæ imperitis mutata oratio­<lb/> ne acclamandum illis foret, Mathematicum e&longs;t, non legitur. </s> <s id="s.000046">Nec mi­<lb/> nus elegans illa altera expo&longs;itio; Diametrum e&longs;&longs;e incommen&longs;urabilem <lb/> co&longs;tæ; quod &longs;æpe apud Ari&longs;t. legentibus occurrit, nihil aliud &longs;ibi velle, <lb/> quam Diametrum e&longs;&longs;e longiorem co&longs;ta, quam quidem a&longs;ymetriæ huius <lb/> ignorantiam Plato de legibus dial. 7. non hominum, &longs;ed &longs;uum, <expan abbr="peco-rumq;">peco­<lb/> rumque</expan> appellare non dubitauit. </s> <s id="s.000047">Quid illa? </s> <s id="s.000048">cum Ari&longs;t. ait duo cubi, cu­<lb/> bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in­<lb/> uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/> </s> <s id="s.000049">Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. <!-- REMOVE S-->15. quàm &longs;e Mathematicis, <lb/> reliqui&longs;que Philo&longs;ophis irridendum præbet dum à permutata propor­<lb/> tione putat &longs;erectè in hunc modum pluribus apud ip&longs;um verbis explica­<lb/> tum, argumentari,</s> </p> <p type="main"> <s id="s.000050"><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/> It a voluntas antiqua ad effectum antiquum. <lb/> </s> <s id="s.000051">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"> <s id="s.000052"><expan abbr="Spectatũ">Spectatum</expan> admi&longs;&longs;i ri&longs;um teneatis amici? </s> <s id="s.000053">nego, ait; qui&longs;piam con&longs;equen­ <pb pagenum="8" xlink:href="009/01/008.jpg"/>tiam, non enim hoc e&longs;t argumentari à permutata ratione, deberet enim <lb/> inferre, &longs;ic, ergo ita &longs;e habebit voluntas noua ad antiquam, quemad­<lb/> modum effectus nouus ad antiquum. </s> <s id="s.000054">quæ vitio&longs;a argumentatio quan­<lb/> tumuis læuis &longs;it, & manife&longs;ta, quo&longs;dam tamen magni nominis philo&longs;o­<lb/> phantes adeò tor&longs;it, vt adhuc torqueat.</s> </p> <p type="main"> <s id="s.000055">Quanta autem mi&longs;eratione digni, qui publicè aliquando apud &longs;uos <lb/> auditores totam Per&longs;pectiuam, qua nihil iucundius e&longs;t, de medio tolle­<lb/> re conati &longs;unt, propterea quod illæ vi&longs;uales lineæ, illi anguli, illæ pyra­<lb/> mides, aut coni, quibus vi&longs;io perficitur nullibi extarent, &longs;ed e&longs;&longs;ent vana <lb/> quædam opticorum figmenta. </s> <s id="s.000056">Quì verò fieri potuit, vt non aduerterint <lb/> i&longs;ti &longs;e Ari&longs;toteli &longs;uo manife&longs;te repugnare, qui &longs;æpius 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, & <lb/> opticam a&longs;&longs;ignat, <expan abbr="ip&longs;ius&qacute;">ip&longs;iusque</expan>; optices tanquam veræ &longs;cientiæ mentionem <lb/> &longs;æpius facit.</s> </p> <p type="main"> <s id="s.000057">Alij ex altera parte contra A&longs;tronomos in &longs;urgunt, eccentricos, <expan abbr="atq;">atque</expan> <lb/> epiciclos omnes de cœlo detrahere cupientes. </s> <s id="s.000058">Verum id i&longs;ti nulla ex­<lb/> pre&longs;&longs;a nedum probabili ratione faciunt, falsò exi&longs;timantes A&longs;tronomos <lb/> admirandam illam Cœlorum 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="appellãt">appellant</expan>, <lb/> non a&longs;&longs;erunt. </s> <s id="s.000059">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> <s id="s.000060">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;æpè hi &longs;unt, vt non &longs;atis intelligant, quid &longs;it Aequa­<lb/> tor, aut Zodiacus, ne dum quid Epiciclus, aut Eccentricus. </s> <s id="s.000061">Nec defuit <lb/> qui viginti duo argumenta excogitarit, <expan abbr="atq;">atque</expan> in medium protulerit, qui­<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, & proprio ab occidente in orientem. </s> <s id="s.000062">Sed exi&longs;timandum <lb/> e&longs;t <expan abbr="i&longs;tũ">i&longs;tum</expan> Lunam nouam à Sole quotidie magis, ac magis ver&longs;us orientem <lb/> recedere, nunquam animaduerti&longs;&longs;e; ab ea enim hanc motuum concor­<lb/> diam didici&longs;&longs;et.</s> </p> <p type="main"> <s id="s.000063">Quid tandem <expan abbr="dic&etilde;dum">dicendum</expan> de quodam magni nominis Philo&longs;opho, om­<lb/> nium tamen <expan abbr="Mathematicarũ">Mathematicarum</expan> experte, qui in publica di&longs;putatione axio­<lb/> ma illud Mathematicum, omne totum e&longs;t maius &longs;ua parte, in &longs;en&longs;u in <lb/> quo à Mathematicis effertur negare non erubuit, eò, quod in infinito, <lb/> vt aiebat non concederetur ab omnibus. </s> <s id="s.000064">&longs;cilicet non intelligebat ma­<lb/> thematicum tantummodo tractare de Quantitate finita, ac terminata, <lb/> in qua axioma prædictum ab omnibus conceditur. </s> <s id="s.000065">Neque vero hic <lb/> nonnullorum infen&longs;us in Mathematicas animus quieuit, verum etiam <lb/> eò progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien­ <pb pagenum="9" xlink:href="009/01/009.jpg"/>tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu­<lb/> gnante, expungere conati &longs;int; <expan abbr="idq;">idque</expan> ne&longs;cio an vlla alia de cau&longs;a egerint, <lb/> quàm quod eas non &longs;atis calerent; non &longs;ecus <expan abbr="atq;">atque</expan> Ae&longs;opica illa Vulpes, <lb/> quæ cum cauda mutilata e&longs;&longs;et, caudarum mutilationem reliquis vulpi­<lb/> bus vafrè per&longs;uadere conabatur. </s> <s id="s.000066">Verum enim verò optimè &longs;cio, ea, <lb/> qu&etail; hactenus dicta &longs;unt non in omnes no&longs;tri temporis Philo&longs;ophos qua­<lb/> drare, cum non pauci hodie quoque &longs;int, qui more antiquorum Mathe­<lb/> maticis &longs;uffulti, optimè &longs;uis &longs;tudijs con&longs;ulentes, reliquam Philo&longs;ophiam <lb/> non &longs;ine magno compendio aggrediuntur. </s> <s id="s.000067">Quo fit, vt cæteros ageo­<lb/> metretos ita antecellant, vt eorum Magi&longs;tri appellari po&longs;&longs;int, & <expan abbr="debeãt">debeant</expan>; <lb/> tales fuerunt in primis Vicomercatus, Cardanus, Zabarella, Toletus, <lb/> Bonamicus, & alij, quibus paulo antiquiores fuerunt D. Tho. <!-- REMOVE S-->& Scotus, <lb/>Hi omnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o­<lb/> phantes excelluerint, nemo e&longs;t qui non nouerit. </s> <s id="s.000068">Illud hoc loco minimè <lb/> tacendum, Iacobum Zabarellam in &longs;uis logicæ commentarijs te&longs;tari &longs;e <lb/> bis &longs;umma diligentia totum Euclidem perlegi&longs;&longs;e, vt perfectè Ari&longs;t. de <lb/> demon&longs;tratione &longs;ententiam a&longs;&longs;equi po&longs;&longs;et.</s> </p> <p type="main"> <s id="s.000069">Hi ridiculas illas, ac pueriles expo&longs;itiones &longs;uperius allatas minimè <lb/> effutierunt, neque reliquis &longs;upra recen&longs;itis incommodis obnoxij fue­<lb/> runt, quibus magno etiam cum dedecore alij Mathematicarum ope ca­<lb/> rentes afficiuntur.</s> </p> <p type="main"> <s id="s.000070">In horum igitur gratiam operam diligenter dedi, vt quantum in me <lb/> e&longs;&longs;et damna à me &longs;upra enarrata aliqua ex parte re&longs;arcirem. </s> <s id="s.000071">Quaprop­<lb/> ter loca hæc mathematica num rectè e&longs;&longs;ent è græco in latinum tran&longs;lata <lb/> diligenter prius expendi. </s> <s id="s.000072">Deinde claritate, quàm potui maxima eadem <lb/> loca interpretatus &longs;um, & in horum, de quibus dixi gratiam, quædam <lb/> fanè tenuia pro&longs;equutus &longs;um, quæ alioquin libenter omi&longs;i&longs;&longs;em. </s> <s id="s.000073">Tum fi­<lb/> guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s> <s id="s.000074">Hoc igitur <lb/> no&longs;tro qualicunque labore poterit qui&longs;que omnia illa facile intelligere, <lb/> <expan abbr="atq;">atque</expan> enumerata incommoda euitare, vnum tantummodo à Lectore ma­<lb/> thematicarum experte requiram, vt principia &longs;altem illa, &longs;cilicet defini­<lb/> tiones, po&longs;tulata, & axiomata, quæ primò Euclideis libro præponuntur, <lb/> diligenter prius perlegat cum illa &longs;ua per&longs;picuitate omnibus &longs;int obuia; <lb/> cætera ego explicanda recipio. </s> <s id="s.000075">Obiter etiam auctaria nonnulla partim <lb/> mathematica, partim naturalia in&longs;erui, quæ ob nouitatem, ac pulchri­<lb/> tudinem grata Lectori, atque iucunda fore exi&longs;timaui.</s> </p> <p type="main"> <s id="s.000076">Sciat præterea Lector no&longs;trum in&longs;titutum e&longs;&longs;e loca hæc mathemati­<lb/> ca, quatenus mathematica &longs;unt declarare, &longs;iue ea &longs;upplere, quæ ex ma­<lb/> thematicis petenda e&longs;&longs;ent: reliqua autem me tantum attingere, quan­<lb/> tum harum rerum cum illis connexio po&longs;tulat.</s> </p> <pb pagenum="10" xlink:href="009/01/010.jpg"/> <p type="main"> <s id="s.000077">His omnibus placuit appendices opportune nonnullas addere, qua­<lb/> rum prima de natura mathematicarum &longs;cientiarum: altera, qua omnes <lb/> demon&longs;trationes primi libri Euclidis breuiter ad Logicam normam ex­<lb/> penduntur, vt pateat, quonam demon&longs;trationis genere <expan abbr="c&etilde;&longs;eri">cen&longs;eri</expan> <expan abbr="vnaqu&etail;q;">vnaqu&etail;que</expan> <lb/> debeat, & ex illis de cæteris iudicium fiat. </s> <s id="s.000078">Tandem in gratiam etiam <lb/> Mathematicorum tertiam appendicem appendi, qua omnia loca Ari&longs;t. <lb/> <!-- REMOVE S-->Geometrica ad Euclidis ordinem referuntur; vnde & ip&longs;i ad &longs;uas pr&etail;le­<lb/> ctiones exornandas aliquid &longs;ubinde depromere queant.</s> </p> <p type="main"> <s id="s.000079">Fruere igitur amice Lector hoc no&longs;tro qua liquali labore, quo ad ple­<lb/> nam totius Ari&longs;t. 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<lb/> dam Philo&longs;ophus, cum totum hunc librum perlegi&longs;&longs;et, effatus e&longs;t, vide­<lb/> licet, opus hoc <emph type="italics"/>Aristotelicæ expo&longs;itionis complementum ad hanc v&longs;que <lb/> diem de&longs;ideratum<emph.end type="italics"/> iure ac meritò nuncupari po&longs;&longs;e.</s> </p> <p type="main"> <s id="s.000080">Illud demum tanquam parergon addam, quod ego his elucubran­<lb/> dis experientia didici, ad veram &longs;cilicet, ac perfectam to­<lb/> tius Ari&longs;totelis intelligentiam linguæ in primis <lb/> græcæ, necnon mathematicarum om­<lb/> nium di&longs;ciplinarum haud medio­<lb/> crem cognitionem ne­<lb/> ce&longs;&longs;ariam e&longs;&longs;e. <lb/> </s> <s id="s.000081">Vale.<!-- KEEP S--></s> </p> </section> <pb pagenum="11" xlink:href="009/01/011.jpg"/> <section> <p type="head"> <s id="s.000082">Pr&etail;cipua qu&etail;dam, aut noua, aut re&longs;taurata, <lb/> quæ 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, & 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 quædam 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, quæ aquæ in&longs;ident, vnà 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 Terræ 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 quæ, & 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 quæ,<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, & 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. propè 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" xlink:href="009/01/012.jpg"/> <section> <p type="head"> <s id="s.000083"><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000084"><emph type="italics"/>Quæ 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"> <s id="s.000085">In Prædicamentis.</s> </p> <p type="main"> <s id="s.000086"><emph type="italics"/>Capite s. </s> <s id="s.000087">de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000088"><emph type="italics"/>Cap. de Priori, vbi de Principijs Mathematicarum,<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000089"><emph type="italics"/>Cap. de Motu, vbi de Gnomone.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000090">In Primo Priorum Re&longs;olutoriorum.</s> </p> <p type="main"> <s id="s.000091"><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000092"><emph type="italics"/>Cap. 23. &longs;ect 1. libri 1. de Incommen&longs;urabilibus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000093"><emph type="italics"/>Cap. 24. &longs;ecti 1. lib. 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000094"><emph type="italics"/>Cap. 2. &longs;ect 2. lib. 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000095"><emph type="italics"/>Cap. 3. &longs;ecti 2. lib. 1. de Incommen&longs;urabili.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000096"><emph type="italics"/>Cap. 1. &longs;ecti 3. lib. 1. de eo, quod est, omnis triangulus habet tres angulos æquales <lb/> æquales duobus rectis: Aequalitas Geometrica, quæ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000097"><emph type="italics"/>Cap. eodem, de exemplis, quibus vtuntur Geometræ.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000098">In &longs;ecundo Priorum Re&longs;ol.<!-- REMOVE S--><emph type="italics"/>Cap. 21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000099"><emph type="italics"/>Cap. eodem. </s> <s id="s.000100">de Paralellis, & de triangulo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000101"><emph type="italics"/>Cap. 26. Quod omnis triangulus habet tres, & c.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000102"><emph type="italics"/>Cap. 31. de Abductione.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000103"><emph type="italics"/>Cap. codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000104">In primo Po&longs;teriorum.</s> </p> <p type="main"> <s id="s.000105"><emph type="italics"/>Textu primo, De Præcognitis Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000106"><emph type="italics"/>T. 2. Omnis triangulus habet tres, & c.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000107"><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s> <s id="s.000108">Item De Mathematicarum Principijs.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000109"><emph type="italics"/>T. eodem, De Indiui&longs;ibilitate vnitatis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000110"><emph type="italics"/>T. 9. De Puncto, & linea. </s> <s id="s.000111">Item de recto, & circulari. </s> <s id="s.000112">Item de numero pari, impari; <lb/> primo, & compo&longs;ito; æquilatero, & altera parte longiore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000113"><emph type="italics"/>T. 11. Lineæ punctum inest per &longs;e, & c.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000114"><emph type="italics"/>T. 13. De Parallelis. <!-- KEEP S--></s> <s id="s.000115">De I&longs;o&longs;cele. </s> <s id="s.000116">De Alterna Proportione, <lb/> Item quod omnis triangulus habet tres, & c.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000117"><emph type="italics"/>T. 14. De ij&longs;dem cum præcedentibus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000118"><emph type="italics"/>T. 20. Magnitudines euadunt numeri. </s> <s id="s.000119">Item, quod non duo cubi cubus. </s> <s id="s.000120">Item de <lb/> Mathematicis &longs;ubalternatis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000121"><emph type="italics"/>T. 23. Quadratura circuli &longs;ecundum Bry&longs;onem. </s> <s id="s.000122">Item per&longs;ectam illam e&longs;&longs;e Demon­<lb/> &longs;trationem, qua Geometræ o&longs;tendunt, quod Omnis triangulus habet tres, & c. <lb/> <!-- KEEP S--></s> <s id="s.000123">Per&longs;pectiuam, & Mechanicam &longs;ubalternari Geometriæ, Mu&longs;icam, Arithmeticæ.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000124"><emph type="italics"/>T. 24. De numero pari, impari, quadrangulo, cubo. </s> <s id="s.000125">In Geometria quid irrationale, <lb/> refrangi, concurrere. </s> <s id="s.000126">Quid Astronomia con&longs;ideret.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000127"><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000128"><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <pb pagenum="13" xlink:href="009/01/013.jpg"/> <p type="main"> <s id="s.000129"><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. <!-- KEEP S--></s> <s id="s.000130">Item quid multiplicata propor­<lb/> tio. </s> <s id="s.000131">Quid Cæneus dixerit. </s> <s id="s.000132">Cur Affectiones <expan abbr="Mathematicorũ">Mathematicorũ</expan> maximè <expan abbr="conuertãtur">conuertantur</expan>.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000133"><emph type="italics"/>T. 30. De Lunæ &longs;phæricitate. </s> <s id="s.000134">Quid &longs;tereometria. </s> <s id="s.000135">& De &longs;ubalternatione, &c. </s> <s id="s.000136">& Ma­<lb/> thematicorum e&longs;t &longs;cire Propter quid: &longs;en&longs;itiuorum verò &longs;cire Quod.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000137"><emph type="italics"/>T. 37. I&longs;o&longs;celes, & Scalenum habere tres æquales, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000138"><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000139"><emph type="italics"/>T. 39. Habere tres angulos æquales, &c. </s> <s id="s.000140">Item, quod omnis figura habet &longs;uos angu­<lb/> los externos æquales quatuor tantum rectis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000141"><emph type="italics"/>T. 43. Triangulum tres æquales, &c. </s> <s id="s.000142">De Eclyp&longs;i.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000143"><emph type="italics"/>De combu&longs;tione per refractionem ex &longs;phæra vitrea. </s> <s id="s.000144">De principijs &longs;cientiarum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000145"><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000146">In 2. Po&longs;teriorum.</s> </p> <p type="main"> <s id="s.000147"><emph type="italics"/>T. 1. Aequalitas, & inæqualitas. </s> <s id="s.000148">Terram e&longs;&longs;e in medio mundi ab A&longs;tronomis per­<lb/> fectè demon&longs;tratur. </s> <s id="s.000149">Item Quid con&longs;onantia.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000150"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &c. </s> <s id="s.000151">Item de Definitionibus Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000152"><emph type="italics"/>T. 7. Geometra, quædam accipit, quædam demon&longs;trat.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000153"><emph type="italics"/>T. 11. Angulum in &longs;emicirculo rectum e&longs;&longs;e probari à Geometra per cau&longs;am materia­<lb/> lem. </s> <s id="s.000154">Zabarella correctus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000155"><emph type="italics"/>T. 24. Echo, Imago è &longs;peculo, Iris.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000156"><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000157">In primo lib. <!-- REMOVE S-->Topicorum.</s> </p> <p type="main"> <s id="s.000158"><emph type="italics"/>Cap. 13. Diameter est incommen&longs;urabilis. </s> <s id="s.000159">Vox acuta velox, cur. </s> <s id="s.000160">&c. </s> <s id="s.000161">Colores in <lb/> Mu&longs;ica, qui. </s> <s id="s.000162">tria genera veteris Mu&longs;icæ.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000163">In 4. libro.</s> </p> <p type="main"> <s id="s.000164"><emph type="italics"/>Cap. 1. loco 1. lineæ in&longs;ecabiles.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000165">In 6. libro.</s> </p> <p type="main"> <s id="s.000166"><emph type="italics"/>Cap. 2. loco 32. Definitio lineæ.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000167">In 8. libro.</s> </p> <p type="main"> <s id="s.000168"><emph type="italics"/>Cap. 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000169"><emph type="italics"/>Cap. 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000170">In Elenchorum lib. 1.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000171"><emph type="italics"/>Cap. 10. Quid P&longs;eudographia. </s> <s id="s.000172">Quadratura rur&longs;us Hippocratis, & Bry&longs;onis. </s> <s id="s.000173">Mathe­<lb/> maticæ non contentio&longs;æ. </s> <s id="s.000174">Quadratio Antiphontis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000175">Ex 1. Phy&longs;ic.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000176"><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, & Antiphontis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000177">Ex 2. Phy&longs;ic.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000178"><emph type="italics"/>T. 20. Quatenus Per&longs;pectiuus con&longs;ideret lineam.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000179"><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000180"><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes habere cau&longs;am, quæ reducitur ad defini­<lb/> tionem.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000181"><emph type="italics"/>T. 8. De nece&longs;&longs;ario, quod e&longs;t in Mathematicis. <!-- KEEP S--></s> <s id="s.000182">& omnis triangulus habet tres an­<lb/> gulos, &c.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000183">Ex 3. Phy&longs;ic.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000184"><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000185"><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000186"><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/><!-- KEEP S--></s> </p> <pb pagenum="14" xlink:href="009/01/014.jpg"/> <p type="head"> <s id="s.000187">Ex 4. Phy&longs;ic.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000188"><emph type="italics"/>T. 120. De commen&longs;urab. </s> <s id="s.000189">& incommen&longs;.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000190">Ex 5. Phy&longs;ic.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000191"><emph type="italics"/>T. 6. De chordis, graui, acuta; media, & vltima.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000192">Ex 8. Phy&longs;ic.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000193"><emph type="italics"/>T. 15. Omnis triangulus habet tres æquales, &c.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000194">Ex 1. de Cœlo.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000195"><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000196"><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"> <s id="s.000197"><emph type="italics"/>T. 48. Commen&longs;urab. <!-- REMOVE S-->& incommen&longs;urab. </s> <s id="s.000198">quid.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000199"><emph type="italics"/>T. 119. Omnis triangulus habet tres, &c. </s> <s id="s.000200">Item de commen&longs;urabili.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000201">Ex 2. de Cœlo.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000202"><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, quì.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000203"><emph type="italics"/>T. 25. Ordo figurarum planarum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000204"><emph type="italics"/>T. 31. Aquæ &longs;uperficiem e&longs;&longs;e &longs;phæricam.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000205"><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s> <s id="s.000206">Recentiorum ob&longs;eruationes.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000207"><emph type="italics"/>T. 57. De ordine Cœlorum ex &longs;ententia A&longs;tronomorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000208"><emph type="italics"/>T. 59. De rotunditate Lunæ, bis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000209"><emph type="italics"/>T. 107. Centrum duplex grauit: & molis. </s> <s id="s.000210">Qua ratione grauia ad mundi centrum <lb/> aptarentur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000211"><emph type="italics"/>T. 109. Terram e&longs;&longs;e rotundam. </s> <s id="s.000212">alio item modo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000213"><emph type="italics"/>T. 110. Terram e&longs;&longs;e paruam re&longs;pectu Cœli.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000214"><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000215"><emph type="italics"/>T. 112. De quantitate Terræ.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000216">Ex 3. de Cœlo.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000217"><emph type="italics"/>T. 40. Vt componatur &longs;phæra.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000218"><emph type="italics"/>T. 66. Omne corpus diui&longs;ibile.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000219"><emph type="italics"/>T. 66. Quænam planarum figurarum totum &longs;patium repleant. </s> <s id="s.000220">Hinc de admirabili <lb/>Apum ingenio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000221"><emph type="italics"/>T. eodem. </s> <s id="s.000222">Num plures Pyramides locum replere valeant, vbi Ari&longs;toteles, & omnes <lb/> expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000223"><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000224">Ex 4. de Cœlo.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000225"><emph type="italics"/>T. 33. Extare centrum Mundi, quò grauia tendunt, à quo leuia abeant.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000226"><emph type="italics"/>T. 44. & <expan abbr="&longs;eq.">&longs;eque</expan> Cur quædam grauiora quàm aqua, &longs;upernatent.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000227">Ex 2. de Generatione, & Corruptione.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000228"><emph type="italics"/>Tex. 56. Cur Planetæ duobus motibus moueri dicantur.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000229">Ex 1. Meteororum.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000230"><emph type="italics"/>Summa prima cap. 3. De magnitudine Terræ ad a&longs;tra, & &longs;olem collata.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000231"><emph type="italics"/>Cap. eodem. </s> <s id="s.000232">De magnitudine A&longs;trorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000233"><emph type="italics"/>Cap. 4. De ordine Luminarium Solis, & Lunæ.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000234"><emph type="italics"/>Summa 2. cap. 3. de Mercurij stella. </s> <s id="s.000235">Item de Cometa: e&longs;&longs;e in Cœlo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000236"><emph type="italics"/>Cap. 5. De Magnitudine Solis, & de vmbra Terræ.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000237"><emph type="italics"/>Cap. 5. De Glaxia.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000238"><emph type="italics"/>Cap. 6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde <lb/> aperitur.<emph.end type="italics"/></s> </p> <pb pagenum="15" xlink:href="009/01/015.jpg"/> <p type="main"> <s id="s.000239"><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s> <s id="s.000240">Mare extraneum, quod. </s> <s id="s.000241">Errata quæ­<lb/> dam veterum Geographorum, & Ari&longs;t. corriguntur. </s> <s id="s.000242">Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000243"><emph type="italics"/>Cap. 2. De permutatione Aquarum, & continentis. </s> <s id="s.000244">Noua ob&longs;eruatio de rotundi­<lb/> tate Terræ, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000245">Ex 2. Meteororum.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000246"><emph type="italics"/>Summa 1. cap. 1. De Mari rubro.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000247"><emph type="italics"/>Summa 2. cap. 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000248"><emph type="italics"/>Cap. eodem, De Canicula. </s> <s id="s.000249">De Zonis temperatis. </s> <s id="s.000250">Corona Ariadnæ. </s> <s id="s.000251">Zonam torridam <lb/> falsò putabant inho&longs;pitalem. </s> <s id="s.000252">cur habitabilis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000253"><emph type="italics"/>Cap. 3. De Ventorum &longs;itu.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000254">Ex 3. Meteor.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000255"><emph type="italics"/>Summa 2. cap. 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;tratio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000256"><emph type="italics"/>Cap. 4. De Iridis figura Mathematica demon&longs;tratio, &longs;ed deficiens. </s> <s id="s.000257">Noua de eadem <lb/> tractatio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000258"><emph type="italics"/>Cap. 5. De Parelio. <!-- KEEP S--></s> <s id="s.000259">Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000260">Ex 1. De Anima.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000261"><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s> <s id="s.000262">& omnis triangulus habet tres, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000263"><emph type="italics"/>T. 13. Sphæra planum tangit in puncto.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000264">Ex 2. De Anima.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000265"><emph type="italics"/>T. 12. Definitionem formalem, & cau&longs;alem explicat exemplo Quadrationis Geo­<lb/> metricæ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000266"><emph type="italics"/>T. 86. Acutum, & Graue, vt differant.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000267"><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000268">Ex 3. De Anima.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000269"><emph type="italics"/>T. 21. Incommen&longs;urabile.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000270"><emph type="italics"/>T. 25. Indiui&longs;ibilia e&longs;&longs;e priuationes.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000271"><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000272">Ex lib. <!-- REMOVE S-->De Sen&longs;u.</s> </p> <p type="main"> <s id="s.000273"><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000274"><emph type="italics"/>Cap. 8. Nete. </s> <s id="s.000275">Diapa&longs;on. <!-- KEEP S--></s> <s id="s.000276">Diapen&longs;e.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000277">Ex lib. <!-- REMOVE S-->De Memoria, & Rem.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000278"><emph type="italics"/>Cap. 1. Omnis triangulus habet tres, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000279"><emph type="italics"/>Cap. 3. Mathemata facile remini&longs;cibilia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000280">Ex lib. <!-- REMOVE S-->De Somnijs.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000281"><emph type="italics"/>Cap. 2. Terra, cur nauigantibus moueri videatur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000282"><emph type="italics"/>Cap. 3. Cur Oculus digito dimotus res geminatas videat.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000283">Ex 1. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000284"><emph type="italics"/>Cap. 1. Initium Mathematicarum ab Aegyptiorum Sacerdotibus. </s> <s id="s.000285">Item, Automata, <lb/> quæ &longs;olstitia. </s> <s id="s.000286">Diameter incommen&longs;.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000287"><emph type="italics"/>Summa 2. cap. 3. Pythagorei Mathematicas cæteris præferebant.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000288"><emph type="italics"/>T. 47. Geometria habet &longs;uas præcognitiones.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000289">Ex 2. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000290"><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000291">Ex 3. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000292"><emph type="italics"/>Tex. <!-- KEEP S--></s> <s id="s.000293">Mathematicas puras carere cau&longs;is efficiente, & finali. </s> <s id="s.000294">Ari&longs;tippus, vt Mathe­<lb/> maticas &longs;ugillaret. </s> <s id="s.000295">Tetragoni&longs;mus est inuentio mediæ.<emph.end type="italics"/></s> </p> <pb pagenum="16" xlink:href="009/01/016.jpg"/> <p type="main"> <s id="s.000296"><emph type="italics"/>Tex. 8. Geodæ&longs;ia quid.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000297">Ex 4. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000298"><emph type="italics"/>T. 4. Quæ &longs;int primæ, & quæ &longs;ecundæ inter Mathematicas.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000299"><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000300">Ex 5. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000301"><emph type="italics"/>T. 2. Exemplum cau&longs;æ formalis ex Diapa&longs;on. <!-- KEEP S--></s> <s id="s.000302">Quæ &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000303"><emph type="italics"/>T. 3. Quæ &longs;it Materia in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000304"><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000305"><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000306"><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s> <s id="s.000307">Quid potentia vnius lineæ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000308"><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000309">Ex 6. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000310"><emph type="italics"/>T. 1. Principia, elementa, & cau&longs;æ in Mathem.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000311"><emph type="italics"/>T. 8. Diameter. </s> <s id="s.000312">commen&longs;urab.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000313"><emph type="italics"/>T. 20. De&longs;criptiones. </s> <s id="s.000314">Omnis triangulus habet tres, &c. </s> <s id="s.000315">Cur Angulus in &longs;emicir­<lb/> culo rectus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000316"><emph type="italics"/>T. 22. Omnis triangulus habet tres, &c.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000317">Ex 10. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000318"><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s> <s id="s.000319">Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000320"><emph type="italics"/>T. 11. Similes figuræ quæ. </s> <s id="s.000321">Diuer&longs;um in Math. quid.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000322">Ex 11. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000323"><emph type="italics"/>Cap. 2. Ortus punctorum, linearum, &longs;uperficierum.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000324">Ex 12. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000325"><emph type="italics"/>T. 44. Peculiari&longs;&longs;imam Philo&longs;ophiam, Mathematicorum videlicet, A&longs;tronomiam <lb/> pluralitatem Cœlorum docere.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000326"><emph type="italics"/>T. 45. Numerus orbium cœle&longs;tium &longs;ecundum Eudoxum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000327"><emph type="italics"/>T. 46. Itidem ex Eudoxo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000328"><emph type="italics"/>T. 47. Orbium cœle&longs;tium numerus, & fabrica ex Calippo.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000329">Ex 13. Methaphy&longs;.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000330"><emph type="italics"/>Cap. 3. Qua ratione Mathematici tractant de Bono.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000331">In Mechanicas Quæ&longs;tiones.</s> </p> <p type="main"> <s id="s.000332"><emph type="italics"/>Cap. 1. Quæ &longs;it Mechanica facultas.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000333"><emph type="italics"/>Cap. 2. De Admirandis circuli.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000334"><emph type="italics"/>Quæ&longs;tio 1. De Libra. <!-- KEEP S--></s> <s id="s.000335">cur maior, exactior. </s> <s id="s.000336">inibi Ari&longs;t. lap&longs;us.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000337"><emph type="italics"/>Quæ&longs;t. 2. Duplex Libra. <!-- KEEP S--></s> <s id="s.000338">Piccolomineus reiectus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000339"><emph type="italics"/>Quæ&longs;t. 3. De Vecte.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000340"><emph type="italics"/>Quæ&longs;t. 4. De Remo; Petri Nonÿ in Arist. correctio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000341"><emph type="italics"/>Quæ&longs;t. 5. De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000342"><emph type="italics"/>Quæ&longs;t. 6. De Antenna.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000343"><emph type="italics"/>Quæ&longs;t. 8 De Rota.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000344"><emph type="italics"/>Quæ&longs;t. 9. De Trochlea, & Scytali. figura antiquæ &longs;cytalis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000345"><emph type="italics"/>Quæ&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000346"><emph type="italics"/>Qùæ&longs;t. <!-- REMOVE S-->11. De Curru, & &longs;cytala.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000347"><emph type="italics"/>Quæ&longs;t. 13. De lugo. </s> <s id="s.000348">De Succula.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000349"><emph type="italics"/>Quæ&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000350"><emph type="italics"/>Quæ&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s> </p> <pb pagenum="17" xlink:href="009/01/017.jpg"/> <p type="main"> <s id="s.000351"><emph type="italics"/>Quæ&longs;t. 17. De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000352"><emph type="italics"/>Quæ&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000353"><emph type="italics"/>Quæ&longs;t. 19. De Securi. </s> <s id="s.000354">Securis veteris figura, & con&longs;tructio; vnà cum affectione <lb/> eius mirabili.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000355"><emph type="italics"/>Quæ&longs;t. 20. De Statera. <!-- KEEP S--></s> <s id="s.000356">Veteris stateræ figura restaurata.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000357"><emph type="italics"/>Quæ&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000358"><emph type="italics"/>Quæ&longs;t. 22. De Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000359"><emph type="italics"/>Quæ&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000360"><emph type="italics"/>Quæ&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000361"><emph type="italics"/>Quæ&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000362"><emph type="italics"/>Quæ&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000363"><emph type="italics"/>Quæ&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000364"><emph type="italics"/>Quæ&longs;t. 28. De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000365"><emph type="italics"/>Quæ&longs;t. 29. De onere à duobus phalanga ge&longs;tato.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000366"><emph type="italics"/>Quæ&longs;t. 30. De &longs;urgente à &longs;e&longs;&longs;ione.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000367">In libello De Mundo ad Alex.<!-- REMOVE S--><emph type="italics"/>Cap. 2. Ordo Planetarum.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000368"><emph type="italics"/>Cap. 3. De Cometis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000369"><emph type="italics"/>Cap. 5. De fluxu maris. </s> <s id="s.000370">noua de maris æ&longs;tu &longs;ententia.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000371">In libro De Admirandis audit.</s> </p> <p type="main"> <s id="s.000372"><emph type="italics"/>Num. <!-- REMOVE S-->8. De nouo orbe.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000373"><emph type="italics"/>Nu. </s> <s id="s.000374">100. De I&longs;tro, error Ari&longs;t. & veterum Geographorum.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000375">In libello De lineis in&longs;ecabilibus.</s> </p> <p type="main"> <s id="s.000376"><emph type="italics"/>Primus locus. </s> <s id="s.000377">De commen&longs;urabili, & incommen&longs;urabili.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000378"><emph type="italics"/>2. locus. </s> <s id="s.000379">De figuris incommen&longs;.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000380"><emph type="italics"/>3. locus. </s> <s id="s.000381">Quæ linea rationalis, quæ irrationalis. </s> <s id="s.000382">Binomio, Apotome.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000383"><emph type="italics"/>4. locus. </s> <s id="s.000384">De communi men&longs;ura.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000385"><emph type="italics"/>5. locus. </s> <s id="s.000386">Lineæ rectæ motus in &longs;emicirculum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000387"><emph type="italics"/>6. locus. </s> <s id="s.000388">Circulorum æqualium ab inuicem motus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000389"><emph type="italics"/>7. locus. </s> <s id="s.000390">Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000391"><emph type="italics"/>8. locus. </s> <s id="s.000392">Si extarent indiuidua, omnes lineæ e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000393"><emph type="italics"/>9. locus. </s> <s id="s.000394">Idem probat aliteŕ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000395"><emph type="italics"/>10. locus. </s> <s id="s.000396">Idem ex triangulo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000397"><emph type="italics"/>11. locus. </s> <s id="s.000398">Idem ex quadrato.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000399"><emph type="italics"/>12. Ex diui&longs;ione lineæ idem confirmatur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000400"><emph type="italics"/>13. Idem eodem ferè modo cum præcedenti.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000401"><emph type="italics"/>14. A quadrato cuiu&longs;uis lineæ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000402"><emph type="italics"/>15. Idem probat ex &longs;uperficie, & ex corpore.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000403"><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000404">Ex lib. 9. Hi&longs;toriæ Animalium.</s> </p> <p type="main"> <s id="s.000405"><emph type="italics"/>Cap. 39. error Ari&longs;t. & noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000406">De Ince&longs;&longs;u Animal.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000407"><emph type="italics"/>Cap. 7. qua ratione in gre&longs;&longs;u fiat hypotenu&longs;a. </s> <s id="s.000408">& ea quid &longs;it.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000409">De Motu Animal.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000410"><emph type="italics"/>Cap. 1. in flexuris animalium e&longs;&longs;e centrum, & circulum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000411"><emph type="italics"/>Cap. 3. Automata.<emph.end type="italics"/><!-- KEEP S--></s> </p> <pb pagenum="18" xlink:href="009/01/018.jpg"/> <p type="head"> <s id="s.000412">De Generatione Animal.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000413"><emph type="italics"/>Lib. 2. cap. 1. Automata.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000414"><emph type="italics"/>Lib. 2. cap. 4. Omnis triangulus habet tres, &c. </s> <s id="s.000415">Ibidem Diametrum e&longs;&longs;e incommen­<lb/> &longs;urabilem co&longs;tæ, habet cau&longs;am, & demon&longs;trationem.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000416">In Ethicis ad Nicom.</s> </p> <p type="main"> <s id="s.000417"><emph type="italics"/>Lib. 1. cap. 7. Faber, & Geometra diuersè con&longs;iderant angulum rectum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000418"><emph type="italics"/>Lib. 2. cap. 6. De Arithmetica proportione.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000419"><emph type="italics"/>cap. 9. Centrum circuli reperire.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000420"><emph type="italics"/>Lib. 3. cap. 3. Diameter, & latus incommen&longs;urabilis: Item quid re&longs;olutio Geome­<lb/> trica: Quid de&longs;ignatio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000421"><emph type="italics"/>Lib. 5. cap. 3. Vnitarius numerus. </s> <s id="s.000422">Quid Proportionalitas. <!-- KEEP S--></s> <s id="s.000423">Eam in 4. terminis con­<lb/> &longs;i&longs;tere. </s> <s id="s.000424">Item quid Permutata proportio. </s> <s id="s.000425">Item quid Geometrica proportio. </s> <s id="s.000426">Propor­<lb/> tio continuata, & di&longs;iuncta quid.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000427"><emph type="italics"/>cap. 6. Proportio Geometrica, & Arithmetica.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000428"><emph type="italics"/>Lib. 6. cap. 5. Omnis triangulus, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000429"><emph type="italics"/>cap. 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000430"><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000431">Ex 1. Magnorum Moralium.</s> </p> <p type="main"> <s id="s.000432"><emph type="italics"/>Cap. 1. Numerus pariter par.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000433"><emph type="italics"/>Cap. 2. Omnis triangulus habet, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000434"><emph type="italics"/>Cap. 10 Omnis triangulus habet, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000435"><emph type="italics"/>Cap. 16. Quadratum quatuor rectis æquales habere.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000436"><emph type="italics"/>Cap. 30. Proportionale in quatuor terminis con&longs;i&longs;tit.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000437">Ex 1. lib. <!-- REMOVE S-->Moralium Eudemiorum.</s> </p> <p type="main"> <s id="s.000438"><emph type="italics"/>Cap. 5. Duplum inter multiplices rationes primum tenet locum.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000439">Ex 1. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s> </p> <p type="main"> <s id="s.000440"><emph type="italics"/>Cap. Omnis triangulus habet tres, &c.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000441"><emph type="italics"/>Cap. 10. Diametrum commen&longs;. </s> <s id="s.000442">e&longs;&longs;e. </s> <s id="s.000443">Circuli quadratio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000444"><emph type="italics"/>Cap. 12. Triangulus habet tres, &c.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000445">Ex 7. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s> </p> <p type="main"> <s id="s.000446"><emph type="italics"/>Cap. 12. Diametralis oppo&longs;itio.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000447">Ex 3. lib. <!-- REMOVE S-->Politicorum.</s> </p> <p type="main"> <s id="s.000448"><emph type="italics"/>Cap. 2. Modi Dorius, & Phrygius apud Mu&longs;icos, quì.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000449">Ex 4. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000450"><emph type="italics"/>Cap. 3. Modus Doricus, & Phrygius.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000451">Ex 5. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000452"><emph type="italics"/>Cap. 1. Aequitas Arithmetica, & quæ &longs;ecundum dignitatem.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000453">Ex 8. Polit.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000454"><emph type="italics"/>Cap. 5. Mu&longs;ica nuda, & cum melodia. </s> <s id="s.000455">Rithmus quid.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000456"><emph type="italics"/>Harmonia lydia. </s> <s id="s.000457">Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000458"><emph type="italics"/>Cap. 7. Harmoniæ, & Rithmi, vt in præcedenti.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000459">Ex Problematibus.</s> </p> <p type="main"> <s id="s.000460"><emph type="italics"/>Sectione 1. num. </s> <s id="s.000461">3. De ortu &longs;yderum inerrantium: Succulæ, Hypades, Atlantides, <lb/> Virgiliæ, Pleiades. </s> <s id="s.000462">num. </s> <s id="s.000463">17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000464"><emph type="italics"/>Sectione 15. num. </s> <s id="s.000465">1. Diametri ethymon.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000466"><emph type="italics"/>num. </s> <s id="s.000467">2. Iterum Diametri ethymologia.<emph.end type="italics"/></s> </p> <pb pagenum="19" xlink:href="009/01/019.jpg"/> <p type="main"> <s id="s.000468"><emph type="italics"/>num. </s> <s id="s.000469">3. Denarius numerus cur perfectus. </s> <s id="s.000470">eius dignitates. </s> <s id="s.000471">Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000472"><emph type="italics"/>4. De inæquali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000473"><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotundæ, quamuis per angulo&longs;a foramina ingre­<lb/> diantur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000474"><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s> <s id="s.000475">vbi de illuminatione Lunæ, <lb/> quæ experientia docetur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000476"><emph type="italics"/>7. Cur Sol, & Luna videantur plana?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000477"><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000478"><emph type="italics"/>9. Cur Lunæ, quàm Solis minores vmbræ?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000479"><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiuæ &longs;unt? </s> <s id="s.000480">modus commodè <lb/> videndi eclyp&longs;im Solis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000481"><emph type="italics"/>Sect. <!-- REMOVE S-->16. nu. </s> <s id="s.000482">1. Cur ba&longs;es bullarum in aquis &longs;unt albæ?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000483"><emph type="italics"/>3. Opplumbati tali.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000484"><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000485"><emph type="italics"/>5. Cur conus, & cylindrus diuersè moueantur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000486"><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000487"><emph type="italics"/>12. Idem cum præcedenti 3.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000488"><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s> <s id="s.000489">reflexio radiorŭm pulchrè comparatur corporŭm re&longs;ultationi.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000490">Ex &longs;ectione 19. De Mu&longs;ica.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000491"><emph type="italics"/>num. </s> <s id="s.000492">2. Lineæ duplæ quadratum quadruplum. </s> <s id="s.000493">Hoc loco &longs;equentium probl. </s> <s id="s.000494">cau&longs;a, <lb/> præmittitur totius Mu&longs;icæ ortus breuis tractatio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000495"><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000496"><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000497"><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000498"><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000499"><emph type="italics"/>8. Cur grauis &longs;onum potest acutæ?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000500"><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000501"><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000502"><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000503"><emph type="italics"/>12. Grauior è fidibus cantilenam &longs;u&longs;cipit.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000504"><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000505"><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s> <s id="s.000506">Punicum quid.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000507"><emph type="italics"/>15. Leges Mu&longs;icæ, quæ. </s> <s id="s.000508">Genera, Diatonicum, Chromaticum, Encharmonium. <lb/> </s> <s id="s.000509">Tetrachorda quæ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000510"><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000511"><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s> <s id="s.000512">Magadis quid. </s> <s id="s.000513">Magadare.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000514"><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000515"><emph type="italics"/>19. Cur Diapente, & Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000516"><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"> <s id="s.000517"><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000518"><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000519"><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000520"><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000521"><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s> <s id="s.000522">Rithmus quid.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000523"><emph type="italics"/>28. Cur cantilenæ quædam leges decebantur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000524"><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s> </p> <pb pagenum="20" xlink:href="009/01/020.jpg"/> <p type="main"> <s id="s.000525"><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melopæos.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000526"><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000527"><emph type="italics"/>33. Cur aptè de acuto in graue, non è contra canitur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000528"><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"> <s id="s.000529"><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"> <s id="s.000530"><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"> <s id="s.000531"><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000532"><emph type="italics"/>38. Cur Rythmo, & harmonij omnes gaudent?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000533"><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000534"><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000535"><emph type="italics"/>41. Idem cum 5.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000536"><emph type="italics"/>42. Idem cum 34.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000537"><emph type="italics"/>43. Idem cum 24. Iugum in lyra veteri quodnam fuerit, vna cum figura vete­<lb/> ris lyræ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000538"><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000539"><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000540"><emph type="italics"/>46. Idem cum 22.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000541"><emph type="italics"/>47. Idem cum 26.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000542"><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000543"><emph type="italics"/>49. Idem cum 30. In choris tragœdiarum, nec &longs;ubdorius, nec &longs;ubphrygius modus <lb/> erat in v&longs;u.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000544"><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000545"><emph type="italics"/>51. Dolia duo æqualia, quorum alterum plenum &longs;it, alterum dimidium, Diapa&longs;on <lb/> re&longs;onant.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000546">Ex &longs;ectione 23.</s> </p> <p type="main"> <s id="s.000547"><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000548">Ex &longs;ectione 30.</s> </p> <p type="main"> <s id="s.000549"><emph type="italics"/>6. Omnis triangulus habet tres æquales, &c.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000550">Ex &longs;ectione 31.</s> </p> <p type="main"> <s id="s.000551"><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"> <s id="s.000552"><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s> <s id="s.000553">Cur aliquando rei vi&longs;æ gemina­<lb/> tio accidat.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000554"><emph type="italics"/>11. Cur di&longs;tractis oculis res vna duæ apparent?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000555"><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000556"><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000557">Auctarium De Oculi Pupilla.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000558"><emph type="italics"/>Oculi fabrica præmittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000559"><emph type="italics"/>Primo. </s> <s id="s.000560">De pupillæ voce.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000561"><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000562"><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000563"><emph type="italics"/>4. Pupillæ definitio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000564"><emph type="italics"/>5. Cur nigra in omnibus hominibus.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000565"><emph type="italics"/>6. Cur in Sole euane&longs;cat.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000566"><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000567"><emph type="italics"/>8. Cur modo maior, modo minor videatur, & cui&longs;dam lepida deceptio.<emph.end type="italics"/></s> </p> <pb pagenum="21" xlink:href="009/01/021.jpg"/> <p type="main"> <s id="s.000568">Additamentum de natura Mathematicarum di&longs;ciplinarum.</s> </p> <p type="main"> <s id="s.000569"><emph type="italics"/>Primo. </s> <s id="s.000570">De &longs;ubiecto Mathem. &longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio­<lb/> nes Mathematicæ e&longs;&longs;e perfecti&longs;&longs;imæ.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000571">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"> <s id="s.000572">3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumniæ diluuntur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000573">4. <emph type="italics"/>De præstantia cognitionis, quam Geometria, & Arithmetica gignunt.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000574">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"> <s id="s.000575">6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000576">7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000577"><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s> </p> </section> <pb pagenum="22" xlink:href="009/01/022.jpg"/> <section> <p type="head"> <s id="s.000578"><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000579"><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/> ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe­<lb/> runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/> vnde &longs;uas prælectiones aliquando valeant locupletare.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000580"><emph type="italics"/>In Primo Elem. Euclidis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000581">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> </p> <p type="main"> <s id="s.000582">Ad principia primi elementorum, vide infra tex. <!-- REMOVE S-->5. pri. <!-- REMOVE S-->Po&longs;ter.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000583">Ad definitionem 10. pri. <!-- REMOVE S-->pro angulo recto, vide 30. quæ&longs;t. </s> <s id="s.000584">Mecha­<lb/> nic. <!-- REMOVE S-->& cap. 7. lib. 1. Eth.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000585">Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/> hoc vno axiomate qu&etail;&longs;tionem <expan abbr="quãdam">quandam</expan> inter Philo&longs;ophos valdè difficilem, <lb/> facile di&longs;&longs;olui. </s> <s id="s.000586">ea e&longs;t, vtrum marmor, aut adamas, aliudue quidpiam infle­<lb/> xibile &longs;ucce&longs;&longs;iuè findi, & aperiri po&longs;&longs;it. </s> <s id="s.000587">qui enim aiunt, &longs;ic refelluntur, quia <lb/> nimirum &longs;equeretur, duas rectas lineas habere &longs;egmentum commune: in­<lb/> telligantur enim duæ lineæ, vna in vna &longs;uperficie, altera vero in altera, quæ <lb/> antequam incipiat apertio, congruant; Quoniam igitur tota illa apertio <lb/> non fit in in&longs;tanti, &longs;ed &longs;ucce&longs;&longs;iuè, facta iam aliqua apertionis parte con&longs;i­<lb/> derentur prædictæ lineæ, erit igitur earum pars aliqua ab inuicem &longs;epara­<lb/> ta, altera verò 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"> <s id="s.000588">Ad Calcem axiomatum primi accommodetur tex. <!-- REMOVE S-->1. primi Po&longs;ter.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000589">Ad primam primi, po&longs;t ip&longs;ius explicationem, commodè declarari pote&longs;t, cur <lb/> Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, & De&longs;igna­<lb/> tiones, vide cap. de Priori, & cap. 24. &longs;ecti primi, libri primi Priorum, & <lb/> tex. <!-- REMOVE S-->4. quinti Methaph. <!-- REMOVE S-->& tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->& cap. 3. lib. 3. Ethic. <lb/> <!-- KEEP S--></s> <s id="s.000590">Item ad primam primi, vide tex. <!-- REMOVE S-->7. &longs;ecundi Po&longs;ter. loco 2.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000591">Ad 5. primi, vide cap. 24. &longs;ecti 1 lib. 1. Priorum.</s> </p> <p type="main"> <s id="s.000592">Ad 21. primi, vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000593">Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s> </p> <p type="main"> <s id="s.000594">Ad 28. primi, vide cap. 21. & cap. 22. &longs;ecundi <expan abbr="Priorũ">Priorum</expan>, & tex. <!-- REMOVE S-->13. primi Po&longs;ter.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000595">Ad 32. primi, vide cap. 1. &longs;ecti 3. lib. 1. Prior. <!-- REMOVE S-->& cap. 26. &longs;ecundi <expan abbr="Priorũ">Priorum</expan>, & tex. <!-- REMOVE S-->2. <lb/> primi Po&longs;ter. loco 4. & tex. <!-- REMOVE S-->23. primi Po&longs;ter. <!-- REMOVE S-->vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam <lb/> <expan abbr="demõ&longs;trationem">demon&longs;trationem</expan>. </s> <s id="s.000596">& tex. <!-- REMOVE S-->37. primi Po&longs;ter. & tex. <!-- REMOVE S-->39. primi Po&longs;ter. <!-- KEEP S--></s> <s id="s.000597">Ibidem <lb/> loco 4. & tex. <!-- REMOVE S-->43. primi Po&longs;ter. <!-- REMOVE S-->& tex. <!-- REMOVE S-->2. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->bis. </s> <s id="s.000598">& tex. <!-- REMOVE S-->89. &longs;e­<lb/> cundi Phy&longs;. & tex. <!-- REMOVE S-->15. octaui Phy&longs;. <!-- REMOVE S-->& tex. <!-- REMOVE S-->119. primi de Cœlo. <!-- KEEP S--></s> <s id="s.000599">& tex. <!-- REMOVE S-->25. <lb/> &longs;ecundi de Cœlo. <!-- KEEP S--></s> <s id="s.000600">tex 11. primi de Anima. <!-- REMOVE S-->& cap. 1. de mem. </s> <s id="s.000601">& remini&longs;c. <lb/> </s> <s id="s.000602">& tex. <!-- REMOVE S-->35. quinti Methaphy&longs;. & tex. <!-- REMOVE S-->20. &longs;exti Methaphy&longs;. <!-- REMOVE S-->& tex. <!-- REMOVE S-->22. &longs;exti <lb/> Methaphy&longs;. <!-- REMOVE S-->& cap. 4. lib. 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s> <s id="s.000603">& cap. 5. lib. 6. Ethic. <!-- REMOVE S-->& <lb/> cap. 2. Magnorum Moral. & cap. 10. Mag. Moral. & cap. 16. Mag. Moral. <lb/> <!-- REMOVE S-->& cap. <!-- REMOVE S-->7. &longs;ecundi Eudem. & cap. <!-- REMOVE S-->12. &longs;ecundi Eudem. <!-- REMOVE S-->& problema 6. &longs;ectio­ <pb pagenum="23" xlink:href="009/01/023.jpg"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica hæc Euclidis Demon&longs;tratio.</s> </p> <p type="main"> <s id="s.000604">Ad &longs;cholion præcedentis 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> </p> <p type="main"> <s id="s.000605">Ad 45. primi, vide locum 9. de lineis in&longs;ecabilibus.</s> </p> <p type="main"> <s id="s.000606">Ad 46. primi, vide locum 11. de lineis in&longs;ecabilibus.</s> </p> <p type="main"> <s id="s.000607">Ad 47. primi, vide locum 11. de lineis in&longs;ecab. </s> <s id="s.000608">Item locum 14. de ij&longs;dem.</s> </p> <p type="head"> <s id="s.000609"><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000610">Ad 2. definitionem 2. Gnomonis, vide cap. de Motu in Po&longs;tprædicam. </s> <s id="s.000611">Qua­<lb/> dratum augetur Gnomone circumpo&longs;ito.</s> </p> <p type="main"> <s id="s.000612">Ad 14. propo&longs;. </s> <s id="s.000613">2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/> vide igitur cap. de relatione in prædicam. </s> <s id="s.000614">& cap. 31. &longs;ecundi Priorum, & <lb/> tex. <!-- REMOVE S-->23. primi Po&longs;ter. & finem 1. cap. primi Elenchorum. </s> <s id="s.000615">lege primam Ar­<lb/> chimedis de dimen&longs;ione circuli.</s> </p> <p type="head"> <s id="s.000616"><emph type="italics"/>In tertio Elem.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000617">Ad primam 3. vide cap. 9. lib. 2. Ethycorum.</s> </p> <p type="main"> <s id="s.000618">Ad 2. tertij, vide tex. <!-- REMOVE S-->13. lib. 1. de Anima. <!-- REMOVE S-->& locum 16. de lineis in&longs;ecab.</s> </p> <p type="main"> <s id="s.000619">Ad 31. tertij, vide tex. <!-- REMOVE S-->11. &longs;ecundi Po&longs;ter. & tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000620"><emph type="italics"/>In quarto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000621">Ad commentarium P. <!-- REMOVE S-->Clauij extremum lib. 4. elementorum. </s> <s id="s.000622">lege tex. <!-- REMOVE S-->66. <lb/> tertij de Cœlo.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000623"><emph type="italics"/>In quinto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000624">Ad 4. definitionem 5. vide cap. 3. lib. 2. Ethyc.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000625">Ad 9. definitionem 5. vide cap. 3. lib. 5. Ethyc. <!-- REMOVE S-->loco 4. & cap. 31. primi Ma­<lb/> gnorum Moralium.</s> </p> <p type="main"> <s id="s.000626">Ad 10. definitionem 5. vide tex. <!-- REMOVE S-->29. primi Po&longs;ter. loco 2.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000627">Ad 12. definitionem 5. vide tex. <!-- REMOVE S-->13. primi Po&longs;ter. <!-- REMOVE S-->loco 3. & tex. <!-- REMOVE S-->25. &longs;ecundi <lb/> Po&longs;ter. <!-- REMOVE S-->& tex. <!-- REMOVE S-->32. tertij de Anima. <!-- REMOVE S-->& cap. 3. lib. 5. Ethyc. <!-- REMOVE S-->loco 4.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000628">Ad 16. propo&longs;. </s> <s id="s.000629">5. vide tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon­<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> </p> <p type="main"> <s id="s.000630">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> <s id="s.000631">Quemadmodum voluntas noua ad effectum antiquum.</s> </p> <p type="main"> <s id="s.000632">Non enim in permutando confert antecedentem ad antecedentem, & con­<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"> <s id="s.000633"><emph type="italics"/>In &longs;exto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000634">Ad 2. propo&longs;it. </s> <s id="s.000635">6. vide cap. 2. lib. 8. Topicorum loco 41.</s> </p> <p type="main"> <s id="s.000636">Ad 13. &longs;exti, vide tex. <!-- REMOVE S-->12. &longs;ecundi de Anima, & tex. <!-- REMOVE S-->3. tertij Methaphy&longs;.<!-- REMOVE S--><emph type="italics"/>In &longs;eptimo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000637">Ad primam definitionem 7. vide tex. <!-- REMOVE S-->5. primi Po&longs;ter.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000638">Ad 8. definitionem 7. vide cap. 1. lib. 1. Magnorum Moral.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000639"><emph type="italics"/>In octauo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000640">Ad 4. propo&longs;. </s> <s id="s.000641">9. vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. loco 2.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000642">Ad 8. propo&longs;. </s> <s id="s.000643">9. vide problem. </s> <s id="s.000644">3. &longs;ectionis 15. loco 4.<!-- KEEP S--></s> </p> <pb pagenum="24" xlink:href="009/01/024.jpg"/> <p type="head"> <s id="s.000645"><emph type="italics"/>In decimo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000646">Ad primam definitionem 10. vide cap. 23. &longs;ecti 1. primi Priorum. </s> <s id="s.000647">& tex. <!-- REMOVE S-->48. <lb/> primi de Cœlo.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000648">Ad 118. decimi, vide cap. 23. &longs;ecti 1. libri 1. Priorum. </s> <s id="s.000649">& &longs;ecto 2. cap. 23. li­<lb/> bri 1. Priorum. </s> <s id="s.000650">& cap. 22. lib. 2. Priorum. </s> <s id="s.000651">& tex. <!-- REMOVE S-->5. primi Po&longs;ter. & tex. <!-- REMOVE S-->44. <lb/> primi Po&longs;ter. <!-- REMOVE S-->& cap. 15. primi Po&longs;ter. <!-- REMOVE S-->& tex. <!-- REMOVE S-->119. primi de Cœlo. <!-- KEEP S--></s> <s id="s.000652">& tex. <lb/> <!-- REMOVE S-->120. quarti Phy&longs;. & tex. <!-- REMOVE S-->21. tertij de Anima. <!-- REMOVE S-->& cap. 1. primi Methaphy&longs;. <lb/> <!-- REMOVE S-->& tex. <!-- REMOVE S-->28. quarti Met. <!-- REMOVE S-->& tex. <!-- REMOVE S-->34. quinti Met. <!-- REMOVE S-->& tex. <!-- REMOVE S-->8. &longs;exti Met. <!-- REMOVE S-->& cap. 4. <lb/> lib. 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s> <s id="s.000653">& lib. 3. cap. 3. Ethyc. <!-- REMOVE S-->& cap. 10. &longs;ecundi Eu­<lb/> dem. <!-- KEEP S--></s> <s id="s.000654">tot Ari&longs;t. loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s> </p> <p type="head"> <s id="s.000655"><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000656">Ad primam propo&longs;. </s> <s id="s.000657">13. &longs;ecundum editionem Commandini, aut Zamberti. <lb/> <!-- KEEP S--></s> <s id="s.000658">vide initio Priorum, in verbum (Re&longs;olutio)</s> </p> <p type="main"> <s id="s.000659">Atque hæc &longs;unt, quæ ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit, <lb/> quæque nos infra explicabimus.</s> </p> <p type="head"> <s id="s.000660"><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s> </p> <p type="main"> <s id="s.000661">Quæ verò ad alias Mathematicas, Mu&longs;icam &longs;cilicet, Per&longs;pe­<lb/> ctiuam, Mechanicam, & A&longs;tronomiam pertinens, facilè <lb/> poterunt ex primo Indice ad vnamquamque earum &longs;eor­<lb/> &longs;um cum libuerit, &longs;ecerni.</s> </p> </section> <pb pagenum="25" xlink:href="009/01/025.jpg"/> <section> <p type="head"> <s id="s.000662"><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000663"><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, quæ.<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, & æquitas &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 variè con&longs;ideratur à Geometra, & à 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"/>Antennæ nauis problema.<emph.end type="italics"/></cell> <cell>248</cell> </row> <row> <cell><emph type="italics"/>Antiphonæ 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, quæ.<emph.end type="italics"/></cell> <cell>279</cell> </row> <row> <cell><emph type="italics"/>Aquæ &longs;uperficiem e&longs;&longs;e &longs;phæricam 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"/>Astronomiæ principia duo, Apparentia, & Ob&longs;eruatio.<emph.end type="italics"/></cell> <cell>8</cell> </row> <row> <cell><emph type="italics"/>Automata, quæ.<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, & cur non faciat vmbram.<emph.end type="italics"/></cell> <cell>351</cell> </row> <row> <cell><emph type="italics"/>Binomium linea, quæ.<emph.end type="italics"/></cell> <cell>279</cell> </row> <row> <cell><emph type="italics"/>Bra&longs;ilien&longs;es, qua ratione numerare &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 Cœlorum.<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 mathematicè o&longs;tenditur. 123. Cen-trum grauitatis, & 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"/>Coalternæ lineæ, quæ.<emph.end type="italics"/> 12. 14.</cell> <cell>44</cell> </row> <row> <cell><emph type="italics"/>Cœlorum 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 Cœlo collocant. 136. e&longs;&longs;e &longs;u-pra aerem longi&longs;&longs;imo &longs;altem interuallo o&longs;tenditur mathematicè. 129. in additione.<emph.end type="italics"/></cell> <cell/> </row> <row> <cell><emph type="italics"/>Con&longs;onantia, quid. 64. quibus numeris con&longs;onantiæ con&longs;tent.<emph.end type="italics"/></cell> <cell>210</cell> </row> <row> <cell><emph type="italics"/>Conus, & cylindrus, cur variè mouentur.<emph.end type="italics"/></cell> <cell>355</cell> </row> <pb pagenum="26" xlink:href="009/01/026.jpg"/> <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, & 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 mathematicæ e&longs;&longs;e e&longs;&longs;entiales, & 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, & 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 perfectæ exemplum. 36. demon&longs;trationum mathematicarum præ-&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 denariŭ 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"/>&c.<emph.end type="italics"/></cell> </row> <row> <cell><emph type="italics"/>Diameter incommen&longs;urabilis costæ. 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 pulcherrima.<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, quæ.<emph.end type="italics"/></cell> <cell>359</cell> </row> <row> <cell><emph type="italics"/>Diate&longs;&longs;aron con&longs;onantia, quæ.<emph.end type="italics"/></cell> <cell>359</cell> </row> <row> <cell><emph type="italics"/>Di&longs;d apa&longs;on con&longs;onantia, quæ.<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, quæ.<emph.end type="italics"/> 82.</cell> <cell>213</cell> </row> <row> <cell><emph type="italics"/>Eudoxi opinio de numero Cœlorum.<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, & 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="quotcŭmq;">quotcŭmque</expan> æquales quatuor rectis angulis, quæ e&longs;t mira proprietas.<emph.end type="italics"/></cell> <cell>59</cell> </row> <row> <cell><emph type="italics"/>Figuræ &longs;imiles, quæ.<emph.end type="italics"/></cell> <cell>70</cell> </row> <row> <cell><emph type="italics"/>Figurarum planarum ordo 88. quæ nam totum locum repleant.<emph.end type="italics"/></cell> <cell>96</cell> </row> <row> <cell><emph type="italics"/>Figurarum &longs;olidarum, quænam totum locum repleant: vbi Ari&longs;t. & omnium expo&longs;i-torum ratum 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 demon&longs;trationibus Mathem.<emph.end type="italics"/></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"/>Filum Araneorum, ex qua parte corporis exeat, & 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;icæ veteris. 78. Fusè explicantur.<emph.end type="italics"/></cell> <cell>371</cell> </row> <row> <cell><emph type="italics"/>Geodæ&longs;ia.<emph.end type="italics"/></cell> <cell>207</cell> </row> <row> <cell><emph type="italics"/>Geographiæ veteris plura errata,<emph.end type="italics"/> 145. 146. 147. 148.</cell> <cell>149</cell> </row> <pb pagenum="27" xlink:href="009/01/027.jpg"/> <row> <cell><emph type="italics"/>Gnomon, quid. 3. &<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, eiqué 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 demon&longs;tratio.<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 lunulæ optima.<emph.end type="italics"/></cell> <cell>17</cell> </row> <row> <cell><emph type="italics"/>Hyades, Atlantides, & Succulæ.<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 defectiuæ.<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"/>& <expan abbr="&longs;eqq.">&longs;eqque</expan><emph.end type="italics"/></cell> </row> <row> <cell><emph type="italics"/>Incommen&longs;urabilia, quæ, & 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. & &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, & 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 quæ&longs;t.<emph.end type="italics"/></cell> <cell/> </row> <row> <cell><emph type="italics"/>Linea, quæ 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"/>Lineæ rationales, & irrationales, &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;phærica. 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;phæricam. 48. illuminari &longs;phæricè quid: ibidem & de illuminatione Lu-næ. iterum e&longs;&longs;e &longs;phæricam ab eclyp&longs;ibus.<emph.end type="italics"/></cell> <cell>111</cell> </row> <row> <cell><emph type="italics"/>Luminarium Solis, & Lunæ 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"/>Lyræ 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, & magadi&longs;&longs;are.<emph.end type="italics"/> 373.</cell> <cell>393</cell> </row> <row> <cell><emph type="italics"/>Materia intelligibilis. fusè verò. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell> <cell/> </row> <row> <cell><emph type="italics"/>Mathematicæ mediæ, &longs;eu &longs;ubalternatæ 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"/>Mathematicæ non &longs;unt contentio&longs;æ. 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"/>Mathematicæ o&longs;tendunt per cau&longs;am materialem, & formalem. 205. earum vtilitas. ibidem. De earum natura. in proprio tractatu.<emph.end type="italics"/></cell> <cell/> </row> <pb pagenum="28" xlink:href="009/01/028.jpg"/> <row> <cell><emph type="italics"/>Mathematicæ maximè tractant de Bono, & Pulcro, qua ratione.<emph.end type="italics"/></cell> <cell>237</cell> </row> <row> <cell><emph type="italics"/>Mechanica facultas, quæ.<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, & 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, &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 cœlestium motuum.<emph.end type="italics"/></cell> <cell>225</cell> </row> <row> <cell><emph type="italics"/>Mu&longs;ici recentiores reprehen&longs;i. 331. & in fine Chronologiæ.<emph.end type="italics"/></cell> <cell/> </row> <row> <cell><emph type="italics"/>Mu&longs;icæ totius elementa.<emph.end type="italics"/></cell> <cell>359</cell> </row> <row> <cell><emph type="italics"/>Mu&longs;ica nuda, & 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, & compo&longs;itus, quadratus, &longs;eu æquilaterus, 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 verò 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"/>&c.<emph.end type="italics"/></cell> </row> <row> <cell><emph type="italics"/>Omophonæ 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, & occa&longs;us &longs;yderum, quid, & quotuplex: vbide Orione, & 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 quæ voces, aut chordæ.<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"/>Planetæ, 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" xlink:href="009/01/029.jpg"/> <row> <cell><emph type="italics"/>Principia &longs;cientiarum duplicia. Ex quibus, & 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 Cæneum.<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, & 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 à 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"/>Pupillæ oculi etymon., & natura. 408. cur in oculo no&longs;tro imago pupillæ 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="operã">operam</expan> dedere, easqué ceteris &longs;cientijs præponebat.<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, & quadraturæ duplex definitio cau&longs;alis, & formalis.<emph.end type="italics"/></cell> <cell>185</cell> </row> <row> <cell><emph type="italics"/>Quantitas an con&longs;tet 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, & mathematica, vt conueniant. 4. &<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 fusè 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, & eius figura 250. &<emph.end type="italics"/></cell> <cell>252</cell> </row> <row> <cell><emph type="italics"/>Securis problema, vbi de antiquæ &longs;ecuris figura, & 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"/>Sphæram planum tangit in puncto. demon&longs;tratur.<emph.end type="italics"/></cell> <cell>184</cell> </row> <row> <cell><emph type="italics"/>Statera antiqua, quæ: eius figura, & problema.<emph.end type="italics"/></cell> <cell>259</cell> </row> <row> <cell><emph type="italics"/>Stereomatria, vt differat à 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"/>Symphonæ 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 Cœli 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"/>Terræ quantitas.<emph.end type="italics"/></cell> <cell>115</cell> </row> <row> <cell><emph type="italics"/>Terram paulatim reduci ad pefféctam 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" xlink:href="009/01/030.jpg"/> <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"/>Trochleæ problemata.<emph.end type="italics"/> 249. 250.</cell> <cell>251</cell> </row> <row> <cell><emph type="italics"/>Tunicæ 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, & &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, & 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"/>Virgiliæ, Pleiades.<emph.end type="italics"/></cell> <cell>335</cell> </row> <row> <cell><emph type="italics"/>Vi&longs;æ res gemmantur di&longs;tractis oculis.<emph.end type="italics"/></cell> <cell>406</cell> </row> <row> <cell><emph type="italics"/>Vi&longs;æ 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 terræ parum &longs;upra Lunam tran&longs;cendere.<emph.end type="italics"/></cell> <cell>137</cell> </row> <row> <cell><emph type="italics"/>Vmbrarum incrementa, & decrementa, cur inæqualia.<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 antiquæ appellationes.<emph.end type="italics"/></cell> <cell>360</cell> </row> <row> <cell><emph type="italics"/>Vox acuta velocior, grauis verò 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 terræ, vt Arist. de&longs;ignet: & quæ &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"> <s id="s.000664">Finis Tertij Indicis.</s> </p> <pb pagenum="31" xlink:href="009/01/031.jpg"/> </section> <section> <p type="main"> <s id="s.000665">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<lb/> thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&etail;&longs;ertim Peripa­<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. & 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 demon&longs;tratione ostenditur.<emph.end type="italics"/></cell> </row> <row> <cell><emph type="italics"/>147<emph.end type="italics"/></cell> <cell><emph type="italics"/>Ait Tanaim, & Indum oriri ex monte Paropami&longs;&longs;o. & 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 à 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, & 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 inhabitabilem 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 cœle&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, à Nonio erroris manifestè 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 benè videtur a&longs;signare cau&longs;am variæ im-mer&longs;ionis nauigij.<emph.end type="italics"/></cell> </row> </table> <pb xlink:href="009/01/032.jpg"/> <!--blank page --> </section> </front> <body> <chap> <pb pagenum="33" xlink:href="009/01/033.jpg"/> <p type="head"> <s id="s.000666">LOCA <lb/>MATHEMATICA <lb/>EX LIBRO <lb/>PRÆDICAMENTORVM <lb/> Per ordinem declarata.</s> </p> <p type="main"> <s id="s.000667"><arrow.to.target n="marg1"/></s> </p> <p type="margin"> <s id="s.000668"><margin.target id="marg1"/>1</s> </p> <p type="main"> <s id="s.000669">Ex c. <!-- REMOVE S-->3. De his, quæ ad aliquid. </s> <s id="s.000670">Porrò quemadmodum vnus angulus vni angulo æqualis e&longs;t, ita <lb/> <expan abbr="aliquãdo">aliquando</expan> duo anguli &longs;unt vni angulo æquales, vt patet, &longs;i vnus angulus, v.g. <lb/> <!-- REMOVE S-->angulus B A C, vbi ait <emph type="italics"/>(Scientia verò &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. o&longs;tendere, <lb/> nó omnia correlatiua &longs;imul e&longs;&longs;e natura, id de &longs;cibili, & &longs;cien­<lb/> tia variè probat, præ&longs;ertim verò, quia multa &longs;int &longs;cibilia, <lb/> quæ tamen nondum &longs;ciantur, vt patet, inquit, in Quadratu­<lb/> ra circuli, & &longs;cientia ip&longs;ius, quia quamuis ip&longs;a circuli quadratura &longs;it &longs;cibi­<lb/> lis, nondum tamen &longs;imul cum ip&longs;a, &longs;cientia illius extat. </s> <s id="s.000671">Quæ vt perfectè <lb/> intelligantur, &longs;ciendum e&longs;t, quadraturam circuli, quæ à Græcis tetrago­<lb/> ni&longs;mus dicitur, nihil aliud e&longs;&longs;e, quàm propo&longs;ito cuilibet circulo exhibere <lb/> quadratum æquale. </s> <s id="s.000672">Quæ æqualitas 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 æqualis <lb/> areæ, &longs;eu &longs;uperficiei quadratæ. </s> <s id="s.000673">Qua in re plurimi decipiuntur exi&longs;timantes <lb/> per quadraturam cir culi inquiri æqualitatem linearum, ita vt circumferen­<lb/> tia circuli debeat e&longs;&longs;e æqualis ambitui, &longs;eu quatuor lateribus quadrati: <lb/> quod omnino fal&longs;um e&longs;t.</s> </p> <p type="main"> <s id="s.000674">Quadratio porrò circuli dupliciter proponi pote&longs;t, vel tanquam Theo­<lb/> rema, vel tanquam Problema <emph type="italics"/>(theorema autem e&longs;t propo&longs;itio, in qua nihil fa­<lb/> ciendum proponitur; problema verò aliquid fieri expo&longs;cit)<emph.end type="italics"/> neutrum autem tem­<lb/> pore Ari&longs;t. erat adinuentum nam theorema inuentum e&longs;t po&longs;t ip&longs;um ducen­<lb/> tis circiter annis ab Archimede: problema verò nondum à quoquam per­<lb/> fectè potuit reperiri. </s> <s id="s.000675">qua di&longs;tinctione &longs;aluari po&longs;&longs;unt nonnulli, vt Boetius <lb/> hoc loco, qui aiunt, &longs;e vidi&longs;&longs;e Demon&longs;trationem quadraturæ huius, &longs;i nimi­<lb/> rum intelligant theorema. </s> <s id="s.000676">& alij etiam verum a&longs;&longs;erunt, dum negant hacte­<lb/> nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi­ <pb pagenum="34" xlink:href="009/01/034.jpg"/>medis e&longs;t propo&longs;itio prima acuti&longs;&longs;imi libelli de Dimen&longs;ione circuli; e&longs;t au­<lb/> tem huiu&longs;modi. </s> <s id="s.000677">Quilibet circulus æqualis e&longs;t triangulo rectangulo, cuius <lb/> quidem &longs;emidiameter vni laterum, quæ circa rectum angulum &longs;unt, ambi­<lb/> tus verò ba&longs;i eius e&longs;t æqualis.</s> </p> <figure id="id.009.01.034.1.jpg" place="text" xlink:href="009/01/034/1.jpg"/> <p type="main"> <s id="s.000678">Sit, v.g. <!-- REMOVE S-->datus circulus, cuius &longs;emidiameter A B; & fit triangulum rectangu­<lb/> lum A B C, cuius angulus B, &longs;it rectus, & latus B A, <expan abbr="con&longs;titu&etilde;s">con&longs;tituens</expan> angulum re­<lb/> ctum B, cum ba&longs;i B C, &longs;it æquale &longs;emidiametro A B; ba&longs;is verò B C, &longs;it æqua­<lb/> lis peripheriæ eiu&longs;dem circuli dati. </s> <s id="s.000679">demon&longs;trat iam ibi Archimedes acuta <lb/> æquè, ac euidenti demon&longs;tratione triangulum i&longs;tud æquale e&longs;&longs;e circulo illi. <lb/> </s> <s id="s.000680">quod perinde e&longs;t, ac &longs;i o&longs;tendi&longs;&longs;et cuinam quadrato &longs;it æqualis, cum per vl­<lb/> timam 2. Eucl. <!-- REMOVE S-->po&longs;&longs;imus triangulo huic quadratum æquale con&longs;truere, quod <lb/> con&longs;equenter dato circulo æquale erit. </s> <s id="s.000681">Quod &longs;i in modum Problematis ita <lb/> proponatur: Dato circulo æquale quadratum con&longs;truere, nondum inuenta <lb/> e&longs;t ratio, quæ demon&longs;tratione confirmetur, qua id geometricè penitus, hoc <lb/> e&longs;t ad æqualitatem mathematicam, &longs;eu exacti&longs;&longs;imam effici po&longs;&longs;it, <expan abbr="tota&qacute;">totaque</expan>; dif­<lb/> ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li­<lb/> neam rectam B C, æqualem peripheriæ circuli dati. </s> <s id="s.000682">quam nullus hactenus <lb/> geometricè illi æqualem potuit exhibere, <expan abbr="atq;">atque</expan> exhibita <expan abbr="euid&etilde;ti">euidenti</expan> demon&longs;tra­<lb/> tione comprobare; Quamuis Archimedes acumine &longs;anè mirabili in lib. de <lb/> lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematicè, non tamen problematicè inue­<lb/> &longs;tigauit. </s> <s id="s.000683">nam propo&longs;itione 18. illius <expan abbr="admirãdi">admirandi</expan> operis inuenit lineam rectam <lb/> æqualem circumferentiæ primi circuli &longs;piralis lineæ; propo&longs; verò 19. repe­<lb/> rit aliam rectam æqualem circumferentiæ &longs;ecundi circuli. </s> <s id="s.000684">tu ip&longs;um con&longs;ule, <lb/> &longs;i admirandarum rerum contemplatione delectaris. </s> <s id="s.000685">Multa hac de re Pap­<lb/> pus Alexandrinus lib. 4. Math. coll. </s> <s id="s.000686">& Ioannes Buteo vnico volumine om­<lb/> nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="cõprehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s> <s id="s.000687">Qua­<lb/> re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/> illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, & Hippocratis quadra­<lb/> turas, quamuis fal&longs;as, <expan abbr="quarũ">quarum</expan> &longs;æpe meminit Ari&longs;t. & alij. </s> <s id="s.000688">&longs;olet autem à non­<lb/> nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/> cum videant eam à nemine, quamuis diu magno labore perqui&longs;itam, hacte­<lb/> nus adinuentam e&longs;&longs;e. </s> <s id="s.000689">ego quidem e&longs;&longs;e po&longs;&longs;ibilem exi&longs;timo, quis enim dubi­<lb/> tare pote&longs;t, po&longs;&longs;e exi&longs;tere quadratum æquale circulo propo&longs;ito? </s> <s id="s.000690">Quod &longs;i po­<lb/> te&longs;t fieri, quare non etiam demon&longs;trari? </s> <s id="s.000691">pr&etail;fertim cum videamus ab Archi­<lb/> mede iam inuentam e&longs;&longs;e, quatenus Theorema e&longs;t. </s> <s id="s.000692">& præterea con&longs;tet, Hip­<lb/> pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, & Archimedem in libel­ <pb pagenum="35" xlink:href="009/01/035.jpg"/>lo de quadratura Paraboles, quadra&longs;&longs;e ip&longs;am Parabolem, quæ tamen duæ fi­<lb/> guræ, lunula &longs;cilicet, & parabola &longs;unt curuilineæ.</s> </p> <p type="main"> <s id="s.000693"><arrow.to.target n="marg2"/></s> </p> <p type="margin"> <s id="s.000694"><margin.target id="marg2"/>2</s> </p> <p type="main"> <s id="s.000695">Ex cap. de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, & po&longs;terius ordine, <lb/> elementa enim priora &longs;unt ijs, quæ de&longs;cribuntur, nam principia prior a &longs;unt theore­<lb/> matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &c. </s> <s id="s.000696">quæ non &longs;unt in antiqua tran­<lb/> &longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo græco codice editionis Francfor­<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/ch. </foreign> per &longs;cientias autem demon&longs;tra­<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<lb/> nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu­<lb/> rationes, & De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver­<lb/> ba illa à nobis addita ex græco, optimè <expan abbr="præced&etilde;tia">præcedentia</expan> exponunt, cum per ele­<lb/> menta intelligantur principia, qualia &longs;unt initio Euclidis, & per de&longs;criptio­<lb/> nes exponant theoremata. </s> <s id="s.000697">quod autem principia illa ordine priora &longs;int de­<lb/> mon&longs;trationibus, &longs;iue ip&longs;as præcedant, ex ip&longs;a primi Euclidis in&longs;pectione <lb/> patere pote&longs;t.</s> </p> <p type="main"> <s id="s.000698"><arrow.to.target n="marg3"/></s> </p> <p type="margin"> <s id="s.000699"><margin.target id="marg3"/>3</s> </p> <p type="main"> <s id="s.000700">Ex cap. de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox <lb/> græca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/> <figure id="id.009.01.035.1.jpg" place="text" xlink:href="009/01/035/1.jpg"/><lb/> tum normam appellant, Itali verò, Squadra, ad <lb/> cuius &longs;imilitudinem Geometræ denominarunt fi­<lb/> guram quandam, &longs;eu portionem cuiu&longs;uis paralle­<lb/> logrammi, vt videre e&longs;t in definitione &longs;ecunda <lb/> 2. elem. </s> <s id="s.000701">& in præ&longs;enti figura, in qua quadratum <lb/> A B C D, circumpo&longs;ito gnomone E F G, augetur, <lb/> & fit maius quadratum H B I L.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000702">Idem etiam verum e&longs;t in quadrato arithmeti­<lb/> co, &longs;iue in numero quadrato: is enim pariter ad­<lb/> dito Gnomone augetur. </s> <s id="s.000703">i. </s> <s id="s.000704">addito numero impari. <lb/> </s> <s id="s.000705">quemadmodum infra 3. Phy&longs;. tex. <!-- REMOVE S-->26. fusè explicabimus.</s> </p> </chap> <chap> <p type="head"> <s id="s.000706"><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000707"><arrow.to.target n="marg4"/></s> </p> <p type="margin"> <s id="s.000708"><margin.target id="marg4"/>4</s> </p> <p type="main"> <s id="s.000709">Aliquorum opinio e&longs;t, Ari&longs;totelem ho&longs;ce libros appella&longs;&longs;e re&longs;olu­<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<lb/> nem meum non e&longs;t, nunc refellere. </s> <s id="s.000710">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<lb/> tiori Mathematicorum eruditione. </s> <s id="s.000711">Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/> Alex. initio &longs;eptimi Mathem. collect. </s> <s id="s.000712">antiqui&longs;&longs;imos videlicet Geometras, <lb/> Euclidem, Apollonium Pergæum, & Ari&longs;t&etail;um &longs;crip&longs;i&longs;&longs;e libros de re&longs;olutio­<lb/> ne, in quibus ars tradebatur, qua propo&longs;ito quouis theoremate, aut proble­<lb/> mate po&longs;&longs;ent facile ex eo, tanquam vero accepto inue&longs;tigare aliquam veri­<lb/> tatem, per quam deinde componerent illius, quod quærebatur, Demon&longs;tra­<lb/> tionem; inue&longs;tigationem illam appellabant re&longs;olutionem: compo&longs;itionem <lb/> verò nominabant di&longs;cur&longs;um <expan abbr="illũ">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb pagenum="36" xlink:href="009/01/036.jpg"/>o&longs;tendebant conclu&longs;ionem. </s> <s id="s.000713">Porrò Diogenes Laert. <!-- REMOVE S-->huius re&longs;olutionis in­<lb/> uentorem facit Platonem: à quo eam Leodamas Tha&longs;ius didicit, cuius be­<lb/> neficio, pluries deinde Geometricas demon&longs;trationes adinuenit. </s> <s id="s.000714">definitio <lb/> <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t apud Euclidem ad primam propo&longs;. 13. Elem. iuxta tran&longs;latio­<lb/> nem Zamberti, & Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri­<lb/> mò per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, quæ tan­<lb/> quam per&longs;picua exempla rei propo&longs;itæ in&longs;eruire po&longs;&longs;unt. </s> <s id="s.000715">&longs;unt præterea fre­<lb/> quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, & Pap­<lb/> pi. </s> <s id="s.000716">extat adhuc liber Datorum Euclidis, qui geometricis re&longs;olutionibus in­<lb/> &longs;eruiebat. </s> <s id="s.000717">vtinam extarent etiam alij de re&longs;olutione, quorum auxilio non <lb/> tantopere recentiores Mathematici in inueniendis Demo&longs;trationibus la­<lb/> borarent; hanc re&longs;olutionem, &longs;ic Pappus fu&longs;ius, quam Euclides explicat; <lb/> re&longs;olutio e&longs;t via à quæ&longs;ito tanquam conce&longs;&longs;o per ea, quæ ex ip&longs;o con&longs;equun­<lb/> tur ad aliquod certum, & conce&longs;&longs;um: in re&longs;olutione enim id, quod quæritur <lb/> tanquam factum, & verum &longs;upponentes, quid ex hoc &longs;equatur, con&longs;idera­<lb/> mus, quou&longs;que incidamus in aliquod iam cognitum, vel quod &longs;it è numero <lb/> principiorum. </s> <s id="s.000718">Quod quidem erat &longs;ignum euidens, quæ&longs;itum quoque verum <lb/> e&longs;&longs;e. </s> <s id="s.000719">eadem omnino habet Proclus in comm. <!-- REMOVE S-->ad &longs;extam primi elem. </s> <s id="s.000720">Quod <lb/> porrò 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, quærere videtur, & re&longs;oluere prædicto modo, quemadmodum de&longs;igna­<lb/> tiones)<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt <lb/> &longs;upra innuimus, & 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 Geometricæ, 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> <s id="s.000721">Exi&longs;timo igitur <lb/> cum docti&longs;&longs;imis Zabarella, Burana, Toleto, & 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/>præ&longs;ertim cum argumentum e&longs;&longs;et ferè idem vtrobique, &longs;ed Ari&longs;t. intentio <lb/> fuerit accommodare re&longs;olutionem omnibus <expan abbr="&longs;ci&etilde;tijs">&longs;cientijs</expan>; Euclidis verò, & alio­<lb/> rum Geometriæ &longs;oli. </s> <s id="s.000722">hinc patere pote&longs;t, cur hi libri re&longs;olutorij in&longs;cribantur, <lb/> quod &longs;cilicet tradunt methodum, qua valeamus quæ&longs;itum quoduis re&longs;olue­<lb/> re, ide&longs;t, ex quæ&longs;ito tanquam vero inue&longs;tare aliquam veritatem, per quam <lb/> deinde propo&longs;itæ quæ&longs;tionis rationem methodo compo&longs;itiua reddamus. </s> <s id="s.000723">Et <lb/> verò cum reliquas appellationes Problematis, Theorematis, Propo&longs;itionis, <lb/> definitionum, po&longs;tulatorum, axiomatum, & alia huiu&longs;modi ex Geometri­<lb/> cis ad omnes &longs;cientias tran&longs;tulerit, quid ni etiam re&longs;olutionem? </s> <s id="s.000724">maximè <lb/> verò, quia &longs;i horum lib. 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; imò nec vtilis, &longs;ed &longs;uperfluum quid. <lb/> </s> <s id="s.000725">at verò vbinam docuit hanc re&longs;olutionem? </s> <s id="s.000726">profecto nullibi. </s> <s id="s.000727">quid opus e&longs;t <lb/> iam factum &longs;yllogi&longs;mum re&longs;oluere? </s> <s id="s.000728">at verò propo&longs;itam quæ&longs;tionem re&longs;ol­<lb/> uere veterum mathematicorum more, hoc opus, hic labor e&longs;t.</s> </p> <p type="main"> <s id="s.000729">Hanc porrò re&longs;olutionem attendendam e&longs;&longs;e primò penes formam, quam <lb/> docet primis duobus analyticis; &longs;ecundò penes materiam, quam tradit duo­ <pb pagenum="37" xlink:href="009/01/037.jpg"/>bus vltimis, non prætereundum. </s> <s id="s.000730">reliquas duas logicæ partes, Topicam &longs;ci­<lb/> licet, & Elenchos, quæ &longs;yllogi&longs;mos probabilem, & apparentem docent, no­<lb/> luit appellare re&longs;olutorios, quamuis inuentionem mediorum doceant, quia <lb/> iam mos i&longs;te inoleuerat apud Philo&longs;ophos, & Mathematicos, vt illa &longs;ola <lb/> pars, quæ ex materia nece&longs;&longs;aria doceret &longs;yllogi&longs;mum demon&longs;tratiuum con­<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"> <s id="s.000731"><arrow.to.target n="marg5"/></s> </p> <p type="margin"> <s id="s.000732"><margin.target id="marg5"/>5</s> </p> <p type="main"> <s id="s.000733">Ex cap. 23. &longs;ecti primi lib. 1. <emph type="italics"/>(Vt quod diameter incommen&longs;urabilis eo, quod <lb/> imparia æqualia paribus fiant, &longs;i fuerit po&longs;ita commen&longs;urabilis. </s> <s id="s.000734">æqualia igitur fieri <lb/> imparia paribus ratiocinantur, diametrum vtrò incommen&longs;urabilem e&longs;&longs;e ex &longs;uppo­<lb/> &longs;itione <expan abbr="mon&longs;trãt">mon&longs;trant</expan>, quoniam fal&longs;um accidit propter contradictionem)<emph.end type="italics"/> Euclides pri­<lb/> mis duabus definitionibus 10. elem. </s> <s id="s.000735">definit, quæ nam &longs;int magnitudines <lb/> commen&longs;. </s> <s id="s.000736">& quæ incommen&longs;. </s> <s id="s.000737">&longs;ic; commen&longs;. </s> <s id="s.000738">magnitudines dicuntur, quas <lb/> <figure id="id.009.01.037.1.jpg" place="text" xlink:href="009/01/037/1.jpg"/><lb/> eadem men&longs;ura metitur, vt &longs;i fuerint duæ magnitu­<lb/> dines, A, & B, quas eadem men&longs;ura C, ide&longs;t quan­<lb/> titas C, metiatur, ide&longs;t <expan abbr="quãtitas">quantitas</expan> C, applicata quan­<lb/> titati A, & per ip&longs;am aliquoties replicata ip&longs;am ad­<lb/> æquatè ab&longs;umat, vt &longs;i linea C, quinquies &longs;uper li­<lb/> neam A, replicata eam præcisè, & perfectè omninò <lb/> adæquaret: & eadem linea C, applicata lineæ B, & &longs;uper illam ter, v.g. <!-- REMOVE S-->re­<lb/> petita ip&longs;am con&longs;umeret, diceretur <expan abbr="vtranq;">vtranque</expan> metiri, & proinde duas lineas <lb/> A, & 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<lb/> rum nullam contingit communem men&longs;uram reperiri; vt &longs;i duarum linea­<lb/> <figure id="id.009.01.037.2.jpg" place="text" xlink:href="009/01/037/2.jpg"/><lb/> rum, A, B, nunquam po&longs;&longs;et reperiri aliqua men&longs;u­<lb/> ra, quæ <expan abbr="vtranq;">vtranque</expan> adæquatè 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 adæquaret omnino <expan abbr="lineã">lineam</expan> B, &longs;ed deficeret, vel ex­<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 perfectè metiretur, e&longs;&longs;ent duæ illæ lineæ <lb/> incommen&longs;. </s> <s id="s.000739">Extare porrò tales lineas, & &longs;uperficies, & corpora, <expan abbr="ea&qacute;">eaque</expan>; quam­<lb/> plurima, ac penè infinita ex 10. Elem. manife&longs;tum e&longs;t. </s> <s id="s.000740">inuentum autem hu­<lb/> ius a&longs;ymmetriæ, 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<lb/> &longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s> <s id="s.000741">Quapropter <lb/> non immeritò diuinus ille Plato lib. 7. de legib. </s> <s id="s.000742">huius a&longs;ymmetriæ ignora­<lb/> tionem, adeo dete&longs;tatus e&longs;t, vt eam non hominum, &longs;ed &longs;uum, pecorumque <lb/> ignorantiam cen&longs;uerit. </s> <s id="s.000743">inter lineas incommen&longs;. &longs;unt diameter, & latus eiu&longs;­<lb/> dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti <lb/> <figure id="id.009.01.037.3.jpg" place="text" xlink:href="009/01/037/3.jpg"/><lb/> e&longs;t lineola E, in præ&longs;enti quadrato, etiam&longs;i illam in <lb/> infinitum &longs;ubdiuidas, quæ <expan abbr="vtranq;">vtranque</expan> lineam, diame­<lb/> trum &longs;cilicet A C, & latus quoduis ex quatuor, v.<!-- REMOVE S-->g. <lb/> <!-- REMOVE S-->latus B C, præcisè omnino metiatur. </s> <s id="s.000744">theorema <lb/> i&longs;tud demon&longs;tratur in vltima 10. Elem. eodem me­<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" xlink:href="009/01/038.jpg"/>propo&longs;itionis, quæ fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito prædictas lineas e&longs;&longs;e comm. <lb/> <!-- REMOVE S-->deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t. fal&longs;um ratiocinatur, quod &longs;ci­<lb/> licet idem numerus e&longs;&longs;et par, & impar, quod Ari&longs;t. &longs;ignificat, quando ait, <lb/> imparia æqualia paribus fiunt. </s> <s id="s.000745">ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e prædi­<lb/> ctam &longs;uppo&longs;itionem, quæ a&longs;truebat e&longs;&longs;e comm. <!-- REMOVE S-->& proinde altera pars con­<lb/> tradictionis, quæ e&longs;t, e&longs;&longs;e incomm. <!-- REMOVE S-->vera a&longs;truitur. </s> <s id="s.000746">ex quibus &longs;atis videtur ex­<lb/> plicari hic locus. </s> <s id="s.000747">videas igitur, quàm leuiter nonnulli no&longs;træ tempe&longs;tatis <lb/> ageometreti i&longs;tud exponant, dicentes diametrum e&longs;&longs;e incomm. <!-- REMOVE S-->co&longs;tæ, nihil <lb/> aliud &longs;ignificare, quam diametrum e&longs;&longs;e longiorem co&longs;ta, qua expo&longs;itione <lb/> nihil ineptius. </s> <s id="s.000748">Aduerte tandem figuram vulgatæ 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"> <s id="s.000749"><arrow.to.target n="marg6"/></s> </p> <p type="margin"> <s id="s.000750"><margin.target id="marg6"/>6</s> </p> <p type="main"> <s id="s.000751">Et cap. 24. &longs;ecti primi libri primi <emph type="italics"/>(Sed magis efficitur manife&longs;tum in de&longs;cri­<lb/> ptionibus, vt quod æquicruris, qui ad ba&longs;im æquales &longs;int, ad centrum ductæ A B, <lb/>A C, &longs;i igitur æqualem accipiat A G, angulum ip&longs;i A B D, non omnino exi&longs;timans <lb/> æquales, qui &longs;emicirculorum, & rur&longs;us G, ip&longs;i D, non omnem a&longs;&longs;umens eum, qui &longs;e­<lb/> cti. </s> <s id="s.000752">amplius ab æqualibus existentibus totis angulis, & ablatorum æquales e&longs;&longs;e re­<lb/> liquos E, F, quod ex principio petet, ni&longs;i acceperit ab æqualibus demptis æqualia <lb/> derelinqui.)<emph.end type="italics"/> Primum &longs;cias characteres vulgatæ editionis, vna cum figura ip­<lb/> &longs;is re&longs;pondente, e&longs;&longs;e mendo&longs;os; propterea ex textu græco vtrunque corri­<lb/> gendum putaui in hunc, quem vidi&longs;ti modum. </s> <s id="s.000753">Secundo, per de&longs;criptiones <lb/> Ari&longs;t. intelligere <expan abbr="demõ&longs;trationes">demon&longs;trationes</expan> Geometricas &longs;upra diximus, quod ex hoc <lb/> loco euidenter confirmatur, vbi manife&longs;tè loco de&longs;criptionis &longs;upponit li­<lb/> nearem demon&longs;trationem. </s> <s id="s.000754">In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t. illud demon­<lb/> &longs;trare, quod Euclides in 5. primi o&longs;tendit, alio tamen modo, &longs;cilicet I&longs;o&longs;ce­<lb/> lium triangulorum, qui ad ba&longs;im &longs;unt anguli, inter &longs;e &longs;unt æquales. </s> <s id="s.000755">e&longs;t au­<lb/> tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="rè&longs;tītuendam">rè&longs;tituendam</expan> e&longs;&longs;e <lb/> ex quodam græco codice, qui characteres hoc modo appo&longs;uerat. </s> <s id="s.000756">&longs;it I&longs;o&longs;ce­<lb/> <figure id="id.009.01.038.1.jpg" place="text" xlink:href="009/01/038/1.jpg"/><lb/> les C A B, cuius ba&longs;is C B, Dico angulos &longs;upra ba&longs;im, <lb/> in quibus literæ E F, e&longs;&longs;e inuicem æquales. </s> <s id="s.000757">facto centro <lb/> in A, de&longs;cribatur circulus A B C, tran&longs;iens per puncta <lb/> C B, iam &longs;ic. </s> <s id="s.000758">omnes anguli &longs;emicirculi &longs;unt æquales in­<lb/> ter &longs;e, ergo anguli A C G, A B D, &longs;unt æquales. </s> <s id="s.000759">Præte­<lb/> rea cùm anguli eiu&longs;dem &longs;ectionis &longs;int æquales ad inui­<lb/> cem, erunt anguli &longs;ectionis C B D G, nimirum anguli, <lb/> in quibus &longs;unt G, & D, inter &longs;e æquales: <expan abbr="cum&qacute;">cumque</expan>; hi duo <lb/> anguli &longs;ectionis &longs;int partes <expan abbr="angulorũ">angulorum</expan> &longs;emicirculi A C G, <lb/> A B D, &longs;i illi ab his auferantur, auferuntur æquales anguli ab æqualibus an­<lb/> gulis, ergo anguli, qui remanent, &longs;cilicet E, & F, erunt æquales, quod erat <lb/> demon&longs;trandum. </s> <s id="s.000760">hinc Ari&longs;t. infert manife&longs;tum e&longs;&longs;e oportere in omni &longs;yllo­<lb/> gi&longs;mo, reperiri vniuer&longs;ales, & affirmatiuas propo&longs;itiones, vt Factum e&longs;t in <lb/> præcedenti aliter e&longs;&longs;et petitio principij. </s> <s id="s.000761">Quænam vero &longs;it æqualitas, quam <lb/> Geometræ con&longs;iderant, infra cap. 1. &longs;ecti 3. explicabitur.</s> </p> <p type="main"> <s id="s.000762"><arrow.to.target n="marg7"/></s> </p> <p type="margin"> <s id="s.000763"><margin.target id="marg7"/>7</s> </p> <p type="main"> <s id="s.000764">Ex cap. 2. &longs;ecti 2. lib. 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, quæ &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, quæ <expan abbr="&longs;ecundũ">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39" xlink:href="009/01/039.jpg"/>ine&longs;&longs;e; &longs;ic græcè, <foreign lang="greek">e/k tw=n kata\ alhqei/an diagegramme/non </foreign> vbi manife&longs;tè 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<lb/> quentibus verbis, cum dixit (ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;i­<lb/> tionibus &longs;ecundum opinionem) hac adhibita con&longs;ideratione, quam inter­<lb/> pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s> </p> <p type="main"> <s id="s.000765"><arrow.to.target n="marg8"/></s> </p> <p type="margin"> <s id="s.000766"><margin.target id="marg8"/>8</s> </p> <p type="main"> <s id="s.000767">Ex eodem loco paulo po&longs;t <emph type="italics"/>(Quare principia quidem, quæ &longs;ecundum <expan abbr="vnum-quodq;">vnum­<lb/> quodque</expan> &longs;unt experimenti est tradere: dico autem, vt a&longs;trologicam experientiam <lb/> a&longs;trologicæ &longs;cientiæ: acceptis enim apparentibus <expan abbr="&longs;uffici&etilde;ter">&longs;ufficienter</expan>, ita inuentæ &longs;unt a&longs;tro­<lb/> logicæ demonstrationes)<emph.end type="italics"/> Cum rationem tradat inueniendorum mediorum ad <lb/>quodlibet problema demon&longs;trandum; nunc docet, non omnia in &longs;cientijs <lb/>po&longs;&longs;e probari, aut demoν&longs;trari: principia enim &longs;cientiarum <expan abbr="nõ">non</expan> demon&longs;tran­<lb/> tur, &longs;ed &longs;ola experientia manife&longs;ta &longs;unt; vt patet in A&longs;tronomia, quæ ab ex­<lb/> perientia &longs;ua &longs;olet &longs;tabilire principia: principijs autem <expan abbr="experim&etilde;to">experimento</expan> con&longs;ti­<lb/> tutis ex ip&longs;is reliqua problemata <expan abbr="demon&longs;trãtur">demon&longs;trantur</expan>. </s> <s id="s.000768">duo autem &longs;unt apud a&longs;tro­<lb/> nomos genera experimenti, primum dicitur Phænomena, ide&longs;t, <expan abbr="appar&etilde;tiæ">apparentiæ</expan>; <lb/> & &longs;unt ea, quæ vulgo omnibus patent, vt Solem oriri, & occidere; a&longs;tra fer­<lb/> ri circulariter, diem augeri modo, modo minui: & his &longs;imilia. </s> <s id="s.000769">alterum ge­<lb/> nus dicitur ob&longs;eruationes, quæ tantummodo a&longs;tronomiæ peritis per ob&longs;er­<lb/> uationem innote&longs;cunt, vt Solem inæqualiter ferri proprio motu per Zodia­<lb/> cum; aliquando maiorem, aliquando minorem videri; plures dies immo­<lb/> rari citra æquatiorem in parte Zodiaci boreali, quam in altera vltra æqua­<lb/> torem au&longs;trali. </s> <s id="s.000770">dies naturales e&longs;&longs;e inuicem inæquales, &c. </s> <s id="s.000771">ex quibus deinde <lb/> ponunt eccentricos, & augem, ad &longs;aluandas tum apparentias, tum ob&longs;erua­<lb/> tiones; & hac ratione a&longs;trologica &longs;cientia paulatim reperta e&longs;t, ac in dies <lb/> reperitur.</s> </p> <p type="main"> <s id="s.000772"><arrow.to.target n="marg9"/></s> </p> <p type="margin"> <s id="s.000773"><margin.target id="marg9"/>9</s> </p> <p type="main"> <s id="s.000774">Ex cap. 3. &longs;ecti 2. lib. 1. <emph type="italics"/>(Vt an ne diameter incomm.)<emph.end type="italics"/> loquitur de a&longs;ymme­<lb/> tria diametri, & co&longs;tæ eiu&longs;dem quadrati, de qua fusè egimus &longs;uperius in <lb/> cap. 23. &longs;ecti 1. huius libri; quæ &longs;i repetantur, optimè hunc <expan abbr="locũ">locum</expan> declarant.</s> </p> <p type="main"> <s id="s.000775"><arrow.to.target n="marg10"/></s> </p> <p type="margin"> <s id="s.000776"><margin.target id="marg10"/>10</s> </p> <p type="main"> <s id="s.000777">Ex cap. 1. &longs;ecti 3. lib. 1. <emph type="italics"/>(Sit A, duo recti, in quo B, triangulus, in quo C, <lb/> æquicrus, 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<lb/> lo, &longs;cilicet, omnis triangulus habet tres angulos æquales duobus rectis an­<lb/> gulis, cuius Demon&longs;tratio e&longs;t in 32. primi Elem. quod, vt probè intelliga­<lb/> tur, explicandum e&longs;t penes quid attendenda &longs;it æqualitas inter angulum, & <lb/> angulum, quod facile a&longs;&longs;equemur, &longs;i meminerimus angulum e&longs;&longs;e inclinatio­<lb/> nem illam, quam duæ lineæ non in directum po&longs;itæ faciunt: &longs;iue etiam (vt <lb/> melius percipiamus) angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="illũ">illum</expan>, quem <lb/> duæ lineæ non in directum con&longs;titutæ faciunt, vt duarum linearum A B, A C, <lb/> <figure id="id.009.01.039.1.jpg" place="text" xlink:href="009/01/039/1.jpg"/><lb/> inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/> e&longs;t ratio anguli. </s> <s id="s.000778">&longs;olum igitur duo anguli erunt æqua­<lb/> les, <expan abbr="quãdo">quando</expan> vnius acumen æquale erit acumini alterius; <lb/> etiam &longs;i lineæ con&longs;tituentes vnum angulum &longs;int lon­<lb/> giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb pagenum="40" xlink:href="009/01/040.jpg"/><expan abbr="linearũ">linearum</expan>, &longs;ed penes inclinationem, & mucronem, quem faciunt: vnde etiam&longs;i <lb/> duæ lineæ prædictæ A B, A C, productæ, &longs;iue etiam decurtatæ fuerint, dum­<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> <s id="s.000779">Aduertendum præterea rationem <lb/> anguli non po&longs;&longs;e &longs;aluari in &longs;olo puncto A, in quo lineæ concurrunt, &longs;ed ne­<lb/> ce&longs;&longs;ariam e&longs;&longs;e aliquam quantitatem, quamuis exiguam, linearum A B, A C. <lb/> <!-- KEEP S--></s> <s id="s.000780">Notandum etiam, quod in nominatione angulorum, quæ fit per tres lite­<lb/> ras, &longs;emper literam illam e&longs;&longs;e medio loco proferendam, quæ ad acumen ip­<lb/> &longs;um po&longs;ita e&longs;t, vt in &longs;uperiori, litera A, debet &longs;emper media proferri, dicen­<lb/> do angulum B A C, &longs;iue C A B, <expan abbr="nũquam">nunquam</expan> tamen licet dicere angulum A C B, <lb/> vel C B A. <!-- KEEP S--></s> <s id="s.000781">Porrò quemadmodum vnus angulus vni angulo æqualis e&longs;t, ita <lb/> <expan abbr="aliquãdo">aliquando</expan> duo anguli &longs;unt vni angulo æquales, vt patet, &longs;i vnus angulus, v.g. <lb/> <!-- REMOVE S-->angulus B A C, diuidatur in duos angulos à linea A D. tunc enim duo angu­<lb/> <figure id="id.009.01.040.1.jpg" place="text" xlink:href="009/01/040/1.jpg"/><lb/> li partiales B A D, D A C, erunt æquales totali angulo <lb/> B A C, cum partes omnes &longs;imul &longs;umptæ &longs;int &longs;uo toti æqua­<lb/> les. </s> <s id="s.000782">pariter tres anguli po&longs;&longs;unt æquari & vni, & duobus <lb/> alijs angulis, quando nimirum a cumina, &longs;iue mucrones il­<lb/> li &longs;imul ad vnum punctum con&longs;tituti <expan abbr="adæquar&etilde;tur">adæquarentur</expan> mucro­<lb/> ni illi, 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 id="id.009.01.040.2.jpg" place="text" xlink:href="009/01/040/2.jpg"/><lb/> quos linea perpendicularis D E, facit cum li­<lb/> nea F G; &longs;it <expan abbr="inquã">inquam</expan> anguli recti D E F, D E G, <lb/> tunc tres anguli illius <expan abbr="triãguli">trianguli</expan> <expan abbr="dic&etilde;tur">dicentur</expan> æqua­<lb/> les duobus hi&longs;ce rectis, &longs;i tres illi mucrones <lb/> trianguli &longs;imul &longs;umpti, & vniti ad punctum <lb/> E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum <lb/> <figure id="id.009.01.040.3.jpg" place="text" xlink:href="009/01/040/3.jpg"/><lb/> rectorum coeunt, congruent omnino duobus <lb/> prædictis angulis rectis, &longs;iue duobus illis mu­<lb/> cronibus angulorum rectorum, &longs;iue con&longs;ti­<lb/> tuent lineam rectam F E G, &longs;icuti faciunt <lb/> etiam duo illi anguli recti; &longs;iue etiam dica­<lb/> mus, occupabunt idem &longs;patium omninò, & <lb/> præcisè, quod occupant duo recti: v.g. <!-- REMOVE S-->&longs;i mucro B, ibi poneretur, faceret <lb/> angulum F E H, & &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-quũ">reli­<lb/> quum</expan> angulum I E G. iam, vt vides, illi tres anguli ad E, tran&longs;lati, &longs;unt æqua­<lb/> les duobus rectis ad E, pariter con&longs;titutis, cum illi tres fiant partes duorum <lb/>rectorúm, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G, <lb/> con&longs;tituant. </s> <s id="s.000783">habet igitur omne triangulum &longs;iue &etail;quilaterum, &longs;iue &longs;calenum, <lb/> &longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian­<lb/> guli &longs;int æquales duobus rectis angulis. </s> <s id="s.000784">Quam demon&longs;trationem primi om­<lb/> nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli­<lb/> des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s> <s id="s.000785">Quod &longs;i <lb/> quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam (cum æqua­<lb/> litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe quæ in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, & cuius <pb pagenum="41" xlink:href="009/01/041.jpg"/>æqualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/> vitare ob &longs;ui imperfectionem non licet: vnde inter eæ, quæ mathematicè <lb/> &longs;unt æqualia, nullus intellectus aliquam valeat reperire differentiam) &longs;umat <lb/> inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po­<lb/>te&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/> quæ &longs;cilicet faciat, cum illa duos angulos rectos. </s> <s id="s.000786">po&longs;tea ab&longs;cindat tres an­<lb/> gulos trianguli materialis, <expan abbr="eos&qacute;">eosque</expan>; ita &longs;imul componat, vt mucrones illorum <lb/> &longs;int vniti, & contigui ad punctum lineæ perpendicularis cum altera, vti e&longs;t <lb/>in &longs;uperiori figura punctum E; & illicò apparebit tres illos angulos mate­<lb/> riales obtegere adæquatè totum illud &longs;patium duorum rectorum, quos per­<lb/> pendicularis con&longs;tituit. </s> <s id="s.000787">Hoc autem experiri poteris in diuer&longs;is admodum <lb/> triangulis Scalenis, Rectangulis, I&longs;o&longs;celibus, Aequilateris, &c. </s> <s id="s.000788">non &longs;ine de­<lb/> lectatione, atque hic e&longs;t &longs;en&longs;us illorum verborum, omnis triangulus habet <lb/> tres &etail;quales duobus rectis. </s> <s id="s.000789">Ab&longs;tineo à demon&longs;trationibus geometricis, quo­<lb/> niam ij, qui Mathematicis &longs;unt imbuti, no&longs;tra hac opera parum indigent. <lb/> </s> <s id="s.000790">&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. <!-- KEEP S--></s> <s id="s.000791">Ex hac igitur declaratione <lb/> licet cogno&longs;cere nonnullos ageometretos locum hunc, & &longs;imiles &longs;ub&longs;equen­<lb/> tes non &longs;atis intelligere, dicentes, nihil aliud verba illa Ari&longs;t. velle &longs;ignifi­<lb/> care, quàm omnem triangulum habere tres angulos, quod inquiunt, noti&longs;­<lb/> &longs;imum e&longs;t. </s> <s id="s.000792">Sed &longs;i incidant in &longs;equentia; æquales duobus rectis, tunc, cum <lb/> hæc non intelligant, ab&longs;tinent etiam à priorum declaratione, quibus præ­<lb/> mi&longs;&longs;is facile e&longs;t Ari&longs;t. textum percipere. </s> <s id="s.000793">&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, æquicrus. </s> <s id="s.000794">ip&longs;i <lb/> itaque C, ide&longs;t triangulo æquicru&longs;i, ine&longs;t A, &longs;cilicet duo recti, hoc e&longs;t, ine&longs;t <lb/> æquicru&longs;i hæc, pa&longs;&longs;io habere tres angulos æquales duobus rectis per B, ide&longs;t <lb/> per <expan abbr="triangulũ">triangulum</expan> vniuer&longs;ale, quia hæc proprietas e&longs;t trianguli propria, & <expan abbr="cõpe-tit">compe­<lb/> tit</expan> æquicru&longs;i, non vt æquicrus e&longs;t, &longs;ed, vt triangulum e&longs;t; quare B, non erit <lb/> medium ip&longs;ius A, quia prædicta pa&longs;&longs;io. </s> <s id="s.000795">A, non competit triangulo B, per <lb/> aliud, &longs;ed per &longs;e, de eo enim primo, & per &longs;e demon&longs;tratur in 32. primi Elem. <lb/> optimè Aegydius, & Niphus in hunc locum.</s> </p> <p type="main"> <s id="s.000796"><arrow.to.target n="marg11"/></s> </p> <p type="margin"> <s id="s.000797"><margin.target id="marg11"/>11</s> </p> <p type="main"> <s id="s.000798">Ex eodem cap. <emph type="italics"/>(Non oportet autem exi&longs;timare penes id, quod exponimus, ali­<lb/> quid accidere ab&longs;urdum, nihil enim vtimur eo, quod e&longs;t hoc aliquid e&longs;&longs;e. </s> <s id="s.000799">&longs;ed &longs;icut <lb/> Geometra pedalem, & rectam hanc, & &longs;ine latitudine dicit, quæ non &longs;unt. </s> <s id="s.000800">verum <lb/> non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t. 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. re&longs;pondet, dicens, nihil inde ab&longs;ur­<lb/> di accidere po&longs;&longs;e, quoniam ip&longs;e vtitur hi&longs;ce literis, <expan abbr="nõ">non</expan> quatenus literæ &longs;unt, <lb/> &longs;ed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum <lb/> etiam Geometræ faciunt, qui lineam, quæ pedalis non e&longs;t, pedalem, & quæ <lb/> non e&longs;t recta, rectam; & quæ lata e&longs;t, non latam, &longs;upponunt, & tamen nihil <lb/> inde ab&longs;urdi contingit. </s> <s id="s.000801">Ex quibus intelligimus per lineas illas &longs;en&longs;ibiles, & <lb/> phy&longs;icas, quas Geometræ in &longs;uis figuris ducunt, intelligendas e&longs;&longs;e lineas ve­<lb/> rè Mathematicas omni latitudine carentes; vtitur enim inquit Ari&longs;t. <!-- REMOVE S-->Geo­<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 verè mathematicis. </s> <s id="s.000802">idem dicen­<lb/>dum e&longs;t de &longs;uperficiebus, necnon de corporibus, quæ ijdem Geometræ de­<lb/> &longs;cribunt, vt per ea, de verè mathematicis di&longs;currant.</s> </p> </chap> <pb pagenum="42" xlink:href="009/01/042.jpg"/> <chap> <p type="head"> <s id="s.000803"><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000804"><arrow.to.target n="marg12"/></s> </p> <p type="margin"> <s id="s.000805"><margin.target id="marg12"/>12</s> </p> <p type="main"> <s id="s.000806">Ex cap. 21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;e<lb/>&longs;e ip&longs;os talia accipientes, quæ non est po&longs;&longs;ibile monstrare uon exi&longs;tentibus <lb/> coalternis)<emph.end type="italics"/> Vult Ari&longs;t. exemplo mathematico explicare, quid &longs;it pe­<lb/> titio principij. </s> <s id="s.000807">vbi per coalternas intelligit parallelas lineas, vox <lb/> enim græca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, & coalternus. </s> <s id="s.000808">quoad <lb/> exempli explicationem vtor figura textibus apponi &longs;olita, quæ e&longs;t præ&longs;ens. <lb/> <figure id="id.009.01.042.1.jpg" place="text" xlink:href="009/01/042/1.jpg"/><lb/> probat Euclides in 28. primi Elem. quod &longs;i <lb/> linea recta quædam, vti E F, cadens &longs;uper <lb/> duas rectas, vti &longs;unt A B, C D, fecerit angu­<lb/> los alternos &etail;quales, angulos <expan abbr="nimirũ">nimirum</expan> A G H, <lb/> G H D, ij enim dicuntur alterni; &longs;iue alios <lb/> duos, nimirum B G H, G H C, hi enim &longs;unt <lb/> <expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li­<lb/> neas A B, C D, e&longs;&longs;e inuicem parallelas. </s> <s id="s.000809">Iam &longs;i quis vellet probare, &longs;e duas <lb/> parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet faciunt prædictos angulos al­<lb/> ternos æquales; & probaret facere angulos alternos æquales, quia &longs;unt pa­<lb/> rallelæ, hic peteret principium, ide&longs;t, illud, quod principio <expan abbr="probandũ">probandum</expan> erat, <lb/> afferret pro ratione, & cau&longs;a, quod dicitur peti principium, quia tunc pe­<lb/> timus, vt concedatur nobis, id, quod principio, & primo omnium demon­<lb/> &longs;trare propo&longs;ueramus. </s> <s id="s.000810">aduerte, quod characteres, qui &longs;unt in &longs;equentibus <lb/> verbis huius loci, non appellant characteres figuræ appo&longs;itæ; in quo quidam <lb/> decepti, nullo pacto poterant locum hunc intelligere.</s> </p> <p type="main"> <s id="s.000811"><arrow.to.target n="marg13"/></s> </p> <p type="margin"> <s id="s.000812"><margin.target id="marg13"/>13</s> </p> <p type="main"> <s id="s.000813">Ex cap. 22. lib. 2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom­<lb/> men&longs;. argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. 1. <lb/> fusè explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea­<lb/> dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com­<lb/>munis, quæ debet vtramque, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, nimirum medietates medietatum in infinitum, <lb/> e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, & propterea <lb/> non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="quãtitatibus">quantitatibus</expan>, quæ putaban­<lb/> tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t. non cau&longs;am pro cau&longs;a.</s> </p> <p type="main"> <s id="s.000814"><arrow.to.target n="marg14"/></s> </p> <p type="margin"> <s id="s.000815"><margin.target id="marg14"/>14</s> </p> <p type="main"> <s id="s.000816">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; & &longs;i maior e&longs;t extrin&longs;ecus <lb/> angulus intrin&longs;eco; & &longs;i triangulus habet plures rectos duobus)<emph.end type="italics"/> per plures po&longs;i­<lb/> tiones &longs;ubaudi fal&longs;as. </s> <s id="s.000817">per coalternas intellige lineas æquidi&longs;tantes, &longs;eu pa­<lb/> rallelas, vt in &longs;uperiori cap. monuimus. </s> <s id="s.000818">Cæterum Euclides propo&longs;. </s> <s id="s.000819">28. pri­<lb/> mi Elem. o&longs;tendit, quod &longs;i fuerint duæ parallelæ veluti in præcedenti figura, <lb/> A B, C D, &longs;uper quas alia recta E F, incidat, nece&longs;&longs;ario faciet angulum ex­<lb/> trin&longs;ecum E G B, v. <!-- REMOVE S-->g. <!-- REMOVE S-->æqualem interno, & oppo&longs;ito, & 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<lb/> gulum &longs;cilicet E G B, externum e&longs;&longs;e maiorem angulo interno G H D, &longs;equi­<lb/> tur etiam fal&longs;um, videlicet lineas <expan abbr="æquidi&longs;tãtes">æquidi&longs;tantes</expan> A B, C D, concurrere. </s> <s id="s.000820">& pro­<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb pagenum="43" xlink:href="009/01/043.jpg"/>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 inæqualibus <lb/> æqualia addantur, tota erunt inæqualia, vt prius per 4, axioma: hoc loco <lb/> communis angulus additur &longs;emel maiori angulo, & &longs;emel minori; & 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> <s id="s.000821">at illi duo E G B, B G H, per 13. primi, &longs;unt <lb/> æquales 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> <s id="s.000822">At quando hi duo interni &longs;unt minores duobus rectis, tunc lineæ A B, C D, <lb/> &longs;unt concurrentes, &longs;i protrahantur ad partes prædictorum <expan abbr="angulorũ">angulorum</expan>. </s> <s id="s.000823">quod <lb/> P. <!-- REMOVE S-->Clauius luculenti, & hactenus de&longs;iderata demon&longs;tratione ad 28. primi <lb/> demon&longs;trauit. </s> <s id="s.000824"><expan abbr="Atq;">Atque</expan> hoc pacto ex prima fal&longs;a &longs;uppo&longs;itione, nimirum angu­<lb/> lum illum externum e&longs;&longs;e maiorem interno, & oppo&longs;ito; &longs;equitur fal&longs;um, ni­<lb/> mirum lineas parallelas concurrere.</s> </p> <p type="main"> <s id="s.000825">Præterea &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<lb/> <figure id="id.009.01.043.1.jpg" place="text" xlink:href="009/01/043/1.jpg"/><lb/> rallelas coincidere, & probatur &longs;ic; &longs;int enim <lb/> <expan abbr="triãguli">trianguli</expan> A B C, tres anguli maiores, quam duo <lb/> recti anguli, & per punctum C, ducta &longs;it recta <lb/> C D, parallela lateri B A. quia ergo angulus <lb/> A, æqualis e&longs;t angulo &longs;ibi alterno A C D, per <lb/> 29. primi, & quia totalis angulus B C D, æqua­<lb/> lis e&longs;t duobus angulis B C A, A C D, quos tanquam &longs;uas partes adæquatas <lb/> continet, quorum alter, &longs;cilicet A C D, e&longs;t æqualis angulo A. erit idem to­<lb/> talis angulus B C D, æqualis duobus angulis A, & A C B, trianguli propo&longs;i­<lb/> ti. </s> <s id="s.000826">ergo totus i&longs;te angulus B C D, &longs;imul cum reliquo <expan abbr="triãguli">trianguli</expan> angulo B. con­<lb/> &longs;tabit compo&longs;itionem ex tribus angulis trianguli dati: & con&longs;equenter ta­<lb/> lis compo&longs;itio trium angulorum erit maior, quam &longs;int duo anguli recti. </s> <s id="s.000827">ex <lb/> quo &longs;equitur duas rectas B A, C D, &longs;uper quas cadit linea B C, faciens duos <lb/> angulos internos, & ad ea&longs;dem partes, &longs;cilicet A B D, maiores duobus re­<lb/> ctis non e&longs;&longs;e parallelas, &longs;ed concurrentes (vt patet ex nuper citata demon­<lb/> &longs;tratione P. Clauij) quod fal&longs;um e&longs;t. </s> <s id="s.000828">& &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio­<lb/> ne. </s> <s id="s.000829">ex quibus textus Ari&longs;t. videtur &longs;atis clarus.</s> </p> <p type="main"> <s id="s.000830"><arrow.to.target n="marg15"/></s> </p> <p type="margin"> <s id="s.000831"><margin.target id="marg15"/>15</s> </p> <p type="main"> <s id="s.000832">Ex cap. 26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C, <lb/>&longs;en&longs;ibilis 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, & ignorabit idem. </s> <s id="s.000833">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> <s id="s.000834">&longs;ic igitur, vt vni­<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, quæ diximus lib. 1. &longs;ecto 3. cap. 1. ex quibus quidquid Ma­<lb/> thematicum e&longs;t hic, clarum redditur. </s> <s id="s.000835">reliqua verò, quæ ad Logicum &longs;pe­<lb/> ctant, huius loci commentatores pro&longs;equuntur.</s> </p> <p type="main"> <s id="s.000836">In cap. 31. de Abductione.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000837"><arrow.to.target n="marg16"/></s> </p> <p type="margin"> <s id="s.000838"><margin.target id="marg16"/>16</s> </p> <p type="main"> <s id="s.000839">Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/> cap. agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">eamque</expan>; Ari&longs;t. quemadmodum multa <lb/> alia à Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s> <s id="s.000840">e&longs;&longs;e <pb pagenum="44" xlink:href="009/01/044.jpg"/>autem terminum mathematicum colligitur manife&longs;tè ex Proelo, qui lib. 3. <lb/> in comm. <!-- REMOVE S-->Elem. Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/> </s> <s id="s.000841">121. &longs;ic ait, Abductio verò e&longs;t tran&longs;itus à propo&longs;ito problemate, vel theo­<lb/> remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi­<lb/> cuum e&longs;t. </s> <s id="s.000842">Exempli cau&longs;a, cum cubi duplicatio propo&longs;ita e&longs;&longs;et ad inue&longs;ti­<lb/> gandam quæ&longs;tionem in aliud tran&longs;tulere, quod illud propo&longs;itum con&longs;equi­<lb/> tur, ad duarum nempe mediarum linearum inuentionem tran&longs;lata e&longs;t quæ­<lb/> &longs;tio, & &longs;ic quærebant deinceps, quonam modo datis duabus rectis lineis, <lb/> duæ mediæ proportionales reperirentur. </s> <s id="s.000843">Primum autem dicunt Hippocra­<lb/> tem Chium pr&etail;dictorum titulorum, Abductionem feci&longs;&longs;e, qui & lunulæ qua­<lb/> dratum fecit æquale, & alia multa in Geometria inuenit. </s> <s id="s.000844">hæc Proclus. <!-- KEEP S--></s> <s id="s.000845">vbi <lb/> non di&longs;&longs;imulandum nos re&longs;titui&longs;&longs;e verbum, Abductionem, cuius loco inter­<lb/> pres Procli vtitur inductionis voce, &longs;equuti & rationem, & græcum textum, <lb/> qui no&longs;tram hanc expo&longs;itionem euidenter po&longs;tulat, <foreign lang="greek">apagwgh\</foreign> enim valet & <lb/> inductionem, & abductionem, &longs;ed abductio omnino rei propo&longs;itæ quadrat.</s> </p> <p type="main"> <s id="s.000846">Notandum præterea Hippocratem Chium fui&longs;&longs;e auctorem huius Abdu­<lb/> ctionis, <expan abbr="eum&qacute;">eumque</expan>; feci&longs;&longs;e Abductionem à propo&longs;ito Problemate quadrandi cir­<lb/> culi, vnde manife&longs;tè apparet, Ari&longs;totelem ex Mathematicis hunc terminum <lb/> mutuò accepi&longs;&longs;e, quandoquidem ex ij&longs;dem accepit etiam exemplum Abdu­<lb/>ctionis Mathematicæ, imò etiam exemplum ip&longs;ius authoris Abductionis <lb/> Mathematicæ. </s> <s id="s.000847">&longs;yllogi&longs;mus autem Hippocratis, quo o&longs;tendebat circuli qua­<lb/> draturam reducebatur ad has propo&longs;itiones, omnis rectilinea figura qua­<lb/> dratur, &longs;ed circulus reducitur ad figuram rectilineam, ergo circulus qua­<lb/> dratur. </s> <s id="s.000848">in probatione minoris facta e&longs;t Abductio, cum enim ip&longs;e vellet re­<lb/> ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam, <lb/> quandam quadratricem, vt e&longs;t apud Pappum <expan abbr="Alexandrinũ">Alexandrinum</expan>, & apud P. <!-- REMOVE S-->Cla­<lb/> uium in fine &longs;exti Elem. & alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio <lb/>circa probationem minoris, in qua adhuc Mathematici ver&longs;antur; quæ pro­<lb/> batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;itũ">propo&longs;itum</expan> pro­<lb/> blema, nimirum circulus quadraretur; vide quæ &longs;crip&longs;imus in cap. 3. Præ­<lb/> dicam. <!-- REMOVE S-->de hac re, quia plurimum hunc conferunt. </s> <s id="s.000849">&longs;ed iam ad textus expli­<lb/> cationem veniamus.</s> </p> <p type="main"> <s id="s.000850"><arrow.to.target n="marg17"/></s> </p> <p type="margin"> <s id="s.000851"><margin.target id="marg17"/>17</s> </p> <p type="main"> <s id="s.000852">Ex eodem cap. <emph type="italics"/>(Veluti &longs;i K, e&longs;&longs;et quadrari, in quo autem E, rectilineum, in <lb/> quo verò 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 æqualem fieri circulum rectilineo, e&longs;&longs;e po&longs;&longs;et propè 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<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/> vulgatæ editionis e&longs;&longs;e mendo&longs;am, & propterea re&longs;tituendam e&longs;&longs;e, qualis pri­<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<lb/> drandus; con&longs;tituatur <expan abbr="itaq;">itaque</expan> &longs;uper diametro eius B C, quadratum B C D F, <lb/> cuius diameter B D, &longs;ecatur bifariam in G, à circumferentia circuli dati, <lb/> quod patet ducta &longs;emidiametro H G, perpendiculari ex B C, quæ &longs;uo extre­<lb/> mo puncto G, &longs;ecat bifariam, & <expan abbr="diametrũ">diametrum</expan> B D, & 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<lb/> ctaturque</expan>; recta G C. in triangulo orthogonio B C D, latus B D, &longs;ubtenditur <pb pagenum="45" xlink:href="009/01/045.jpg"/><figure id="id.009.01.045.1.jpg" place="text" xlink:href="009/01/045/1.jpg"/><lb/> angulo recto C, ergo quadratum eius ex corol­<lb/> lario 47. primi, duplum erit quadrati B C, quare <lb/> etiam circulus B C D F, duplus erit circuli A B­<lb/> G C, per 2. duodecimi, & &longs;emicirculus B C D, <lb/> duplus erit &longs;emicirculi B A C: & quadrans B E­<lb/> C G, æqualis erit &longs;emicirculo B A C: ablato igi­<lb/> tur communi &longs;egmento B E C H, remanet lunu­<lb/> la B A C E, æqualis triangulo B C G, quod trian­<lb/> gulum &longs;i per vltimam &longs;ecundi quadretur, erit lu­<lb/> nula B A C, con&longs;equenter quadrata. </s> <s id="s.000853"><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be­<lb/> nè procedit Hippocrates. <!-- KEEP S--></s> <s id="s.000854">&longs;ed vt reliquum circu­<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 id="id.009.01.045.2.jpg" place="text" xlink:href="009/01/045/2.jpg"/><lb/> L O M, cui in&longs;cribatur hexagoni <lb/> æquilateri dimidium L Q S M, & &longs;u­<lb/> per tribus hexagoni lateribus, &longs;int <lb/> tres &longs;emicirculi, vt in figura. </s> <s id="s.000855">& <expan abbr="quo-niã">quo­<lb/> niam</expan> diameter L M, dupla e&longs;t <expan abbr="vniu&longs;-cuiu&longs;q;">vniu&longs;­<lb/> cuiu&longs;que</expan> <expan abbr="diametrorũ">diametrorum</expan> B C, L Q, Q S, <lb/> S M, erit &longs;emicirculus L O M, &etail;qua­<lb/> lis quatuor &longs;emicirculis prædictis <lb/> per 2. duodecimi, & per 4. &longs;ecundi <lb/> ablatis igitur tribus <expan abbr="&longs;egm&etilde;tis">&longs;egmentis</expan> com­<lb/> munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, æquale &longs;e­<lb/> micirculo B A C, & tribus lunulis L H Q N, Q R S O, S X M P, ab&longs;cindan­<lb/> tur <expan abbr="itaq;">itaque</expan> de trapezio tria triangula æqualia tribus lunulis, eo modo, quo &longs;u­<lb/> pra in prima figura factum e&longs;t, & quod relinquetur æquale erit &longs;emicirculo <lb/> B A C. quod deinde quadretur per vlt. </s> <s id="s.000856">&longs;ecundi, &longs;ed aduerte, quod quando <lb/> ait, ab&longs;cindantur de trapezio tria triangula æqualia lunulis, eo modo, quo <lb/> &longs;upra, committit deceptionem, quia eodem modo, quo &longs;upra minimè id fa­<lb/> cere po&longs;&longs;umus, quia in &longs;uperiori figura triangula erant con&longs;tituta &longs;uper la­<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;egmentũ">&longs;egmentum</expan>, quam faciat &longs;emicirculus L O M, cum lateribus L Q, <lb/> Q S, S M. & 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> hæc e&longs;t fallacia, quam authorem &longs;uum mi­<lb/> nimè latui&longs;&longs;e putandum, cuius Ari&longs;t. &longs;æpius mentionem in &longs;equentibus fa­<lb/> ciet : quì enim fieri pote&longs;t, vt tam acutus inuentor, adeo manife&longs;tum erro­<lb/> rem non vidi&longs;&longs;et, verum propter adinuenti excellentiam, authori &longs;uo pla­<lb/> cuit paralogy&longs;mus. </s> <s id="s.000857">mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunulæ <lb/> quadratio. </s> <s id="s.000858">Ex quibus &longs;atis clara e&longs;&longs;e po&longs;&longs;unt ea, quæ ad <expan abbr="Mathematicũ">Mathematicum</expan> per­<lb/> tinent, ad locum hunc de Abductione declarandum. </s> <s id="s.000859">facta e&longs;t igitur abdu­<lb/> ctio ab Hippocrate in quadratione trium po&longs;teriorum lunularum, in qua­<lb/> rum quadratione diu immoratus, nunquam ni&longs;i cum paralogy&longs;mo quadra­<lb/> re valuit. </s> <s id="s.000860">Hæc pluribus, vt &longs;equentibus etiam textibus, in quibus huius te­<lb/> tragoni&longs;mi fit mentio &longs;atisfacere po&longs;&longs;imus. </s> <s id="s.000861">Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46" xlink:href="009/01/046.jpg"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/> Aphrod. <!-- REMOVE S-->in Primum Meteororum de Cometis.<!-- KEEP S--></s> </p> </chap> <chap> <p type="head"> <s id="s.000862"><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000863"><arrow.to.target n="marg18"/></s> </p> <p type="margin"> <s id="s.000864"><margin.target id="marg18"/>18</s> </p> <p type="main"> <s id="s.000865">Textu primo <emph type="italics"/>(Omnis doctrina, & omnis di&longs;ciplina di&longs;cur&longs;iua ex præexi­<lb/> &longs;tenti fit cognitione. </s> <s id="s.000866">manife&longs;tum autem hoc &longs;peculantibus in omnibus, <lb/> Mathematicæ <expan abbr="namq;">namque</expan> &longs;cientiarum per hunc modum accedunt)<emph.end type="italics"/> quo mo­<lb/> do Mathematicæ fiant ex præcedenti cognitione, &longs;cilicet Princi­<lb/> piorum per&longs;picuè quilibet videbit, qui &longs;altem primum <expan abbr="Elem&etilde;torum">Elementorum</expan> Eucli­<lb/> dis, vel è ianuis in&longs;pexerit; pr&etail;cedunt enim primo principiorum tria gene­<lb/> ra, quorum primum continet definitiones &longs;ubiecti Geometriæ, vt definitio­<lb/> nes lineæ, &longs;uperficiei, trianguli, &c: Secundum continet Po&longs;tulata. </s> <s id="s.000867">Tertium <lb/> Axiomata, &longs;eu communes omnium conceptiones, & &longs;ententias, ex quibus <lb/>tanquam ex vberrimis, & chri&longs;tallinis fontibus Demon&longs;trationes Geome­<lb/> tricæ deriuantur. </s> <s id="s.000868">Idem vìdere licet in operibus aliorum Geometrarum, <lb/> Archimedis, Apollonij, Pappi, & cæterorum. </s> <s id="s.000869">Aliæ &longs;imiliter mathematicæ, <lb/> vt Arithmetica, Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia, non ni&longs;t ex <lb/> præmi&longs;&longs;is, ac manife&longs;ti&longs;simis principijs &longs;uas demon&longs;trationes deducunt. <lb/> </s> <s id="s.000870">Nulla porrò alia &longs;cientia tam di&longs;tinctè &longs;ua præmittit principia, <expan abbr="tam&qacute;">tamque</expan>; per­<lb/> &longs;picua, &longs;icuti Mathematicæ, vt non immeritò Philo&longs;ophus eas, tamquam <lb/> veræ &longs;cientiæ <expan abbr="typũ">typum</expan>, <expan abbr="eum&qacute;">eumque</expan>; omnibus numeris ab&longs;olutum &longs;ibi ob oculos pro­<lb/> po&longs;uerit, ex quo veræ &longs;cientiæ de&longs;criptionem hi&longs;ce libris complecteretur.</s> </p> <p type="main"> <s id="s.000871"><arrow.to.target n="marg19"/></s> </p> <p type="margin"> <s id="s.000872"><margin.target id="marg19"/>19</s> </p> <p type="main"> <s id="s.000873">Tex. 2. <emph type="italics"/>(Quod enim omne triangulum habet duobus rectis æquales, præ&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, quæ &longs;upra libro 1. Prior. <!-- REMOVE S-->&longs;ecto 3. cap. 1. explicaui de angulis <lb/> trianguli. </s> <s id="s.000874">deinde &longs;cias, quod quando Ari&longs;t. ait, hoc, quod e&longs;t in &longs;emicircu­<lb/> lo triangulum, &c. </s> <s id="s.000875">alludit ad demon&longs;trationem quandam, quam ip&longs;e infe­<lb/> rius in exemplum adducet, & quæ e&longs;t in 3. Elem. Euclidis 31. in qua talis fi­<lb/> gura proponitur qualis e&longs;t præ&longs;ens, in qua vides triangulum A B C. in &longs;e­<lb/> <figure id="id.009.01.046.1.jpg" place="text" xlink:href="009/01/046/1.jpg"/><lb/> micirculo. </s> <s id="s.000876">tunc autem dicitur triangulum in <lb/> &longs;emicirculo, quando ba&longs;is ip&longs;ius e&longs;t diameter <lb/> &longs;emicirculi, & reliqua duo latera ita concur­<lb/>runt &longs;imul in angulum B, vt ip&longs;um pariter in <lb/> circumferentia con&longs;tituant, quibus pr&etail;mi&longs;sis <lb/> &longs;ic textum explicaueris: quod enim omne <lb/> triangulum habet tres angulos æquales duo­<lb/> bus rectis angulis præ&longs;ciuit vniuer&longs;aliter per <lb/> 32. primi; quod autem hoc particulare triangulum A B C, quod e&longs;t in &longs;e­<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<lb/> te illius maioris propo&longs;itionis; omne triangulum habet tres, &c.</s> </p> <p type="main"> <s id="s.000877"><arrow.to.target n="marg20"/></s> </p> <p type="margin"> <s id="s.000878"><margin.target id="marg20"/>20</s> </p> <p type="main"> <s id="s.000879">Tex. 5. <emph type="italics"/>(Vera quidem igitur oportet e&longs;&longs;e, quoniam non e&longs;t non ens &longs;cire, vt quod <lb/>diameter &longs;it commen&longs;urabilis)<emph.end type="italics"/> con&longs;ule ea, quæ &longs;crip&longs;imus ad cap. 23. primi <lb/> Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per­<lb/> ceptis &longs;ic <expan abbr="locũ">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom­ <pb pagenum="47" xlink:href="009/01/047.jpg"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com­<lb/> men&longs;urabilem prædicto 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"> <s id="s.000880"><arrow.to.target n="marg21"/></s> </p> <p type="margin"> <s id="s.000881"><margin.target id="marg21"/>21</s> </p> <p type="main"> <s id="s.000882">Hoc eodem cap. plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien­<lb/> tiæ, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, & &longs;imilia, quæ quo modo <lb/> &longs;e habeant, & quo modo illis Demon&longs;trationes innitantur, optimè ex con­<lb/> templatione primi libri Elem. Euclidis percipi pote&longs;t. </s> <s id="s.000883">vt propterea benè ij <lb/> &longs;entiant, inter quos præcipui &longs;unt Toletus, & 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 veræ &longs;cientiæ de&longs;criptionem his li­<lb/> bris complectaretur.</s> </p> <p type="main"> <s id="s.000884"><arrow.to.target n="marg22"/></s> </p> <p type="margin"> <s id="s.000885"><margin.target id="marg22"/>22</s> </p> <p type="main"> <s id="s.000886">Eodem tex. <!-- REMOVE S-->5. <emph type="italics"/>(Ponit enim Arithmeticus vnitatem indiui&longs;ibilem e&longs;&longs;e &longs;ecun­<lb/> dum quantum)<emph.end type="italics"/> hoc quamquam non ponatur ab Arithmeticis expre&longs;sè, præ­<lb/> &longs;upponitur tamen ab eis: nu&longs;quam enim Euclides in totis tribus Arithme­<lb/> ticis libris, infra vnitatem de&longs;cendit, vt propterea appareat, ip&longs;am in quan­<lb/> titate di&longs;creta e&longs;&longs;e minimum, & indiui&longs;ibile. </s> <s id="s.000887">Verum dubitabit fortè qui&longs;­<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<lb/> tem, in quadrantem, & alijs &longs;imiliter modis, vnde numeri illi, qui fractio­<lb/> nes appellantur, exurgunt? </s> <s id="s.000888">Re&longs;pondemus, <expan abbr="quotie&longs;eunq;">quotie&longs;cunque</expan> vnitas diuiditur ab <lb/> Arithmeticis, tunc ip&longs;i eam accipiunt tanquam totum quoddam <expan abbr="cõtinuum">continuum</expan> <lb/> in plures partes diui&longs;ibile: &longs;iue tanquam aggregatum quoddam vnitatum, <lb/> quæ vnitates &longs;unt partes illius, vt quando dicunt, vnum horæ quadrantem, <lb/> vel duos horæ quadrantes, vel tres horæ quadrantes, accipiunt horam tan­<lb/> quam aggregatum quatuor quadrantum, & propterea numeri illi 1/4. 2/4. 3/4. <lb/> & &longs;imiles fractiones, nihil aliud &longs;unt, quam numeri partium vnius horæ: 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<lb/> ligitur diui&longs;um e&longs;&longs;e in 4. æquales partes, ex quibus illæ tres tantummodo <lb/> numerat.</s> </p> <p type="main"> <s id="s.000889"><arrow.to.target n="marg23"/></s> </p> <p type="margin"> <s id="s.000890"><margin.target id="marg23"/>23</s> </p> <p type="main"> <s id="s.000891">Tex. 9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="quæcunq;">quæcunque</expan> & in&longs;unt in eo, quod quid e&longs;t, vt triangulo li­<lb/> nea, & lineæ punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, & in oratione dicen­<lb/> te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare quænam &longs;int ea, quæ per &longs;e dicun­<lb/> tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s> <s id="s.000892">quorum primus e&longs;t, ea &longs;cilicet, <lb/> per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="quæcunq;">quæcunque</expan> in definitione illius ponuntur, cu­<lb/> iu&longs;modi &longs;unt linea, & punctum, quæ per &longs;e prædicantur, illa de triangulo, <lb/>i&longs;tud de linea; in definitione enim trianguli ponitur linea recta, quia linea <lb/> recta dum terminat illam &longs;uperficiem, quæ dicitur triangulus illi trianguli <lb/> naturam impertitur, & ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/> tribus lineis rectis terminata. </s> <s id="s.000893">&longs;imiliter in definitione lineæ, non infinitæ, <lb/> &longs;ed finitæ, & terminatæ ponitur punctum, quia duo puncta, quæ &longs;unt extre­<lb/> ma illius, faciunt, vt ea &longs;it line a finita, & definitur &longs;ic, linea finita e&longs;t lon­<lb/>gitudo, cuius extrema &longs;unt puncta. </s> <s id="s.000894">quamuis autem hæc definitio apud Eu­<lb/> clidem expre&longs;&longs;a non habeatur, tamen ex definitionibus ip&longs;ius præ&longs;ertim &longs;e­<lb/> cunda, tertia, & quarta elici pote&longs;t.</s> </p> <p type="main"> <s id="s.000895"><arrow.to.target n="marg24"/></s> </p> <p type="margin"> <s id="s.000896"><margin.target id="marg24"/>24</s> </p> <p type="main"> <s id="s.000897">Eodem tex. <!-- REMOVE S-->9. <emph type="italics"/>(Et <expan abbr="quibu&longs;cunq;">quibu&longs;cunque</expan> inexi&longs;tentium ip&longs;is, ip&longs;æ &longs;unt in oratione, quid<emph.end type="italics"/> <pb pagenum="48" xlink:href="009/01/048.jpg"/><emph type="italics"/>est declarante, quemadmodum rectum ine&longs;t lineæ, & circulare: & impar, & par <lb/> numero, & primum, & compo&longs;itum, & æquilaterum, & altera parte longius. & <lb/> <expan abbr="oĩbus">omnibus</expan> bis in&longs;unt in oratione, quid e&longs;t <expan abbr="declarãte">declarante</expan>, ibi quidem linea, hic vero numerus)<emph.end type="italics"/><lb/> quia locus hic benè exponitur à Toleto, & melius etiam à Conymbr. </s> <s id="s.000898">addam <lb/> tantummodo quædam, quæ ad perfectam eius intelligentiam de&longs;iderantur. <lb/> </s> <s id="s.000899">Sciendum igitur primò, nu&longs;quam ab Euclide definiri rectum, circulare, <lb/> impar, par, primum, compo&longs;itum, æquilaterum, nec altera parte longius: <lb/> <expan abbr="verũ">verum</expan> ab ip&longs;o in definitionibus primi definiri lineam rectam, non tamen cir­<lb/> cularem expre&longs;sè. </s> <s id="s.000900">in definitionibus deinde &longs;eptimi definiri <expan abbr="numerũ">numerum</expan> parem, <lb/> & imparem, item numerum primum, & compo&longs;itum, & æquilaterum, & al­<lb/> tera parte longiorem. </s> <s id="s.000901">ex quibus definitionibus po&longs;&longs;unt erui definitiones re­<lb/> cti, circularis, imparis, & cæterorum, quorum hic Ari&longs;toteles meminit. <lb/> </s> <s id="s.000902">Cæterum Euclides definitione 11. &longs;eptimi, &longs;ic definit numerum primum: <lb/> primus numerus e&longs;t, quem vnitas &longs;ola metitur. </s> <s id="s.000903">numerus autem, vel vnitas <lb/> metiri dicitur alium numerum, quando &longs;æpius repetita ip&longs;um omnino ad­<lb/> æquat, vt ternarius metitur nouenarium, quia ter repetitus ip&longs;um ad vn­<lb/> guem explet. </s> <s id="s.000904">illi igitur numeri dicuntur ab Arithmeticis primi, qui à nullo <lb/> alio, præterquam ab vnitate men&longs;urantur, quales &longs;unt, 2. 3. 5. 7. &c. </s> <s id="s.000905">Defi­<lb/> nitione verò 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 perfectè adæquatur.</s> </p> <p type="main"> <s id="s.000906">Per æquilaterum, intelligit quadratum, quadratus autem numerus defi­<lb/> nitione 18. &longs;eptimi &longs;ic explicatur: Quadratus numerus e&longs;t, qui &longs;ub duobus <lb/> æqualibus numeris continetur, ide&longs;t, qui fit ex ductu vnius numeri in &longs;e ip­<lb/> <figure id="id.009.01.048.1.jpg" place="text" xlink:href="009/01/048/1.jpg"/><lb/> &longs;um, vt &longs;i ducantur 3. in 3. fient 9. qui continetur &longs;ub duobus <lb/> ternarijs; omnes autem ternarij &longs;unt æquales. </s> <s id="s.000907">is autem nu­<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; & &longs;icuti quadratum geometricum ha­<lb/> bet latera æqualia, ita etiam quadratum arithmeticum: &longs;i­<lb/> ue numerus quadratus, habet &longs;ua latera æqualia, quot enim vnitates &longs;unt <lb/> in vno, tot etiam &longs;unt in reliquis, vt in præ&longs;enti &longs;unt tres vnitates in &longs;ingulis <lb/> lateribus. </s> <s id="s.000908">pr&etail;terea quemadmodum quadratum geometricum re&longs;olui pote&longs;t <lb/> in plura quadrata, ita etiam arithmeticum, vt præ&longs;ens, qui re&longs;oluitur in <lb/> quatuor quadrata arithmetica. </s> <s id="s.000909"><expan abbr="Neq;">Neque</expan> enim pote&longs;t quilibet numerus, vt opi­<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"> <s id="s.000910">Per altera parte longius, intelligit numerum, qui producitur à duobus <lb/> <figure id="id.009.01.048.2.jpg" place="text" xlink:href="009/01/048/2.jpg"/><lb/> numeris inæqualibus inuicem multiplicatis, qualis e&longs;t <lb/> duodenarius, qui ex ductu trium in quatuor produci­<lb/> tur, & 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> <s id="s.000911">atque hæc <lb/> &longs;unt, quæ ex Mathematicis petenda erant, ad huius <lb/> loci intelligentiam.</s> </p> <p type="main"> <s id="s.000912"><arrow.to.target n="marg25"/></s> </p> <p type="margin"> <s id="s.000913"><margin.target id="marg25"/>25</s> </p> <p type="main"> <s id="s.000914">Tex. 11. <emph type="italics"/>(Per &longs;e autem, & &longs;ecundum quod ip&longs;um, idem, vt per &longs;e lineæ inest<emph.end type="italics"/> <pb pagenum="49" xlink:href="009/01/049.jpg"/><emph type="italics"/>punctum, & rectum; etenim &longs;ecundum quod linea, & triangulo, &longs;ecundum quod <lb/> triangulum duo recti: etenim per &longs;e triangulum duobus rectis æquale. </s> <s id="s.000915">Vniuer&longs;ale <lb/> autem e&longs;t tunc, quando in quolibet, & primo mon&longs;tratur, vt duos rectos habere, <lb/> <expan abbr="neq;">neque</expan> figuræ e&longs;t vniuer&longs;ale, quamuis e&longs;t mon&longs;trare 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 æquales. </s> <s id="s.000916">Aequicrus verò <lb/>habet quidem <expan abbr="quodcunq;">quodcunque</expan> duobus rectis æquales, &longs;ed non primò, &longs;ed triangulum <lb/> prius. </s> <s id="s.000917">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, & demonstratio de hoc vniuer&longs;aliter e&longs;t, de alijs <lb/> verò quodammodo, non per &longs;e, <expan abbr="neq;">neque</expan> de æquicrure 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, quæ primo Priorum &longs;ecto 3. cap. 1. <lb/> &longs;crip&longs;imus. </s> <s id="s.000918">deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, & tri­<lb/> angulum vniuer&longs;alius æquicrure. </s> <s id="s.000919">quando ait (vt duos rectos habere) vult <lb/> dicere, habere duos angulos rectos non actu, &longs;ed potentia; quæ affectio e&longs;t <lb/> trianguli, quia, vt &longs;uperius diximus, habet tres angulos æquales duobus <lb/> rectis angulis: quæ proprietas vniuer&longs;aliter, & primò competit triangulo. <lb/> </s> <s id="s.000920">non autem figuræ, quia figura e&longs;t vniuer&longs;alior. </s> <s id="s.000921"><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> <s id="s.000922">omittimus reliqua &longs;ingillatim exponere, tum quia &longs;a­<lb/> tis clara &longs;unt, tum quia ab interpretibus benè explicantur.</s> </p> <p type="main"> <s id="s.000923"><arrow.to.target n="marg26"/></s> </p> <p type="margin"> <s id="s.000924"><margin.target id="marg26"/>26</s> </p> <p type="main"> <s id="s.000925">Tex. 13. <emph type="italics"/>(Si quis igitur mon&longs;trauerit, quod rectæ <expan abbr="nõ">non</expan> coincidunt, videbitur <expan abbr="vtiq;">vtique</expan> <lb/>huius 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 æquales, fit hoc, &longs;ed &longs;ecundum quod <expan abbr="quomodocunq;">quomodocunque</expan> æquales)<emph.end type="italics"/> pro­<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 præmi&longs;&longs;is verbis continetur, <expan abbr="atq;">atque</expan> <lb/> ex 28. primi Elem. de&longs;umitur, quam propterea primo loco exponendam <lb/> <figure id="id.009.01.049.1.jpg" place="text" xlink:href="009/01/049/1.jpg"/><lb/> cen&longs;ui. </s> <s id="s.000926">Quando igitur duæ rectæ con&longs;titu­<lb/> tæ fuerint, vt A B, C D, in quas alia recta, <lb/> vt G F, incidens, faciat duos angulos in­<lb/> ternos, re&longs;pectu rectarum A B, C D, & ad <lb/> ea&longs;dem partes rectæ E F, vt &longs;unt ex parte <lb/> &longs;ini&longs;tra anguli A G H, C H G; exparte ve­<lb/> rò dextra B G H, D H G; &longs;i <expan abbr="inquã">inquam</expan> linea E F, <lb/> fecerit duos illos angulos ex parte &longs;ini&longs;tra &longs;imul &longs;umptos, æquales duobus <lb/> rectis angulis, vel duos ex parte dextra pariter æquales duobus rectis, pro­<lb/> bat Euclides rectas A B, C D, non concurrere, &longs;iue parallelas e&longs;&longs;e. </s> <s id="s.000927">Verum, <lb/> quia linea E F, pote&longs;t facere aliquando prædictos angulos non <expan abbr="tantũ">tantum</expan> æqua­<lb/> les duobus rectis, verum etiam rectos, quo etiam modo <expan abbr="probar&etilde;tur">probarentur</expan> cædem <lb/> lineæ e&longs;&longs;e parallelæ, vt in &longs;equenti figura, cum &longs;int anguli A G I, C I G, re­<lb/> <figure id="id.009.01.049.2.jpg" place="text" xlink:href="009/01/049/2.jpg"/><lb/> cti, probabitur de rectis A B, C D, æquidi&longs;tan­<lb/> tia. </s> <s id="s.000928">Ex his facile textum in hunc modum expo­<lb/> nemus; &longs;i quis igitur mon&longs;trauerit, quod rectæ <lb/>A B, C D, nunquam coincidunt, etiam&longs;i in infi­<lb/> nitum producantur, &longs;eu quod &longs;unt æquidi&longs;tantes, <lb/> quando anguli prædicti 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, & de primo &longs;u­ <pb pagenum="50" xlink:href="009/01/050.jpg"/>biecto, vel &longs;ecundum quod ip&longs;um, eò quod probatur vniuer&longs;aliter de lineis <lb/> omnibus habentibus prædictos angulos rectos. </s> <s id="s.000929">non autem de omni, &longs;ecun­<lb/> dum quod ip&longs;um, &longs;i quidem non competit affectio hæc, e&longs;&longs;e parallelas, li­<lb/> neis habentibus illos angulos rectos actu; &longs;ed primò, & vniuer&longs;aliter, & &longs;e­<lb/> cundum quod ip&longs;um competit lineis habentibus illos angulos æquales duo­<lb/> bus rectis, <expan abbr="quomodocunq;">quomodocunque</expan> æquales &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 æquentur duobus re­<lb/> ctis, quales &longs;unt lineæ primæ figuræ. </s> <s id="s.000930">In tertio igitur errore, vniuer&longs;ale exi­<lb/> &longs;tit quidem, & habet nomen, &longs;ed tamen prætermittetur, &longs;eu &longs;trictius &longs;ume­<lb/> tur, quam oportet. </s> <s id="s.000931">alij latini, quos quidem viderim, præter Zabarellana <lb/> perperam omnino ob mathematicarum ignorantiam, exemplum i&longs;tud in­<lb/> terpretantur.</s> </p> <p type="main"> <s id="s.000932"><arrow.to.target n="marg27"/></s> </p> <p type="margin"> <s id="s.000933"><margin.target id="marg27"/>27</s> </p> <p type="main"> <s id="s.000934">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<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> <s id="s.000935">Por­<lb/> rò cum tres &longs;int &longs;pecies triangulorum, æquilaterum, 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<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, & 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, & per &longs;e, & &longs;ecundum quod ip&longs;um conuenit. </s> <s id="s.000936">hoc <lb/> loco di&longs;ce&longs;&longs;imus à 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<lb/> tant. </s> <s id="s.000937">&longs;unt autem hæc textus verba <emph type="italics"/>(Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o­<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;tè <lb/> apparet Ari&longs;t. 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> <s id="s.000938">ait enim, &longs;i <lb/> non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, <expan abbr="&longs;ecundũ">&longs;ecundum</expan> quod I&longs;o&longs;celes: quibus verbis cla­<lb/>rè &longs;peciem, non indiuiduum, &longs;ignificat, 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"/>(vel contingit etiam, vt in parte totum, in quo mon&longs;tratur: ijs enim, <lb/> quæ &longs;unt in parte inerit quidem demon&longs;tratio, & erit de omni, &longs;ed tamen non erit <lb/> huius primi vniuer&longs;aliter demon&longs;tratio. </s> <s id="s.000939">dico autem huius primi, &longs;ecundum quod <lb/> huius 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<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 primò de ip&longs;o vniuer&longs;ali, cum illi primò competat.</s> </p> <p type="main"> <s id="s.000940"><arrow.to.target n="marg28"/></s> </p> <p type="margin"> <s id="s.000941"><margin.target id="marg28"/>28</s> </p> <p type="main"> <s id="s.000942">Ibidem <emph type="italics"/>(Et proportionale, quod alternatim, &longs;ecundum quod numeri, & &longs;ecun­<lb/> dum quod lineæ, & &longs;ecundum quod &longs;olida, & &longs;ecundum quod tempora: quemad­<lb/> modum & mon&longs;trabatur aliquando &longs;eor&longs;um, contingens <expan abbr="vtiq;">vtique</expan> de omnibus vnica <lb/>demon&longs;tratione mon&longs;trari; &longs;ed quia non &longs;unt nominatum quidam omnia hæc vnum, <lb/> numeri, longitudines, tempora &longs;olida, & &longs;pecie differunt à &longs;einuicem &longs;eor&longs;um <expan abbr="ac-cipiebãtur">ac­<lb/> cipiebantur</expan>. </s> <s id="s.000943">nunc autem vniuer aliter mon&longs;tratur, <expan abbr="neq;">neque</expan> enim &longs;ecundum quod lineæ, <lb/>aut &longs;ecundum quod numeri, inerat; &longs;ed &longs;ecundum quod hoc, quod vniuer&longs;ale &longs;up­<lb/> ponunt e&longs;&longs;e)<emph.end type="italics"/> affert exemplum &longs;ecundi erroris, qui accidit, quando vniuer&longs;a­<lb/> le exi&longs;tit quidem, &longs;ed tamen e&longs;t innominatum, pro cuius explicatione &longs;cien­ <pb pagenum="51" xlink:href="009/01/051.jpg"/>dum quid &longs;it alterna proportio. </s> <s id="s.000944">Alternam igitur proportionem definit Eu­<lb/> clides definitione 12. quinti, &longs;ic, e&longs;t &longs;umptio antecedentis ad <expan abbr="anteced&etilde;tem">antecedentem</expan>, <lb/> <figure id="id.009.01.051.1.jpg" place="text" xlink:href="009/01/051/1.jpg"/><lb/> & con&longs;equentis ad con&longs;equentem. </s> <s id="s.000945">Explico, exponantur qua­<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<lb/> ternatim erit, vt 6. ad 4. ita 3. ad 2. &longs;iue dixerimus, vt pri­<lb/> mum ad &longs;ecundum, ita tertium ad quartum, igitur alterna­<lb/> tim erit, vt primum ad tertium, ita &longs;ecundum ad quartum: valebit con&longs;e­<lb/> quentia; quæ quidem probatur deinde propo&longs;itione 16. quinti de magnitu­<lb/> dinibus, hoc e&longs;t in vniuer&longs;um de lineis, &longs;uperficiebus, & &longs;olidis. </s> <s id="s.000946">quando igi­<lb/> tur Ari&longs;t. ait, mon&longs;tramus proportionale, ide&longs;t, qua&longs;uis quatuor quantita­<lb/> tes proportionales, habere hanc proprietatem, vt &longs;int etiam alternatim <lb/> proportionales, & 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, & &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 magnitudines, aut tempora &longs;unt, &longs;ed <lb/> &longs;ecundum quandam naturam illis omnibus communem, cui primò illa pa&longs;­<lb/> &longs;io debetur; quæ quidem natura communis nomine caret, & propterea e&longs;t <lb/> cau&longs;a erroris.</s> </p> <p type="main"> <s id="s.000947"><arrow.to.target n="marg29"/></s> </p> <p type="margin"> <s id="s.000948"><margin.target id="marg29"/>29</s> </p> <p type="main"> <s id="s.000949"><emph type="italics"/>Nunc autem vniuer&longs;aliter demon&longs;tratur)<emph.end type="italics"/> nu&longs;quam apud Mathematicos in­<lb/> uenio hanc demon&longs;trationem vniuer&longs;alem de illo communi omnibus præ­<lb/> dictis, quare dicendum cum Zabarella, illud, nunc, e&longs;&longs;e intelligendum &longs;ic, <lb/> nunc autem, ide&longs;t, in præ&longs;entia autem deberet vniuer&longs;aliter demon&longs;trari, <lb/> quod tamen cum non fiat, contingit nos decipi putantes vniuer&longs;aliter de­<lb/> mon&longs;tra&longs;&longs;e. </s> <s id="s.000950">vel dicendum i&longs;tud verificari tantum de lineis, &longs;uperficiebus, & <lb/> &longs;olidis, de quibus &longs;imul in vnica natura communi, quæ e&longs;t magnitudo, de­<lb/> mon&longs;tratur in 16. quinti vniuer&longs;aliter. </s> <s id="s.000951"><expan abbr="atq;">atque</expan> hoc modo explicatum e&longs;t exem­<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"> <s id="s.000952"><arrow.to.target n="marg30"/></s> </p> <p type="margin"> <s id="s.000953"><margin.target id="marg30"/>30</s> </p> <p type="main"> <s id="s.000954">Ibidem <emph type="italics"/>(Propter hoc &longs;i quis mon&longs;trauerit &longs;ingulum triangulum. </s> <s id="s.000955">demon&longs;tratio­<lb/> ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="æquilateiũ">æquilaterum</expan> &longs;eor&longs;um, <lb/> & &longs;calenum, & æquicrus: nondum nouit triangulum, quod duobus rectis, ni&longs;i &longs;o­<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 præter prædicta <lb/> triangulum alterum. </s> <s id="s.000956">non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omne triangulum, <lb/> ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; & &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<lb/> lis <emph type="italics"/>(Quando vel nihil &longs;it accipere &longs;uperius, præter &longs;ingulare)<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/> vt benè intelligamus, opus e&longs;t ea, legere, quæ libro primo Priorum &longs;ecto 3. <lb/> cap. 1. &longs;crip&longs;imus de proprietate illa trianguli, quod &longs;cilicet habet tres an­<lb/> gulos æquales duobus rectis angulis, quibus præmi&longs;&longs;is, &longs;ic deinde locum <lb/> hunc interpretaberis; Propter hoc, quod præcedenti textu dictum e&longs;t; no­<lb/> tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten­<lb/> ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian­<lb/> gulo in &longs;ingulari, &longs;cilicet de vno æquilatero, tantum, & de vno Scaleno, & <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens aut eadem demon&longs;tratione dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52" xlink:href="009/01/052.jpg"/>&longs;eparatim o&longs;tendit, aut vtens diuer&longs;is demon&longs;trationibus, vna pro æquila­<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 æquales duobus rectis angulis; i&longs;te nondum no­<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="cõpetere">competere</expan> propter naturam illam com­<lb/> munem trianguli, cui primo, & per &longs;e competit; & neque vniuer&longs;aliter co­<lb/> gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian­<lb/> gulum, præter illud æquilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/> quibus &longs;eparatim <expan abbr="demõ&longs;trauit">demon&longs;trauit</expan>, & &longs;ecundum numerum, ide&longs;t de vnoquoque, <lb/> quatenus e&longs;t vnum numero. </s> <s id="s.000957">non nouit autem &longs;ecundum &longs;peciem, idest fecun­<lb/> dum naturam, & formam communem illis tribus indiuiduis, quæ e&longs;t natu­<lb/> ra trianguli. </s> <s id="s.000958">hoc autem e&longs;&longs;e exemplum primi erroris manife&longs;tè conuincitur, <lb/> tum ex verbis illis, quando nihil &longs;it &longs;uperius, præter &longs;ingulare, tum ex hu­<lb/> ius textus verbis illis <emph type="italics"/>(Singulum triangulum)<emph.end type="italics"/> & ex illis <emph type="italics"/>(Ni&longs;i &longs;ecundum nume­<lb/> rum)<emph.end type="italics"/> ide&longs;t, ni&longs;i de vno, quod &longs;it vnum numero. </s> <s id="s.000959">propterea nos de &longs;ingulari <lb/> triangulo omi&longs;&longs;a Zabarellæ &longs;ententia explicauimus tandem in confirma­<lb/>tionem no&longs;træ expo&longs;itionis in hæc tria errata illud non omittendum, &longs;atius <lb/> e&longs;&longs;e dicere, Ari&longs;t. attuli&longs;&longs;e pro tribus erratis tria exempla ordine retrogra­<lb/> do, quàm, quod facit Zabarella, primum e&longs;&longs;e pro tertio, &longs;ecundum pro pri­<lb/> mo, tertium verò pro &longs;ecundo; eo enim modo, Ari&longs;t. confu&longs;ionem nulla ra­<lb/> tione, imò contra omnem rationem imponimus.</s> </p> <p type="main"> <s id="s.000960"><arrow.to.target n="marg31"/></s> </p> <p type="margin"> <s id="s.000961"><margin.target id="marg31"/>31</s> </p> <p type="main"> <s id="s.000962">Textu 14. continet quidem quædam mathematica, &longs;ed ferè eadem cum <lb/> &longs;uperioribus, quæ quia tum ex prædictis facile intelligi po&longs;&longs;unt, tum quia <lb/> benè ab expo&longs;itoribus explicantur, ne actum agamus, prætermittimus.</s> </p> <p type="main"> <s id="s.000963"><arrow.to.target n="marg32"/></s> </p> <p type="margin"> <s id="s.000964"><margin.target id="marg32"/>32</s> </p> <p type="main"> <s id="s.000965">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<lb/> feretæ, ita vt cadant &longs;ub numerum, vt &longs;i linea quæpiam diuidatur in partes <lb/> decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s> <s id="s.000966">& tunc <lb/> linea numerus e&longs;t. </s> <s id="s.000967">idem de &longs;uperficie, ac &longs;olido intelligendum.</s> </p> <p type="main"> <s id="s.000968"><arrow.to.target n="marg33"/></s> </p> <p type="margin"> <s id="s.000969"><margin.target id="marg33"/>33</s> </p> <p type="main"> <s id="s.000970">Ibidem <emph type="italics"/>(Propter hoc Geometriæ 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/> quæ ad nos pertinent, vult Ari&longs;t. docere, quod non debet Geometra o&longs;ten­<lb/>dere numerorum affectiones (per cubos enim intelligit numeros quo&longs;dam <lb/> &longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometricè o&longs;tendere id, <lb/> quod o&longs;tenditur in 4. noni Elem. &longs;cilicet, &longs;i cubus numerus cubum numerum <lb/> multiplicauerit, productus numerus erit pariter cubus. </s> <s id="s.000971">nonnulli latinorum <lb/> perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/> geometricos, at Euclides definit. </s> <s id="s.000972">19. &longs;eptimi, &longs;ic arithmeticum cubum de­<lb/> finit, cubus numerus e&longs;t, qui &longs;ub tribus numeris æqualibus continetur, qua­<lb/> lis e&longs;t. </s> <s id="s.000973">8. qui e&longs;t ad in&longs;tar cubi geometrici, & continetur &longs;ub tribus binarijs <lb/> multiplicatis inuicem, quæ multiplicatio &longs;ic in&longs;tituitur, exponuntur tres bi­<lb/> <figure id="id.009.01.052.1.jpg" place="text" xlink:href="009/01/052/1.jpg"/><lb/> narij, 2, 2, 2, primus ducitur in &longs;ecundum, & producitur. <lb/> </s> <s id="s.000974">4. qui e&longs;t numerus quadratus huius figuræ, <figure id="id.009.01.052.2.jpg" place="text" xlink:href="009/01/052/2.jpg"/>, deinde <lb/> tertius binarius ducitur in prædictum quadratum 4. & pro­<lb/> ducitur 8. qui dicitur cubus, quia &longs;i intelligantur duo qua­<lb/> ternarij, vnus &longs;upra alterum, vt in præ&longs;enti figura refe­<lb/> runt cubicam figuram, cuius tam longitudo, quam latitudo, <pb pagenum="53" xlink:href="009/01/053.jpg"/>& altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna­<lb/> rijs inuicem modo prædicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis &longs;it 9. <lb/> <figure id="id.009.01.053.1.jpg" place="text" xlink:href="009/01/053/1.jpg"/><lb/> qui e&longs;t quadratus. </s> <s id="s.000975">quo deinde ducto in tertium ter­<lb/> narium, producitur 27. qui e&longs;t cubus, & refert figu­<lb/> ram cubicam hanc. </s> <s id="s.000976">Iam verò &longs;i cubus 8. multipli­<lb/> cet cubum 27. procreabitur 216. qui pariter cubus <lb/> e&longs;t. </s> <s id="s.000977"><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 mutuò, cu­<lb/> bus alter producetur; ex quibus videas, quam in­<lb/> eptè illi <expan abbr="interpret&etilde;tur">interpretentur</expan> hunc locum, qui dicunt, Ari­<lb/> &longs;totilem velle dicere non pertinere ad Geometram <lb/> probare duos cubos geometricos &longs;ibi additos face­<lb/> re alium cubum, quod erat problema Delphicum de <lb/> duplatione cubi, nondum inuentum; bis enim i&longs;ti peccant, primo in Logi­<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;ecundò in Mathematicas, cum nondum noue­<lb/>rint arithmeticos cubos; & præterea ignorent duos cubos &longs;ibi additos, non <lb/> facere alium cubum. </s> <s id="s.000978">Quod præterea hoc loco intelligendi &longs;int cubi arith­<lb/> metici certò 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"> <s id="s.000979"><arrow.to.target n="marg34"/></s> </p> <p type="margin"> <s id="s.000980"><margin.target id="marg34"/>34</s> </p> <p type="main"> <s id="s.000981">Ibidem <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> alij &longs;cientiæ quod alterius, ni&longs;i <expan abbr="quæcunq;">quæcunque</expan> ita &longs;e habent inter &longs;e, <lb/> vt &longs;it alterum &longs;ub altero, vt per&longs;pectiua ad Geometriam, & harmonica ad Arith­<lb/> meticam)<emph.end type="italics"/> excipit ab illa regula (qua prohibetur, quamuis &longs;cientiam in alie­<lb/> nam falcem immittere) &longs;cientias &longs;ubalternatas, quæ propriè in Mathemati­<lb/> cis reperiuntur, Per&longs;pectiua enim propriè &longs;ubalternatur Geometriæ, quia <lb/> vtitur Demon&longs;trationibus linearibus, quas applicat lineis vi&longs;ualibus, & Mu­<lb/> &longs;ica &longs;ubalternatur Arithmeticæ, quia ab ip&longs;a mutuatur <expan abbr="demõ&longs;trationes">demon&longs;trationes</expan> nu­<lb/> merorum, quas applicat numeris &longs;onoris. </s> <s id="s.000982">v.g. <!-- REMOVE S-->Per&longs;pectiua dicit, ea, quæ vi­<lb/> dentur eminus videri minora, quam quæ videntur cominus, quia illa viden­<lb/> tur &longs;ub angulo minori, hæc verò &longs;ub angulo maiori, quod verò remotiora <lb/> videantur &longs;ub angulo minori, quam propinquiora cæteris paribus probat <lb/> <figure id="id.009.01.053.2.jpg" place="text" xlink:href="009/01/053/2.jpg"/><lb/> per 21. primi Elem. &longs;it enim ma­<lb/> gnitudo vi&longs;a A B, remotior ab o­<lb/> culo in C, po&longs;ito, & vi&longs;a propin­<lb/> quior ab oculo in D. ductis lineis <lb/> vi&longs;ualibus C A, C B: D A, D B; ab <lb/> oculis C, & D, ad extremitates <lb/> &longs;pectatæ magnitudinis, erit remo­<lb/> tioris vi&longs;ionis angulus C, minor <lb/> angulo D, propinquioris, vt ex præallegata Demon&longs;tratione pater. </s> <s id="s.000983">Hine <lb/> per&longs;picuè vides, qua ratione Per&longs;pectiua Geometriæ &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> <s id="s.000984">Exemplum &longs;ubalternationis Mu&longs;icæ &longs;it, <expan abbr="con&longs;onãtia">con&longs;onantia</expan> Diapa&longs;on, quam <lb/> vulgò octauam appellant in data chorda collocare, hoc e&longs;t, vocem grauio­<lb/> rem facere duplam vocis acutioris &longs;umatur chorda A B, & diuidatur bifa­<lb/>riam, &longs;ine in æqualia in C; tota igitur chorda A B, ad dimidium A C, habet <pb pagenum="54" xlink:href="009/01/054.jpg"/><figure id="id.009.01.054.1.jpg" place="text" xlink:href="009/01/054/1.jpg"/><lb/> proportionem, quam 2. ad 1. <lb/> &longs;iue duplam, ergo etiam &longs;o­<lb/> nus totius chordæ A B, ad <expan abbr="&longs;o-nũ">&longs;o­<lb/> num</expan> chordæ dimidiæ A C, ha­<lb/> bebit eandem rationem, <expan abbr="nimirũ">nimirum</expan> quam 2. ad 1. &longs;iue duplam. </s> <s id="s.000985">&longs;ed &longs;onus chor­<lb/> dæ A B, ad &longs;onum chordæ 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> <s id="s.000986">vides me­<lb/> dium e&longs;&longs;e arithmeticam, conclu&longs;ionem verò harmonicam. </s> <s id="s.000987">Aliud exemplum <lb/> Tonus, quod e&longs;t <expan abbr="interuallũ">interuallum</expan> primæ vocis, Vt, ad &longs;ecundam, Rè, in duo æqua­<lb/> lia &longs;emitonia diuidi nequit, ratio e&longs;t Arithmetica, quia proportio &longs;uper­<lb/> particularis in duo æqualia arithmeticè &longs;ecari nequit; at Tonus con&longs;i&longs;tit in <lb/> ratione &longs;uperparticulari, nempè in &longs;e&longs;quioctaua, ergo Tonus bifariam diui­<lb/> di nequit. </s> <s id="s.000988">de&longs;umptum e&longs;t ex Boetio.</s> </p> <p type="main"> <s id="s.000989"><arrow.to.target n="marg35"/></s> </p> <p type="margin"> <s id="s.000990"><margin.target id="marg35"/>35</s> </p> <p type="main"> <s id="s.000991">Tex. 23. <emph type="italics"/>(Est autem &longs;ic mon&longs;trare, quemadmodum Bry&longs;o quadraturam, &longs;ecun­<lb/> dum enim commune mon&longs;trant tales rationes)<emph.end type="italics"/> cum velit o&longs;tendere veram de­<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, quæ ex com­<lb/> munibus procedat, vt autem benè intelligamus, quale&longs;nam &longs;int huiu&longs;modi <lb/> demon&longs;trationes, quæ per communia o&longs;tendunt, legenda prius ea &longs;unt, quæ <lb/> &longs;crip&longs;imus de quadratura circuli in pr&etail;dicamento relationis. </s> <s id="s.000992">Bry&longs;o itaque, <lb/> vt tradit Alexander, in hunc modum conabatur quadrare <expan abbr="circulũ">circulum</expan>. </s> <s id="s.000993">&longs;it qua­<lb/>drandus circulus A B C D, cui circum&longs;cribatur quadratum E F G H. per <lb/> 7 quarti, & alterum quadratum I L M N, eidem in&longs;cribatur per 6. quarti, <lb/> quid autem &longs;it circum&longs;cribere, & in&longs;cribere figuram circulo, ex definitione <lb/> <figure id="id.009.01.054.2.jpg" place="text" xlink:href="009/01/054/2.jpg"/><lb/> 3. & 4. eiu&longs;dem libri petatur, quamuis <lb/> ex in&longs;pectione figuræ <expan abbr="pr&etail;s&etilde;tis">pr&etail;sentis</expan> &longs;atis per­<lb/> cipi po&longs;&longs;it; deinde aliud <expan abbr="quadratũ">quadratum</expan> me­<lb/> dium inter prædicta duo con&longs;tituatur, <lb/> <expan abbr="&longs;it&qacute;">&longs;itque</expan>; O P Q R. </s> <s id="s.000994">Iam &longs;ic o&longs;tendebat i&longs;tud <lb/> medium quadratum e&longs;&longs;e æquale circu­<lb/> lo propo&longs;ito. </s> <s id="s.000995"><expan abbr="Quæcunq;">Quæcunque</expan> &longs;unt, &longs;imul ma­<lb/> iora eodem, & minora eodem, &longs;unt in­<lb/> uicem æqualia, &longs;ed circulus, & quadra­<lb/> tum medium, &longs;unt ambo maiora qua­<lb/> drato in&longs;cripto, & ambo minora qua­<lb/> drato circum&longs;cripto, ergo circulus, & <lb/> quadratum medium, &longs;unt æqualia. </s> <s id="s.000996">vte­<lb/> batur, inquit Ari&longs;t pr&etail;dicto principio, <lb/> etiam numeris, lineis, temporibus, & <lb/> qualitatibus communi, <expan abbr="neq;">neque</expan> deducto ex natura circuli, aut quadrati, de qui­<lb/> bus erat demon&longs;tratio. </s> <s id="s.000997">præterea aduertendum e&longs;t, illud e&longs;&longs;e fal&longs;um, nam &longs;ex, <lb/> & quinque, ambo &longs;unt maiores, quam quatuor, & minores, quam &longs;eptem, <lb/> & tamen non &longs;unt æquales.</s> </p> <p type="main"> <s id="s.000998"><arrow.to.target n="marg36"/></s> </p> <p type="margin"> <s id="s.000999"><margin.target id="marg36"/>36</s> </p> <p type="main"> <s id="s.001000">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 æquales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/> <pb pagenum="55" xlink:href="009/01/055.jpg"/><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, quæ non <lb/> ex communibus, vt præcedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/> affectionem de &longs;ubiecto proprio. </s> <s id="s.001001">E&longs;t autem illud exemplum toties decan­<lb/> tatum de triangulo habente tres angulos æquales duobus rectis angulis; id­<lb/> circo operæpretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli­<lb/> dis, quæ i&longs;tud ex proprijs principijs demon&longs;trat, & quam hoc loco Ari&longs;to­<lb/> teles innuit, hoc enim modo ip&longs;ius Ari&longs;t. mentem probè penetrare poteri­<lb/> <figure id="id.009.01.055.1.jpg" place="text" xlink:href="009/01/055/1.jpg"/><lb/> mus. </s> <s id="s.001002">&longs;it ergo <expan abbr="triãgulum">triangulum</expan> A B C. <!-- KEEP S--></s> <s id="s.001003">Dico ag­<lb/> gregatum <expan abbr="triũ">trium</expan> ip&longs;ius angulorum A, B, C, <lb/> e&longs;&longs;e æquale aggregato ex duobus angu­<lb/> lis rectis (vt autem melius intelligas, quæ <lb/> &longs;equuntur, lege prius ea, quæ dicta &longs;unt <lb/> in lib. 1. Priorum &longs;ecto 3. cap. 1.) produ­<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-batũ">pro­<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: & quia pariter in prima parte huius propo&longs;. </s> <s id="s.001004">32. probatum <lb/> e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e æquales externo angulo A C D: &longs;i ter­<lb/> tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/> & &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> æqualia æqualibus, & propterea tres <lb/> anguli A, B, A C B, &longs;imul &longs;umpti, erunt æquales duobus A C D, A C B, &longs;imul <lb/> &longs;umptis; &longs;ed his duobus &longs;unt æquales duo recti, ergo cum quæ &longs;unt æqualia <lb/> vni tertio, &longs;int etiam æqualia inuicem, erit aggregatum trium angulorum <lb/> A, B, A C B, æquale aggregato duorum rectorum; quod erat demon&longs;tran­<lb/> dum. </s> <s id="s.001005">Medium <expan abbr="itaq;">itaque</expan> huius demon&longs;trationis, &longs;i res ad trutinam Logicam ex­<lb/> pendatur, e&longs;t, quod partes aggregati <expan abbr="triũ">trium</expan> <expan abbr="angulorũ">angulorum</expan> A, B, A C B, &longs;unt æqua­<lb/> les partibus aggregati <expan abbr="duorũ">duorum</expan>, & ideo <expan abbr="aggregatũ">aggregatum</expan>, aggregato æqua­<lb/> le e&longs;t. </s> <s id="s.001006">quod medium e&longs;t in genere cau&longs;æ materialis. </s> <s id="s.001007">quod verò partes illius <lb/> &longs;int æquales partibus huius, probatur, per dignitatem <expan abbr="illã">illam</expan>, quæ &longs;unt æqualia <lb/> vni tertio, &longs;unt etiam inter &longs;e. </s> <s id="s.001008">partes porrò aggregati trium angulorum <lb/> erant hæ, anguli A, B, vna; altera verò angulus A C B; partes verò aggre­<lb/> gati duorum rectorum erant A C B, A C D, quibus partibus, illæ &longs;unt æqua­<lb/> les, & ideo totum toti æquale. </s> <s id="s.001009">quod medium e&longs;t omnino intrin&longs;ecum, & ex <lb/> proprijs ip&longs;ius trianguli, &longs;iue ex proprijs angulorum ip&longs;ius, cum &longs;int ip&longs;ius <lb/> partes. </s> <s id="s.001010">quod pariter medium ex parte pa&longs;&longs;ionis, quæ demon&longs;tratur, e&longs;t ex <lb/> proprijs, cum &longs;int partes illius materiales. </s> <s id="s.001011">per materiam autem oportet <lb/> hoc loco intelligere materiam intelligibilem, ide&longs;t quantitatem à qualita­<lb/>tibus ab&longs;tractam, & terminatam, de qua pluribus agemus infra in tractatu <lb/> de natura mathematicarum. </s> <s id="s.001012">Hinc videas eos magnopere decipi, qui pu­<lb/> tant, hanc demon&longs;trationem e&longs;&longs;e per extrin&longs;eca, eò quod ad demon&longs;tran­<lb/> dum producatur linea B C, in D, putantes lineam illam productam C D, <lb/> e&longs;&longs;e demon&longs;trationis medium; lineæ <expan abbr="namq;">namque</expan> huiu&longs;modi, quæ in demon&longs;tra­<lb/> tionibus geometricis con&longs;truuntur, nunquam &longs;unt media propria demon­<lb/> &longs;trationum, &longs;ed tantummodo a&longs;&longs;umuntur ad probandum medium iam ex­<lb/> cogitatum e&longs;&longs;e veram cau&longs;am conclu&longs;ionis. </s> <s id="s.001013">Hinc etiam manife&longs;tè colligas <pb pagenum="56" xlink:href="009/01/056.jpg"/>Mathematicas facultates habere demon&longs;trationes perfecti&longs;&longs;imas, quod <lb/> ageometreti negare &longs;olent, &longs;ed audacter aiunt exempla Ari&longs;t. non e&longs;&longs;e vera: <lb/> <expan abbr="neq;">neque</expan> requiri veritatem exemplorum; in <expan abbr="quorũ">quorum</expan> <expan abbr="vtroq;">vtroque</expan> peccant, nam dictum <lb/> illud v&longs;urpari &longs;olet, & debet de exemplis moralibus. </s> <s id="s.001014">at vero requiri confor­<lb/> mitatem exemplorum cum regulis traditis, nemo &longs;anæ mentis dubitabit. <lb/> </s> <s id="s.001015">Verum i&longs;ti confundunt conformitatem cum veritate. </s> <s id="s.001016">Veritas exemplo tunc <lb/> ine&longs;t, quando illud, quod in exemplo narratur, verè extitit, vt &longs;i quis in <lb/> exemplum pudicitiæ afferret hi&longs;toriam Io&longs;ephi, <expan abbr="verũ">verum</expan> i&longs;tud e&longs;&longs;et exemplum. <lb/> </s> <s id="s.001017">quæ veritas in exemplis moralibus non &longs;emper e&longs;t nece&longs;&longs;aria, talia exempla <lb/> &longs;unt &longs;æpè parabolæ, & fabulæ, quæ nunquam extiterunt, v. <!-- REMOVE S-->g. <!-- REMOVE S-->narratur ab <lb/> Ari&longs;t. 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 impiè raptauerat. </s> <s id="s.001018">non e&longs;t nece&longs;&longs;e, ta­<lb/> lem extiti&longs;&longs;e filium, <expan abbr="neq;">neque</expan> patrem. </s> <s id="s.001019">Verumtamen &longs;emper conformitas exem­<lb/> pli cum regulis, & præceptis, quæ traduntur nece&longs;&longs;aria e&longs;t, alioquin exem­<lb/> pla de&longs;truerent id, quod præceptio con&longs;truit, <expan abbr="illi&qacute;">illique</expan> contraria e&longs;&longs;et, quod om­<lb/> nino ab&longs;urdum foret. </s> <s id="s.001020">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> <s id="s.001021">re­<lb/> quiritur igitur &longs;emper in omni exemplo conformitas cum eo, quod doce­<lb/> tur; in moralibus tamen non &longs;emper requiritur veritas, vti diximus; Alij <lb/> verò 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="quorũ">quorum</expan> &longs;ententiam <lb/> non improbamus. </s> <s id="s.001022">Exempla igitur ab Ari&longs;t. pa&longs;&longs;im ex mathematicis allata, <lb/> congrua, <expan abbr="conformia&qacute;">conformiaque</expan>; omninò &longs;unt ip&longs;ius doctrinæ, aliter ip&longs;um perpetuò <lb/> mentientem facimus. </s> <s id="s.001023">Po&longs;tremò illud etiam e&longs;t aduertendum, fortè Ari&longs;t. in <lb/> præ&longs;enti textu &longs;pecta&longs;&longs;e <expan abbr="nõ">non</expan> ad hanc Euclidianam demon&longs;trationem, &longs;ed po­<lb/> tius ad Pithagoricam. </s> <s id="s.001024">Pithagorei enim eam aliter, quamuis per idem me­<lb/> dium, &longs;cilicet à cau&longs;a materiali, demon&longs;trabant; con&longs;truebant enim aliter, <lb/> <expan abbr="neq;">neque</expan> vlla vtebantur diui&longs;ione. </s> <s id="s.001025">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<lb/> ni per eas plurimum derogetur. </s> <s id="s.001026">Pithagoreorum demon&longs;trationem vide <lb/> apud Clauium in &longs;cholio 32. primi Euclidis, quam ex Eudemo etiam Pro­<lb/> clus in comm. <!-- REMOVE S-->eiu&longs;dem recitat.</s> </p> <p type="main"> <s id="s.001027"><arrow.to.target n="marg37"/></s> </p> <p type="margin"> <s id="s.001028"><margin.target id="marg37"/>37</s> </p> <p type="main"> <s id="s.001029">Ibidem <emph type="italics"/>(Sed quemadmodŭm harmonica per Arithmeticam)<emph.end type="italics"/> vide &longs;upra tex. <!-- REMOVE S-->20.</s> </p> <p type="main"> <s id="s.001030"><arrow.to.target n="marg38"/></s> </p> <p type="margin"> <s id="s.001031"><margin.target id="marg38"/>38</s> </p> <p type="main"> <s id="s.001032">Ibidem <emph type="italics"/>(Demon&longs;tratio autem non computatur in aliud genus; ni&longs;i, vt dictum <lb/>e&longs;t geometricæ demon&longs;trationes in Per&longs;pectiuas, aut Mechanicas, & arithmeticæ in <lb/> harmonicas)<emph.end type="italics"/> exempla &longs;ubalternationis Per&longs;pectiuæ, & Mu&longs;icæ in tex. <!-- REMOVE S-->20. at­<lb/> tulimus; nunc Mechanicæ &longs;ubalternationis, quam hic Ari&longs;t. in&longs;inuat, exem­<lb/> plum &longs;it illud, quod Archimedes prop. 14. primi Aequep. <!-- REMOVE S-->demon&longs;trat, ni­<lb/> mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rectæ <lb/> lineæ ab angulis trianguli ad dimidia latera oppo&longs;ita ductæ concurrunt. </s> <s id="s.001033">&longs;it <lb/> triangulum A B C, à cuius angulis A, & B, ducantur duæ rectæ A D, B E, ita <lb/> vt bifariam &longs;ecent latera A C, B C, in punctis D, & E, & concurrant in F. <lb/> <!-- KEEP S--></s> <s id="s.001034">Dico F, e&longs;&longs;e centrum grauitatis propo&longs;iti trianguli. </s> <s id="s.001035">Quoniam enim in 13. <lb/> Aequep. <!-- REMOVE S-->probauit centrum grauitatis e&longs;&longs;e in ea linea, quæ ducta ab angulo <lb/> quouis &longs;ecat oppo&longs;itum latus bifariam, crit in linea A D, <expan abbr="centrũ">centrum</expan> grauitatis. <pb pagenum="57" xlink:href="009/01/057.jpg"/><figure id="id.009.01.057.1.jpg" place="text" xlink:href="009/01/057/1.jpg"/><lb/> &longs;ed eadem ratione erit etiam in linea B E, er­<lb/> go non ni&longs;i in puncto F, quod <expan abbr="&longs;olũ">&longs;olum</expan> e&longs;t in vtra­<lb/> que, quod erat demon&longs;trandum. </s> <s id="s.001036">ex quibus ap­<lb/> paret, qua ratione mechanica conclu&longs;io Geo­<lb/> metriæ &longs;ubiaceat, dum lineari di&longs;cur&longs;u ip&longs;a <lb/> demon&longs;tratio perficitur. </s> <s id="s.001037">Scias præterea cen­<lb/> trum grauitatis e&longs;&longs;e tale punctum, ex quo &longs;i &longs;u­<lb/> &longs;pendatur corpus triangulare vniformis cra&longs;­<lb/> &longs;itici, manet &longs;emper horizonti parallelum, &longs;i <lb/> tamen antequam &longs;u&longs;penderetur, iacebat plano horizontis, æquidi&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"> <s id="s.001038"><arrow.to.target n="marg39"/></s> </p> <p type="margin"> <s id="s.001039"><margin.target id="marg39"/>39</s> </p> <p type="main"> <s id="s.001040">Tex. 24. <emph type="italics"/>(Veluti Arithmetica quidem quid impar, aut par; aut quadrangu­<lb/> lum, aut cubus)<emph.end type="italics"/> cogno&longs;cas hinc certò certius quadrangulum, & cubum e&longs;&longs;e <lb/> &longs;pecies numerorum, &longs;icuti &longs;upra tex. <!-- REMOVE S-->9. & 20. explicauimus, quò nunc te vi­<lb/> ci&longs;&longs;im, vt præ&longs;entem locum intelligas, remittimus.</s> </p> <p type="main"> <s id="s.001041"><arrow.to.target n="marg40"/></s> </p> <p type="margin"> <s id="s.001042"><margin.target id="marg40"/>40</s> </p> <p type="main"> <s id="s.001043">Ibidem <emph type="italics"/>(Geometrica verò quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/> verbum, irrationale, non videtur Ari&longs;t. intellexi&longs;&longs;e proprietatem illam duo­<lb/> rum linearum incommen&longs;urabilium longitudine, & potentia, quia v&longs;us fui&longs;­<lb/> &longs;et verbo, <foreign lang="greek">a/orhton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio­<lb/> ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latinè redditur improportionale.</s> </p> <p type="main"> <s id="s.001044"><arrow.to.target n="marg41"/></s> </p> <p type="margin"> <s id="s.001045"><margin.target id="marg41"/>41</s> </p> <p type="main"> <s id="s.001046">Per verbum <emph type="italics"/>(Refrangi)<emph.end type="italics"/> &longs;eu frangi, intelligit lineam aliquam rectam, non <lb/>in directum tendere, &longs;ed in aliquo puncto frangi, &longs;eu declinari à rectitudine, <lb/> ita vt con&longs;tituat angulum.</s> </p> <p type="main"> <s id="s.001047">Per verbum <emph type="italics"/>(Concurrere)<emph.end type="italics"/> intelligit, non e&longs;&longs;e parallelas, &longs;ed ad idem ali­<lb/> quod punctum coire, &longs;i protrahantur.</s> </p> <p type="main"> <s id="s.001048"><arrow.to.target n="marg42"/></s> </p> <p type="margin"> <s id="s.001049"><margin.target id="marg42"/>42</s> </p> <p type="main"> <s id="s.001050">Ibidem <emph type="italics"/>(Et Astrologia &longs;imiliter)<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t. non iu­<lb/> diciariam, quamuis à 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<lb/> tum, & locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt Cœli, <lb/> & Elementa.</s> </p> <p type="main"> <s id="s.001051"><arrow.to.target n="marg43"/></s> </p> <p type="margin"> <s id="s.001052"><margin.target id="marg43"/>43</s> </p> <p type="main"> <s id="s.001053">Tex. 25. <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> Geometra fal&longs;a &longs;upponit, quemadmodum quidam a&longs;&longs;eruere di­<lb/> centes, quod non oportet fal&longs;o vti: Geometram verò mentiri dicentem pedalem, non <lb/> pedalem, aut rectam de&longs;criptam, non rectam <expan abbr="exist&etilde;tem">existentem</expan>: Geometra verò nihil con­<lb/>cludit eò, quod hæc e&longs;t linea, &longs;ed quæ per hæc o&longs;tenduntur)<emph.end type="italics"/> innuit his verbis eam <lb/> materiam intelligibilem, quæ e&longs;t &longs;ubiectum Geometriæ: eam &longs;cilicet, quæ <lb/> &longs;ub figuris Geometricis &longs;en&longs;ibilibus, & <expan abbr="plerunq;">plerunque</expan> fal&longs;is latet; nam &longs;æpè Geo­<lb/> metra vtitur linea quadam &longs;en&longs;ibili pro recta, quæ verè nec e&longs;t linea mathe­<lb/> matica, nec recta; &longs;upponit aliquando talem lineam e&longs;&longs;e pedalem, quæ ve­<lb/> rè non e&longs;t pedalis: Verumtamen non mentitur, quia re&longs;picit ad veram li­<lb/> neam mathematicam, quæ &longs;ub illa intelligitur, & quæ recta concipitur; & <lb/> quidem hæc omnia verè concipiuntur, quoniam ita e&longs;&longs;e re vera po&longs;&longs;unt.</s> </p> <p type="main"> <s id="s.001054"><arrow.to.target n="marg44"/></s> </p> <p type="margin"> <s id="s.001055"><margin.target id="marg44"/>44</s> </p> <p type="main"> <s id="s.001056">Tex. 28. <emph type="italics"/>(Coaltern as verò coincidere)<emph.end type="italics"/> per coalternas intelligendas e&longs;&longs;e pa­<lb/> rallelas lineas, alias, & nunc <expan abbr="quoq;">quoque</expan> monemus.</s> </p> <p type="main"> <s id="s.001057"><arrow.to.target n="marg45"/></s> </p> <p type="margin"> <s id="s.001058"><margin.target id="marg45"/>45</s> </p> <p type="main"> <s id="s.001059">Tex. 29. <emph type="italics"/>(In Mathematicis verò non est &longs;imiliter paralogi&longs;mus, quoniam me­<lb/> diŭ e&longs;t &longs;emper, quod duplex, de hoc enim omni, & 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" xlink:href="009/01/058.jpg"/>di&longs;ciplinis, idem tamen apud græcos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci­<lb/> plinæ; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.001060">Porrò non <lb/> e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra­<lb/> tione maius extremum dicitur de omni medio, & rur&longs;us medium dicitur de <lb/> omni minori extremo, ac &longs;i diceret mathematicæ demon&longs;trationes &longs;unt in <lb/> primo modo, qui barbarè à latinis recentioribus Barbara appellatur. </s> <s id="s.001061">Hæc <lb/> e&longs;t autem pulcherrima mathematicarum commendatio, quippe præclarum <lb/> e&longs;t à laudato laudari. </s> <s id="s.001062">In mathematicis, inquit, non accidit &longs;imiliter para­<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 primæ figuræ.</s> </p> <p type="main"> <s id="s.001063"><arrow.to.target n="marg46"/></s> </p> <p type="margin"> <s id="s.001064"><margin.target id="marg46"/>46</s> </p> <p type="main"> <s id="s.001065">Eodem tex. <emph type="italics"/>(Contingit autem quo&longs;dam non &longs;yllogi&longs;ticè dicere, & quod ex vtri&longs;­<lb/> que con&longs;equentia accipiunt, quemadmodum & Cæneus facit, quod ignis in multi­<lb/> plici proportione: etenim ignis celeriter gignitur, vt ait: & hæc est proportio. </s> <s id="s.001066">&longs;ic <lb/>autem non e&longs;t &longs;yllogi&longs;mus, ni&longs;i celerrimam proportio &longs;equatur multiplex: & ignem <lb/> celerrima in motu proportio)<emph.end type="italics"/> verba illa (in multiplici proportione) græcè &longs;ic <lb/> &longs;e habent, <foreign lang="greek">en th| pollaplasioni analogia|,</foreign> quod melius redditur latinè in mul­<lb/> tiplici proportione, quemadmodum fecimus, quam in multiplicata, quem­<lb/> admodum in vulgata editione. </s> <s id="s.001067">porrò quid inter multiplicem, & multipli­<lb/> catam rationem inter&longs;it, optimè declarat no&longs;ter Clauius ad 4. definit. </s> <s id="s.001068">lib. 5. <lb/> Elem. ex quo etiam loco pauca decerpam, quæ huic loco declarando con­<lb/> ducunt. </s> <s id="s.001069">Proportio igitur multiplex e&longs;t habitudo inter duas quantitates in­<lb/> æquales, quarum maior continet minorem, bis, vel ter, vel quater, &c. </s> <s id="s.001070">vn­<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: & &longs;ic in infinitum: v. <!-- REMOVE S-->g. <!-- REMOVE S-->2. ad 1. e&longs;t proportio dupla; 3. ad 1. tri­<lb/> pla; 4. ad 1. quadrupla, &c. </s> <s id="s.001071">omnes tamen continentur &longs;ub genere multipli­<lb/> cis rationis. </s> <s id="s.001072">porrò &longs;i qu&etail;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. &c. </s> <s id="s.001073">fit, vt &longs;ub&longs;equentes termini mirum in modum augean­<lb/> tur. </s> <s id="s.001074">hic vides primum ip&longs;am quadruplam rationem in di&longs;po&longs;itis terminis <lb/> progredi, quia quilibet &longs;equens terminus ad præcedentem e&longs;t quadruplus. <lb/> </s> <s id="s.001075">cernis etiam in paucis terminis, quinque &longs;cilicet magnum factum e&longs;&longs;e incre­<lb/> mentum, cum <expan abbr="v&longs;q;">v&longs;que</expan> ad 256. excreuerint. </s> <s id="s.001076">Cæneus igitur dicens ignem augeri <lb/> &longs;ecundum multiplicem rationem, vnam ex prædictis intelligebat aliquam, <lb/> quia quælibet illarum magnopere cre&longs;cit, &longs;i propagetur, vt ad 10. quinti <lb/> definit. </s> <s id="s.001077">traditur: & vt paulo ante exemplo licuit per&longs;picere. </s> <s id="s.001078">argumentaba­<lb/> tur igitur Cæneus in hunc modum; quod in multiplici ratione augetur, ce­<lb/> lerrimè augetur: ignis celerrimè augetur, ergo ignis in multiplici ratione <lb/> augetur, quæ argumentatio vitio&longs;a e&longs;t, ex duabus quippe affirmatiuis in &longs;e­<lb/> cunda figura procedens, vt colligitur ex verbis illis tex. <emph type="italics"/>(Ex viri&longs;que con&longs;e­<lb/> quentia accipiunt<emph.end type="italics"/>) ex his mathematica huius locis patere &longs;atis po&longs;&longs;unt.</s> </p> <p type="main"> <s id="s.001079"><arrow.to.target n="marg47"/></s> </p> <p type="margin"> <s id="s.001080"><margin.target id="marg47"/>47</s> </p> <p type="main"> <s id="s.001081">Ibidem (<emph type="italics"/>Conuertuntur autem magis, quæ&longs;unt in mathematicis, quoniam nul­<lb/> lum accidens accipiunt (in quo quidem ijs præ&longs;tăt, quæ di&longs;putationibus traduntur) <lb/> &longs;ed definitiones<emph.end type="italics"/>) Hæc e&longs;t altera mathematicarum laus, vnde earum quoque <lb/> præ&longs;tantia elucet, quia &longs;cilicet mathematicæ pro medijs vtuntur definitio­ <pb pagenum="59" xlink:href="009/01/059.jpg"/>nibus &longs;ubiecti, aut pa&longs;&longs;ionis, quæ nullo 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 lineæ e&longs;&longs;e æquales, quia nimirum &longs;int &longs;emidiametri circulorum æqua­<lb/> lium, quæ e&longs;t ip&longs;arum definitio. </s> <s id="s.001082">& in 4. primi probantur ba&longs;is, & anguli <lb/> vnius trianguli æquales e&longs;&longs;e ba&longs;i, & angulis alterius trianguli per formalem <lb/> definitionem pa&longs;&longs;ionis, videlicet æqualitatis, quæ traditur in octauo axio­<lb/> mate &longs;ic, quæ &longs;ibi mutuo congruunt, ea inter &longs;e &longs;unt æqualia. </s> <s id="s.001083">probat igitur <lb/> Euclides in quarta ba&longs;im, & angulos vnius trianguli e&longs;&longs;e æqualia ba&longs;i, & an­<lb/> gulis alterius trianguli, quia o&longs;tendit, quod, &longs;i ba&longs;is illa huic ba&longs;i, & illi an­<lb/> guli hi&longs;ce angulis &longs;uperponantur, congruunt; ex qua congruentia mutua, <lb/> quæ e&longs;t æqualitatis definitio, infert æqualitatem ip&longs;arum ba&longs;ium, necnon <lb/> angulorum. </s> <s id="s.001084">eadem deinde æqualitatis definitione totam demon&longs;trationem <lb/> concludit, &longs;cilicet totum triangulum toti triangulo æquale e&longs;&longs;e, quia vnum <lb/> alteri congruat. </s> <s id="s.001085">A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in­<lb/> terpo&longs;itionem terræ inter Lunam, & Solem, quæ interpo&longs;itio e&longs;t definitio <lb/> cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s> <s id="s.001086">huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/> Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="cæteros&qacute;">cæterosque</expan>; Mathematicas demon­<lb/> &longs;trationes: ita vt meritò dixerit Ari&longs;t. Mathematicas alias omnes natura­<lb/> les &longs;cientias, quæ di&longs;putabilibus rationibus traduntur ex hac parte antecel­<lb/> lere. </s> <s id="s.001087">a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;æpè definitio­<lb/> nes ad demon&longs;trandum. </s> <s id="s.001088">Reliqua logici expo&longs;itores declarant.</s> </p> <p type="main"> <s id="s.001089"><arrow.to.target n="marg48"/></s> </p> <p type="margin"> <s id="s.001090"><margin.target id="marg48"/>48</s> </p> <p type="main"> <s id="s.001091">Tex. 30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;phærica &longs;it per aug­<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;phæricum; augetur autem Luna; planŭm quod <lb/> &longs;phærica<emph.end type="italics"/>) Illius demon&longs;trationis, quæ ab effectu procedit, affert exemplum <lb/> ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;phæricam ab ef­<lb/> fectu ip&longs;ius &longs;phæricitatis, qui e&longs;t illuminatio &longs;phærica: &longs;ic enim ratiocinan­<lb/> tur: ea, quæ &longs;phæricè illuminantur &longs;unt &longs;phærica, Luna &longs;phæricè illumina­<lb/> tur, ergo &longs;phærica e&longs;t: quæ argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/> quod ita augetur, ide&longs;t, &longs;phæricè, e&longs;t &longs;phæricum, ide&longs;t, quia lumen nouæ Lu­<lb/> næ augetur &longs;phæricè, hoc e&longs;t, ad eum modum, quo quæuis &longs;phæra obiecta <lb/> corpori lumino&longs;o &longs;olet illuminari. </s> <s id="s.001092">illuminatio porrò Lunæ in &longs;e &longs;emper e&longs;t <lb/> eadem, quia &longs;emper dimidium Lunæ quod Solem a&longs;picit, illuminatur; dici­<lb/> tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto à 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 ferè Lunæ <expan abbr="illuminatũ">illuminatum</expan> con&longs;picitur. </s> <s id="s.001093">Vt autem <lb/> huius illuminationis non iniucundam facias experientiam; cape &longs;phæram <lb/> quampiam &longs;olidam manu, cum qua recede ad medium cubiculi, & pone lu­<lb/> men &longs;eor&longs;um ad partem aliquam: deinde brachio exten&longs;o oppone &longs;phæram <lb/> lumini, quo &longs;itu nihil de illuminatione videbis, quamuis dimidium ferè il­<lb/> lius illuminetur. </s> <s id="s.001094">po&longs;tea conuerte te ip&longs;um ibidem paulatim, ita vt aliquid <lb/> illuminationis oculo tuo appareat; & videbis partem illam illuminationis, <lb/> falcatæ, &longs;eu nouæ Lunæ &longs;imilem. </s> <s id="s.001095">Deinde adhuc magis te conuerte, & cer­<lb/> nes illuminationem dimidiatæ Lunæ &longs;imilem: verte adhuc te ip&longs;um donec <lb/> &longs;it &longs;phæra ita lumini oppo&longs;ita, vt inter ip&longs;am, & lumen oculus tuus &longs;it me­<lb/> dius; apparebit tunc tota illuminatio, quæ erit in&longs;tar plenilunij. </s> <s id="s.001096">perge ad­ <pb pagenum="60" xlink:href="009/01/060.jpg"/>huc te ip&longs;um conuertere, & videbis paulatim lumen oculo tuo decre&longs;cere <lb/> non aliter ac in Luna &longs;ene&longs;cente. </s> <s id="s.001097"><expan abbr="atq;">atque</expan> hoc e&longs;t &longs;phæricè illuminari, fierique <lb/> &longs;phærica illuminationis augmenta. </s> <s id="s.001098">cum ergo videamus Lunam eo modo lu­<lb/> mine augeri, quo &longs;phæra, hinc ip&longs;am <expan abbr="quoq;">quoque</expan> &longs;phæricam e&longs;&longs;e argumentamur.</s> </p> <p type="main"> <s id="s.001099"><arrow.to.target n="marg49"/></s> </p> <p type="margin"> <s id="s.001100"><margin.target id="marg49"/>49</s> </p> <p type="main"> <s id="s.001101">Po&longs;t nonnulla (<emph type="italics"/>Vt Per&longs;pectiua ad Geometriam, & Mechanica ad Stereome­<lb/> tricam, & 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;pectiuæ, & Mechanicæ cum Geo­<lb/> metria &longs;unt allata. </s> <s id="s.001102">hic primo notandum Stereometriam non e&longs;&longs;e &longs;cientiam <lb/> di&longs;tinctam à Geometria, ni&longs;i &longs;icuti partem à toto: nam cum Geometria <lb/> con&longs;ideret quantitatem, &longs;ecundum tres dimen&longs;iones, longitudinem, latitu­<lb/>dinem, & profunditatem, oritur triplex illius diui&longs;io, de lineis, de &longs;uperfi­<lb/> ciebus, de &longs;olidis. </s> <s id="s.001103">pars igitur, quæ de &longs;olidis tractat, <expan abbr="partim&qacute;">partimque</expan>; continetur <lb/> 11. 12. 13. 14. & 15. Euclidis, partim aliorum Geometrarum libris, vt li­<lb/> bro Archim. <!-- REMOVE S-->de Sphæra, & Cyl. <!-- REMOVE S-->& &longs;imilibus, dicitur Stereometria à græco <lb/> <foreign lang="greek">stereon,</foreign> ide&longs;t &longs;olidum. </s> <s id="s.001104">Porrò cur malit Ari&longs;t. Mechanicam &longs;ubalternari Ste­<lb/> reometriæ, quam toti Geometriæ, qua tamen, vt videre e&longs;t apud Archime­<lb/> dem, innititur, fortè ea ratio e&longs;t, quia Mechanica præcipuè con&longs;iderat ma­<lb/> chinas, quæ corpora &longs;unt, & propterea præcipuè, & primò debet Stereome­<lb/> triæ, quæ corpora pariter contemplatur, &longs;ubalternari. </s> <s id="s.001105">Quod ait Apparen­<lb/>tia ad A&longs;trol. <!-- KEEP S--></s> <s id="s.001106">intelligit per Apparentia vulgarem quandam Nautarum, & <lb/> Agricolarum a&longs;tronomiam, quæ quodammodo &longs;ubalternatur, & pendet ex <lb/> &longs;cientia A&longs;trologiæ; indiget enim cognitione ortus, & motus a&longs;trorum, <lb/> præ&longs;ertim Lunæ, Hyadum, Pleiadum, & Canis. </s> <s id="s.001107">Reliqua <expan abbr="v&longs;q;">v&longs;que</expan> ad finem ca­<lb/> pitis optimè à Zabarella explicantur, <expan abbr="neq;">neque</expan> ad nos pertinet, cum de Mathe­<lb/> maticis agant, quatenus ad Logicum &longs;pectant.</s> </p> <p type="main"> <s id="s.001108"><arrow.to.target n="marg50"/></s> </p> <p type="margin"> <s id="s.001109"><margin.target id="marg50"/>50</s> </p> <p type="main"> <s id="s.001110">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<lb/> rò Propter quid Mathematicorum; hi <expan abbr="namq;">namque</expan> habent cau&longs;arum demon&longs;trationes, <lb/> &c.<emph.end type="italics"/>) &longs;en&longs;us e&longs;t in &longs;ubalternatis, & 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 vi&longs;ibi­<lb/> libus, & 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 à <lb/> &longs;cientijs &longs;ubalternantibus. </s> <s id="s.001111">v. <!-- REMOVE S-->g. <!-- REMOVE S-->alicuius effectus in Per&longs;pectiua cau&longs;a inqui­<lb/>ritur, & inuenitur ope Geometriæ, cui illa &longs;ubiacet. </s> <s id="s.001112">Hic obiter notandum, <lb/> Ari&longs;t. fateri manife&longs;tè 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"> <s id="s.001113"><arrow.to.target n="marg51"/></s> </p> <p type="margin"> <s id="s.001114"><margin.target id="marg51"/>51</s> </p> <p type="main"> <s id="s.001115">Et po&longs;tea (<emph type="italics"/>Se habet autem & ad Per&longs;pectiuam, vt hæc ad Geometriam, alia ad <lb/>hanc, vt quod e&longs;t de Iride ip&longs;um enim quod Naturalis e&longs;t &longs;cire, ip&longs;um verò Prop­<lb/> ter quid Per&longs;pectiui<emph.end type="italics"/>) &longs;icut &longs;e habet, inquit, <expan abbr="&longs;ci&etilde;tià">&longs;cientià</expan> Naturalis de Iride ad Per­<lb/> &longs;pectiuam, ita Per&longs;pectiua ad Geometriam. </s> <s id="s.001116">qua verò ratione cau&longs;a Iridis <lb/> pertineat ad opticam, <expan abbr="atq;">atque</expan> hine tandem ad Geometriam, optimè patebit <lb/> in Meteoris, cum ip&longs;ius demon&longs;trationem afferemus.</s> </p> <p type="main"> <s id="s.001117"><arrow.to.target n="marg52"/></s> </p> <p type="margin"> <s id="s.001118"><margin.target id="marg52"/>52</s> </p> <p type="main"> <s id="s.001119">Tex. 37. (<emph type="italics"/>Vt æquicruri, & Scaleno hoc, quod e&longs;t duobus rectis æquales habere <lb/> &longs;ecandum commune aliquod ine&longs;t<emph.end type="italics"/>) quid &longs;it habere tres æquales duobus rectis <lb/> &longs;atis explicatum e&longs;t lib. r. </s> <s id="s.001120">Priorum &longs;ecto 3. cap. r. </s> <s id="s.001121">nunc igitur paraphra&longs;im <lb/> &longs;olum huius loci dabo. </s> <s id="s.001122">Triangulo I&longs;o&longs;celi, & Scaleno convenit pa&longs;&longs;io illa,<lb/> habere tres angulos æquales duobus rectis angulis &longs;ecundum aliquod com­ <pb pagenum="61" xlink:href="009/01/061.jpg"/>mune, quia illis competit, quatenus ambo &longs;unt figura quædam, ide&longs;t, qua­<lb/> tenus <expan abbr="vtrumq;">vtrumque</expan> illorum triangulum e&longs;t; triangulo <expan abbr="namq;">namque</expan> omni primo com­<lb/> petit habere tres angulos æquales duobus rectis.</s> </p> <p type="main"> <s id="s.001123"><arrow.to.target n="marg53"/></s> </p> <p type="margin"> <s id="s.001124"><margin.target id="marg53"/>53</s> </p> <p type="main"> <s id="s.001125">Tex. 38. (<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, hoc autem non idem <lb/> vbique, &longs;ed in pondere quidem mina, in cătu verò die&longs;is<emph.end type="italics"/>) Die&longs;is apud Mu&longs;icos e&longs;t <lb/> pars Toni. </s> <s id="s.001126">Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri­<lb/> mam vocem, Vt, & &longs;ecundam Rè, vt modo loquuntur. </s> <s id="s.001127">i&longs;tud interuallum <lb/> diuidunt Mu&longs;ici primum in &longs;emitonia, non tamen æqualia, &longs;ed vnum maius <lb/> altero. </s> <s id="s.001128">minus iterum in duas partes æquales &longs;ubdiuidunt, quarum <expan abbr="vtramq;">vtramque</expan> <lb/> veteres harmonici die&longs;im dixerunt. </s> <s id="s.001129">& h&etail;c die&longs;is e&longs;t minima vox ab eis con­<lb/> &longs;iderata; & quæ prima cadit &longs;ub &longs;en&longs;um; & propterea veluti &longs;implex prin­<lb/>cipium, & elementum, ex quo alia maiora interualla con&longs;tent; & in quod <lb/> re&longs;oluuntur. <foreign lang="greek">die/ois</foreign> porrò græcè valet inter alia, diui&longs;ionem. </s> <s id="s.001130">igitur interual­<lb/> lum i&longs;tud minimum dictum e&longs;t die&longs;is, quod &longs;it quædam diui&longs;io, &longs;eu &longs;egmen­<lb/>tum Toni (<emph type="italics"/>Quemadmodum in pondere mina<emph.end type="italics"/>) qui de ponderibus antiquis tra­<lb/> ctant, a&longs;&longs;erunt, Minam fui&longs;&longs;e maiorem libra per &longs;emunciam, æquipondera­<lb/> bat enim centum drachmis: quæ refragantur huic loco. </s> <s id="s.001131">&longs;ed fortè <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/> Ari&longs;t. 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 id="id.009.01.061.1.jpg" place="text" xlink:href="009/01/061/1.jpg"/> <p type="main"> <s id="s.001132"><arrow.to.target n="marg54"/></s> </p> <p type="margin"> <s id="s.001133"><margin.target id="marg54"/>54</s> </p> <p type="main"> <s id="s.001134">Tex. 39. <emph type="italics"/>(Si enim quod duobus rectis ine&longs;t, non in <lb/> quantum æquicrus, &longs;ed in quantum triangulus, no­<lb/> &longs;cens, &c.)<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha­<lb/> bere tres angulos æquales duobus rectis conuenit <lb/> æquicruri, non quatenus æquicrus e&longs;t, &longs;ed quate­<lb/> nus triangulus e&longs;t, &c. </s> <s id="s.001135">quid &longs;it habere tres æqua­<lb/> les duobus rectis, &c. </s> <s id="s.001136">fusè explicatum e&longs;t in lib. 1. <lb/> Priorum &longs;ecto 3. cap. 1. quò te nunc mitto.</s> </p> <p type="main"> <s id="s.001137"><arrow.to.target n="marg55"/></s> </p> <p type="margin"> <s id="s.001138"><margin.target id="marg55"/>55</s> </p> <p type="main"> <s id="s.001139">Po&longs;t pauca <emph type="italics"/>(Ine&longs;t omni triangulo hoc quod est <lb/> duos, &c.)<emph.end type="italics"/> ide&longs;t, hæc proprietas, quæ e&longs;t habere <lb/> duos angulos rectos non actu, &longs;ed per æquiualen­<lb/> tiam trium angulorum trianguli. </s> <s id="s.001140">Vide quæ im­<lb/>mediatè &longs;upra de hac re dixi, & quò te remi&longs;i.</s> </p> <p type="main"> <s id="s.001141"><arrow.to.target n="marg56"/></s> </p> <p type="margin"> <s id="s.001142"><margin.target id="marg56"/>56</s> </p> <p type="main"> <s id="s.001143">Eodem tex <emph type="italics"/>(Quando igitur cogno&longs;cimus, quod <lb/> quatuor exteriores &longs;unt æquales, quoniam I&longs;o&longs;celes, <lb/>adhuc deficit, propier quid I&longs;o&longs;celes? </s> <s id="s.001144">quoniam trian­<lb/> gulus: & hoc quoniam figura rectilinea, &c.)<emph.end type="italics"/> exem­<lb/> plo geometrico vult o&longs;tendere demon&longs;trationem <lb/> vniuer&longs;alem e&longs;&longs;e particulari præ&longs;tantiorem: e&longs;t <lb/> autem exemplum de pulcherrima, <expan abbr="atq;">atque</expan> admira­<lb/> bili proprietate, quæ omnibus figuris rectilineis <lb/> conuenit, e&longs;t <expan abbr="&qacute;">que</expan>; huiu&longs;modi: Omnis figuræ rectili­<lb/>neæ anguli externi omnes &longs;imul &longs;umpti, &longs;unt æqu<lb/> les quatuor rectis angulis, quæ affectio demon­<lb/> &longs;tratur in &longs;cholio 32. primi Elem. dicuntur autem <lb/> anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo præ&longs;enti anguli externi &longs;unt, B D C,<pb pagenum="62" xlink:href="009/01/062.jpg"/>D F E, F B A, ita vt quælibet figura tot angulos externos &longs;ortiatur, quot <lb/> habet latera; cum exproductis lateribus oriantur. </s> <s id="s.001145">Vt autem propo&longs;itio ve­<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> <s id="s.001146">Quæuis igitur figura rectilinea, &longs;iue <lb/> trilatera &longs;it, &longs;iue quadrilatera, vel etiam millelatera, & proinde mille quo­<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 æquales <lb/> quatuor rectis angulis. </s> <s id="s.001147">vnde tres externi anguli trianguli, & quatuor exter­<lb/> ni quadranguli, & quinque externi <expan abbr="p&etilde;tagoni">pentagoni</expan>, &c. </s> <s id="s.001148">&longs;unt æquales quatuor tan­<lb/> tum rectis, nec aliter res &longs;e habet in figura millelatera. </s> <s id="s.001149">Ex quo fit, vt an­<lb/>guli externi cuiu&longs;uis figuræ &longs;int æquales angulis omnibus externis alterius <lb/> cuiu&longs;libet figuræ. </s> <s id="s.001150">Ari&longs;t. igitur inquit, quando cogno&longs;cimus, quod quatuor <lb/> angulis rectis &longs;unt æquales exteriores omnes anguli alicuius figuræ, quo­<lb/> niam figura illa e&longs;t triangulum &longs;calenum, adhuc talis cognitio e&longs;t defecti­<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/> figuræ rectilineæ, cui hæc proprietas ine&longs;t primo, & vniuer&longs;aliter: qui igi­<lb/> tur &longs;cit, &longs;calenum habere prædictam affectionem, ex eo, quod &longs;it figura re­<lb/> ctilinea, perfectius &longs;cit, quia nihil amplius quæri pote&longs;t, quia illa figura re­<lb/> ctilinea illud vniuer&longs;ale e&longs;t, cui primo competit; reliquis autem per illam. <lb/> </s> <s id="s.001151">qui igitur vniuer&longs;ale &longs;cit, perfectius &longs;cit; quod volebat Ari&longs;t. demon&longs;trare.</s> </p> <p type="main"> <s id="s.001152"><arrow.to.target n="marg57"/></s> </p> <p type="margin"> <s id="s.001153"><margin.target id="marg57"/>57</s> </p> <p type="main"> <s id="s.001154">Eodem tex. <emph type="italics"/>(Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/> æquales)<emph.end type="italics"/> nihil frequentius. </s> <s id="s.001155">vide &longs;upra lib. 1. Priorum &longs;ecto 3. cap. 1.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001156"><arrow.to.target n="marg58"/></s> </p> <p type="margin"> <s id="s.001157"><margin.target id="marg58"/>58</s> </p> <p type="main"> <s id="s.001158">Tex. 43. <emph type="italics"/>(Sed planum, quod et&longs;i e&longs;&longs;et &longs;entire triangulum, quod duobus rectis <lb/> æquales habet angulos)<emph.end type="italics"/> vide &longs;upra lib. 1. Priorum &longs;ecto 3. cap. 1.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001159"><arrow.to.target n="marg59"/></s> </p> <p type="margin"> <s id="s.001160"><margin.target id="marg59"/>59</s> </p> <p type="main"> <s id="s.001161">Po&longs;t pauca <emph type="italics"/>(Quare & &longs;i &longs;upra Lunam e&longs;&longs;emus, & 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 Lunæ, qui fit, quando <lb/> terra inter Lunam, & Solem po&longs;ita, impedit, ne lumen Solis feratur in Lu­<lb/> nam, &longs;ed efficit, vt vmbra ip&longs;ius terræ eam contegat.</s> </p> <p type="main"> <s id="s.001162"><arrow.to.target n="marg60"/></s> </p> <p type="margin"> <s id="s.001163"><margin.target id="marg60"/>60</s> </p> <figure id="id.009.01.062.1.jpg" place="text" xlink:href="009/01/062/1.jpg"/> <p type="main"> <s id="s.001164">Et paulo po&longs;t <emph type="italics"/>(Quemadmodŭm &longs;i vi­<lb/> trum perforatum videremus, & lumen <lb/> permeans, planum vtique e&longs;&longs;et propter <lb/> quid comburit)<emph.end type="italics"/> Ioquitur de ea com­<lb/> bu&longs;tione, cuæ fit per refractionem <lb/> media &longs;phæra vitrea. </s> <s id="s.001165">de qua Vitel­<lb/> lio propo&longs;. </s> <s id="s.001166">48. decimi libri; non au­<lb/> tem de ea, quæ fit per reflexionem <lb/> ex &longs;peculo concauo quando combu­<lb/> &longs;tio fit per refractionem, cau&longs;atur à <lb/> radijs Solis vitrum permeantibus, <lb/> in quo ita franguntur, vt egredien­<lb/> tes è vitro &longs;imul vniantur, ex qua <lb/> vnione ita calor intenditur, vt ibi <lb/> comburat. </s> <s id="s.001167">vt in appo&longs;ita figura cer­<lb/> nere facile e&longs;t; in qua radij à Sole <lb/> manentes, &longs;phæram vitream perua­ <pb pagenum="63" xlink:href="009/01/063.jpg"/>dunt, <expan abbr="atq;">atque</expan> in exitu ita refraguntur, vt ad A, punctum coaceruati, ibi po&longs;­<lb/> &longs;int, &longs;i quid combu&longs;tibile occurrat, comburere. </s> <s id="s.001168">Si igitur, inquit Ari&longs;t. vide­<lb/> remus illos radios &longs;ic permeare, & refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro­<lb/> pter quid incendant.<lb/> <arrow.to.target n="marg61"/></s> </p> <p type="margin"> <s id="s.001169"><margin.target id="marg61"/>61</s> </p> <p type="main"> <s id="s.001170">Ad finem tex. <!-- REMOVE S-->43. <emph type="italics"/>(Principia enim duplicia &longs;unt, ex quibus, & circa quod: <lb/> quæ quidem igitur, ex quibus, communia &longs;unt: quæ autem circa quod propria, vt <lb/> numerus, magnitudo)<emph.end type="italics"/> nonnulli codices corruptè legunt (vt numerus magni­<lb/> tudine) &longs;ed ex græco tex. <!-- REMOVE S-->corrigendi &longs;unt, vti fecimus. </s> <s id="s.001171">Cæterum per prin­<lb/> cipia, ex quibus intelligit Dignitates, quia ex illis di&longs;currimus. </s> <s id="s.001172">per princi­<lb/> pia verò circa quod, intelligit Definitiones, quibus, vt apparet apud Eucli­<lb/> dem, explicatur &longs;ubiectum, circa quod &longs;cientia ver&longs;atur; vt in definitioni­<lb/> bus primi Elem. docemur, quid &longs;it linea, quid triangulum, quid circulus, <lb/> quid magnitudines reliquæ, quæ &longs;unt materia, circa quam Geometria &longs;pe­<lb/> culatur. </s> <s id="s.001173">In &longs;eptimo verò traduntur definitiones numerorum, quid &longs;it nu­<lb/> merus, quid impar, quid compo&longs;itus, quadratus, cubus, & reliquæ nume­<lb/> rorum &longs;pecies, quæ &longs;unt materia &longs;eptimi, octaui, & noni, in quibus de Arith­<lb/> metica tractatur.</s> </p> <p type="main"> <s id="s.001174"><arrow.to.target n="marg62"/></s> </p> <p type="margin"> <s id="s.001175"><margin.target id="marg62"/>62</s> </p> <p type="main"> <s id="s.001176">Tex. 44. <emph type="italics"/>(Commen&longs;urabilem namq; e&longs;&longs;e diametrum verè opinari, ab&longs;urdum e&longs;t)<emph.end type="italics"/><lb/> vide, quæ de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/> lib. 1. Priorum &longs;ecto 1. cap. 23. ait igitur Ari&longs;t. ab&longs;urdum e&longs;&longs;e opinari dia­<lb/> metrum e&longs;&longs;e commen&longs;urabilem co&longs;tæ, &longs;eu lateri eiu&longs;dem quadrati, reli­<lb/> qua &longs;unt Logica.</s> </p> </chap> <chap> <p type="head"> <s id="s.001177"><emph type="italics"/>Ex Secundo Posteriorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001178"><arrow.to.target n="marg63"/></s> </p> <p type="margin"> <s id="s.001179"><margin.target id="marg63"/>63</s> </p> <p type="main"> <s id="s.001180">Tex. 1. <emph type="italics"/>(Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter­<lb/> ram, aut Solem, aut triangulum; aliquid verò defectum, æqualitatem, <lb/> inæqualitatem. </s> <s id="s.001181">&longs;i in medio, aut non)<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/> quatenus ad Mathematicum attinet, optimè declarat. </s> <s id="s.001182">In quæ­<lb/> &longs;tionibus, & demon&longs;trationibus duo &longs;unt, &longs;ubiectum, & <expan abbr="prædicatũ">prædicatum</expan>, <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/> cau&longs;æ exi&longs;tunt, & quæruntur: v. <!-- REMOVE S-->g. <!-- REMOVE S-->Luna, terra, Sol, & triangulum &longs;unt &longs;u­<lb/> biectum in demon&longs;tratione, quorum prædicata &longs;unt, Lunæ quidem, & So­<lb/> lis, eclyp&longs;is. </s> <s id="s.001183">terræ 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;phæra. </s> <s id="s.001184">in quo Zabarella non probatur, qui &longs;olum <lb/> ait, terram e&longs;&longs;e in medio mundi, à Phy&longs;icis demon&longs;trari. </s> <s id="s.001185"><expan abbr="triãgulum">triangulum</expan> autem, <lb/> &longs;eu angulorum ip&longs;ius <expan abbr="prædicatũ">prædicatum</expan> e&longs;t æqualitas, & inæqualitas: vt cum in 32. <lb/> primi Elem. demon&longs;trat Euclides, omne triangulum habere tres angulos <lb/> æquales duobus rectis.</s> </p> <p type="main"> <s id="s.001186"><arrow.to.target n="marg64"/></s> </p> <p type="margin"> <s id="s.001187"><margin.target id="marg64"/>64</s> </p> <p type="main"> <s id="s.001188">Ibidem <emph type="italics"/>(Quid e&longs;t con&longs;onantia? </s> <s id="s.001189">ratio numerorum in acuto, & graui, &c)<emph.end type="italics"/> tan­<lb/> git breuiter Ari&longs;t. cau&longs;am formalem con&longs;onantiæ, & con&longs;equenter defini­<lb/> tionem ip&longs;ius. </s> <s id="s.001190">definiunt igitur Mu&longs;ici con&longs;onantiam hoc modo; Con&longs;onan­<lb/> tia e&longs;t compo&longs;itio &longs;oni grauis, & acuti, quæ &longs;uauiter auribus accidit; & quo­<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;cunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64" xlink:href="009/01/064.jpg"/>ex <expan abbr="quinq;">quinque</expan> prædictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnus <lb/> tantum &longs;onus efficiatur; &longs;onus ille erit concordans, & auribus gratus. </s> <s id="s.001191"><expan abbr="atq;">atque</expan> <lb/> hæc e&longs;t &longs;ententia pri&longs;corum præ&longs;ertim Pythagoreorum, qui propterea di­<lb/> cebant non licere Mu&longs;ico vltra quaternarium pertran&longs;ire, eò quod &longs;olæ pro­<lb/> portiones, vt diximus, numerorum quaternario contentorum, concordem, <lb/> ac con&longs;onantem concentum efficere poterant: quod vt adhuc melius per­<lb/> <figure id="id.009.01.064.1.jpg" place="text" xlink:href="009/01/064/1.jpg"/><lb/> cipiamus, accipe exemplum. </s> <s id="s.001192">Sint duæ chordæ <lb/> A, & B, æqualis cra&longs;&longs;itici, & æquè ten&longs;æ. </s> <s id="s.001193">qua­<lb/> rum A, dupla &longs;it ip&longs;ius B, quia igitur corpora <lb/> &longs;onantia &longs;unt in dupla proportione, erunt pa­<lb/> riter eorum &longs;oni in ratione dupla (vt patet ex <lb/> principijs harmonicæ) hoc e&longs;t, <expan abbr="eorũ">eorum</expan> &longs;oni erunt, <lb/> vt 2. ad 1. quia &longs;cilicet &longs;onus maioris chordæ A, erit duplus ad &longs;onum mi­<lb/> noris chordæ B. hoc e&longs;t, erit, vt 2. ad 1. & propterea, &longs;i &longs;imul ambæ chordæ <lb/> pul&longs;entur, &longs;onus, quem ex duobus mixtum edent, con&longs;onans, <expan abbr="atq;">atque</expan> grati&longs;&longs;i­<lb/> mus auribus no&longs;tris perueniet. </s> <s id="s.001194">huiu&longs;modi porrò con&longs;onantia, quæ e&longs;t in <lb/> proportione dupla, <expan abbr="quæ&qacute;">quæque</expan> omnium &longs;uaui&longs;&longs;ima e&longs;t, à græcis dicebatur Dia­<lb/>pa&longs;on. </s> <s id="s.001195"><expan abbr="atq;">atque</expan> hæc in præ&longs;entia &longs;ufficiant, cum plura de his ad &longs;ectionem pro­<lb/> blematum 19. quæ tota e&longs;t de Mu&longs;ica, dicenda &longs;int.</s> </p> <p type="main"> <s id="s.001196"><arrow.to.target n="marg65"/></s> </p> <p type="margin"> <s id="s.001197"><margin.target id="marg65"/>65</s> </p> <p type="main"> <s id="s.001198">Tex. 2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis æquales habet)<emph.end type="italics"/> vide anno­<lb/> tata lib. 1. Priorum &longs;ecto 3. cap. 1.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001199"><arrow.to.target n="marg66"/></s> </p> <p type="margin"> <s id="s.001200"><margin.target id="marg66"/>66</s> </p> <p type="main"> <s id="s.001201">Eodem tex. <emph type="italics"/>(Definitiones verò apparent omnes &longs;upponentes, & accipientes <lb/> ip&longs;um quid e&longs;t, vt Mathematicæ, quid vnitas, quid par, & impar)<emph.end type="italics"/> alludit ad de­<lb/> finitiones 7. Elem. vbi agitur de numeris. </s> <s id="s.001202">Quæ verò hoc loco de principijs <lb/> dicuntur, luculenti&longs;&longs;imè patent con&longs;ideranti definitiones, & axiomata, quæ <lb/> Mathematicis demon&longs;trationibus in omnibus ferè libris præmittuntur; ex <lb/> quibus &longs;tatim demon&longs;trationes deriuantur.</s> </p> <p type="main"> <s id="s.001203"><arrow.to.target n="marg67"/></s> </p> <p type="margin"> <s id="s.001204"><margin.target id="marg67"/>67</s> </p> <p type="main"> <s id="s.001205">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<lb/> gura planum)<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu­<lb/> lus, cuius definitio e&longs;t inter definitiones primi Elem. 15. & e&longs;t huiu&longs;modi: <lb/> circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, quæ periphæria ap­<lb/> pellatur, ad quam ab vno puncto eorum, quæ intra figuram &longs;unt po&longs;ita, ca­<lb/> dentes omnes rectæ lineæ inter &longs;e &longs;unt æquales: in qua quidem definitione <lb/> non prædicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/> &longs;eu 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 plurimæ &longs;int figuræ curuæ, & præterea &longs;olidæ quam­<lb/> plurimæ.</s> </p> <p type="main"> <s id="s.001206"><arrow.to.target n="marg68"/></s> </p> <p type="margin"> <s id="s.001207"><margin.target id="marg68"/>68</s> </p> <p type="main"> <s id="s.001208">Ibidem <emph type="italics"/>(Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos æquales duo­<lb/> bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it)<emph.end type="italics"/> ex dictis lib. 1. Priorum &longs;ecto <lb/> 3. cap. 1. petatur huius loci declaratio.</s> </p> <p type="main"> <s id="s.001209"><arrow.to.target n="marg69"/></s> </p> <p type="margin"> <s id="s.001210"><margin.target id="marg69"/>69</s> </p> <p type="main"> <s id="s.001211">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. definitione primi Elem.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001212"><arrow.to.target n="marg70"/></s> </p> <p type="margin"> <s id="s.001213"><margin.target id="marg70"/>70</s> </p> <p type="main"> <s id="s.001214">Ibidem <emph type="italics"/>(Quod autem &longs;it, monstrat)<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="demõ&longs;tra-tione">demon&longs;tra­<lb/> tione</expan> primi Elem. vbi triangulum æquilaterum con&longs;truit, & po&longs;tea probat <lb/> illud e&longs;&longs;e triangulum æquilaterum. </s> <s id="s.001215">Certum tamen e&longs;t, Geometram &longs;uppo­<lb/> nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur, <pb pagenum="65" xlink:href="009/01/065.jpg"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="cõ&longs;trni">con&longs;trui</expan>, <lb/> & e&longs;&longs;e aliquod particulare triangulum, vt fit in prædicta demon&longs;tratione, <lb/> Euclidis.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001216"><arrow.to.target n="marg71"/></s> </p> <p type="margin"> <s id="s.001217"><margin.target id="marg71"/>71</s> </p> <p type="main"> <s id="s.001218">Tex. 11. <emph type="italics"/>(Manife&longs;tum autem, & &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> <s id="s.001219">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. cui a&longs;cripta e&longs;t figura &longs;imilis huic no&longs;træ; <lb/> in editione Clauiana. </s> <s id="s.001220">quod fortè non benè aduertens Iacobus Zabarella, <lb/> alioquin in his &longs;atis oculatus incidit in errorem, dicens, &longs;e nullo pacto vi­<lb/> dere medium Euclidianæ demon&longs;trationis e&longs;&longs;e cau&longs;am materialem; quod <lb/> tamen nos mox aperiemus. </s> <s id="s.001221">per angulum in &longs;emicirculo intelligas eum, qui <lb/> fit à lineis ductis ab extremitatibus diametri, & &longs;imul in quoduis punctum <lb/> <figure id="id.009.01.065.1.jpg" place="text" xlink:href="009/01/065/1.jpg"/><lb/> circumferentiæ coeuntibus, vt in figura <lb/> præ&longs;enti vides lineas A C, B C, ad C, pun­<lb/> ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/> A C B, qui dicitur angulus in &longs;emicircu­<lb/> lo, quia de&longs;criptus e&longs;t in &longs;emicirculo A­<lb/> C B. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;anè mirabilis hæc &longs;emicirculi <lb/> proprietas, cum <expan abbr="vbicunq;">vbicunque</expan> punctum C, in <lb/> periphæria &longs;umptum fuerit, &longs;emper ta­<lb/> men angulus A C B, fiat rectus. </s> <s id="s.001222">quod Euclides eodem pror&longs;us medio, quod <lb/> Ari&longs;t. hic innuit, hoc modo demon&longs;trat. </s> <s id="s.001223">ducta enim recta D C, à 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 æquales: pariter anguli D C B, D B C, <lb/> æquales &longs;unt. </s> <s id="s.001224">& quia per 32. primi, anguli D A C, D C A, &longs;imul &longs;unt æqua­<lb/> les angulo externo C D B, & inter &longs;e æquales, erit angulus A C D, dimidium <lb/> anguli C D B. eadem ratione probatur angulus D C B, e&longs;&longs;e dimidium an­<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="æquiual&etilde;t">æquiualent</expan>. <lb/> </s> <s id="s.001225">Sequitur igitur, angulum A C B, in &longs;emicirculo e&longs;&longs;e dimidium duorum re­<lb/> ctorum; & quia omnes recti &longs;unt æquales, &longs;equitur dimidium duorum re­<lb/> ctorum, nihil aliud e&longs;&longs;e, quam vnum rectum angulum, ergo angulus in &longs;e­<lb/> micirculo, cum &longs;it &longs;emi&longs;&longs;is duorum <expan abbr="rectorũ">rectorum</expan>, erit vnus rectus angules; quod <lb/> erat probandum. </s> <s id="s.001226">ex quibus vides medium illud, quod Ari&longs;t. 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, & propterea e&longs;&longs;e rectum: quod etiam medium in toto demon­<lb/> &longs;trationis decur&longs;u e&longs;t vltimum, & principale, quod proximè conclu&longs;ionem <lb/> attingit, & propterea dici meretur e&longs;&longs;e medium huius demon&longs;trationis. <lb/> </s> <s id="s.001227">Cæterum, quod medium i&longs;tud &longs;it in genere cau&longs;æ materialis, patet ex eo, <lb/> quod e&longs;t, e&longs;&longs;e dimidium; nam e&longs;&longs;e dimidium, vel e&longs;&longs;e tertiam partem, & &longs;i­<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. ex hac præterea materia conflatur <lb/> definitio minoris extremi, vel &longs;ubiecti; dum dicitur, angulus in &longs;emicircu­<lb/> lo e&longs;t dimidium duorum rectorum. </s> <s id="s.001228">&longs;yllogi&longs;mus enim reducitur tandem ad <pb pagenum="66" xlink:href="009/01/066.jpg"/>hanc formam, dimidium duorum rectorum e&longs;t rectus, angulus in &longs;emicir­<lb/> culo e&longs;t dimidium duorum <expan abbr="rectorũ">rectorum</expan>, ergo angulus in &longs;emicirculo e&longs;t rectus. <lb/> </s> <s id="s.001229">vides in minori propo&longs;itione contineri definitionem &longs;ubiecti materialem? <lb/> </s> <s id="s.001230">adeò vt hæc &longs;it demon&longs;tratio omnibus numeris ab&longs;oluta per cau&longs;am mate­<lb/> rialem, vt benè &longs;entit Ari&longs;t. <!-- KEEP S--></s> <s id="s.001231">Reliqua ad logicum pertinent, etiam&longs;i per cha­<lb/> racteres more mathematicorum exponantur.</s> </p> <p type="main"> <s id="s.001232"><arrow.to.target n="marg72"/></s> </p> <p type="margin"> <s id="s.001233"><margin.target id="marg72"/>72</s> </p> <p type="main"> <s id="s.001234">Tex. 24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s> <s id="s.001235">aut propter quid apparet? </s> <s id="s.001236">aut propter quid <lb/> Iris? <!-- KEEP S--></s> <s id="s.001237">omnia enim hæc 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> <s id="s.001238">&longs;cilicet echo; propter quid apparet? <lb/> </s> <s id="s.001239">&longs;cilicet imago in &longs;peculo. </s> <s id="s.001240">dicit cau&longs;am echo, imaginis in &longs;peculo, & iridis <lb/> in nubibus e&longs;&longs;e eandem; nimirum refractionem; quamuis tres illæ refractio­<lb/> nes, &longs;eu; vt melius loquamur, reflexiones differant &longs;pecie ab inuicem, illa <lb/> enim e&longs;t repercu&longs;&longs;io vocis; hæc 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> <s id="s.001241">qua <lb/> ratione autem i&longs;ta omnia fiant, longum e&longs;&longs;et exponere, & ab intelligentia <lb/> huius loci fortè alienum. </s> <s id="s.001242">Illud tamen non prætereundum, quod &longs;i propriè <lb/> cum Per&longs;pectiuis loqui velimus, dicendum e&longs;&longs;e, omnia illa e&longs;&longs;e reflexionem, <lb/> non refractionem. </s> <s id="s.001243">nam reflexio e&longs;t, quando linea vi&longs;ualis, per quam fertur <lb/>&longs;pecies in aliquod corpus ter&longs;um, impingit, ex quo deinde ad oculos refle­<lb/> ctitur. </s> <s id="s.001244">refractio tunc e&longs;t, quando &longs;pecies obiecti vi&longs;ibilis tran&longs;it per media <lb/> diuer&longs;æ cra&longs;&longs;itiei., vt quando &longs;pecies lapilli per aquam primùm, deinde per <lb/>aerem means ad oculum peruenit; tunc enim linea, per quam &longs;pecies pro­<lb/> greditur, frangitur in confinio aquæ, & aeris, ita vt &longs;pecies non per vnicam <lb/> lineam rectam, &longs;ed per fractam, &longs;eu refractam in confinio illo, oculis tan­<lb/> dem accidat.</s> </p> <p type="main"> <s id="s.001245">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 Lunæ minus oculis no­<lb/> &longs;tris apparet: decre&longs;cente enim Luna &longs;olent humida augeri.</s> </p> <p type="main"> <s id="s.001246"><arrow.to.target n="marg73"/></s> </p> <p type="margin"> <s id="s.001247"><margin.target id="marg73"/>73</s> </p> <p type="main"> <s id="s.001248">Tex. 25. <emph type="italics"/>(Vt propter quid, & permutatim proportionale? </s> <s id="s.001249">& c.<emph.end type="italics"/>) quod quan­<lb/> titates, quæ &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. quæ etiam nece&longs;&longs;a­<lb/> ria &longs;unt ad hunc locum benè intelligendum. </s> <s id="s.001250">Illud autem commune propter <lb/> quod ea, quæ &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<lb/> neis, & numeris, & tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/> quærit cuinam primò, & per &longs;e conueniat hæc pa&longs;&longs;io, e&longs;&longs;e permutatim pro­<lb/> portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu­<lb/> nicent lineæ, & numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor­<lb/> tionalia.</s> </p> <p type="main"> <s id="s.001251"><arrow.to.target n="marg74"/></s> </p> <p type="margin"> <s id="s.001252"><margin.target id="marg74"/>74</s> </p> <p type="main"> <s id="s.001253">Ibidem (<emph type="italics"/>Hic quidem forta&longs;&longs;e proportionaliter habere latera, & angulos<emph.end type="italics"/>) vult <lb/>indicare, in quonam con&longs;i&longs;tat &longs;imilitudo inter duas figuras rectilineas geo­<lb/> metricas, quam &longs;imilitudinem Euclides definit. </s> <s id="s.001254">1. &longs;exti, &longs;ic explicat: &longs;imi­<lb/> les figuræ rectilíneæ &longs;unt; quæ & angulos &longs;ingulos, &longs;ingulis angulis æquales <lb/> habent, <expan abbr="atq;">atque</expan> etiam latera, quæ circa angulos æquales &longs;unt proportionalia. <lb/> </s> <s id="s.001255">vt &longs;i duo triangula appo&longs;ita habeant angulos æquales, <expan abbr="angulũ">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. & præterea latera, quæ &longs;unt <pb pagenum="67" xlink:href="009/01/067.jpg"/><figure id="id.009.01.067.1.jpg" place="text" xlink:href="009/01/067/1.jpg"/><lb/> circa angulos æquales, v. <!-- REMOVE S-->g. <!-- REMOVE S-->circa an­<lb/> gulos A, & D, habeant proportiona­<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; & &longs;ic de <lb/> lateribus alijs circa reliquos angulos <lb/> æquales; erunt tunc prædicta duo tri­<lb/> angula &longs;imilia.</s> </p> <p type="main"> <s id="s.001256"><arrow.to.target n="marg75"/></s> </p> <p type="margin"> <s id="s.001257"><margin.target id="marg75"/>75</s> </p> <p type="main"> <s id="s.001258">Ibidem (<emph type="italics"/>Vt extrin&longs;ecos æquales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi­<lb/> guræ rectilineæ æquales e&longs;&longs;e quatuor rectis angulis: vide quæ &longs;crip&longs;imus de <lb/> hac re ad tex. <!-- REMOVE S-->39. &longs;ecundi Po&longs;ter. quæ huic pariter loco &longs;atisfaciunt.</s> </p> </chap> <chap> <p type="head"> <s id="s.001259"><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001260"><emph type="italics"/>Ex Primo Libro.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001261"><arrow.to.target n="marg76"/></s> </p> <p type="margin"> <s id="s.001262"><margin.target id="marg76"/>76</s> </p> <p type="main"> <s id="s.001263">Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;tæ incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/> quæ de hac re &longs;crip&longs;i lib. 1. Priorum &longs;ecto 1. cap. 23.</s> </p> <p type="main"> <s id="s.001264"><arrow.to.target n="marg77"/></s> </p> <p type="margin"> <s id="s.001265"><margin.target id="marg77"/>77</s> </p> <p type="main"> <s id="s.001266">Eodem cap. (<emph type="italics"/>Similiter autem & acutum; non enim idem &longs;impliciter <lb/> in omnibus dicitur: nam vox acuta quidem velox (&longs;icut dicunt, qui &longs;e­<lb/>cundum numeros harmonici &longs;unt) angulus autem acutus, qui minor e&longs;t recto; gla­<lb/> dius verò, qui e&longs;t anguli acuti<emph.end type="italics"/>) affert tres &longs;pecies acuti, aliud dicens e&longs;&longs;e acu­<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> <s id="s.001267">nam acumen vocis, & &longs;oni ex celeritate motus, qua aer percu&longs;&longs;us impelli­<lb/> tur; grauitatem autem ex tarditate oriri tradiderunt antiqui Mu&longs;ici om­<lb/> nes: quamuis non ex &longs;ola celeritate, & tarditate, &longs;ed ex alijs etiam cau&longs;is <lb/> oriri po&longs;&longs;e voluerint. </s> <s id="s.001268">Primus <expan abbr="omniũ">omnium</expan> Architas Tarentinus, vt e&longs;t apud Por­<lb/> phirium in harmonicis Ptolæmei, & Zarlinum pag. </s> <s id="s.001269">58. complem. </s> <s id="s.001270">mu&longs;ica­<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<lb/> ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o­<lb/> num grauem, vt experientia docet. </s> <s id="s.001271">Ptolæmeus deinde lib. 1. cap. 3. Harm. <lb/> <!-- REMOVE S-->cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem verò ex tardi­<lb/> tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver­<lb/> berat, & ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/> aerem pul&longs;abit, & proinde citiorem motum illi imprimet, & propterea <lb/> acutiorem &longs;onum reddet. </s> <s id="s.001272">hæc ille. </s> <s id="s.001273">videmus etiam, quod cannæ organo­<lb/> rum maiores cum plus aeris moueant, & idcirco tardius, &longs;onum grauiorem <lb/> emittunt, quàm cannæ graciliores, quæ quia parum aeris cient, & ideo ce­<lb/> lerius, &longs;onum acutum edunt. </s> <s id="s.001274">ab hac &longs;ententia po&longs;teriores Mu&longs;ici non recel&longs;<lb/>&longs;erunt, vt videre e&longs;t apud Zarlinum.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001275">In quo po&longs;tea con&longs;i&longs;tat ratio acuti anguli, explicat <expan abbr="induc&etilde;s">inducens</expan> definitionem <lb/> ip&longs;ius, quæ e&longs;t inter definitiones primi Elem. huiu&longs;modi, Angulus acutus <lb/> e&longs;t, qui minor recto e&longs;t. </s> <s id="s.001276">Demum explicat, cur nam gladius dicatur acutus, <lb/> quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem duæ &longs;uper­<lb/> ficies &longs;imul in acie gladij concurrentes efficiunt.</s> </p> <pb pagenum="68" xlink:href="009/01/068.jpg"/> <p type="main"> <s id="s.001277"><arrow.to.target n="marg78"/></s> </p> <p type="margin"> <s id="s.001278"><margin.target id="marg78"/>78</s> </p> <p type="main"> <s id="s.001279">Eodem cap. (<emph type="italics"/>Rur&longs;um &longs;i eorundem; quæ &longs;unt &longs;ub eodem nomine diuer&longs;æ diffe­<lb/> rentiæ &longs;unt; vt coloris, qui e&longs;t in corporibus, & in melodijs<emph.end type="italics"/>) veteres Mu&longs;ici can­<lb/> tilenas omnes ad tria genera reuocarunt, videlicet Enharmonicum, Chro­<lb/>maticum, & Diatonicum; quæ di&longs;tinguebantur inuicem ex varia diui&longs;ione <lb/>interuallorum, ex quibus ip&longs;orum Monochordia con&longs;tabant: &longs;iue ex varijs <lb/> vocum interuallis, v. <!-- REMOVE S-->g. <!-- REMOVE S-->quia in vno continebantur plures toni, vt in Diato­<lb/> nico; in alio plures die&longs;es, vt in Enharmonico; in tertio verò plura &longs;emito­<lb/> nia, vt in Chromatico: quæ vox deducitur à chroma, græco, quod latinis <lb/> e&longs;t color; quare Chromaticum latinè redditur coloratum. </s> <s id="s.001280">Hic e&longs;t igitur <lb/> color ille, quem hic Ari&longs;t. innuit. </s> <s id="s.001281">quod genus for&longs;itan à calore denomina­<lb/> batur, quòd ip&longs;ius notæ mu&longs;icales e&longs;&longs;ent coloratæ, vt hoc modo ab alijs ge­<lb/> neribus digno&longs;ceretur. quam con&longs;uetudinem exi&longs;timat Zarlinus cap. 46. &longs;e­<lb/> cundæ partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi­<lb/> deamus in organis, & alijs huiu&longs;modi in&longs;trumentis, quæ pinnas, vulgò ta­<lb/>&longs;tos, habent; illas inquam pinnas, quæ chromaticis interuallis deputatæ <lb/> &longs;unt, colore nigro tinctas e&longs;&longs;e.</s> </p> </chap> <chap> <p type="head"> <s id="s.001282"><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001283"><arrow.to.target n="marg79"/></s> </p> <p type="margin"> <s id="s.001284"><margin.target id="marg79"/>79</s> </p> <p type="main"> <s id="s.001285">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<lb/> critus, & Leucippus, & propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam adeò paruis, quæ 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> </p> </chap> <chap> <p type="head"> <s id="s.001286"><emph type="italics"/>Libro Sexto.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001287"><arrow.to.target n="marg80"/></s> </p> <p type="margin"> <s id="s.001288"><margin.target id="marg80"/>80</s> </p> <p type="main"> <s id="s.001289">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;upponimus lectorem intellexi&longs;&longs;e definitiones &longs;altem primi Elem. in­<lb/> ter quas definitio lineæ e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">eademque</expan>; cum hac Ari&longs;totelis.<!-- KEEP S--></s> </p> </chap> <chap> <p type="head"> <s id="s.001290"><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001291"><arrow.to.target n="marg81"/></s> </p> <p type="margin"> <s id="s.001292"><margin.target id="marg81"/>81</s> </p> <p type="main"> <s id="s.001293">Cap. 2. loco 41. (<emph type="italics"/>Videntur autem in di&longs;ciplinis, &longs;eu Mathematicis quædam <lb/>ob definitionis defectum non facile de&longs;cribi; vt & quoniam, quæ ad latus &longs;e­<lb/> cat planum linea, &longs;imiliter diuidit & lineam, & locum: definitione autem dicta, <lb/> &longs;tatim manife&longs;tum e&longs;t, quod dicitur, nam eandem ablationem habent loca, & linea, <lb/> &longs;ive latus planæ figuræ, est autem definitio eiu&longs;dem proportionis hæc<emph.end type="italics"/>) mendosè <lb/>legitur à nonnullis (<emph type="italics"/>E&longs;t distem definitio eiu&longs;dem orationis hæc<emph.end type="italics"/>) quos puto de­<lb/> ceptos ab æquiuoco <foreign lang="greek">lsgous</foreign> quod & orationem, & rationem, &longs;iue proportio­<lb/> nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani­<lb/> fe&longs;tat. </s> <s id="s.001294">Notandum po&longs;tea cum Alexandro (quod & &longs;uperius alias commo­<lb/>nui in cap. de Priori, & alibi) per verbum (De&longs;cribi) &longs;ignificari hoc loco <lb/> geometricè demon&longs;trare, quoniam Geometræ <expan abbr="nõ">non</expan> ni&longs;i adhibitis de&longs;criptio­<lb/>nibus, &longs;eu figuris demon&longs;trant. </s> <s id="s.001295">Vult autem Ari&longs;t. 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 rectè a&longs;&longs;ignetur <pb pagenum="69" xlink:href="009/01/069.jpg"/>definitio illius rei, de qua di&longs;&longs;eritur. </s> <s id="s.001296">Porrò exemplum mathematicum hic <lb/> allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro­<lb/> po&longs;itionem; &longs;i linea ducta fuerit æquidi&longs;tans lateri vnius plani trianguli, &longs;e­<lb/>cabit & latera, & locum, ide&longs;t &longs;uperficiem illam triangularem &longs;imiliter, ide&longs;t <lb/> <figure id="id.009.01.069.1.jpg" place="text" xlink:href="009/01/069/1.jpg"/><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/> & A C, in punctis D, & E, in eadem ratione, <lb/> in qua etiam fecat totum triangulum, ita vt <lb/> eadem &longs;it proportio lineæ A D, ad D B, & lineæ <lb/> A E, ad E C, quæ e&longs;t partium totalis trianguli <lb/>A B C, &longs;cilicet quæ 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> <s id="s.001297">Inquit ergo Ari&longs;t. <!-- KEEP S--></s> <s id="s.001298">Si quis <lb/> vellet hoc demon&longs;trare nondum præmi&longs;&longs;a defi­<lb/> nitione eorum, quæ habent eandem rationem, &longs;iue nondum definitione al­<lb/> lata quantitatum proportionalium, hic difficile id valeret o&longs;tendere: at ve­<lb/>rò allata prius definitione quantitatum proportionalium facile demon&longs;tra­<lb/> bit. </s> <s id="s.001299">Subdit verò Ari&longs;t. dictam definitionem, dicens, tunc quantitates e&longs;&longs;e <lb/> proportionales, quando habent eandem ablationem, ide&longs;t, eandem diui&longs;io­<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<lb/> to probat, latera illius trianguli, & &longs;uperficiem e&longs;&longs;e &longs;imiliter diui&longs;a, ex quo <lb/> &longs;equitur e&longs;&longs;e proportionalia. </s> <s id="s.001300">Porrò Euclides definit. </s> <s id="s.001301">&longs;eptima 5. paulo ali­<lb/> ter definit quantitates proportionales e&longs;&longs;e illas, quæ eandem habent ratio­<lb/> nem, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i &longs;it, vt prima ad &longs;ecundam, ita tertia ad quartam. </s> <s id="s.001302">ex quibus <lb/> quoad Mathematicas &longs;pectat, huic loco &longs;atisfactum &longs;it.</s> </p> <p type="main"> <s id="s.001303"><arrow.to.target n="marg82"/></s> </p> <p type="margin"> <s id="s.001304"><margin.target id="marg82"/>82</s> </p> <p type="main"> <s id="s.001305">Cap. 4. loco 86. <emph type="italics"/>(Tentandum autem, & ea, in quæ &longs;æpi&longs;&longs;imè incidunt di&longs;puta­<lb/> tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer­<lb/> citatum e&longs;&longs;e, & in numeris circa capitales promptè &longs;e habere, & multum refert ad <lb/>hoc, & alium numerum cogno&longs;cere multiplicatum)<emph.end type="italics"/> Elementa vocabant antiqui <lb/> demon&longs;trationes faciliores, & &longs;impliciores, quales propriè &longs;unt omnes, quæ <lb/> &longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele­<lb/> mentis ab&longs;tru&longs;iores, & difficiliores demon&longs;trationes deducebant. </s> <s id="s.001306"><expan abbr="atq;">atque</expan> hæc <lb/> e&longs;t ratio, cur Euclides &longs;uos libros elementa nuncupauerit. </s> <s id="s.001307">ait igitur curan­<lb/> dum e&longs;&longs;e horum elementorum cognitionem in promptu habere, quia fre­<lb/> quens de ip&longs;is incidit di&longs;putatio. </s> <s id="s.001308">Per capitales numeros intelligo &longs;implices <lb/> ab vnitate, <expan abbr="v&longs;q;">v&longs;que</expan> ad nouem inclu&longs;iuè. </s> <s id="s.001309">& quando ait, alium numerum cogno­<lb/> &longs;cere multiplicatum, &longs;ignificat vtile valdè 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<lb/> gnitio facilis, ac leuis &longs;it: qua de cau&longs;a vide­<lb/> mus v&longs;que in hanc diem pueros diu in <lb/> Abaco memoriter perdi&longs;cen­<lb/> do detineri.</s> </p> </chap> <chap> <pb pagenum="70" xlink:href="009/01/070.jpg"/> <p type="head"> <s id="s.001310"><emph type="italics"/>Ex Primo Elenchorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001311"><arrow.to.target n="marg83"/></s> </p> <p type="margin"> <s id="s.001312"><margin.target id="marg83"/>83</s> </p> <p type="main"> <s id="s.001313">Cap. 10. <emph type="italics"/>(Nam p&longs;eudographiæ non contentio&longs;æ (&longs;ecundum enim ea, quæ <lb/> &longs;ub arte &longs;unt, captio&longs;æ &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra­<lb/> phia circa verum, vt Hippocratis quadratura, quæ per lunulas, &longs;ed, vt <lb/> Bry&longs;&longs;o quadrauit circulum; & 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 æquale tentauerit, explicatum e&longs;t abundè in 2. Priorum cap. 31. <lb/> & quo itidem modo Bry&longs;&longs;o lib. 1. Po&longs;ter. tex. <!-- REMOVE S-->23. <expan abbr="&longs;olũmodo">&longs;olummodo</expan> id hoc loco no­<lb/> tandum per p&longs;eudographiam intelligere, vt apertè etiam inferius explicat, <lb/> Geometricam demon&longs;trationem fallacem, eò quod demon&longs;trationes geo­<lb/>metricæ fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;eudographia <lb/> autem latinè idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum è contrariò, &longs;i­<lb/> cuti &longs;upra in Topicis, & alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri­<lb/> cè demon&longs;trare, & per de&longs;criptiones intelligit demon&longs;trationes geometri­<lb/> cas. </s> <s id="s.001314">Qua ratione item Hippocrates ex ijs, quæ &longs;ub arte Geometriæ &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<lb/> &longs;as, quæ non procedunt ex proprijs illius &longs;cientiæ, in qua fiunt, &longs;ed ex com­<lb/> munibus alijs &longs;cientijs: captio&longs;as verò, & &longs;ophi&longs;ticas, quæ ex proprijs &longs;cien­<lb/> tiæ, in qua fiunt, decipiunt. </s> <s id="s.001315">At verò demon&longs;tratio, &longs;eu p&longs;eudographia Bry&longs;­<lb/> &longs;onis erat contentio&longs;a, quia ex communibus, & extra Geometriam petitis <lb/> argumentabatur: quemadmodum ibi explicatum e&longs;t.</s> </p> <p type="main"> <s id="s.001316"><arrow.to.target n="marg84"/></s> </p> <p type="margin"> <s id="s.001317"><margin.target id="marg84"/>84</s> </p> <p type="main"> <s id="s.001318">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, quæ non contentio&longs;a dicitur, quia ex <lb/> proprijs Geometriæ deducebatur.</s> </p> <p type="main"> <s id="s.001319"><arrow.to.target n="marg85"/></s> </p> <p type="margin"> <s id="s.001320"><margin.target id="marg85"/>85</s> </p> <p type="main"> <s id="s.001321">Ibidem <emph type="italics"/>(Bry&longs;&longs;onis autem contentio&longs;a: & 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="quãdo">quando</expan> ait <emph type="italics"/>(& illam qui­<lb/> dem)<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s> <s id="s.001322">vide 2. Prior cap. 31. & quæ pau­<lb/> lo ante in præcedentibus locis diximus.</s> </p> <p type="main"> <s id="s.001323"><arrow.to.target n="marg86"/></s> </p> <p type="margin"> <s id="s.001324"><margin.target id="marg86"/>86</s> </p> <p type="main"> <s id="s.001325">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> <s id="s.001326">lege &longs;uperius dicta in præcedentibus locis hu­<lb/> ius capituli.</s> </p> <p type="main"> <s id="s.001327"><arrow.to.target n="marg87"/></s> </p> <p type="margin"> <s id="s.001328"><margin.target id="marg87"/>87</s> </p> <figure id="id.009.01.070.1.jpg" place="text" xlink:href="009/01/070/1.jpg"/> <p type="main"> <s id="s.001329">Ad finem cap. <emph type="italics"/>(Aut vt Antiphon quadra­<lb/> uit)<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon­<lb/> tem in orbe quadrando, ac Hippocratem, <lb/> Ari&longs;t. his verbis videtur &longs;ignificare, ide&longs;t, <lb/> ip&longs;um, quamuis ex proprijs Geometriæ, <lb/> fal&longs;is tamen ratiocinatum e&longs;&longs;e. </s> <s id="s.001330">Cæterum <lb/> Antiphontem in hunc modum orbem ad <lb/> quadrum redigere tenta&longs;&longs;e, tradit Simpli­<lb/> cius. </s> <s id="s.001331">circulo quadrando in&longs;cribebat pri­<lb/> mò quadratum A B C D. deinde in &longs;ingu­<lb/> lis quatuor &longs;egmentis in&longs;cribebat totidem <lb/>trigona æquilatera, vt patet in ad&longs;cripta <pb pagenum="71" xlink:href="009/01/071.jpg"/>figura. </s> <s id="s.001332">po&longs;tea &longs;uper &longs;ingula latera horum triangulorum in reliquis &longs;egmen­<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 figuræ illius multilateræ <lb/>in circulo delineatæ, circumferentiæ circuli aptaretur. </s> <s id="s.001333">quod fieri po&longs;&longs;e ille <lb/> falsò contra Geometriæ principia a&longs;&longs;umebat; e&longs;t enim principium Geome­<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 totum circu­<lb/> lum, diuidendo illud in triangula &longs;emper minora; vel quia putat, lineam <lb/> curuam con&longs;tare ex minimis lineis rectis. </s> <s id="s.001334">Similiter igitur <expan abbr="atq;">atque</expan> Hippocra­<lb/>tes errauit, qúi pariter in Geometria fallebatur: Antiphon quidem contra <lb/> principia illius: Hippocrates verò a&longs;&longs;umens fal&longs;i quidpiam in Geometria. <lb/> <!-- KEEP S--></s> <s id="s.001335">At Bry&longs;&longs;o, eo quod per communia alijs &longs;cientijs deduceret ratiocinatio­<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<lb/> &longs;criptio, &longs;eu demon&longs;tratio extra Geometriæ li­<lb/> mites, quod cau&longs;a e&longs;t contentionis.</s> </p> <p type="head"> <s id="s.001336"><emph type="italics"/>Logicorum locorum finis.<emph.end type="italics"/></s> </p> </chap> <pb pagenum="72" xlink:href="009/01/072.jpg"/> <chap> <p type="head"> <s id="s.001337">EX PRIMO LIBRO <lb/> PHYSICORVM.<lb/> <arrow.to.target n="marg88"/></s> </p> <p type="margin"> <s id="s.001338"><margin.target id="marg88"/>88</s> </p> <p type="main"> <s id="s.001339">Tex. 11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="quæcunq;">quæcunque</expan> ex <lb/> principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="quæcunq;">quæcunque</expan> verò non, minimè: <lb/> vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;­<lb/> &longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago­<lb/> ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip­<lb/> pocratis Chij exi&longs;timant græci expo&longs;itores, qui per lunulas, quas Ari&longs;t. &longs;e­<lb/> ctiones appellat, orbem quadrare tentabat. </s> <s id="s.001340">Eius demon&longs;trationem expli­<lb/> caui ad cap. 31. de Abductione in 2. Priorum, quam inibi videas. </s> <s id="s.001341">hoc &longs;olum <lb/> hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua­<lb/> dam præmi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet (in­<lb/> quit Ari&longs;t.) Geometra illius deceptionem inuenire. </s> <s id="s.001342">Tetragoni&longs;mum autem <lb/> Antiphontis non e&longs;t Geometræ <expan abbr="cõfutare">confutare</expan>, quia aduer&longs;abatur principijs Geo­<lb/> metriæ, &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. 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. 8. vbi ip&longs;ius p&longs;eudographiam expo&longs;ui. Quemad­<lb/> modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantummodo rationes eas, quæ &longs;er­<lb/> uatis Geometricis principijs procedunt; non autem eas, quæ Geometriæ <lb/> principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="cõtra">contra</expan> Parmenidem, ac Me­<lb/> li&longs;&longs;um naturæ principia de&longs;truentes di&longs;ceptare, aut fallaces eorum rationes <lb/> coarguere. </s> <s id="s.001343">Hoc volebat Ari&longs;toteles inferre.</s> </p> </chap> <chap> <p type="head"> <s id="s.001344"><emph type="italics"/>Ex Secundo Phy&longs;icorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001345"><arrow.to.target n="marg89"/></s> </p> <p type="margin"> <s id="s.001346"><margin.target id="marg89"/>89</s> </p> <p type="main"> <s id="s.001347">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<lb/> maticum, libuit tamen illum in ordinem no&longs;trum recen&longs;ere, ope­<lb/> ræpretium etenim e&longs;t ea, quæ in ip&longs;o continentur à nonnullis recentioribus <lb/> rectè intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab­<lb/> &longs;tineant, ac tandem ex Ari&longs;t. lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/> per&longs;picuè videant. </s> <s id="s.001348">cætera, quæ in præcedentibus locis Ari&longs;t. de Natura Ma­<lb/> thematicarum habet, &longs;unt præter no&longs;trum in&longs;titutum.</s> </p> <p type="main"> <s id="s.001349"><arrow.to.target n="marg90"/></s> </p> <p type="margin"> <s id="s.001350"><margin.target id="marg90"/>90</s> </p> <p type="main"> <s id="s.001351">Tex. 28. (<emph type="italics"/>Alio autem modo, forma, & exemplum: hæc autem e&longs;t ratio ip&longs;ius, <lb/> quod quid erat e&longs;&longs;e, & huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, & omnino <lb/> numerus, & partes, quæ in ratione &longs;unt<emph.end type="italics"/>) vt benè intelligas, quod in præ&longs;enti <lb/> textu <expan abbr="mathematicũ">mathematicum</expan> e&longs;t, con&longs;ule prius, quæ &longs;crip&longs;i ad tex. <!-- REMOVE S-->1. cap. primi 2. Po­<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;picuè videbis, cur <expan abbr="con-&longs;onãtiæ">con­<lb/> &longs;onantiæ</expan>, quæ dicitur Diapa&longs;on, e&longs;&longs;entia, & definitio &longs;it ip&longs;a proportio dupla, <lb/> quæ &longs;ub his num. </s> <s id="s.001352">2.1. continetur: quibus per&longs;pectis facilis erit phy&longs;ico totius <lb/> loci intelligentia.</s> </p> <pb pagenum="73" xlink:href="009/01/073.jpg"/> <p type="main"> <s id="s.001353"><arrow.to.target n="marg91"/></s> </p> <p type="margin"> <s id="s.001354"><margin.target id="marg91"/>91</s> </p> <p type="main"> <s id="s.001355">Tex. 68. (<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo­<lb/>bilibus, 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;tè videas Mathematicas <expan abbr="de-mõ&longs;trare">de­<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> <s id="s.001356">quorum exempla in logicis ex Mathematicis at­<lb/> tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apertè manife­<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 lineæ perpendicularis A C, quod idem e&longs;t.</s> </p> <p type="main"> <s id="s.001357"><arrow.to.target n="marg92"/></s> </p> <p type="margin"> <s id="s.001358"><margin.target id="marg92"/>92</s> </p> <p type="main"> <s id="s.001359">Tex 89. (<emph type="italics"/>E&longs;t autem nece&longs;&longs;arium in Mathematicis, & in his, quæ &longs;ecundum <lb/>naturam fiunt qua&longs;i eodem modo; quoniam enim hoc rectum e&longs;t, nece&longs;&longs;e e&longs;t, trian­<lb/>gulum tres angulos habere æquales 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, & <lb/> difficultatis in exemplo hoc mathematico explicando, ita vt recentiores <lb/> quidam textum <expan abbr="hũc">hunc</expan> pro arbitratu &longs;uo perperam latinè verterint: ideò pri­<lb/> mum ex græcis codicibus interpretationem hanc veram attuli. </s> <s id="s.001360">deinde, quia <lb/> etiam græci in exemplo mathematico enodando, vel malè, vt Simplicius; <lb/> vel ob&longs;curè nimis, vt reliqui; Latini verò vel nihil, vel peius multò loquun­<lb/> tur, ideò &longs;ic ego exponendum cen&longs;ui. </s> <s id="s.001361">cum velit Ari&longs;t. o&longs;tendere nece&longs;&longs;ita­<lb/>tem, quæ in &longs;cientijs inter præmi&longs;&longs;as, &longs;eu medium, & conclu&longs;ionem reperi­<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 æqua­<lb/> les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/> primo Priorum, &longs;ecto 3. cap. 1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s> <s id="s.001362">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 id="id.009.01.073.1.jpg" place="text" xlink:href="009/01/073/1.jpg"/><lb/> A C, &longs;it perpendiculare <expan abbr="cũ">cum</expan> latere B C, & pro­<lb/> ducatur B C, in D; tunc triangulum A B C, <lb/> habere tres angulos, A, B, & A C B, æquales <lb/> duobus rectis planum erit: nam <expan abbr="cũ">cum</expan> latus A C, <lb/> &longs;it perpendiculare (quod Ari&longs;t. dicit, cum <expan abbr="re-ctũ">re­<lb/> ctum</expan> hoc &longs;it) erunt duo anguli deinceps A C B, <lb/> A C D, recti, ex definitione lineæ perpendicu­<lb/> laris, cum ergo duo anguli A, & B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int æquales per <lb/> 32. primi, & reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu­<lb/> li, & angulus vnus lineæ perpendicularis, & ideò rectus; manife&longs;tè apparet, <lb/> tres angulos A, B, A C B, e&longs;&longs;e æquales nece&longs;&longs;ariò duobus rectis, ex po&longs;itio­<lb/> ne illius recti, &longs;iue lateris perpendicularis, quia ex verò, verum nece&longs;&longs;ariò <lb/> &longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/> tres angulos æquales duobus rectis, nece&longs;&longs;ariò &longs;equitur illud e&longs;&longs;e rectum, <lb/>ide&longs;t latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/> &longs;equi pote&longs;t ex verò, & falsò. </s> <s id="s.001363">valebit tamen hæc con&longs;equen­<lb/> tia, &longs;i triangulum non habet hanc proprietatem, ne­<lb/> que illud rectum e&longs;t, ide&longs;t, <expan abbr="neq;">neque</expan> latus prædi­<lb/>ctum erit <expan abbr="perp&etilde;diculare">perpendiculare</expan>, quia fal&longs;um <lb/>non, ni&longs;i ex fal&longs;o &longs;equitur.</s> </p> </chap> <pb pagenum="74" xlink:href="009/01/074.jpg"/> <chap> <p type="head"> <s id="s.001364"><emph type="italics"/>Ex Tertio Phy&longs;icorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001365"><arrow.to.target n="marg93"/></s> </p> <p type="margin"> <s id="s.001366"><margin.target id="marg93"/>93</s> </p> <p type="main"> <s id="s.001367">Tex. 26. <emph type="italics"/>(Et hi quidem infinitum e&longs;&longs;e par; hoc enim compræhen&longs;ura, & <lb/> ab impari terminatum tribuit ijs, quæ &longs;unt, infinitatem. </s> <s id="s.001368">&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numeris, circumpo&longs;itis enim Gnomoni­<lb/>bus circa vnum, & &longs;eor&longs;um, aliquando quidem &longs;emper aliam fieri &longs;pe­<lb/> ciem, aliquando autem vnam)<emph.end type="italics"/> vt melius percipiantur ea, quæ &longs;equuntur, lege <lb/> prius, quæ in cap. de Motu in po&longs;t prædicamentis &longs;crip&longs;i de Gnomone, ad <lb/> &longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu­<lb/> meris Gnomones Arithmetici. </s> <s id="s.001369">Pythagorici enim (à quibus i&longs;ta mutuatus <lb/> e&longs;t Ari&longs;t. numeros impares &longs;olos appellabant Gnomones, eò quod in for­<lb/> mam normæ æquilateræ, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/> <figure id="id.009.01.074.1.jpg" place="text" xlink:href="009/01/074/1.jpg"/><lb/> nimirum in ternario, quinario, &longs;eptenario, & &longs;ic de <lb/> reliquis imparibus. </s> <s id="s.001370">pares autem numeri, quia ne­<lb/> queunt in figuram normæ æquilateræ di&longs;poni, cum <lb/> non habeant vnitatem pro angulo, & paria po&longs;tea la­<lb/> tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di­<lb/> &longs;ponatur &longs;ic <figure id="id.009.01.074.2.jpg" place="text" xlink:href="009/01/074/2.jpg"/> non refert Gnomonem, quia lateribus in&etail;qualibus con­<lb/> &longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="id.009.01.074.3.jpg" place="text" xlink:href="009/01/074/3.jpg"/> quia dee&longs;t huic figuræ angularis vnitas, quæ <lb/>illi nece&longs;&longs;aria e&longs;t. </s> <s id="s.001371">Pythagorici igitur dicebant, numerum parem ideò e&longs;&longs;e <lb/> infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetuæ diui&longs;ionis, cum <lb/> quælibet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/> parem, & &longs;ubdiui&longs;ibilis po&longs;tea bifariam, & &longs;ic in infinitum, vt de linea pro­<lb/> blematicè probatur in 10. primi Elem. quamuis theorematicè &longs;it axioma. <lb/> </s> <s id="s.001372">hunc porrò numerum parem dicebant terminatum e&longs;&longs;e ab impari, quia ori­<lb/> tur ex diui&longs;ione cuiu&longs;uis rei, quæ vna &longs;it, &longs;umentes vnitatem pro impari. <lb/> </s> <s id="s.001373">&longs;ignum præterea huius finitatis ab impari, & infinitatis à pari numero pro­<lb/> cedentis, aiunt e&longs;&longs;e Gnomones, numeros &longs;cilicet impares: Gnomones enim, <lb/> ide&longs;t impares numeri vnitati additi, producunt eandem perpetuò numero­<lb/> rum formam, videlicet quadratum: at verò è contrariò numeri pares vni­<lb/> tati additi, conflant perpetuò varias numerorum formas: quapropter vi­<lb/>dentur numeri impares e&longs;&longs;e finitatis cau&longs;a; &longs;icut pares ex aduersò infinitatis <lb/> principium. </s> <s id="s.001374">quæ vt melius intelligas, declaranda e&longs;t 26. propo&longs;. </s> <s id="s.001375">7. Arith­<lb/> metices lordani, vbi i&longs;tud idem demon&longs;trat, quæ e&longs;t hæc. </s> <s id="s.001376">&longs;it vnitas, & &longs;uo or­<lb/> dine &longs;equantur impares, vt in &longs;equenti hac &longs;erie apparet 1. 3. 5. 7. 9. & c. <lb/> <figure id="id.009.01.074.4.jpg" place="text" xlink:href="009/01/074/4.jpg"/><lb/> &longs;i igitur vnitati addatur ternarius in Gnomo­<lb/> nis modum, vt vides in prima figura, produ­<lb/> cetur quaternarius numerus, qui e&longs;t numerus <lb/> quadratus (quid &longs;it quadratus numerus expli­<lb/> caui in Logicis tex. <!-- REMOVE S-->9. primi Po&longs;ter.) et&longs;i 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> <s id="s.001377">et&longs;i huic &longs;imiliter <lb/>addatur &longs;equens impar, nimirum &longs;eptenarius, conflabitur &longs;edenarius, qui <lb/> numerus pariter quadratus e&longs;t, vt in tertia figura, & hoc modo, &longs;i in infini­ <pb pagenum="75" xlink:href="009/01/075.jpg"/>tum procedatur, numeri &longs;emper quadrati progignentur. </s> <s id="s.001378">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> <s id="s.001379">Po&longs;t prædictam 26. propo&longs;itio­<lb/>nem Iordani, &longs;unt aliquot propo&longs;itiones, quarum &longs;umma hæc e&longs;t: &longs;i pares <lb/> numeri ab vnitate coaceruentur; coaceruati erunt &longs;emper variæ formæ nu­<lb/> merorum. </s> <s id="s.001380">quæ &longs;ic explicantur: &longs;int ab vnitate pares di&longs;po&longs;iti ordinatim <lb/> hoc modo, 1. 2. 4. 6. &c. </s> <s id="s.001381">&longs;i igitur vnitati binarius coaceruetur, fit numerus <lb/> <figure id="id.009.01.075.1.jpg" place="text" xlink:href="009/01/075/1.jpg"/><lb/> triangularis, vt in prima figura. </s> <s id="s.001382">&longs;i huic ternario <lb/> coaceruetur &longs;equens par, fiet altera &longs;pecies, ni­<lb/> mirum hexagonus numerus, vt in &longs;ecunda figu­<lb/> ra. </s> <s id="s.001383">cui &longs;i &longs;equens addatur par, &longs;cilicet &longs;enarius, <lb/> fiet iterum noua numeri forma, v. <!-- REMOVE S-->g. <!-- KEEP S--></s> <s id="s.001384">dodecago­<lb/> nus, vt in tertia figura. </s> <s id="s.001385">& &longs;ic &longs;emper in infinitum nouæ ac variæ numerorum <lb/> formæ ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/> parem infiniti naturam &longs;apere. </s> <s id="s.001386">Porrò reperiri numeros triangulares, pen­<lb/> tagonos, & &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, & Iordani, <lb/>citati in definitionibus 7. &longs;uæ Arithmeticæ, atque ex tractatu Diophantis <lb/> Alex. de numeris rectangulis. </s> <s id="s.001387"><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s> </p> <p type="main"> <s id="s.001388"><arrow.to.target n="marg94"/></s> </p> <p type="margin"> <s id="s.001389"><margin.target id="marg94"/>94</s> </p> <p type="main"> <s id="s.001390">Tex. 31. <emph type="italics"/>(Vtuntur etiam Mathematici infinito)<emph.end type="italics"/> <expan abbr="aliquãdo">aliquando</expan> Mathematici du­<lb/> cunt lineas quantumuis longas, &longs;eu indefinitæ longitudinis, quas etiam in­<lb/> finitas appellant: & hoc modo vtuntur infinito, vt infra tex. <!-- REMOVE S-->71. ip&longs;e Ari&longs;t. <lb/> exponit. </s> <s id="s.001391">alio præterea 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. editionis Clauianæ. </s> <s id="s.001392">numerum <expan abbr="quoq;">quoque</expan> au­<lb/> geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem. 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="infinitũ">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinitũ">infinitum</expan> in v&longs;u e&longs;t.</s> </p> <p type="main"> <s id="s.001393"><arrow.to.target n="marg95"/></s> </p> <p type="margin"> <s id="s.001394"><margin.target id="marg95"/>95</s> </p> <p type="main"> <s id="s.001395">Tex. 68. & 69. plura de magnitudine, & numero continent; &longs;ed quæ non <lb/> indigeant opera no&longs;tra.</s> </p> <p type="main"> <s id="s.001396"><arrow.to.target n="marg96"/></s> </p> <p type="margin"> <s id="s.001397"><margin.target id="marg96"/>96</s> </p> <p type="main"> <s id="s.001398">Tex. 71. <emph type="italics"/>(Non remouet autem ratio Mathematicos à 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;">neque</expan> enim nunc in­<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/> verè 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"> <s id="s.001399"><emph type="italics"/>Ex Quarto Phy&longs;icorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001400"><arrow.to.target n="marg97"/></s> </p> <p type="margin"> <s id="s.001401"><margin.target id="marg97"/>97</s> </p> <p type="main"> <s id="s.001402">Tex. 120. ter in hoc textu meminit commen&longs;urabilitatis, & incommen­<lb/> &longs;urabilitatis, quæ e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/> primo Priorum, &longs;ecto primo, cap. 23.</s> </p> </chap> <pb pagenum="76" xlink:href="009/01/076.jpg"/> <chap> <p type="head"> <s id="s.001403"><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001404"><arrow.to.target n="marg98"/></s> </p> <p type="margin"> <s id="s.001405"><margin.target id="marg98"/>98</s> </p> <p type="main"> <s id="s.001406">Tex. 6. <emph type="italics"/>(Vt media grauis ad vltimam, & acuta ad primam)<emph.end type="italics"/> alludit ad or­<lb/> dinem chordarum in mu&longs;icis in&longs;trumentis, vbi media chorda edit &longs;o­<lb/> num, re&longs;pectu quidem vltimæ, & &longs;upremæ chordæ grauem: re&longs;pectu verò <lb/> primæ, & infimæ acutum.</s> </p> </chap> <chap> <p type="head"> <s id="s.001407"><emph type="italics"/>Ex Octauo Phy&longs;icorum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001408"><arrow.to.target n="marg99"/></s> </p> <p type="margin"> <s id="s.001409"><margin.target id="marg99"/>99</s> </p> <p type="main"> <s id="s.001410">Tex. 15. <emph type="italics"/>(Etenim triangulus habet tres angulos æquales duobus rectis angulis)<emph.end type="italics"/><lb/> lib. 1. Priorum, &longs;ecto 3. cap. 1. huius rei explicationem reperies.</s> </p> </chap> <chap> <p type="head"> <s id="s.001411"><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001412"><arrow.to.target n="marg100"/></s> </p> <p type="margin"> <s id="s.001413"><margin.target id="marg100"/>100</s> </p> <p type="main"> <s id="s.001414">Tex. 33. <emph type="italics"/>(Vt &longs;i quis minimam quădam e&longs;&longs;e dicat magnitudinem, hic enim <lb/> minimum introducens, maxima <expan abbr="vbiq;">vbique</expan> amoueret mathematicorŭm)<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<lb/> tiones, atque etiam effata euerterentur: v. <!-- REMOVE S-->g. <!-- REMOVE S-->10. primi Elem. quæ docet <lb/> quamlibet lineam po&longs;&longs;e diuidi bifariam nulla e&longs;&longs;et, quia linea illa, quæ con­<lb/> &longs;taret ex tribus Democriti atomis, nulla ratione bifariam &longs;ecari po&longs;&longs;et. </s> <s id="s.001415">pa­<lb/> riter totus ferè decimus liber Elem. deceptiuus, & nullus e&longs;&longs;et, &longs;i enim da­<lb/> rentur illæ atomi, ex quibus <expan abbr="quãtitas">quantitas</expan> conflaretur, nullæ e&longs;&longs;ent lineæ incom­<lb/> men&longs;urabiles, quandoquidem omnes communi illa, ac indiuidua, commen­<lb/> &longs;urarentur. </s> <s id="s.001416">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"> <s id="s.001417"><arrow.to.target n="marg101"/></s> </p> <p type="margin"> <s id="s.001418"><margin.target id="marg101"/>101</s> </p> <p type="main"> <s id="s.001419">Tex. 36. <emph type="italics"/>(Sit <expan abbr="itaq;">itaque</expan> linea, in qua A G E, infinita ad partes E; & 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, circa centrum G, fe-<emph.end type="italics"/><lb/> <figure id="id.009.01.076.1.jpg" place="text" xlink:href="009/01/076/1.jpg"/><lb/> <emph type="italics"/>retur circulariter linea A G E, &longs;ecans ali­<lb/> quando lineam <foreign lang="greek">b</foreign> B, tempore finito; totum <lb/> enim tempus, in quo circulariter latum <lb/> e&longs;t Cœlum finitum e&longs;t, & ablatum igitur, <lb/>quo &longs;ecans ferebatur; erit igitur aliquod <lb/>principium, quo primum linea A G E, li­<lb/> neam <foreign lang="greek">b</foreign> B, &longs;ecuit. </s> <s id="s.001420">&longs;ed impo&longs;&longs;ibile est; non <lb/> est igitur circulariter verti <expan abbr="infinitũ">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<lb/> maticam, quæ in codicibus pariter, ac <lb/> commentarijs de&longs;ideratur, illam pla­<lb/> cuit apponere. </s> <s id="s.001421">in qua quidem, quamuis duæ lineæ infinitæ &longs;upponantur, vna <lb/> ad alteram <expan abbr="tãtum">tantum</expan> partem in qua E: altera verò ad <expan abbr="vtramq;">vtramque</expan> partem <foreign lang="greek">b,</foreign> & B, <pb pagenum="77" xlink:href="009/01/077.jpg"/>non potuerunt tamen de&longs;cribi, ni&longs;i finitæ; appo&longs;itæ idcircò &longs;unt ad partes <lb/> illas, ad quas deberent e&longs;&longs;e infinitæ lineolæ quædam infinitatem indicantes. <lb/> </s> <s id="s.001422">debemus po&longs;tea, vt mentem Ari&longs;t. percipiamus concipere lineam A G E, <lb/> moueri circulariter facto centro in G. quæ quia infinita &longs;upponitur ad par­<lb/> tem E, &longs;ecabit nece&longs;&longs;ariò alteram <expan abbr="vtrinq;">vtrinque</expan> infinitam <foreign lang="greek">b</foreign> B, <expan abbr="illam&qacute;">illamque</expan>; nece&longs;&longs;ariò <lb/> finito tempore percurret, finito enim tempore tota mundi circulatio per­<lb/> agitur, &longs;patio videlicet viginti quatuor horarum. </s> <s id="s.001423">ex quo Ari&longs;t. infert mun­<lb/> dum non po&longs;&longs;e e&longs;&longs;e infinitæ magnitudinis; quia &longs;i mundus e&longs;&longs;et infinitus; &. <lb/> </s> <s id="s.001424">duæ lineæ infinitæ, quales &longs;unt prædictæ in ip&longs;o, <expan abbr="atq;">atque</expan> cum ip&longs;o moueri alte­<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<lb/> tudo finito tempore percurratur; quare dicendum e&longs;t, mundum e&longs;&longs;e finita <lb/> magnitudine præditum.</s> </p> <p type="main"> <s id="s.001425"><arrow.to.target n="marg102"/></s> </p> <p type="margin"> <s id="s.001426"><margin.target id="marg102"/>102</s> </p> <p type="main"> <s id="s.001427">Tex. 48. <emph type="italics"/>(Nihil autem refert grauitates, commen&longs;urabiles &longs;int, an incommen­<lb/>&longs;urabiles)<emph.end type="italics"/> quidnam &longs;it commen&longs;urabilitas, & incommen&longs;urabilitas, expli­<lb/> catum e&longs;t lib. 1. Priorum, &longs;ecto 1. cap. 23.</s> </p> <p type="main"> <s id="s.001428"><arrow.to.target n="marg103"/></s> </p> <p type="margin"> <s id="s.001429"><margin.target id="marg103"/>103</s> </p> <p type="main"> <s id="s.001430">Tex. 119. <emph type="italics"/>(Est autem impo&longs;&longs;ibile, & po&longs;&longs;ibile; fal&longs;um, & verum, ex &longs;uppo&longs;itio­<lb/> ne quidem, dico autem, vt triangulum impo&longs;&longs;ibile e&longs;t duos rectos habere, &longs;i hæc)<emph.end type="italics"/><lb/> ide&longs;t, &longs;i &longs;upponantur fal&longs;a quædam, quæ &longs;upponi po&longs;&longs;unt, &longs;equetur impo&longs;&longs;i­<lb/> bile e&longs;&longs;e triangulum habere tres angulos æquales duobus rectis angulis, vi­<lb/> de, quæ &longs;crip&longs;i lib. 1. Priorum, &longs;ecto 3. cap. 1. de hoc, quod e&longs;t, habere tres <lb/> angulos æquales duobus rectis. </s> <s id="s.001431">v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i in triangulo pag. </s> <s id="s.001432">73. producto late­<lb/> re A C, in D. &longs;i &longs;upponatur externus angulus B C D, non e&longs;&longs;e æqualis duobus <lb/>internis, & oppo&longs;itis A, & B, nunquam poterimus eo modo, quo Euclides, <lb/> demon&longs;trare pa&longs;&longs;ionem prædictam de triangulo A B C. huiu&longs;modi impo&longs;&longs;i­<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. impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo­<lb/> dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an­<lb/> gulos æquales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up­<lb/>po&longs;itione, impo&longs;&longs;ibile eua&longs;it.</s> </p> <p type="main"> <s id="s.001433"><arrow.to.target n="marg104"/></s> </p> <p type="margin"> <s id="s.001434"><margin.target id="marg104"/>104</s> </p> <p type="main"> <s id="s.001435">Ibidem <emph type="italics"/>(Et diameter commen&longs;urabilis est co&longs;tæ, &longs;i hæc)<emph.end type="italics"/> vide primo Priorum, <lb/> &longs;ecto 3. cap. 23. hoc &longs;olum nunc addendum <emph type="italics"/>(Si hæc)<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i &longs;upponamus li­<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;tæ, quia indiui&longs;ibile illud, ex quo vtraque linea con­<lb/> &longs;tat, erit <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> men&longs;ura communis.</s> </p> </chap> <chap> <p type="head"> <s id="s.001436"><emph type="italics"/>Ex Secundo de Cælo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001437"><arrow.to.target n="marg105"/></s> </p> <p type="margin"> <s id="s.001438"><margin.target id="marg105"/>105</s> </p> <p type="main"> <s id="s.001439">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;phæram non diuidunt, vt non plures &longs;uperficies. </s> <s id="s.001440">quam vnam <expan abbr="hab&etilde;um">habentem</expan>. <lb/> </s> <s id="s.001441">diui&longs;io enim in plana non perinde efficitur, vt qui&longs;piam <expan abbr="diuid&etilde;s">diuidens</expan> in par­<lb/>tes diuidat totum, &longs;ed vt in &longs;pecie diuer&longs;a: patet igitur &longs;phæram e&longs;&longs;e &longs;olidarum <lb/> primam)<emph.end type="italics"/> qui &longs;olida diuidunt in plana, ea diuidunt <expan abbr="&longs;ecũdum">&longs;ecundum</expan> numerum &longs;uper­<lb/>ficierum, 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 nequeunt <pb pagenum="78" xlink:href="009/01/078.jpg"/>&longs;phæram in plana vlla re&longs;oluere, <expan abbr="neq;">neque</expan> in alias plures &longs;uperficies, quia &longs;phæ­<lb/> ra ambitur vnica tantum &longs;uperficie &longs;phærica. </s> <s id="s.001442">quando verò ex planis corpo­<lb/> ra generant, vt facit Plato in Timæo, accipíunt primò triangulum æquila­<lb/> terum, & ex quatuor triangulis æquilateris &longs;imul compactis conficiunt py­<lb/> ramidem; & hoc modo alia &longs;olida à pluribus &longs;uperficiebus ambita con&longs;ti­<lb/> tuunt: verum hac ratione nullo modo po&longs;&longs;unt &longs;phæram componere, quia <lb/> vnica tantum, <expan abbr="ea&qacute;">eaque</expan>; &longs;phærica &longs;uperficie compræhenditur: <expan abbr="atq;">atque</expan> hoc pacto i&longs;ti <lb/> diuidentes, & componentes corpora fidem faciunt, &longs;phæram, cum ex nullis <lb/> componatur, &longs;olidorum e&longs;&longs;e primam.</s> </p> <p type="main"> <s id="s.001443"><arrow.to.target n="marg106"/></s> </p> <p type="margin"> <s id="s.001444"><margin.target id="marg106"/>106</s> </p> <p type="main"> <s id="s.001445">Tex. 25. <emph type="italics"/>(Est autem, & &longs;ecundum numerorum ordinem a&longs;&longs;ignantibus, &longs;ic po­<lb/> nentibus rationabili&longs;&longs;imam, circulum quidem &longs;ecundum vnum; triangulum autem <lb/> &longs;ecundum dualitatem, quoniam duo recti. </s> <s id="s.001446">&longs;i autem &longs;ecundum triangulum, vnum. <lb/> </s> <s id="s.001447">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<lb/> fecta circulari linea comprehendatur: <expan abbr="Triangulũ">Triangulum</expan> verò &longs;ecundam, quoniam <lb/> duo anguli recti, ide&longs;t, quia triangulum habet tres angulos æquales duobus <lb/>rectis angulis; quod fusè explicatum e&longs;t lib. 1. Priorum, &longs;ecto 3. cap. 1. De­<lb/> mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir­<lb/> culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s> </p> <p type="main"> <s id="s.001448"><arrow.to.target n="marg107"/></s> </p> <p type="margin"> <s id="s.001449"><margin.target id="marg107"/>107</s> </p> <p type="main"> <s id="s.001450">Tex. 31. <emph type="italics"/>(At verò, quod aquæ &longs;uperficies talis &longs;it, manife&longs;tum e&longs;t hac &longs;uppo&longs;i­<lb/> tione &longs;umpta, quod apta natura e&longs;t &longs;emper confluere aqua ad magis concauum: ma­<lb/> gis autem concauum e&longs;t, quod centro propinquius est. </s> <s id="s.001451">ducantur ergo ex centro A,<emph.end type="italics"/><lb/> <figure id="id.009.01.078.1.jpg" place="text" xlink:href="009/01/078/1.jpg"/><lb/> <emph type="italics"/>linea A B, & linea A C, & producatur, in qua B C, <lb/> ducta igitur ad ba&longs;im linea, in qua A D, minor e&longs;t eis, <lb/> quæ ex centro. </s> <s id="s.001452">magis igitur concauus locus e&longs;t, quare <lb/> influet aqua, donec <expan abbr="vtiq;">vtique</expan> æquetur. </s> <s id="s.001453">æqualis e&longs;t autem eis, <lb/> quæ ex centro linea A E, quare nece&longs;&longs;e e&longs;t apud eas, quæ <lb/> ex centro, e&longs;&longs;e aquam, tunc enim quie&longs;cet. </s> <s id="s.001454">linea autem, <lb/> quæ eas, quæ ex centro tangit, circularis e&longs;t, &longs;phærica <lb/> igitur aquæ &longs;uperficies e&longs;t, in qua B E C.)<emph.end type="italics"/> toto hoc <lb/> textu lineari demon&longs;tratione probat aquæ manen­<lb/> tis &longs;uperficiem e&longs;&longs;e &longs;phæricam: quæ demon&longs;tratio <lb/> per&longs;picua euadit, &longs;i figura, quæ in codicibus tam <lb/> græcis, quam latinis, <expan abbr="atq;">atque</expan> etiam in commentarijs de&longs;ideratur, quemadmo­<lb/> dum fecimus, re&longs;tituatur. </s> <s id="s.001455">&longs;it igitur in præcedenti figura A, centrum mundi, <lb/> ex quo educantur duæ rectæ lineæ æquales A B, A C, quæ deinde alia recta <lb/> B C, coniungantur. </s> <s id="s.001456">educatur <expan abbr="quoq;">quoque</expan> recta alia ex centro A, quæ pertingat <lb/> ad B C, quæ ba&longs;is e&longs;t trianguli B A C, & producatur vlterius quantumlibet <lb/> in E. intelligatur demum circumferentia tran&longs;ire per puncta B, & C, quia <lb/> illæ duæ lineæ A B, A C, &longs;unt æquales, quæ circumferentia alteram A D, quæ <lb/> fuit protracta, &longs;ecet in E. <!-- KEEP S--></s> <s id="s.001457">Iam &longs;ic argumentatur: aqua natura &longs;ua &longs;emper <lb/>defluit ad locum magis concauum, ide&longs;t, ad loca centro A, terræ propin­<lb/> quiora, quale e&longs;&longs;et in figura locus D, re&longs;pectu locorum B, & C, quia A D, <lb/> linea minor e&longs;t ijs, quæ ex centro eductæ &longs;unt A B, A C. quapropter aqua <lb/>debet defluere ex B, ad D, vel ex C, ad idem D, donec pertingat ad E. qui <lb/> locus non e&longs;t decliuior punctis B, & C. quare cum loca B, E, C, quæ &longs;unt ex­ <pb pagenum="79" xlink:href="009/01/079.jpg"/>trema linearum, &longs;int æquè decliuia, nece&longs;&longs;e e&longs;t aquæ &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<lb/> mus aquam manentem, & quietam, ergo quie&longs;cit circa puncta B, E, C, à <lb/> centro terræ æquidi&longs;tantia, per quæ 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;phærica: &longs;ed &longs;uperfi­<lb/> cies aquæ tran&longs;it per talia loca, ergo &longs;phærica e&longs;t. </s> <s id="s.001458">Huius etiam habes acu­<lb/> ti&longs;&longs;imam Archimedis demon&longs;trationem initio libelli de ijs, quæ vehuntur <lb/> in aqua, quam in &longs;uam &longs;phæram retulit Clauius.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001459"><arrow.to.target n="marg108"/></s> </p> <p type="margin"> <s id="s.001460"><margin.target id="marg108"/>108</s> </p> <p type="main"> <s id="s.001461">Tex. 46. <emph type="italics"/>(Reliquum e&longs;t orbes quidem moueri, stellas verò quie&longs;cere, & infixas <lb/> ip&longs;is orbibus ferri; &longs;olum enim &longs;ic nullum ab&longs;urdum accidit. </s> <s id="s.001462">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, & in circularibus: maius <lb/> enim e&longs;t eorum, quæ auferuntur ab eis, quæ ex centro, maioris circuli &longs;egmentum)<emph.end type="italics"/><lb/> ex intellectione vltimæ periodi textus totius intelligentia pendet: &longs;it igitur <lb/> <figure id="id.009.01.079.1.jpg" place="text" xlink:href="009/01/079/1.jpg"/><lb/> figura præ&longs;ens, in qua cum &longs;int duo circuli concen­<lb/> trici, vnus altero maior, <expan abbr="eductæ&qacute;">eductæque</expan>; &longs;int ex <expan abbr="c&etilde;tro">centro</expan> duæ <lb/> &longs;emidiametri A D, A E, quæ <expan abbr="vtrunq;">vtrunque</expan> circulum &longs;e­<lb/> cant, apparet maius e&longs;&longs;e <expan abbr="&longs;egmentũ">&longs;egmentum</expan> D E, quod è ma­<lb/> iori circulo &longs;emidiametri ex <expan abbr="c&etilde;tro">centro</expan> eductæ auferunt, <lb/> quam &longs;egmentum B C, minoris circuli, quod ei&longs;dem <lb/>&longs;emidiametris intercipitur. </s> <s id="s.001463">Verumtamen &longs;i circuli <lb/> ambo &longs;imul moueantur, maior circulus æquali tem­<lb/> pore maius illud &longs;patium D E, & minor minus B C, <lb/> pertran&longs;ibit: idem igitur de cœle&longs;tibus orbibus di­<lb/> cendum, qui quamuis omnes diurnum &longs;imul motum <lb/> ab&longs;oluunt, maiores tamen celerius conuertuntur: quo fit, vt &longs;tellæ maiori­<lb/> bus circulis infixæ, <expan abbr="atq;">atque</expan> delatæ, maiori celeritate &longs;uos cur&longs;us peragant, ne­<lb/> que oportet eas, dum mouentur cœlum di&longs;&longs;ecare, quod accideret, &longs;i pro­<lb/>prio motu veluti pi&longs;ces per aquam progrederentur.</s> </p> <p type="main"> <s id="s.001464">Hæc quidem Ari&longs;t. con&longs;entanea ob&longs;eruationibus veterum A&longs;tronomo­<lb/> rum; at verò illis no&longs;træ ætatis ob&longs;eruationes repugnant; præ&longs;ertim illæ, <lb/> quæ fiunt circa &longs;tellas errantes: ex quibus fatendum e&longs;&longs;e videtur, Cœlum, <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> <s id="s.001465">Tycho <expan abbr="namq;">namque</expan> Brahe, <expan abbr="alij&qacute;">alijque</expan>; plures exactè <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&etail;lú deberent perforare; ijdem o&longs;ten­<lb/> dunt nonnullos Planetas, Martem præ&longs;ertim, ac Venerem modo &longs;upra So­<lb/> lem, modo infra a&longs;cendere, & de&longs;cendere. </s> <s id="s.001466">Idem patet ex ob&longs;eruatione no­<lb/> ua per nouum Tele&longs;copij i <expan abbr="&longs;trum&etilde;tum">&longs;trumentum</expan> in Venere facta, quæ lunulata <expan abbr="vtrinq;">vtrinque</expan> <lb/> à Sole apparet: quando nimirum e&longs;t in imo epicyclo. </s> <s id="s.001467"><expan abbr="iterum&qacute;">iterumque</expan>; rotunda ve­<lb/> luti Luna plena, cum in &longs;ummo epicyclo ver&longs;atur: quæ minimè apparerent, <lb/> ni&longs;i &longs;upra, ac infra Solem circumiret. </s> <s id="s.001468">His rationibus conantur ip&longs;i proba­<lb/> re Cœlum e&longs;&longs;e liquidum; <expan abbr="atq;">atque</expan> in eo Planetas, veluti aues in aere, permeare: <lb/>quarum &longs;olutio mihi nulla occurrit, alijs forta&longs;&longs;is occurret.</s> </p> <p type="main"> <s id="s.001469"><arrow.to.target n="marg109"/></s> </p> <p type="margin"> <s id="s.001470"><margin.target id="marg109"/>109</s> </p> <p type="main"> <s id="s.001471">Tex. 57. <emph type="italics"/>(De ordine autem ip&longs;orum, quo quidem modo &longs;ingula di&longs;ponantur, vt <lb/> quædam &longs;int priora, quædam posteriora, & quomodo &longs;patijs &longs;e ă<expan abbr="habeãt">habeant</expan> ad inuicem,<emph.end type="italics"/> <pb pagenum="80" xlink:href="009/01/080.jpg"/><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> <s id="s.001472">Dicit igi­<lb/> tur ordinem cœlorum, ac &longs;yderum, item &longs;itum, & proportiones magnitu­<lb/>dinum eorundem, cum per naturalis &longs;cientiæ principia &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<lb/> &longs;trentur</expan>. </s> <s id="s.001473">& meritò quidem hæc dicuntur; po&longs;teriores enim ab Ari&longs;t. ordines, <lb/> &longs;itus, ac magnitudines tam cœlorum, quam &longs;yderum firmis rationibus, <expan abbr="atq;">atque</expan> <lb/> inuentu peracutis demon&longs;trarunt. </s> <s id="s.001474">quorum princeps fuit ptolæmeus; no&longs;tra <lb/> tamen ætate Tycho Brahe, qui certis ob&longs;eruationibus, quas maximo labo­<lb/> re, ac &longs;umptu exantlauit, in nonnullis à Ptolæmeo, ac reliquis di&longs;&longs;entjt: &longs;tan­<lb/> dum autem e&longs;&longs;e recentioribus ob&longs;eruationibus apud A&longs;tronomiæ peritos in <lb/> confe&longs;&longs;o e&longs;t.</s> </p> <p type="main"> <s id="s.001475"><arrow.to.target n="marg110"/></s> </p> <p type="margin"> <s id="s.001476"><margin.target id="marg110"/>110</s> </p> <p type="main"> <s id="s.001477">Tex. <emph type="italics"/>(Luna autem o&longs;tenditur per ea, quæ circa vi&longs;um, quod &longs;phærica &longs;it: non <lb/> enim <expan abbr="vtiq;">vtique</expan> fieret accre&longs;cens, & decre&longs;cens, plurimŭm quidem alter a ex parte curua, <lb/> altera concaua, aut <expan abbr="vtrmq;">vtrinque</expan> curua, &longs;emel autem bipartita)<emph.end type="italics"/> ait per ea, quæ circa <lb/> vi&longs;um, ide&longs;t per opticem probari Lunam e&longs;&longs;e &longs;phæricam: &longs;ed con&longs;ule, quæ <lb/> primo Po&longs;ter. tex. <!-- REMOVE S-->3. de hac re &longs;crip&longs;i, & plenam etiam huius loci intelligen­<lb/> tiam a&longs;&longs;equeris, præ&longs;ertim &longs;i experimentum ibi traditum inieris.</s> </p> <p type="main"> <s id="s.001478"><arrow.to.target n="marg111"/></s> </p> <p type="margin"> <s id="s.001479"><margin.target id="marg111"/>111</s> </p> <p type="main"> <s id="s.001480">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 lunulæ <lb/>&longs;peciem præfeferentes. </s> <s id="s.001481">Quare &longs;i vnum est tale, palam e&longs;t, quod & alia <expan abbr="vtiq;">vtique</expan> erunt <lb/> talia)<emph.end type="italics"/> &longs;icuti <expan abbr="præced&etilde;s">præcedens</expan> &longs;phæricitatis Lunæ ratio ex Per&longs;pectiua de&longs;umpta e&longs;t, <lb/> ita præ&longs;ens ex A&longs;tronomia, ex eò enim, quod eclyp&longs;is Solis habeat figuram <lb/> lunulæ, ide&longs;t, &longs;i in&longs;tar Lunæ falcatæ, probant A&longs;tronomi Lunam e&longs;&longs;e &longs;phæri­<lb/> cam. </s> <s id="s.001482">intellige tamen partem illam Solis, quæ non eclyp&longs;atur, habere figu­<lb/> ram lunulæ, pars enim à Luna obumbrata non videtur, et&longs;i videretur oua­<lb/>lem quandam &longs;peciem, præ&longs;eferret: pars igitur, illa e&longs;t corniculata, quia <lb/> <figure id="id.009.01.080.1.jpg" place="text" xlink:href="009/01/080/1.jpg"/><lb/> cum Solis defectio ex interpo&longs;itione Lunæ inter nos, & <lb/> Solem contingat, & Luna &longs;it &longs;phærica, nece&longs;&longs;ariò &longs;phæ­<lb/> ricè, & circulariter Solem obumbrabit; quare pars illa <lb/> non obumbrata remanet falcata, & corniculata, vt in <lb/>præ&longs;enti figura videre e&longs;t; vbi cernis, Lunam Solem or­<lb/> biculariter offu&longs;care in linea A D C, partem Solis de­<lb/> tectam <expan abbr="contentã">contentam</expan> lineis curuis A B C D, e&longs;&longs;e lunularem, <lb/> & falcatam; cum ergo in hunc modum fiat Solis deli­<lb/> quium, &longs;ignum certum e&longs;t, Lunam e&longs;&longs;e &longs;phæricam.</s> </p> <p type="main"> <s id="s.001483"><arrow.to.target n="marg112"/></s> </p> <p type="margin"> <s id="s.001484"><margin.target id="marg112"/>112</s> </p> <p type="main"> <s id="s.001485">Tex. 107. <emph type="italics"/>(Quod autem dubitatur, hoc e&longs;t; videre autem non e&longs;t difficile, &longs;i pa­<lb/> rum con&longs;iderauerimus, & di&longs;tinxerimus, quonam modo cen&longs;eamus quantamuis ma­<lb/> gnitudinem grauem ad medium ferri. </s> <s id="s.001486">manife&longs;tum enim e&longs;t, quod non quou&longs;que ex­<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 compræhendat; <expan abbr="hucn&longs;q;">hucu&longs;que</expan> enim habet propen&longs;ionem)<emph.end type="italics"/> &longs;en&longs;us Ari&longs;to­<lb/> telis e&longs;t, debere nos exi&longs;timare, quod &longs;i quæpiam grauis magnitudo de&longs;cen­<lb/>dat ad centrum mundi, eam non perman&longs;uram, &longs;tatim ac ip&longs;ius extremum <lb/>centrum mundi attigent; &longs;ed eò <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 à centro <lb/> mundi æquè emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb pagenum="81" xlink:href="009/01/081.jpg"/><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 reliquæ ip&longs;ius partes <lb/> adhuc grauitarent, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; vlterius primam partem impellerent, donec lapi­<lb/>dis medium, mundi medio congrueret: quo facto lapis quie&longs;ceret. </s> <s id="s.001487">quæ num <lb/> vera &longs;int, vt intelligamus, oportet prius præmittere, 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> <s id="s.001488">centrum molis e&longs;t illud pun­<lb/> ctum, à quo extrema æquidi&longs;tant: centrum grauitatis e&longs;t punctum illud, à <lb/> quo extrema æque ponderant, &longs;iue à quo graue &longs;u&longs;pen&longs;um æquè ponderat, <lb/> &longs;iue in æquilibrio manet. </s> <s id="s.001489">Porrò in corporibus regularibus, &longs;i vniformia &longs;int <lb/> idem, & vnum &longs;unt centrum molis, ac centrum grauitatis: vt in &longs;phæra <lb/>plumbea, idem erit <expan abbr="vtrumq;">vtrumque</expan> centrum: &longs;i verò difformia &longs;int in grauitate, <lb/> vt in &longs;phæra partim plumbea, partim lignea, diuer&longs;um erit centrum molis, <lb/> à centro grauitatis; illud enim erit in medio &longs;phæræ; centrum verò graui­<lb/> tatis in parte plumbea exi&longs;tet. </s> <s id="s.001490">In corporibus deinde irregularibus, etiam&longs;i <lb/> &longs;int vniformis ponderis, aliud tamen e&longs;&longs;e pote&longs;t centrum molis à <expan abbr="c&etilde;tro">centro</expan> gra­<lb/> uitatis, vt in corpore oblongo, cuius alterum extremum &longs;it reliquis parti­<lb/> bus multò maius, vti e&longs;t claua: vbi centrum molis erit in medio longitudi­<lb/> nis clauæ; centrum verò grauitatis, erit propinquius capiti clauæ. </s> <s id="s.001491">quando <lb/> igitur Ari&longs;t. ait, graue de&longs;cen&longs;urum, donec ip&longs;ius medium, &longs;iue centrum, <lb/> mundi centrum attingat; benè dicit, &longs;i de medio grauitatis intelligat; ma­<lb/> lè autem &longs;i de medio molis. </s> <s id="s.001492">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="attingãt">attingant</expan> cen­<lb/> trum mundi &longs;emper grauitabunt, & mouebuntur. </s> <s id="s.001493">Verum enim verò ex an­<lb/> tiquorum monumentis manife&longs;tum e&longs;t, Archimedem, qui multò po&longs;t Ari­<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/> & perinde non <expan abbr="v&longs;quequaq;">v&longs;quequaque</expan> verè.</s> </p> <p type="main"> <s id="s.001494"><arrow.to.target n="marg113"/></s> </p> <p type="margin"> <s id="s.001495"><margin.target id="marg113"/>113</s> </p> <p type="main"> <s id="s.001496">Tex. 109. <emph type="italics"/>(Præterea <expan abbr="quoq;">quoque</expan> & per ea, quæ apparent &longs;ecundum &longs;en&longs;um, neque <lb/> enim Lunæ eclyp&longs;es tales <expan abbr="haber&etilde;t">haberent</expan> deci&longs;iones; nunc enim in ijs, quæ &longs;ecundum men­<lb/> &longs;em fiunt, figurationibus, omnes accipit diui&longs;iones: etenim recta fit, & vtrinque <lb/> curua, & concaua)<emph.end type="italics"/> probat terram e&longs;&longs;e &longs;phæricam ratione a&longs;tronomica, ex <lb/> Lunæ 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, quæ in eclyp&longs;i ob&longs;curantur, & qua&longs;i à Luna re&longs;ecantur. </s> <s id="s.001497">quam­<lb/> uis enim &longs;ingulis men&longs;ibus Luna terminetur modo linea concaua, vt quan­<lb/> do noua e&longs;t; modo recta, vt quando diuidua e&longs;t: modo vtrinque curua, vt <lb/>cum à diuidua ad plenilunium tendit. </s> <s id="s.001498">quod fu&longs;ius primo Po&longs;ter. tex. <!-- REMOVE S-->30. ex­<lb/> po&longs;ui. </s> <s id="s.001499">in eclyp&longs;ibus tamen &longs;emper curuam habet lineam illam, quæ partem <lb/>eclyp&longs;atam de&longs;init; vt paulo po&longs;t explicabo. </s> <s id="s.001500">Vide precedentem textum 59. <lb/> & ca, quæ ibi annotaui, <expan abbr="quæq;">quæque</expan> tibi propo&longs;ui, & plenam huius loci intelligen­<lb/> tiam a&longs;&longs;equeris. </s> <s id="s.001501">vide etiam, quæ mox &longs;ubdam circa huius loci reliquum.</s> </p> <p type="main"> <s id="s.001502"><arrow.to.target n="marg114"/></s> </p> <p type="margin"> <s id="s.001503"><margin.target id="marg114"/>114</s> </p> <p type="main"> <s id="s.001504">Ibidem <emph type="italics"/>(Circa autem eclyp&longs;es, &longs;emper curuam habet terminătem lineam: qua­<lb/>re quoniam eclyp&longs;im patitur propter terræ obiectionem, terræ <expan abbr="circumfer&etilde;tia">circumferentia</expan> &longs;phæ­<lb/> rica exi&longs;tens, figuræ cau&longs;a erit)<emph.end type="italics"/> probat rotunditatem terræ ab eclyp&longs;i lunari, <lb/> ex eo, quod Luna &longs;phæricè eclyp&longs;etur, quod innuitur illis verbis, &longs;emper <pb pagenum="82" xlink:href="009/01/082.jpg"/>curuam habet terminantem lineam, linea &longs;cilicet, quæ terminat partem <lb/> eclyp&longs;atam à non eclyp&longs;ata, &longs;emper apparet circularis; cum autem hæc li­<lb/> nea &longs;it terminus vmbræ terræ, quæ lumen obumbrat, &longs;ignum <expan abbr="manife&longs;tũ">manife&longs;tum</expan> e&longs;t <lb/> vmbram ip&longs;am e&longs;&longs;e rotundam; nam cum Luna deficiat propter terræ obie­<lb/> ctionem inter ip&longs;am, & Solem, ita, vt vmbra terræ protendatur <expan abbr="v&longs;q;">v&longs;que</expan> ad Lu­<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 terræ fiat, orbiculariter eam contegit, &longs;ignum <lb/> per&longs;picuum e&longs;t terram proijcere quoquouer&longs;us vmbram rotundam, quæ vt <lb/> in &longs;phæra o&longs;tenditur, e&longs;t rotunda ad modum coni; cum ergo vmbra terræ <lb/> ex quauis parte proijciatur, &longs;it rotunda, certò certius colligitur, <expan abbr="terram&qacute;">terramque</expan>; <lb/> <expan abbr="quoq;">quoque</expan> ip&longs;am rotunda figura præditam e&longs;&longs;e. </s> <s id="s.001505">hanc eandem rationem, &longs;i libue­<lb/> rit, fu&longs;ius pertractatam videre poteris apud P. <!-- REMOVE S-->Clauium in &longs;phæra.</s> </p> <p type="main"> <s id="s.001506"><arrow.to.target n="marg115"/></s> </p> <p type="margin"> <s id="s.001507"><margin.target id="marg115"/>115</s> </p> <p type="main"> <s id="s.001508">Tex. <emph type="italics"/>(Præterea per astrorum apparentiam, non &longs;olum manife&longs;tum e&longs;t, quod re<lb/>tunda, &longs;ed & quod magnitudine non magna &longs;it; paruo enim facto nobis tran&longs;itu ad <lb/>meridiem, & Vr&longs;am, manife&longs;tè fit alter horizon circulus, ita vt a&longs;tra, quæ &longs;uper <lb/>caput, magnam habeant mutationem, & non eadem appareant, & ad Vr&longs;am, & ad <lb/>meridiem tran&longs;euntibus, quædam enim in Aegypto quidem stellæ <expan abbr="vid&etilde;tur">videntur</expan>, & cir­<lb/> ca Cyprum, in ijs autem, quæ ad Vr&longs;am vergunt regionibus, non <expan abbr="via&etilde;tur">videntur</expan>. </s> <s id="s.001509">& a&longs;tro­<lb/> rum ea, quæ &longs;emper in ijs, quæ ad Vr&longs;am vergunt, apparent, in illis locis occidunt. <lb/> </s> <s id="s.001510">Quare non &longs;olum ex his manife&longs;tum e&longs;t rotundam e&longs;&longs;e figuram terræ, &longs;ed & &longs;phæræ <lb/> non magnæ: non enim tam celeriter in&longs;igne quippiam faceret, tran&longs;latis nobis adeò <lb/> parum)<emph.end type="italics"/> hic textus ei, qui &longs;phæram mundi audiuerit perfacilis e&longs;t: propte­<lb/> rea eum breuiter &longs;ic paraphra&longs;ticè exponam. </s> <s id="s.001511">Terram e&longs;&longs;e rotundam, <expan abbr="atq;">atque</expan> <lb/> re&longs;pectu cœle&longs;tium corporum non magnam, &longs;ignum e&longs;t, quod facto à 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<lb/>tione a&longs;trorum, nam quæ in primo loco &longs;upra no&longs;trum verticem <expan abbr="trã&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 id="id.009.01.082.1.jpg" place="text" xlink:href="009/01/082/1.jpg"/><lb/>ex facto quamuis paruo itinere tran&longs;eunt. </s> <s id="s.001512">&longs;it in <lb/> præ&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;trorũ">a&longs;trorum</expan> ver&longs;icalium B, in C, quæ mul­<lb/> tum ab inuicem di&longs;tant. </s> <s id="s.001513">&longs;i autem terra e&longs;&longs;et <lb/> maior, v. <!-- REMOVE S-->g. <!-- REMOVE S-->circulus medius, tunc facta maio­<lb/> ri mutatione ex D, in E, fieret eadem a&longs;trorum <lb/> variatio ex B, in C; &longs;ed cum nos experiamur <lb/>fieri magnam a&longs;trorum mutationem, ex parua <lb/> locorum intercapedine, &longs;ignum e&longs;t magnope­<lb/> re mutari horizontem, ac proinde terram e&longs;&longs;e <lb/> rotundam, ac re&longs;pectu cœle&longs;tium corporum <lb/> paruam. </s> <s id="s.001514">aliud præterea &longs;ignum huius horizontis permutationis e&longs;t, quod <lb/> &longs;tellæ, quæ in priori loco &longs;upra horizontem apparebant, mutato paululum <lb/> loco ad alterutram plagam, &longs;tatim ab&longs;conduntur; aliæ verò nouæ <expan abbr="appar&etilde;t">apparent</expan> <lb/>vt in Aegypto, & Cypro, &longs;tella, quæ dicitur Canobus &longs;upra horizontem <lb/> a&longs;cendit; quæ &longs;i paululum Vr&longs;am, &longs;eu &longs;eptentrionem ambulaueris, &longs;tatim <lb/> latitabit. </s> <s id="s.001515">Demum eiu&longs;dem citæ mutationis finitoris indicium etiam &longs;it,<pb pagenum="83" xlink:href="009/01/083.jpg"/>quod regiones &longs;eptentrionales incolentibus plurima &longs;unt a&longs;tra, quæ nun­<lb/>quam occidunt, quamuis horizontem leuiter per&longs;tringant, quæ tamen Cy­<lb/> prijs, <expan abbr="atq;">atque</expan> Aegyptijs oriuntur, <expan abbr="atq;">atque</expan> occidunt. </s> <s id="s.001516">ex quibus & rotunditas, & <lb/> paruitas terræ colligi pote&longs;t. </s> <s id="s.001517">has ea&longs;dem rationes fu&longs;ius explicatas repe­<lb/> ries apud P. <!-- REMOVE S-->Clauium in &longs;phæra.</s> </p> <p type="main"> <s id="s.001518"><arrow.to.target n="marg116"/></s> </p> <p type="margin"> <s id="s.001519"><margin.target id="marg116"/>116</s> </p> <p type="main"> <s id="s.001520">Tex. 111. <emph type="italics"/>(Quapropter existimantes eum, qui circa Herculeas columnas e&longs;t lo­<lb/>cum coniungi ei, qui circa Indiam, & hoc modo mare vnum e&longs;&longs;e, non admodum <lb/> incredibilia exi&longs;timare videntur &c.)<emph.end type="italics"/> exi&longs;timatores ho&longs;ce non perperam exi­<lb/> &longs;tima&longs;&longs;e apertè <expan abbr="cõuincunt">conuincunt</expan> Chri&longs;tophori Columbi, Argonautarum principis <lb/> nauigationes; quibus nouus orbis repertus e&longs;t, qui inter columnas Hercu­<lb/> lis, <expan abbr="atq;">atque</expan> orientalem Indiam totus vna <expan abbr="cũ">cum</expan> mari Oceano Atlantico interiacet.</s> </p> <p type="main"> <s id="s.001521"><arrow.to.target n="marg117"/></s> </p> <p type="margin"> <s id="s.001522"><margin.target id="marg117"/>117</s> </p> <p type="main"> <s id="s.001523">Tex. 112. <emph type="italics"/>(Mathematicorum etiam, qui circumferentiæ magnitudinem ratio­<lb/>cinari tentant, ad 400. dicunt &longs;tadiorum millia, &c.)<emph.end type="italics"/> quam &longs;ubtilibus rationi­<lb/> bus inue&longs;tigauerint A&longs;tronomi quantitatem terræ, optimè, ac dilucidè ex­<lb/> ponitur à P. <!-- REMOVE S-->Clauio in &longs;phæra: quem &longs;i libet, con&longs;ule, ne inani labore opu­<lb/> &longs;culum i&longs;tud exere&longs;cat.</s> </p> </chap> <chap> <p type="head"> <s id="s.001524"><emph type="italics"/>Ex Tertio de Cœlo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001525"><arrow.to.target n="marg118"/></s> </p> <p type="margin"> <s id="s.001526"><margin.target id="marg118"/>118</s> </p> <p type="main"> <s id="s.001527">Tex. 40. <emph type="italics"/>(Figuræ autem omnes componuntur ex pyramidibus: rectilinea <lb/>quidem ex rectilineis: &longs;phæra verò ex octo partibus componitur)<emph.end type="italics"/> Ale­<lb/>xander exi&longs;timat, Ari&longs;totelem dicere &longs;phæram con&longs;tare ex octo <lb/> partibus illis, quæ de&longs;ignantur per tres circulos, quorum duo &longs;e­<lb/>cant &longs;e mutuò ad angulos rectos, vt in &longs;phæra mundi faciunt duo coluri; <lb/> tertius verò medios illos diuidit æquidi&longs;tanter à &longs;ectionibus <expan abbr="illorũ">illorum</expan> mutuis, <lb/> quemadmodum æquator in &longs;phæra mundi &longs;ecat duos coluros. </s> <s id="s.001528">ex quibus &longs;e­<lb/> ctionibus tota &longs;phæra in octo partes diuiditur, quibus &longs;phæram componi <lb/> vult Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.001529">aduerte tamen hanc &longs;phæræ compo&longs;itionem nullo modo <lb/> habere partes actu, cum &longs;phæra &longs;it vnica &longs;implici &longs;uperficie terminata; &longs;ed <lb/> quæ tantum &longs;int à prædictis imaginatis circulis de&longs;ignatæ: at verò aliæ fi­<lb/> guræ, quæ pluribus planis terminantur, vt cubus, octaedrum, & &longs;imilia, quæ <lb/>Ari&longs;t. vocat rectilineas, quia terminantur &longs;uperficiebus rectilineis actu di­<lb/> &longs;tinctis ab inuicem ex natura &longs;ua, non per no&longs;tram de&longs;ignationem, ideò re­<lb/> ctè 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<lb/> larum &longs;ingulas pyramides erigi, quarum omnium vertices ad idem punctum <lb/> medium intra cubum imaginatum coeant. </s> <s id="s.001530">& &longs;ic de reliquis &longs;olidis. </s> <s id="s.001531">quæ qua <lb/> ratione re&longs;oluantur in plures pyramides, con&longs;tat ex 10. 11. 12. & 13. Ele­<lb/> mentorum Euclidis, at verò in &longs;phæra nullum reale compo&longs;itionis, aut di­<lb/> ui&longs;ionis fundamentum reperitur.</s> </p> <p type="main"> <s id="s.001532"><arrow.to.target n="marg119"/></s> </p> <p type="margin"> <s id="s.001533"><margin.target id="marg119"/>119</s> </p> <p type="main"> <s id="s.001534">Tex. <emph type="italics"/>(Ad hæc 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;imis &longs;cientijs; nam Mathematicæ ip&longs;um quidem intelligibile, accipiunt diui­<lb/> &longs;ibile)<emph.end type="italics"/> ip&longs;um intelligibile, ide&longs;t, quantitatem ab&longs;tractam tam continuam, <lb/>quam di&longs;cretam, quam &longs;tatuunt Philo&longs;ophi e&longs;&longs;e &longs;ubiectam materiam ma­<lb/> thematicarum. </s> <s id="s.001535">quam ideo appellant intelligibilem, quia cum &longs;it ab&longs;tracta <lb/> per intellectum à &longs;en&longs;ibilibus affectionibus, re&longs;tat vt &longs;it tantummodo intel­ <pb pagenum="84" xlink:href="009/01/084.jpg"/>lectu perceptibilis. </s> <s id="s.001536">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"> <s id="s.001537"><arrow.to.target n="marg120"/></s> </p> <p type="margin"> <s id="s.001538"><margin.target id="marg120"/>120</s> </p> <p type="main"> <s id="s.001539">Tex. 66. <emph type="italics"/>(Omninò autem eniti &longs;implicibus corporibus figuras tribuere irratio­<lb/> nabile e&longs;t. </s> <s id="s.001540">primò quidem, quia accidit non repleri totum; nam in planis tres figuræ <lb/> videntur implere locum, Triangulus, Quadratum, & Sexangulus)<emph.end type="italics"/> per &longs;implicia <lb/> corpora intelligit quatuor elementa. </s> <s id="s.001541">Vult enim probare quatuor elemen­<lb/> ta non habere figuras illas mathematicas, quas illis Plato tribuebat, vt au­<lb/> tem Ari&longs;t. rationem probè percipiamus, &longs;ciendum, quod implere totum, <lb/> &longs;iue locum, illæ figuræ dicuntur, quæ &longs;imul &longs;uis angulis in plano quopiam ad <lb/> vnum, <expan abbr="atq;">atque</expan> idem punctum vnitæ locum illum totum, qui circa punctum il­<lb/> lud con&longs;i&longs;tit, <expan abbr="cõtegunt">contegunt</expan>, ita vt nihil vacui inter ip&longs;as relinquatur. </s> <s id="s.001542">tales &longs;unt, <lb/> quibus fieri po&longs;&longs;unt pauimenta, oportet enim, vt &longs;imul vnitæ nihil vacui in <lb/> pauimento relinquant. </s> <s id="s.001543">huiu&longs;modi &longs;unt triangula æquilatera (de his enim <lb/> intelligendus e&longs;t textus) quadrata, & hexagona, &longs;iue &longs;exilatera regularia; <lb/> <figure id="id.009.01.084.1.jpg" place="text" xlink:href="009/01/084/1.jpg"/><lb/> nam &longs;ex triangula æquilatera &longs;imul iuncta in plano paui­<lb/> re po&longs;&longs;unt, vt patet in figura præ&longs;enti; ratio huius e&longs;t, <lb/> quia omnes anguli circa idem punctum (y. </s> <s id="s.001544">g. <!-- REMOVE S-->A, in hac <lb/> figura) in plano, quotquot fuerint con&longs;tituti, &longs;unt æqua­<lb/> les quatuor rectis, ex coroll. </s> <s id="s.001545">&longs;ecundo 15. primi Elemen­<lb/> ti: cum igitur &longs;ex anguli, trianguli æquilateri <expan abbr="æquiualeãt">æquiualeant</expan> <lb/> quatuor rectis angulis, con&longs;tituti omnes circa punctum <lb/> A, totum locum circa illud implere po&longs;&longs;unt. </s> <s id="s.001546">Quadratum etiam replere lo­<lb/> <figure id="id.009.01.084.2.jpg" place="text" xlink:href="009/01/084/2.jpg"/><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;int recti, &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"> <s id="s.001547">Hexagonum quoque regulare, ide&longs;t æquilaterum, & <lb/> æquiangulum idem præ&longs;tare pote&longs;t; cum enim tres angu­<lb/> li ip&longs;ius æquiualeant quatuor rectis, &longs;i tria hexagona ad <lb/> idem punctum A, vt in figura adaptentur, nece&longs;&longs;ariò ni­<lb/> hil vacui inter ip&longs;a relinquetur, vt in figura hac o&longs;tenditur. </s> <s id="s.001548">præter has tres <lb/> <figure id="id.009.01.084.3.jpg" place="text" xlink:href="009/01/084/3.jpg"/><lb/>figuras, nulla alia reperitur, quæ i&longs;tud efficere po&longs;­<lb/> &longs;it. </s> <s id="s.001549">cuius demon&longs;trationem perfectam videre pote­<lb/> ris in fine commentarij P. <!-- REMOVE S-->Clauij &longs;uper 4. Elem. nos <lb/> ea tantum attingimus, quæ percipi po&longs;&longs;int ab homi­<lb/> ne vix mathematicis tincto: &longs;ed tamen, quæ &longs;en&longs;um <lb/> Ari&longs;totelis patefaciunt. </s> <s id="s.001550">Aliæ porrò figuræ replen­<lb/> tes locum planum, quibus aliquando Architectores <lb/> vtuntur, vel &longs;unt irregulares, vel ad prædictas redu­<lb/> ci po&longs;&longs;unt. </s> <s id="s.001551">cum igitur tres tantum ex figuris planis <lb/> totum repleant, hæ &longs;olæ poterunt elementis attri­<lb/> bui, ac propterea non &longs;ufficient, ni&longs;i pro tribus elementis. </s> <s id="s.001552">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" xlink:href="009/01/085.jpg"/> <p type="head"> <s id="s.001553"><emph type="italics"/>Admirabilis quædam A&pgrave;um industria.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001554">Cæterum occa&longs;ione harum figurarum illud hoc loco apponere vi­<lb/> &longs;um e&longs;t, quod Pappus <expan abbr="Alexãdrinus">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> <s id="s.001555">cum enim vellent omne vacuum excludere, & præterea capaci&longs;&longs;imam <expan abbr="om-niũ">om­<lb/> nium</expan> figuram habere, hexagonam accepere, quæ inter prædictas tres vtrum­<lb/> que præ&longs;tat, nam & inane omne excludit, & 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;phæra, necnon in Geometria pra­<lb/> ctica. </s> <s id="s.001556">hoc ideò libentius recen&longs;ui, quia animaduerti naturales hi&longs;toriogra­<lb/> phos omnes latere, vel ip&longs;um Aldobrandum no&longs;trum, qui quamuis indu­<lb/> &longs;trio&longs;æ Apis in&longs;tar omnia delibauerit, i&longs;tud tamen de Apibus artificium tan­<lb/> ta &longs;apientia plenum, ne&longs;cio quo modo prætermi&longs;it.</s> </p> <p type="main"> <s id="s.001557"><arrow.to.target n="marg121"/></s> </p> <p type="margin"> <s id="s.001558"><margin.target id="marg121"/>121</s> </p> <p type="main"> <s id="s.001559">Ibidem <emph type="italics"/>(In &longs;olidis verò duæ &longs;olum pyramis, & cubus)<emph.end type="italics"/> ide&longs;t replent locum <lb/> &longs;olidum. </s> <s id="s.001560">nullum reperi, qui in hoc loco explicando non errauerit; nam Græ­<lb/> ci, qui alioqui &longs;olent mathematica probè intelligere, hic omnes lap&longs;i &longs;unt, <lb/> <expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; & Arabes, & Latinos in <expan abbr="eãdem">eandem</expan> foueam &longs;upra &longs;e mi&longs;erè traxerunt. <lb/> </s> <s id="s.001561">communis ferè error omnium fuit, pyramides plures &longs;imul compactas po&longs;­<lb/> &longs;e replere &longs;olidum locum. </s> <s id="s.001562">quod vt melius intelligamus, &longs;ciendum e&longs;t, reple­<lb/> re locum <expan abbr="&longs;olidũ">&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<lb/> ctum illud omninò occupent, hoc e&longs;t, nihil vacui inter ip&longs;a relinquatur: &longs;i­<lb/> cut enim prædictæ tres figuræ planæ, de quibus paulò ante, replent locum <lb/>planum, ide&longs;t &longs;uperficiem; 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<lb/>&longs;tituant corpus &longs;olidum ex octo illius con&longs;tatum, <expan abbr="nihil&qacute;">nihilque</expan>; inane inter ip&longs;os <lb/> cubos relinquatur. </s> <s id="s.001563">& &longs;icuti planæ illæ figuræ erant conficiendis pauimentis <lb/> aptæ, ita &longs;olidæ hæ muris, qui corpora &longs;unt &longs;olida, <expan abbr="con&longs;tru&etilde;dis">con&longs;truendis</expan> idonea &longs;unt. <lb/> </s> <s id="s.001564"><expan abbr="Notã">Notam</expan> dum præterea, quod per pyramidem debemus intelligere pyramidem <lb/> regularem, quæ dicitur etiam Tetraedrum, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;ecunda inter <expan abbr="quinq;">quinque</expan> cor­<lb/> pora regularia rectilinea, quæ alias Platonica corpora dicuntur. </s> <s id="s.001565"><expan abbr="eorum&qacute;">eorumque</expan>; <lb/>definitiones &longs;unt in 11. Elem. <!-- KEEP S--></s> <s id="s.001566">Tetraedrum autem &longs;ic definitur, e&longs;t figura &longs;o­<lb/> lida &longs;ub quatuor triangulis æquilateris, <expan abbr="atq;">atque</expan> inuicem æqualibus contenta: <lb/> de hac inquam e&longs;t &longs;ermo. </s> <s id="s.001567">quia &longs;i liceret intelligere de irregularibus figuris, <lb/>infinitæ reperirentur figuræ tam planæ, quam &longs;olidæ, quæ vtrumque locum <lb/> complerent. </s> <s id="s.001568">Aduertendum tandem Ari&longs;t. videri loqui de repletione loci <lb/> &longs;olidi, quia tran&longs;it à planïs figuris ad &longs;olidas. </s> <s id="s.001569">& quia &longs;i hæ duæ pyramis, & <lb/>cubus replent locum &longs;olummodo &longs;ecundum &longs;uas &longs;uperficies, quæ &longs;unt trian­<lb/> gulum, & quadratum, iam de his cum proximè ante dixi&longs;&longs;et, quid opus fui&longs;­<lb/> &longs;et idem po&longs;t modum repetere. </s> <s id="s.001570">ad hæc &longs;i in medium &longs;olida hæc duo profert, <lb/> <expan abbr="ait&qacute;">aitque</expan>; ip&longs;a replere locum, intelligens, planum, profectò non loquitur forma­<lb/>liter, ide&longs;t de ip&longs;is, vt &longs;olida &longs;unt. </s> <s id="s.001571">Quare Ari&longs;t. videretur &longs;ibi non con&longs;tare, <lb/> vel perperam exi&longs;tima&longs;&longs;e plura Tetraedra complere &longs;oliditatem. </s> <s id="s.001572">deceptus <pb pagenum="86" xlink:href="009/01/086.jpg"/>fortè fuit Ari&longs;t. eò quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi­<lb/> bus, verùm illæ non &longs;unt regulares, ide&longs;t <expan abbr="nõ">non</expan> &longs;unt Tetraedra, vt po&longs;tea o&longs;ten­<lb/> dam. </s> <s id="s.001573">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 præbere po&longs;&longs;unt, <lb/> cum anguli ip&longs;orum &longs;int recti, & &longs;olidi. </s> <s id="s.001574">Verum enim verò plures pyramides <lb/> regulares, &longs;iue plura Tetraedra non po&longs;&longs;e replere vacuum, <expan abbr="&longs;olidum&qacute;">&longs;olidumque</expan>; con­<lb/> &longs;tituere, ex eo patet, quia &longs;i id præ&longs;tarent, conflarent nece&longs;&longs;ariò, vel vnum <lb/> ex <expan abbr="quinq;">quinque</expan> corporibus regularibus, de quibus in 13. Elemen. <!-- REMOVE S-->vel aliud quod­<lb/> piam; non aliud, nam, vt patet ex &longs;cholio 13. Elem. non dantur, ni&longs;i illa. <lb/> </s> <s id="s.001575">quinque; <expan abbr="neq;">neque</expan> vllum ex illis, quia diameter huiu&longs;modi corporis, quod com­<lb/> poneretur ex illis pyramidibus, e&longs;&longs;et dupla lateris eiu&longs;dem, vt patet, quia <lb/> pyramides illæ omnes concurrerent ad centrum &longs;phæræ illas omnes com­<lb/> plectentis, quare latus vnius pyramidis à &longs;uperficie &longs;phæræ incipiens de&longs;i­<lb/> neret in centrum, ergo latus i&longs;tud e&longs;&longs;et &longs;emidiameter, quapropter tota dia­<lb/>meter illius &longs;ph&etail;ræ, & con&longs;equenter huius corporis in illa in&longs;cripti, e&longs;&longs;et du­<lb/> pla lateris eiu&longs;dem figuræ &longs;olidæ in&longs;criptæ, &longs;ed nullo talis proportio diame­<lb/> tri alicuius ex illis <expan abbr="quinq;">quinque</expan> &longs;olidis regularibus ad latus eiu&longs;dem reperitur, <lb/> quæ &longs;it nimirum dupla, vt patet ex vltimis demon&longs;trationibus 13. Elem. ini­<lb/> tio facto à 13. demon&longs;tratione, in quibus nulla reperitur proportio dupla <lb/> inter diametrum, & latus eiu&longs;dem alicuius ex illis &longs;olidis; ex quibus mani­<lb/> fe&longs;tum e&longs;t, plures regulares pyramides quouis pacto &longs;imul vnitas nullo mo­<lb/> do replere locum &longs;olidum. </s> <s id="s.001576">cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t. nullo <lb/> modo po&longs;&longs;e verificari de repletione &longs;olidi per plura Tetraedra, & omnes <lb/> tamen commentatores auctoritate Ari&longs;t. decepti pro ip&longs;o &longs;tarent, dubius, <lb/> <expan abbr="anceps&qacute;">ancepsque</expan>; diu hæ&longs;i, neque quid quam mea Minerua a&longs;&longs;erere au&longs;us &longs;um, &longs;ed P. <lb/> <!-- REMOVE S-->Clauium præceptorem meum per literas con&longs;ului, qui in hunc modum hu­<lb/> mani&longs;&longs;imè 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 iunctæ ratione &longs;ub&longs;tantium <expan abbr="triangulorũ">triangulorum</expan> æqui­<lb/> laterorum. </s> <s id="s.001577">Verum hac ratione non videntur implere locum &longs;olidum, fa­<lb/>teor; &longs;ed tamen Ari&longs;t. in eo tex. <!-- REMOVE S-->non loquitur de repletione loci &longs;olidi. </s> <s id="s.001578">hæc <lb/> ip&longs;e. </s> <s id="s.001579">&longs;i igitur libeat Ari&longs;totelem, quod fortè 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, & Tetraedro, quatenus &longs;unt corpora, &longs;ed quatenus habent &longs;uper­<lb/> ficies, cubus quidem &longs;ex quadratas, Tetraedrum autem quatuor æquilate­<lb/> ras &longs;uperficies, quæ duæ figuræ, vt &longs;upra in hoc textu vidimus, replent lo­<lb/> cum: <expan abbr="atq;">atque</expan> hoc modo facimus Ari&longs;totelem non formaliter loquentem. </s> <s id="s.001580">ex­ <lb/> aduersò ne videamur magis Ari&longs;t. quam veritatem &longs;equi, videtur dicen­<lb/> dum, Ari&longs;totilem formaliter locutum e&longs;&longs;e, & 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> <s id="s.001581">Vtrumuis dixerimus, non tamen Ari&longs;t. ab om­<lb/>ni errore vindicabimus. </s> <s id="s.001582">Hoc tamen certum e&longs;t, ex prædictis, Græcos om­<lb/> nes pariter, ac Latinos, illos &longs;equentes, lapos e&longs;&longs;e, a&longs;&longs;erentes duodecim py­<lb/> ramides complere &longs;olidum locum, <expan abbr="atq;">atque</expan> Dodecaedrum con&longs;tituere; nam py­<lb/> ramides Dodecaedron con&longs;tituentes non &longs;unt regulares, ide&longs;t, non &longs;unt Te­ <pb pagenum="87" xlink:href="009/01/087.jpg"/>traedra (de quibus tamen Ari&longs;t. loquitur) vt patet ex &longs;upra dictis. </s> <s id="s.001583">Indul­<lb/> geas Lector, &longs;i hoc loco nece&longs;&longs;e fuit in Geometriæ penetralia ingredi: ope­<lb/> ræpretium enim e&longs;t aliquando ip&longs;is Mathematicis &longs;atisfacere. </s> <s id="s.001584">tu verò, &longs;i <lb/> adeo es mathematicis imbutus, con&longs;ule po&longs;tremas demon&longs;tra. </s> <s id="s.001585">13. Elem. & <lb/> præcipuè &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, quæ no&longs;træ &longs;unt <lb/> partes, per&longs;picuè &longs;atis expo&longs;uimus.</s> </p> <p type="main"> <s id="s.001586">Multo po&longs;t tempore, quàm hæc &longs;crip&longs;eram incidi fortè in cap. 38. &longs;pecu­<lb/> lationem 10. Benedicti de placitis Ari&longs;t. <!-- REMOVE S--><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t. hoc loco <lb/> erroris notari, dum a&longs;&longs;eruit duodecim pyramides replere <expan abbr="locũ">locum</expan> corporeum, <lb/> ide&longs;t, vt exponit ip&longs;e, &longs;ex pyramides &longs;uper hexagonam aliquam figuram <lb/> &longs;uperficialem, & &longs;ex &longs;ub eadem, id præ&longs;tarent, cum potius maius vacuum <lb/> remaneat ad quamlibet partium &longs;upra, & infra, quam plenum. </s> <s id="s.001587">hæc ip&longs;e. </s> <s id="s.001588">&longs;ed <lb/> expo&longs;itio i&longs;ta puerili, ne dum Ari&longs;t. ingenio pror&longs;us indigna e&longs;t: vt propte­<lb/> rea exi&longs;timem ca&longs;u potius eum Ari&longs;t. rectè reprehendi&longs;&longs;e, quam ex certa <lb/> &longs;cientia, cum illius erratum maiori errato conetur corrigere. </s> <s id="s.001589">Incidi po­<lb/> &longs;tremò in Indicem librorum, quem Maurolyius &longs;uæ Co&longs;mographiæ præpo­<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 verò cum octaedris compactas <lb/> dumtaxat implere locum, qua in re Auerroem erra&longs;&longs;e pueriliter manife&longs;tum <lb/> erit. </s> <s id="s.001590">Vides igitur tanti viri auctoritate confirmari no&longs;tram &longs;ententiam, py­<lb/> ramides videlicet per &longs;e, non replere vacuum. </s> <s id="s.001591">cum igitur con&longs;tet vnam tan­<lb/> tum ex figuris &longs;olidis, &longs;iue etiam dicas, vt perperam Ari&longs;t. & alij plures exi­<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"> <s id="s.001592"><arrow.to.target n="marg122"/></s> </p> <p type="margin"> <s id="s.001593"><margin.target id="marg122"/>122</s> </p> <p type="main"> <s id="s.001594">Tex. 71 <emph type="italics"/>(Deinde &longs;i terra e&longs;t cubus &c.)<emph.end type="italics"/> lege definitiones 11. Elem. quæ &longs;unt <lb/>admodum faciles, ibi reperies definitiones quinque corporum regularium, <lb/> quorum figuras Plato elementis tribuebat: qua verò id ratione faceret, ha­<lb/> bes in &longs;phæra Clau. <!-- KEEP S--></s> <s id="s.001595">Simpl. <!-- REMOVE S-->etiam hoc loco &longs;atisfacit.</s> </p> </chap> <chap> <p type="head"> <s id="s.001596"><emph type="italics"/>Ex Quarto de Cœlo.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001597"><arrow.to.target n="marg123"/></s> </p> <p type="margin"> <s id="s.001598"><margin.target id="marg123"/>123</s> </p> <p type="main"> <s id="s.001599">Tex. 33. <emph type="italics"/>(Deinde ad &longs;imiles videtur angulos ignis quidem &longs;ur&longs;um ferri, <lb/>terra autem deor&longs;um, & omninò quod grauitatem habet, quare nece&longs;&longs;e <lb/> est ferri ad medium. </s> <s id="s.001600">hoc autem vtrum accidit ad ip&longs;um terræ 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 id="id.009.01.087.1.jpg" place="text" xlink:href="009/01/087/1.jpg"/><lb/> probare Ari&longs;toteles dari <expan abbr="pũctum">punctum</expan> quoddam in medio <lb/> mundi, ad quod grauia de&longs;cendant, & concurrent: <lb/> & à quo leuia a&longs;cendat; vtitur, præter alias, etiam <lb/> ratione aliqua ex parte mathematica; quæ e&longs;t huiu&longs;­<lb/> modi. </s> <s id="s.001601">videmus ignem, & cætera l&etail;uia a&longs;cendere à <lb/> terra &longs;ur&longs;um ad angulos æquales; &longs;imiliter videmus <lb/>terram, & c&etail;tera grauia de&longs;cendere ad terram deor­<lb/> &longs;um ad angulos æquales, 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 figu­<lb/> ra præ&longs;enti circulus E C D, cuius medium, &longs;ine cen­ <pb pagenum="88" xlink:href="009/01/088.jpg"/>trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, quæ facit angulos in &longs;u­<lb/> perficie terræ æquales, nimirum angulos B C D, B C E. &longs;imiliter terra per <lb/>eandem lineam <expan abbr="faci&etilde;s">faciens</expan> eo&longs;dem angulos æquales de&longs;cendit. </s> <s id="s.001602">linea autem, quæ <lb/> facit tales angulos tendit ad centrum &longs;phæræ A, vt patet ad &longs;en&longs;um in figu­<lb/> ra, & probari pote&longs;t geometricè ex primis tertij Elem. ex quibus patet tam <lb/> læuia, quam grauia, quæ per talem lineam ferantur, re&longs;picere centrum A, <lb/> &longs;phæræ. </s> <s id="s.001603">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> <s id="s.001604">vide igitur hac de re <lb/> pulchram de&longs;&longs;ertationem apud Clauium in &longs;phæra: qui probat euidenter <lb/> e&longs;&longs;e vnum, & idem.</s> </p> <p type="main"> <s id="s.001605"><arrow.to.target n="marg124"/></s> </p> <p type="margin"> <s id="s.001606"><margin.target id="marg124"/>124<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001607"><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap. vlt. </s> <s id="s.001608">de Cœlo. <!-- KEEP S--></s> <s id="s.001609">cuius loco ìn-<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001610"><arrow.to.target n="marg125"/><lb/> <arrow.to.target n="marg126"/><lb/> <emph type="italics"/>terim Lector adeat Di&longs;cur&longs;um Italicum Galilæi Galilæi, de his,<emph.end type="italics"/><lb/> <arrow.to.target n="marg127"/><lb/> <emph type="italics"/>quæ in aqua mouentur, ac natant: ubi propè 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"> <s id="s.001611"><margin.target id="marg125"/>125</s> </p> <p type="margin"> <s id="s.001612"><margin.target id="marg126"/>126</s> </p> <p type="margin"> <s id="s.001613"><margin.target id="marg127"/>127</s> </p> <p type="margin"> <s id="s.001614"><margin.target id="marg128"/>128</s> </p> <p type="margin"> <s id="s.001615"><margin.target id="marg129"/>129</s> </p> </chap> <chap> <p type="head"> <s id="s.001616"><emph type="italics"/>Ex Lib. 2. de Generatione, & Corruptione.<emph.end type="italics"/><lb/> <arrow.to.target n="marg130"/><!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001617"><margin.target id="marg130"/>130</s> </p> <p type="main"> <s id="s.001618">Tex. 56. <emph type="italics"/>(ldeoqué non prima latio cau&longs;a Generationis, & Corruptionis e&longs;t, <lb/> &longs;ed quæ &longs;ecundum obliquum circulum, in hac enim & continuum vnum <lb/> e&longs;t & moueri duobus motibus)<emph.end type="italics"/> per primam lationem intelligit mo­<lb/>tum primi mobilis, qui &longs;it &longs;uper polis mundi, quo Stellæ omnes <lb/> ab oriente in occidentem rectà feruntur. </s> <s id="s.001619">per obliquum verò circulum in­<lb/> telligit Zodiacum, qui obliquus e&longs;t, quia poli eius &longs;unt alij à polis mundi, & <lb/> quia non tendit rectà ab ortu ad occa&longs;um, &longs;ed in &longs;phæra mundi tran&longs;uer­<lb/> &longs;us e&longs;t, & deflectit à &longs;eptentrione in meridiem, quamuis non rectà, vt in <lb/> &longs;phæra explicari &longs;olet. </s> <s id="s.001620">motus ergo Planetarum, qui fit &longs;ecundum hunc cir­<lb/> culum, & ip&longs;e obliquus, & tran&longs;uer&longs;us codem modo erit; ferrentur que per <lb/> eum à Borea ad Au&longs;trum, & è conuer&longs;o; ex quo acce&longs;&longs;u, & rece&longs;&longs;u efficiunt <lb/> æ&longs;tatem, & hyemem, item generationes, & corruptiones. </s> <s id="s.001621">Sol porrò, & pla­<lb/> netæ, qui motibus proprijs hunc circulum peragunt, dicuntur moueri duo­<lb/> bus motibus, & quidem contrarijs: quoniam dum Sol. </s> <s id="s.001622">v. <!-- REMOVE S-->g. <!-- REMOVE S-->per Zodiacum <lb/> graditur motu proprio, interim etiam à primo mobili fertur ab ortu in oc­<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 à 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 à duobus motoribus, qui &longs;unt <lb/> Sol ip&longs;e, mouens &longs;e ip&longs;um per Zodiacum: & primum mobile mouens in&longs;u­<lb/> per ip&longs;um Solem, & Zodiacum ab ortu in occa&longs;um circa mundum.</s> </p> </chap> <pb pagenum="89" xlink:href="009/01/089.jpg"/> <chap> <p type="head"> <s id="s.001623"><emph type="italics"/>EX PRIMO METEORORVM.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001624"><arrow.to.target n="marg131"/></s> </p> <p type="margin"> <s id="s.001625"><margin.target id="marg131"/>131</s> </p> <p type="main"> <s id="s.001626">Svmma 1. cap. 3. <emph type="italics"/>(Moles autem terræ quanta &longs;it ad ambientes magnitudi­<lb/>nes, non immanifestum, iam enim vi&longs;um est per a&longs;trologica theoremata, <lb/> quod multò etiam quibu&longs;dam a&longs;tris est minor)<emph.end type="italics"/> Quantitas terræ non &longs;o­<lb/> lum ab&longs;olutè con&longs;iderata, ab A&longs;tronomis explorata habetur, vt vi­<lb/> dere e&longs;t in &longs;phæra Clauij; &longs;ed etiam re&longs;pectiuè con&longs;iderata, ide&longs;t re&longs;pectu <lb/> aliorum elementorum, & ip&longs;orum etiam a&longs;trorum; cuius demon&longs;trationes <lb/> &longs;unt partim in libello Ari&longs;tarchi Samij, de magnitudine, & di&longs;tantia Solis, <lb/> & Lunæ, partim apud Ptolæmeum in magna Syntaxi, &longs;iue Almage&longs;to: par­<lb/> tim apud Albategnium de &longs;cientia &longs;tellarum: partim demum apud Ticho­<lb/> nem Brahe. </s> <s id="s.001627">Porrò facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra multò maiorem, <lb/> terram verò maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/> in figura &longs;equenti; vbi vmbra terræ e&longs;t D B E, in quam Luna nigricans im­<lb/> mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro­<lb/> nomi ob&longs;eruarunt vmbram terræ paulò &longs;upra Lunam pertingere, cum &longs;upe­<lb/> riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ariò e&longs;&longs;e acuminatam, &longs;eu <lb/> conicam, vt figura refert. </s> <s id="s.001628">Cum ergo terra vmbram proijciat turbinatam, <lb/> nece&longs;&longs;ariò corpus Solis, quod ip&longs;am illuminat, eadem maior erit: quoti­<lb/> diana enim experientia docemur, corpore illuminante exi&longs;tente maiore <lb/> quà &longs;it illuminatum, vmbram proijci fa&longs;tigiatam: cum deinde Solem val­<lb/> de a terra di&longs;tare certum &longs;it, optimè infertur, eum re&longs;pectu terræ e&longs;&longs;e maxi­<lb/> mum: quanto enim duæ lineæ, &longs;iue radij B A, B C. à terra ad partes Solis <lb/> <figure id="id.009.01.089.1.jpg" place="text" xlink:href="009/01/089/1.jpg"/><lb/> magis elongantur, tan­<lb/> to maius corpus <expan abbr="illu-minãs">illu­<lb/> minans</expan> intercipiunt. </s> <s id="s.001629">ha­<lb/> ctenus de magnitudine <lb/> terræ ad Solem. </s> <s id="s.001630">Cum <lb/> verò Luna eclyp&longs;atio­<lb/> nis tempore, aliquan­<lb/> do non &longs;olum tota in <lb/> vmbræ vertice lateat, <lb/> verùm etiam <expan abbr="aliquãdo">aliquando</expan> <lb/> moram trahat, euidens <lb/> e&longs;t, eam e&longs;&longs;e multò mi­<lb/> norem illa vmbræ par­<lb/> te, in quam immergi­<lb/> tur; quæ pars cum &longs;it <lb/> conicæ vmbræ media, <lb/>erit multò gracilior <lb/> quàm &longs;it ip&longs;a terra. <lb/> </s> <s id="s.001631">Ex quo manife&longs;tè apparet, Lunam, quæ illa vmbra minor e&longs;t, e&longs;&longs;e à fortio­<lb/> ri multò minorem ip&longs;a terre&longs;tri mole. </s> <s id="s.001632">Atque hæc de comparatione terræ <lb/> ad Lunam. <!-- KEEP S--></s> <s id="s.001633">harum rerum demon&longs;trationes exactiores pertractare non e&longs;t <lb/> huius loci.</s> </p> <p type="main"> <s id="s.001634"><arrow.to.target n="marg132"/></s> </p> <p type="margin"> <s id="s.001635"><margin.target id="marg132"/>132</s> </p> <p type="main"> <s id="s.001636">Eodem cap. <emph type="italics"/>(Con&longs;iderantes vtique, quæ nunc o&longs;tenduntur per Mathematica<emph.end type="italics"/> <pb pagenum="90" xlink:href="009/01/090.jpg"/><emph type="italics"/>&longs;ufficienter, fortè vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/> e&longs;t putare <expan abbr="vnumquodq;">vnumquodque</expan> eorum quæ feruntur e&longs;&longs;e paruum magnitudinibus, quia vi­<lb/>detur a&longs;picientibus, hinc nobis &longs;ic)<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, quæ <lb/> pa&longs;&longs;im apud Ari&longs;t. occurrunt, <expan abbr="pleriq;">plerique</expan> no&longs;træ ætatis 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<lb/> xies maiorem; &longs;ed etiam, quod peius e&longs;t, negant e&longs;&longs;e maiorem; ad demon­<lb/> &longs;trationes autem a&longs;tronomicas dicunt &longs;e exi&longs;timare eas e&longs;&longs;e fallaces; at que <lb/>impo&longs;&longs;ibile e&longs;&longs;e nos res adeo à nobis di&longs;tantes &longs;ufficienter perue&longs;tigare: <lb/> quanto &longs;apientius, ac prudentius eorum Magi&longs;ter Ari&longs;t. alibi &longs;æpius, &longs;ed hoc <lb/> præcipuè loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/> i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia præceptoris a&longs;&longs;equi poterunt.</s> </p> <p type="main"> <s id="s.001637"><arrow.to.target n="marg133"/></s> </p> <p type="margin"> <s id="s.001638"><margin.target id="marg133"/>133</s> </p> <p type="main"> <s id="s.001639">Summa 1. cap. 4. <emph type="italics"/>(Quæ igitur astrorum e&longs;t, velox quidem; longè autem: quæ <lb/>verò Lunæ deor&longs;um quidem, tarda autem: quæ autem Solis ambo hæc habet &longs;uffi­<lb/> cienter)<emph.end type="italics"/> quæ igitur a&longs;trorum, ide&longs;t latio a&longs;trorum e&longs;t velox, &longs;ed procul à ter­<lb/> ra; Lunæ verò latio terræ quidem proxima, tarda tamen: at verò Solis la­<lb/> tio medio modo &longs;e habet inter vtrumque, ide&longs;t, quia <expan abbr="neq;">neque</expan> nimis vt a&longs;tra di­<lb/> &longs;tat, <expan abbr="neq;">neque</expan> tardè &longs;icut Luna circunfertur. </s> <s id="s.001640">exi&longs;timo Ari&longs;t. loqui de motu diur­<lb/> no, quia &longs;ecundum hunc a&longs;tra inerrantia &longs;unt Sole citatiora, Sol verò ip&longs;a <lb/> Luna citior. </s> <s id="s.001641">Verumenimuerò illud non prætereundum, quod plurium inua­<lb/> luerit opinio exi&longs;timantium Ari&longs;t. his verbis, Solem &longs;upra Lunam proximè <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> <s id="s.001642">quod &longs;i ita &longs;en&longs;i&longs;&longs;et venia dignus haberetur, <lb/> cum tunc temporis nondum fortè adinuentæ e&longs;&longs;ent demon&longs;trationes illæ <lb/> a&longs;tronomicæ, quibus ordo Planetarum certi&longs;&longs;imè con&longs;tat, <expan abbr="Sol&qacute;">Solque</expan>; medius in­<lb/> ter Planetas collocatur. </s> <s id="s.001643">At verò nulla ratione ferendi &longs;unt <expan abbr="quicunq;">quicunque</expan> no&longs;tra <lb/> hac tempe&longs;tate non &longs;olum Ari&longs;t. ita &longs;en&longs;i&longs;&longs;e, &longs;ed etiam contra firmi&longs;&longs;imas <lb/> aftronomorum demon&longs;trationes, quibus adeò Ari&longs;t. deferebat, vnica, vt pu­<lb/> tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum à Luna locum occupare om­<lb/> ni ope defendunt.</s> </p> <p type="main"> <s id="s.001644"><arrow.to.target n="marg134"/></s> </p> <p type="margin"> <s id="s.001645"><margin.target id="marg134"/>134</s> </p> <p type="main"> <s id="s.001646">Summa 2. cap. 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;æpè non apparet, it a vt po&longs;t tempus multum appareat)<emph.end type="italics"/> quod Mer­<lb/> curius non ni&longs;i rarò con&longs;pici po&longs;&longs;it, cau&longs;a e&longs;t, quia parum à Sole elongatur, <lb/> &longs;iue ip&longs;um antecedat, &longs;iue &longs;ub&longs;equatur. </s> <s id="s.001647">ex quo fit, vt diu ferè &longs;imul cum So­<lb/>le circumferatur, & propterea &longs;iue oriatur, &longs;iue occidat, parum &longs;upra ho­<lb/> rizontem eleuatus apparere pote&longs;t, quod Ari&longs;t. ait modicum <expan abbr="&longs;upera&longs;c&etilde;dit">&longs;upera&longs;cendit</expan>. <lb/> </s> <s id="s.001648">vnde fit tum propter nimiam Solis vicinitatem, cuius lumine tegitur; tum <lb/> propter vapores, qui horizonti vt plurimum incumbunt, vt rarò, & po&longs;t ma­<lb/> gna temporis interualla con&longs;piciatur. </s> <s id="s.001649">non me fugit hæc omnia ab a&longs;trono­<lb/> mis per epiciclum excu&longs;ari; &longs;ed ego mediocritati eorum, in quorum gra­<lb/> tiam hæc &longs;cribo, con&longs;ultum volo.</s> </p> <p type="main"> <s id="s.001650"><arrow.to.target n="marg135"/></s> </p> <p type="margin"> <s id="s.001651"><margin.target id="marg135"/>135</s> </p> <p type="main"> <s id="s.001652">Eodem cap. <emph type="italics"/>(Ad au&longs;trum autem quando feratur, copiam quidem habere talís <lb/>humiditatis, &longs;ed quia parua e&longs;t &longs;ectio circuli, quæ &longs;uper terram, quæ autem deor­<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 æ&longs;tiuis ver&longs;ionibus exi&longs;tente Sole. <!-- KEEP S--></s> <s id="s.001653">quapropter in <lb/> lis quidem locis neque fieri cometem ip&longs;um. </s> <s id="s.001654">quando verò ad Boream &longs;ubdefecerit, <lb/>accipere comam, quia magna e&longs;t circunferentia, quæ e&longs;t &longs;upra horizontem; quæ au-<emph.end type="italics"/> <pb pagenum="91" xlink:href="009/01/091.jpg"/><emph type="italics"/>tem e&longs;t &longs;ubtus, pars circuli parua; facilè 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, quem <lb/> motu diurno cometa de&longs;cribebat, ob quam adeò parum &longs;upra horizontem <lb/> attolleretur, vt <expan abbr="nõ">non</expan> po&longs;&longs;et vi&longs;us no&longs;ter ab ip&longs;o ad Solem reflecti; quod &longs;ecun­<lb/> dum ip&longs;um erat nece&longs;&longs;arium ad cometarum apparitionem. </s> <s id="s.001655">loquitur igitur <lb/>Hippocrates de circulis, quos diurna conuer&longs;ione cometes circumducit, qui <lb/> omninò &longs;imiles &longs;unt ijs, quos etiam Sol, <expan abbr="reliqua&qacute;">reliquaque</expan>; a&longs;tra eodem motu de &longs;i­<lb/> gnant. </s> <s id="s.001656">qui quidem omnes in no&longs;tra &longs;phæra obliqua ita &longs;e habent, vt ij, qui <lb/>&longs;unt vltra æquatorem ad Capricorni tropicum, minus &longs;upra horizontem <lb/>extent, quàm infra deprimantur, & tanto minus, quanto magis ab æquato­<lb/>re in au&longs;trum recedunt: contra verò faciunt, qui citra æquatorem ad Can­<lb/>cri conuer&longs;ionem collocantur, quanto enim magis ab æquatore in boream <lb/> remouentur, tantò eorum &longs;ectio, quæ e&longs;t &longs;upra horizontem, maior e&longs;t ea, <lb/> quæ infra horizontem latet. </s> <s id="s.001657">quæ quidem omnia clara &longs;unt adhibita &longs;phæra <lb/> materiali, quam &longs;i ad tuam poli eleuationem accommodaueris, illicò vi­<lb/> debis tropici, Cancri &longs;ectionem, quæ e&longs;t &longs;upra horizontem multo maiorem <lb/> ea, quæ e&longs;t infra. </s> <s id="s.001658">oppo&longs;itum verò in altero Capricorni tropico, cuius mini­<lb/> mam portionem &longs;upra, maximam verò infra horizontem exi&longs;tere videbis. <lb/> </s> <s id="s.001659">Idem proportionaliter imaginari debes de circulis, quos cometa tam vltra <lb/> Capricornum, quàm citra Cancrum delineat; nam eorum, qui &longs;unt vltra <lb/> Capricornum ad au&longs;trum minores adhuc &longs;ectiones &longs;upra horizontem exi­<lb/> &longs;terent, quàm opus &longs;it ad cometen &longs;pectandum. </s> <s id="s.001660"><expan abbr="At&qacute;ue">Atque</expan> hæc cau&longs;a e&longs;t ex &longs;en­<lb/> tentia Hippocr. <!-- REMOVE S-->cur in illa au&longs;trali plaga <expan abbr="nũquam">nunquam</expan> cometes effulgeat. </s> <s id="s.001661">è con­<lb/> trario autem, quia ad boream &longs;ectiones illæ maximæ &longs;unt, <expan abbr="aptæ&qacute;">aptæque</expan>; ad refra­<lb/> ctionem vi&longs;us no&longs;tri v&longs;que ad Solem, idcircò in hac mundi parte cometas <lb/> con&longs;picere &longs;olemus. </s> <s id="s.001662">Reliqua Vicomercatus, <expan abbr="atq;">atque</expan> Alexand. <!-- REMOVE S-->optimè expli­<lb/> cant, quos tu con&longs;ule, ne actum agatur.</s> </p> </chap> <chap> <p type="head"> <s id="s.001663"><emph type="italics"/>In cap. 4. &longs;ummæ 2. lib. 1. Meteor. <!-- REMOVE S-->de Cometis.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001664"><arrow.to.target n="marg136"/></s> </p> <p type="margin"> <s id="s.001665"><margin.target id="marg136"/>136</s> </p> <p type="main"> <s id="s.001666">In præ&longs;enti cap. <!-- REMOVE S-->Ari&longs;t. &longs;uam de Cometis &longs;ententiam exponit: Come­<lb/> tam nimirum infra Lunam in elementari mundo procreari, & ignitum <lb/> quoddam Meteoron, ex lenta, pingui, <expan abbr="&longs;icca&qacute;">&longs;iccaque</expan>; materia à terra in &longs;u­<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> <s id="s.001667">Hanć porrò opinionem & &longs;i probabilibus tantum ra­<lb/> tionibus confirmatam vulgò tamen <expan abbr="v&longs;q;">v&longs;que</expan> ad hanc diem receptam, cum fal­<lb/> &longs;am e&longs;&longs;e a&longs;tronomi exi&longs;timent, non erit abs re rationes eas ex &longs;ecundo pro­<lb/> gymn. </s> <s id="s.001668">Tichonis volumine, de&longs;umptas hic breuiter referre, quibus a&longs;trono­<lb/> mus ille eos &longs;upra Lunam in ætherea regione collocauit: quas quidem ra­<lb/> tiones ille ex diuturnis ob&longs;eruationibus per exqui&longs;ita organa factis adinue­<lb/> nit: ea&longs;que Mathematicis linearum, ac numerorum demon&longs;trationibus <lb/> explicauit.</s> </p> <p type="main"> <s id="s.001669">Prima. <!-- KEEP S--></s> <s id="s.001670">&longs;ed vt ab auctoritate, in quam obiter incidimus <expan abbr="initiũ">initium</expan> faciamus, <lb/>non e&longs;t exi&longs;timandum nonnullos &longs;olum ex recentioribus id con&longs;tanter a&longs;&longs;e­<pb pagenum="92" xlink:href="009/01/092.jpg"/>uera&longs;&longs;e, &longs;ed &longs;uperiori etiam ætate id ip&longs;um Hieron. </s> <s id="s.001671">Cardan. <!-- REMOVE S-->libro de &longs;ubtili­<lb/> tate conatus e&longs;t, <expan abbr="neq;">neque</expan> irrito conatu, demon&longs;trare; qui præterea idem cum <lb/>&longs;e ip&longs;o &longs;en&longs;i&longs;&longs;e ait Albumazar. </s> <s id="s.001672">quibus etiam ex antiquis Seneca annumeran­<lb/> dus e&longs;t. </s> <s id="s.001673">pr&etail;dicti autem recentiores omnes varijs demon&longs;trationibus ex ac­<lb/>curata ob&longs;eruatione erutis illud certò certius confirmare 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> <s id="s.001674">partim in epi&longs;t. <!-- REMOVE S-->fu&longs;ius explicatas reperies.</s> </p> <p type="main"> <s id="s.001675">2. Quarum poti&longs;&longs;ima illa e&longs;t, quæ 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<lb/> norem exhibet parallaxim: expertos autem &longs;e e&longs;&longs;e hi omnes, affirmant ho­<lb/> &longs;ce quinque cometas multò minorem pati parallaxim, quam Lunam; imò <lb/> quempiam minorem, quàm Sol ip&longs;e patiatur, quo po&longs;ito manife&longs;tè conuin­<lb/> ceretur eos omnes &longs;upra Lunam in ætherea regione efful&longs;i&longs;&longs;e.</s> </p> <p type="main"> <s id="s.001676">3. Ratio, qua etiam ante nouas ob&longs;eruationes vti &longs;olebant, de&longs;umitur <lb/> ex motu cometæ diurno, quo &longs;cilicet oritur, & occidit, quemadmodum cæ­<lb/> tera &longs;ydera, hoc e&longs;t &longs;patio 24. horarum diurnam conuer&longs;ionem circa totam <lb/> terram ab&longs;oluit. </s> <s id="s.001677">&longs;i igitur comete e&longs;&longs;et in &longs;ublimiori aeris regione, vbi cæte­<lb/> ra ignita meteora collocantur, <expan abbr="moueretur&qacute;">mouereturque</expan>; diurno motu circa terram, &longs;e­<lb/> queretur nece&longs;&longs;ariò eum tanta velocitate videri à nobis circumferri, vt po­<lb/> tius fulgor quidam, &longs;eu radius pertran&longs;iens ab oriente in occidentem appa­<lb/> reret, quam &longs;tella qu&etail;dam: <expan abbr="id&qacute;">idque</expan>; propter propinquitatem; a&longs;tra enim ob ni­<lb/> miam di&longs;tantiam videntur tardè moueri, quamuis veloci&longs;&longs;imè moueantur.</s> </p> <figure id="id.009.01.092.1.jpg" place="text" xlink:href="009/01/092/1.jpg"/> <p type="main"> <s id="s.001678">Quod melius ex &longs;equenti figura <lb/> <expan abbr="cõuincitur">conuincitur</expan>, vbi circulus interior e&longs;t <lb/> terra, cuius &longs;emidiameter A B. cir­<lb/> culus verò exterior e&longs;t cometæ gy­<lb/> rus, quem ip&longs;e &longs;patio 24. horarum <lb/> percurrit, qui &longs;ecundum veram pro­<lb/> portionem deberet adhuc ip&longs;i terræ <lb/> propinquior, ac proinde minor e&longs;&longs;e, <lb/> iuxta aeris &longs;upremam partem. </s> <s id="s.001679">hori­<lb/> zon e&longs;t recta D C, tangens terram in <lb/> B, vbi e&longs;t oculus no&longs;ter, qui nihil in­<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; quæ quidem por­<lb/> tio, <expan abbr="neq;">neque</expan> &longs;emihoræ re&longs;ponderet, &longs;i fi­<lb/> gura iuxta veram proportionem con&longs;trueretur. </s> <s id="s.001680">experientia tamen con&longs;tat, <lb/> cometas videri &longs;upra horizontem tot horis, quot &longs;tellæ fixæ, &longs;ub quibus mo­<lb/> uentur: non ergo e&longs;t in &longs;upremo aere. </s> <s id="s.001681">Quod &longs;i fiat figura, in qua exterior <lb/> cometæ ambitus adeò 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<lb/> tem &longs;pectatur, ea figura terræ &longs;emidiametrum A B. toties multiplicabit, vt <lb/> ip&longs;i Lunæ circuitui proximè accedat.</s> </p> <pb pagenum="93" xlink:href="009/01/093.jpg"/> <p type="main"> <s id="s.001682">Præterea aiunt, quis &longs;anæ mentis dixerit, Meteoron vllum ex materia <lb/> vaga, ac fluxa con&longs;tans, po&longs;&longs;e tanta pernicitate moueri, vt diurnam con­<lb/> uer&longs;ionem ab&longs;oluat? </s> <s id="s.001683">vnde illi motus i&longs;te? </s> <s id="s.001684">præ&longs;ertim cum videamus cætera <lb/> ignita meteora e&longs;&longs;e ad modum temporanea, <expan abbr="atq;">atque</expan> euanida.</s> </p> <p type="main"> <s id="s.001685">4. Comprobationem nobis &longs;uppeditant ex via, &longs;eu ductus circuli, quem <lb/> toto durationis tempore proprio cur&longs;u de&longs;ignarunt: prædicti <expan abbr="namq;">namque</expan> quin­<lb/> que cometæ motu &longs;ibi proprio, quo ab occidente non omninò orientem <lb/> ver&longs;us, &longs;ed ad aquilonem deflectentes ab initio &longs;uæ apparitionis, <expan abbr="v&longs;q;">v&longs;que</expan> ad vl­<lb/>timum finem exqui&longs;iti&longs;&longs;imè portionem circuli maximi in c&etail;lo de&longs;ignarunt; <lb/>non aliter quàm Sol proprio motu per eclypticam in cœlo mundi &longs;phæram <lb/> in duo æqualia diuidentem de&longs;cribit. </s> <s id="s.001686">necnon aliter ac Luna &longs;uum iter per <lb/> circulum maximum cœlum bifariam diuidentem perficit. </s> <s id="s.001687">quapropter co­<lb/> metas ho&longs;ce <expan abbr="nõ">non</expan> minus quam Sol, vel Luna in ip&longs;o æthere &longs;patiatos e&longs;&longs;e con­<lb/> tendunt. </s> <s id="s.001688">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 exactè <lb/> delinea&longs;&longs;ent, quam quidem inter elementa vagum, <expan abbr="atq;">atque</expan> in&longs;tabilem pro ma­<lb/> teriæ in&longs;tabilitate exercere debui&longs;&longs;ent?</s> </p> <p type="main"> <s id="s.001689">5. Adde, quod in maximo hoc circulo de&longs;cribendo, etiam &longs;i inæquali ve­<lb/> locitate vi&longs;i &longs;int moueri, inæqualitatem tamen illam regularem <expan abbr="vbiq;">vbique</expan> &longs;em­<lb/> per &longs;eruauerunt, in principio quidem velociores, deinde &longs;ucce&longs;&longs;iuè, & pro­<lb/> portionaliter velocitatem illam &longs;imili analogia &longs;emper &longs;eruata <expan abbr="inhibuerũt">inhibuerunt</expan>, <lb/> nullo igitur pacto inordinatam inæqualitatem, qua à tardiore motu &longs;ubito <lb/> in celeriorem, & rur&longs;us &longs;tatim ab hoc in <expan abbr="illũ">illum</expan> pro&longs;ilirent exhibuerunt: prout <lb/> omnia Meteora, quæ in mundi parte elementari ex flammanti materia ge­<lb/> nerantur, talem di&longs;parem, <expan abbr="atq;">atque</expan> incon&longs;tantem motum obtinere cernuntur.</s> </p> <p type="main"> <s id="s.001690">6. Argumento præterea e&longs;t cometas ho&longs;ce minimè elementares fui&longs;&longs;e, <lb/>quod hic eorum proprius motus, quo maximo illo tramite ferebantur, nun­<lb/> quam tantus fuit, vt proprium Lunæ motum, vel tardi&longs;&longs;imum adæquauerit, <lb/> quæ quidem cum lenti&longs;&longs;ima e&longs;t plus denis gradibus vna die promouetur; <lb/> cum tamen cometæ 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 longè &longs;upra Lunam cur&longs;um &longs;uum <lb/> ab&longs;olui&longs;&longs;e manife&longs;tè comprobari po&longs;&longs;it: quo enim &longs;ydera magis à terra at­<lb/> tolluntur, <expan abbr="octauæ&qacute;">octauæque</expan>; &longs;phæræ propius accedunt, eò tardioribus proprijs la­<lb/>tionibus proferuntur: ita vt &longs;tellæ i&longs;tæ cœlo ad&longs;cititiæ &longs;upra Lunam admo­<lb/> dum euehendæ videantur. </s> <s id="s.001691">Quod &longs;i in &longs;uprema aeris regione conflagrarent, <lb/> qua nam ratione vnà cum toto cœlo 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 perne citate, <lb/> qua cœle&longs;tes orbes, verum minori admodum imò tardi&longs;&longs;imè à diurno mo­<lb/> tu, &longs;i tamen eo rapitur circumduci.</s> </p> <p type="main"> <s id="s.001692">7. Tandem argumentum ex ip&longs;orum duratione de&longs;umatur. </s> <s id="s.001693">cætera nam­<lb/> que meteora &longs;tatim <expan abbr="atq;">atque</expan> apparuerint, veluti temporanea pror&longs;us, <expan abbr="atq;">atque</expan> eua­<lb/> nida extinguuntur: At verò cometæ ad men&longs;em aliquando integrum per­<lb/> &longs;euerant. </s> <s id="s.001694">quì igitur fieri potuerit, vt in hac corruptibili <expan abbr="mũdi">mundi</expan> parte ex ma­<lb/>teria adeò fluxa, & vaga, quam illis Ari&longs;toteles &longs;upponit, tandiu perdura­<lb/> re potui&longs;&longs;ent.</s> </p> <p type="main"> <s id="s.001695"><expan abbr="Atq;">Atque</expan> hæ &longs;unt rationes, quibus plurimi a&longs;tronomorum recentiorum, co­ <pb pagenum="94" xlink:href="009/01/094.jpg"/>metas ho&longs;ce motum æthereæ regioni conformem, contrà quam Ari&longs;t. opi­<lb/>natus e&longs;t, obtinui&longs;&longs;e, manife&longs;tum e&longs;&longs;e volunt; ac proinde eorum locum, & <lb/> cur&longs;um in cœle&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"> <s id="s.001696">Verumenimuerò Peripatetica omnis &longs;chola reclamat; Cœlum e&longs;t inge­<lb/>nerabile, & incorruptibile, nihil igitur noui cœlo pote&longs;t accidere. </s> <s id="s.001697">&longs;ed age <lb/> re&longs;pondent, nonne omnium a&longs;tronomorum con&longs;en&longs;u &longs;tellæ tres nouæ no&longs;tro <lb/> hoc &longs;æculo in cœlo toti mundo con&longs;picuæ illuxerunt? </s> <s id="s.001698"><expan abbr="eas&qacute;">easque</expan>; in octaua &longs;phæ­<lb/>ra re&longs;edi&longs;&longs;e con&longs;tans e&longs;t omnium a&longs;&longs;ertio? </s> <s id="s.001699">quarum prior anno 1572. in con­<lb/> &longs;tellatione Ca&longs;&longs;iopeæ apparuit. </s> <s id="s.001700">Secunda anno 1600. in Cygno, quæ nec dum <lb/> extinguitur. </s> <s id="s.001701">Tertia anno 1604. inter Sagittarij &longs;tellas vi&longs;a e&longs;t, de quibus vi­<lb/> de P. <!-- REMOVE S-->Clauium in &longs;phæra breuiter de illis tractantem: aut &longs;i mauis, & 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> <s id="s.001702">con&longs;ule etiam de reliquis duabus Ioannis Kepleri Cæ&longs;areæ Maie­<lb/> &longs;tatis Mathematici commentaria; & coactus libenter fateberis noui ali­<lb/> quid cœlo aduenire po&longs;&longs;e.</s> </p> <p type="main"> <s id="s.001703">Po&longs;tremò tandem po&longs;&longs;et qui&longs;piam in hunc <expan abbr="modũ">modum</expan> opponere: etiam &longs;i con­<lb/> &longs;tet <expan abbr="quinq;">quinque</expan> cometas c&etail;lo oberra&longs;&longs;e, non propterea dicemus reliquos omnes <lb/> e&longs;&longs;e pariter cœle&longs;tes, <expan abbr="nullum&qacute;">nullumque</expan>; proinde &longs;ublunarem. </s> <s id="s.001704">Huic memorati A&longs;tro­<lb/> nomi &longs;ic re&longs;ponderent; id quidem mathematica, & infallibili ratione non <lb/> colligi, imò aliquot parum infra Lunam extiti&longs;&longs;e, non omninò negandum <lb/> videri: at verò in &longs;uperiori aeris plaga, in tam fluxa, ac in&longs;tabili mundi par­<lb/> te, cometas vnquam efful&longs;i&longs;&longs;e, nemo &longs;ibi ob allatas rationes meritò per&longs;ua­<lb/> dere po&longs;&longs;e.</s> </p> <p type="main"> <s id="s.001705"><arrow.to.target n="marg137"/></s> </p> <p type="margin"> <s id="s.001706"><margin.target id="marg137"/>137</s> </p> <p type="main"> <s id="s.001707">Summæ 2. cap. 5. <emph type="italics"/>(Ad hæc autem &longs;i quemadmodum o&longs;tenditur in ijs, quæ cir­<lb/>ca Astrologiam &longs;peculationibus, Solis magnitudo maior e&longs;t quàm terræ; & di&longs;tan­<lb/> tia multò maior a&longs;trorum ad terram quàm So is; &longs;icut Solis ad terram quàm Lu­<lb/> næ; non <expan abbr="vtiq;">vtique</expan> longè alicubi à terra conus, qui à Sole, conijciet radios, <expan abbr="neq;">neque</expan> vtique <lb/>vmbra terræ, quæ vocatur nox, erit apud astra; &longs;ed nece&longs;&longs;e Solem omnia a&longs;tra cir­<lb/> cun&longs;picere, & nulli ip&longs;orum terram ob&longs;istere)<emph.end type="italics"/> ex dictis &longs;umma 1. cap. 3. huius, <lb/> & ex figura ibi de&longs;cripta, facilè e&longs;t intelligere præ&longs;entem locum; nam cum <lb/> Sol &longs;it multò maior terra, vt ibi probatur, ac minus di&longs;ter à terra quàm fixæ <lb/> &longs;tellæ, magis tamen quàm Luna, vt patet ex &longs;olari eclyp&longs;i, &longs;equitur nece&longs;&longs;a­<lb/> riò vmbram terræ, quæ nox e&longs;t ip&longs;a, effici turbinatam, & valdè procul à ter­<lb/> ra acumen coni vmbræ a&longs;cendet, &longs;ed paulò &longs;upra Lunam conus hic vmbræ <lb/> permittet radios Solis &longs;e ip&longs;um ambientes iterum &longs;imul committi, quod il­<lb/> lis verbis <emph type="italics"/>(Conijciet radios)<emph.end type="italics"/> ide&longs;t committet radios expre&longs;&longs;it Ari&longs;t. cum igi­<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 tenebras offundet. </s> <s id="s.001708">quod <lb/> etiam experientia confirmat, cum nunquam a&longs;tra illa, quæ Soli opponuntur, <lb/> <expan abbr="quæ&qacute;">quæque</expan>; vertex vmbræ collimat, vllam <expan abbr="patiãtur">patiantur</expan> eclyp&longs;im. </s> <s id="s.001709">quare &longs;ine vllo ter­<lb/>ræ impedimento Sol pote&longs;t affixa omnia &longs;ydera per lu&longs;trare. </s> <s id="s.001710">Exactiores ha­<lb/> rum rerum demon&longs;trationes &longs;unt alterius loci.</s> </p> <p type="main"> <s id="s.001711"><arrow.to.target n="marg138"/></s> </p> <p type="margin"> <s id="s.001712"><margin.target id="marg138"/>138</s> </p> <p type="main"> <s id="s.001713">Eodem cap. <emph type="italics"/>(Amplius autem e&longs;t tertia quædam opinio de ip&longs;o, dicunt enim<emph.end type="italics"/> <pb pagenum="95" xlink:href="009/01/095.jpg"/><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut & &longs;tellam comatam; im­<lb/> po&longs;&longs;ibile autem e&longs;t & hoc, &longs;i enim videns quieuerit & &longs;peculum, & quod videtur <lb/> omne in eodem puncto &longs;peculi eadem apparebit <expan abbr="vtiq;">vtique</expan> pars imaginis, &longs;i autem mo­<lb/> ueatur &longs;peculum, & quod videtur, in eadem quidem di&longs;tantia ad videns, & quie­<lb/> &longs;cens; ad inuicem autem <expan abbr="neq;">neque</expan> æquè velociter, <expan abbr="neq;">neque</expan> in eadem &longs;emper di&longs;tantia im­<lb/> po&longs;&longs;ibile eandem imaginem in eadem e&longs;&longs;e parte &longs;peculi. </s> <s id="s.001714">Quæ autem in lactis circu­<lb/> lo feruntur a&longs;tra, & Sol, ad quem fit reflexio, mouentur manentibus nobis, & &longs;i­<lb/> militer, & æqualiter ad nos di&longs;tantia; à &longs;e ip&longs;is autem non æqualiter: aliquando <lb/> enim medijs noctibus Delphin oritur, aliquando verò diluculo. </s> <s id="s.001715">partes autem lactis <lb/> eædem manent in vnoquoque; atqui non oportebat, &longs;i erat imago, &longs;ed non in ei&longs;dem <lb/> adhuc e&longs;&longs;et hæc pa&longs;&longs;io locis)<emph.end type="italics"/> in his Ari&longs;t. confutat opinionem dicentium Gala­<lb/> xiam apparere per quandam reflexionem vi&longs;us no&longs;tri ab illa parte c&etail;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, quæ dicitur Catoptrica, &longs;iue &longs;pecularia, quia <lb/> tractat de vi&longs;ione reflexa, quæ fit mediante &longs;peculo, quam quidem rationem <lb/> &longs;i vellem mathematicè explicare, longa nimis, ac præter in&longs;titutum fieret <lb/> tractatio. </s> <s id="s.001716">Pauca tamen addam, quæ Ari&longs;totelis <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> &longs;atis per&longs;picuam <lb/> reddant. </s> <s id="s.001717">&longs;i igitur inquit, Galaxia nihil aliud e&longs;&longs;et quàm reflexio no&longs;tri vi&longs;us <lb/> ex illa cœli 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, quàm Sol vi&longs;us per reflexionem ex illa cœli parte tan­<lb/> quam &longs;peculo; &longs;equeretur eam non &longs;emper in eadem cœli parte apparere, <lb/> &longs;ed modo in vna, modo in alia, ita vt &longs;patio vnius anni totum cœlum perua­<lb/> garetur: quod tamen non accidit. </s> <s id="s.001718">quod autem illud con&longs;equatur manife­<lb/> &longs;tum e&longs;&longs;e pote&longs;t ex ob&longs;eruatione eorum, quæ ex &longs;peculis videntur: tunc enim <lb/> res per &longs;pe culum vi&longs;a in eadem &longs;peculi parte apparet, quando & videns, & <lb/> &longs;peculum, & obiectum immota manent: quod &longs;i & &longs;peculum, & obiectum ad <lb/> inuicem accedant, vel recedant, &longs;eruata tamen eadem ab in&longs;pectore di&longs;tan­<lb/> tia, nullo modo fieri pote&longs;t, vt eadem imago, in eadem &longs;peculi parte &longs;pe­<lb/> ctanti videatur, ni&longs;i obiectum &longs;peculo per eandem lineam accedat, &longs;ecun­<lb/> dum quam illi incidebat. </s> <s id="s.001719">At verò partibus illis lactei circuli, &longs;iue a&longs;tris, quæ <lb/> in eo fulgent, Sol perpetuò accedit, vel recedit, <expan abbr="neq;">neque</expan> per lineam incidentiæ <lb/> <expan abbr="eãdem">eandem</expan>, &longs;eruata tamen eadem à nobis di&longs;tantia, quod quidem inde patet, quia <lb/> Delphini con&longs;tellatio, qui in ip&longs;o ferè lacte exi&longs;tit, <expan abbr="aliquãdo">aliquando</expan> medijs noctibus, <lb/> aliquando verò mane, aliquando etiam ve&longs;peri oritur; quod inde accidit, <lb/> quia illi Sol modò appropinquat, modò coniungitur, modò 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<lb/> tuò in alijs, <expan abbr="atq;">atque</expan> alijs cerneretur, cuius tamen contrarium videmus. </s> <s id="s.001720">ex qui­<lb/> bus con&longs;tat fal&longs;am omninò e&longs;&longs;e eorum &longs;ententiam, qui Galaxiam per huiu&longs;­<lb/>modi reflexionem fieri opinabantur. </s> <s id="s.001721">Quæ dicta &longs;unt de &longs;peculo, & obiecto <lb/> &longs;atius e&longs;t a&longs;&longs;umpto aliquo &longs;peculo experiri, quàm ea pluribus ob&longs;curare: qua <lb/>etiam experientia Ari&longs;t. ratio confirmabitur.</s> </p> <p type="main"> <s id="s.001722"><arrow.to.target n="marg139"/></s> </p> <p type="margin"> <s id="s.001723"><margin.target id="marg139"/>139</s> </p> <p type="main"> <s id="s.001724">Ibidem <emph type="italics"/>(Quæ autem in lactis cir culo feruntur astra, & Sol, ad quem fit refle­<lb/>xio, mouentur manentibus nobis, & &longs;imiliter, & æqualiter ad nos di&longs;tantia à &longs;e <lb/> ip&longs;is autem non æqualiter)<emph.end type="italics"/> quæ hic ab Ari&longs;totele dicuntur <expan abbr="nõ">non</expan> &longs;unt v&longs;que quaque <lb/>vera propter apogæum, ac perigæum Solis, quæ quidem duo ab omnibus <lb/> a&longs;tronomis a&longs;&longs;eruatur: quando igitur Sol e&longs;t in apogæo, maiori multo in­ <pb pagenum="96" xlink:href="009/01/096.jpg"/>teruallo di&longs;tat à nobis, quàm quando e&longs;t in perigæo, interuallum enim illud <lb/> con&longs;tat diametris terræ duobus, & quadraginta, hoc e&longs;t milliarijs 208000. <lb/> ferè, ide&longs;t octonis millibus &longs;upra ducenta millia. </s> <s id="s.001725">quæ differentia facit vt Sol <lb/> manife&longs;tè appareat nobis minor apogæus, quàm perigæus. </s> <s id="s.001726">Sol præterea &longs;i­<lb/> militer ip&longs;is inerrantibus &longs;tellis fit tantumdem modo remotior, modo pro­<lb/> pinquior: &longs;ed fortè Ari&longs;t. i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/> per&longs;pecta erant.</s> </p> <p type="main"> <s id="s.001727"><arrow.to.target n="marg140"/></s> </p> <p type="margin"> <s id="s.001728"><margin.target id="marg140"/>140</s> </p> <p type="main"> <s id="s.001729">Ibidem <emph type="italics"/>(Aliquando enim medijs noctibus Delphin oritur)<emph.end type="italics"/> vt probet, Gala­<lb/> xiam non &longs;emper &longs;eruare à Sole di&longs;tantiam eandem, accipit tanquam huius <lb/> rei &longs;ignum, manife&longs;tum, quod Delphini con&longs;tellatio aliquando medijs no­<lb/> ctibus oriatur &longs;upra horizontem, aliquando verò diluculo; non ideò 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 cœlo, vel etiam &longs;i mauis in globo a&longs;tronomico: non ta­<lb/> men ob id Ari&longs;t. ratio minus valida redditur, cum Delphinus &longs;emper Gala­<lb/> xiæ eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s> </p> <p type="main"> <s id="s.001730"><arrow.to.target n="marg141"/></s> </p> <p type="margin"> <s id="s.001731"><margin.target id="marg141"/>141</s> </p> <p type="main"> <s id="s.001732">Summæ 2. cap. 6. Sunt qui velint Ari&longs;t. <!-- REMOVE S-->Galaxiam nihil aliud e&longs;&longs;e, quàm <lb/> quandam refractionem lucis &longs;tellarum illarum, quæ &longs;unt in ætherea Gala­<lb/> xia, quæ inquam refractio fiat circa &longs;upremam aeris regionem ex occur&longs;u <lb/> exhalationum, quæ ibi perpetuò con&longs;eruantur, & vi earumdem &longs;tellarum <lb/> &longs;ur&longs;um &longs;emper attrahuntur, quæ refractio fiat ad eum modum, quo halo cir­<lb/> ca Solem, & Lunam. <!-- KEEP S--></s> <s id="s.001733">& quemadmodum halo, &longs;iue area omnibus <expan abbr="vndecunq;">vndecunque</expan> <lb/> a&longs;picientibus &longs;emper videntur in eodem cœli loco, hoc e&longs;t è regione Solis, <lb/> vel Lunæ; &longs;imiliter Galaxia in aere omnibus <expan abbr="vndecunq;">vndecunque</expan> intuentibus appa­<lb/> reat in eadem cœli parte, ide&longs;t ex aduersò eorumdem &longs;yderum, quæ cœle­<lb/> &longs;tem lacteam viam conficiunt. </s> <s id="s.001734">Porrò qui &longs;ic mentem Ari&longs;t. exponunt, nul­<lb/> lo modo po&longs;&longs;unt à Mathematicis redargui per rationem de&longs;umptam à di­<lb/> uer&longs;itate a&longs;pectus (quam po&longs;tea explicabo) quamuis phy&longs;icis rationibus re­<lb/> fellantur. </s> <s id="s.001735">Alij &longs;unt, quorum &longs;ententia magis videtur <expan abbr="improbãda">improbanda</expan>, eò quod <lb/> Ari&longs;t. &longs;ummum Philo&longs;ophum pueriliter in a&longs;tronomia lap&longs;um fateri cogan­<lb/> tur. </s> <s id="s.001736">Exi&longs;timant hi Galaxiam hanc Ari&longs;totelicam nihil aliud e&longs;&longs;e, quàm ip­<lb/> &longs;as tenues exhalationes in aere &longs;ubuectas, directèque infra &longs;tellas illas la­<lb/> cteum circulum in cœlo con&longs;tituentes nobis obiectas. </s> <s id="s.001737">qui præter innumera, <lb/> ac magna ab&longs;urda è naturali Philo&longs;ophia petita, vnum maximum ex A&longs;tro­<lb/> nomia, nempè ex diuer&longs;itate a&longs;pectus de&longs;umptum, nullo modo vitare po&longs;­<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<lb/> nibus, <expan abbr="neq;">neque</expan> ex omni terræ loco per eadem &longs;ydera commeare cerneretur, &longs;ed <lb/> è diuer&longs;is, & præcipuè ab inuicem valde di&longs;&longs;itis, circa diuer&longs;a a&longs;tra &longs;e &longs;e ocu­<lb/> lis no&longs;tris obijceret: at te&longs;timonio &longs;en&longs;us con&longs;tat, Galaxiam &longs;emper in eo­<lb/> dem loco; <expan abbr="eadem&qacute;">eademque</expan>; à &longs;yderibus fixis di&longs;tantia albicare, ergò nullo modo <lb/> viam hanc in aere qua&longs;i pendulam fabricare debemus. </s> <s id="s.001738">rationem hanc di­<lb/> uer&longs;itatis a&longs;pectus a&longs;tronomicè magis explicatam reperies apud Clauium <lb/> in &longs;phæra. </s> <s id="s.001739">Porrò hæc ratio quamuis adeo certa, ac no&longs;tra tempe&longs;tate vul­<lb/> gata, parum tamen à nonnullis de rebus Meteorologicis commentaria con­<lb/> farcinantibus intellecta, minimè eos ab&longs;terrere potuit, quin prædictam opi­<lb/> nionem, non &longs;olum Ari&longs;toteli imponerent, verum etiam ip&longs;i <expan abbr="tãquam">tanquam</expan> veram <pb pagenum="97" xlink:href="009/01/097.jpg"/>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"> <s id="s.001740"><arrow.to.target n="marg142"/></s> </p> <p type="margin"> <s id="s.001741"><margin.target id="marg142"/>142</s> </p> <p type="main"> <s id="s.001742">Eodem cap. <emph type="italics"/>(Ad hæc autem locus plenus e&longs;t a&longs;tris maximis, & fulgidi&longs;&longs;imis, <lb/> & adhuc &longs;par&longs;is vocatis)<emph.end type="italics"/> non &longs;olum viam hanc lacteam a&longs;tris plurimis refer­<lb/> ti&longs;&longs;imam e&longs;&longs;e videmus, &longs;ed præterea eandem &longs;tellarum admodum feracem <lb/> appellare licebit, &longs;i quidem &longs;tellæ omnes illæ nouæ, quæ no&longs;tra tempe&longs;tate <lb/> apparuerunt, omnes in hac via exortæ &longs;unt. </s> <s id="s.001743">prima enim anno 1572. efful&longs;it <lb/> in Ca&longs;&longs;iopea; altera anno 1600. in Cygno. </s> <s id="s.001744">tertia demum anno 1604. in Sa­<lb/> gittario, quæ omnes con&longs;tellationes intra lacteum circulum continentur. <lb/> </s> <s id="s.001745">Veri&longs;&longs;imum præterea e&longs;&longs;e hoc idem confirmatur in&longs;trumenti illius mirabi­<lb/> lis auxilio, quod &longs;uperiori anno in Belgio excogitatum, & po&longs;tea in Italia <lb/> à Galilæo perfectius <expan abbr="redditũ">redditum</expan> e&longs;t, <expan abbr="quod&qacute;">quodque</expan>; ip&longs;e primum Italicè Cannocchiale, <lb/> Latinè verò, & quidem aptè à Græcis 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, certò certius <lb/> con&longs;tat; &longs;ed &longs;atius e&longs;t ip&longs;ius Galilæi verba ex Nuncio &longs;ydereo referre: Quod <lb/> tertio inquit, loco à nobis fuit ob&longs;eruatum e&longs;t ip&longs;iu&longs;met lactei circuli e&longs;&longs;en­<lb/> tia, &longs;en materies, quam Tele&longs;copij beneficio adeò ad &longs;en&longs;um licet intueri, <lb/> vt & altercationes omnes, quæ per tot &longs;æcula Philo&longs;ophos excruciarunt ab <lb/> oculata certitudine <expan abbr="dirimãtur">dirimantur</expan>, <expan abbr="nos&qacute;">nosque</expan>; à verbo&longs;is di&longs;putationibus liberemur: <lb/> e&longs;t enim Galaxia nihil aliud, quàm innumerarum &longs;tellarum coaceruatim <lb/> con&longs;itarum congeries, in <expan abbr="quãcunq;">quancunque</expan> enim regionem illius &longs;pecillum dirigas, <lb/>&longs;tatim &longs;tellarum ingens frequentia &longs;e &longs;e in con&longs;pectum profert, <expan abbr="quarũ">quarum</expan> com­<lb/> plures &longs;atis magnæ, ac valdè con&longs;picuæ videntur; &longs;ed exiguarum multitudo <lb/> pror&longs;us inexplorabilis e&longs;t. </s> <s id="s.001746">hæc ille.</s> </p> <p type="main"> <s id="s.001747"><arrow.to.target n="marg143"/></s> </p> <p type="margin"> <s id="s.001748"><margin.target id="marg143"/>143</s> </p> <p type="main"> <s id="s.001749">Eodem cap. <emph type="italics"/>(Con&longs;ideretur autem & circulus, & quæ &longs;unt in ip&longs;o a&longs;tra ex de­<lb/> &longs;criptione)<emph.end type="italics"/> id e&longs;t, con&longs;ideretur Galaxia, & 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<lb/> culum graphicè effingere. </s> <s id="s.001750">huiu&longs;modi globum veteres &longs;ph&etail;ram Aratæam di­<lb/> cebant ab Arato Poeta græco, qui <expan abbr="cõ&longs;tellationes">con&longs;tellationes</expan> omnes carmine pro&longs;equu­<lb/> tus e&longs;t, ac proinde globum hunc ordine expo&longs;uit:</s> </p> <p type="main"> <s id="s.001751"><arrow.to.target n="marg144"/></s> </p> <p type="margin"> <s id="s.001752"><margin.target id="marg144"/>144</s> </p> <p type="main"> <s id="s.001753">Eodem cap. <emph type="italics"/>(Spar&longs;a autem vocata)<emph.end type="italics"/> putò &longs;par&longs;a hæc &longs;ydera illa e&longs;&longs;e, quæ <lb/> recentiores informia appellant, eò quod ad aliorum a&longs;teri&longs;morum formas <lb/> minimè reuocentur.</s> </p> <p type="main"> <s id="s.001754"><arrow.to.target n="marg145"/></s> </p> <p type="margin"> <s id="s.001755"><margin.target id="marg145"/>145</s> </p> <p type="main"> <s id="s.001756">Summa 4. cap. 1. <emph type="italics"/>(In A&longs;ia igitur plurimi ex Parna&longs;&longs;o vocato monte videntur <lb/>fluentes)<emph.end type="italics"/> rectè dubitat Alexander, qua ratione mons Parna&longs;&longs;us ab Ari&longs;t. po­<lb/> natur in A&longs;ia, cum certò certius con&longs;tet, ip&longs;um in Græcia Europæ regione <lb/> &longs;itum e&longs;&longs;e. </s> <s id="s.001757">fortè legendum e&longs;t, vt vult Vicomercatus, ex Paropame&longs;&longs;o, non <lb/> autem ex Parna&longs;&longs;o, quamuis Græci codices aduer&longs;entur; Paropame&longs;&longs;um <lb/> <expan abbr="namq;">namque</expan> Plinius, & Strabo in A&longs;ia collocant, <expan abbr="volunt&qacute;">voluntque</expan>; ip&longs;um e&longs;&longs;e iugum quod­<lb/>dam montis Cauca&longs;i: Cauca&longs;um autem &longs;upra Pontum oriri, & <expan abbr="v&longs;q;">v&longs;que</expan> ad Hir­<lb/> canum, & vltra mare per totam A&longs;iam &longs;e proferre, tradunt veteres Geo­<lb/> graphi. </s> <s id="s.001758">vide The&longs;aurum geographicum Abrahami Ortelij. </s> <s id="s.001759">Strabo lib. 15. <lb/> &longs;ic: Indiam à &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/> orientale mare, quæ extrema indigenæ particulatim nominant Poropami&longs;­ <pb pagenum="98" xlink:href="009/01/098.jpg"/>&longs;um, Emodum, Imauum, & alijs nominibus: Macedones verò Cauca&longs;um <lb/> vocant.</s> </p> <p type="main"> <s id="s.001760"><arrow.to.target n="marg146"/></s> </p> <p type="margin"> <s id="s.001761"><margin.target id="marg146"/>146</s> </p> <p type="main"> <s id="s.001762">Ibidem <emph type="italics"/>(Apparet mare, quod e&longs;t extra)<emph.end type="italics"/> intelligit illud mare <expan abbr="Oceanũ">Oceanum</expan>, quod <lb/> Arabiam, ac Per&longs;iam alluit, <expan abbr="Indico&qacute;">Indicoque</expan>; Oceano committitur: <expan abbr="quod&qacute;">quodque</expan>; à pri­<lb/> &longs;cis Geographis Rubrum mare appellatur, cuius alterum Rubrum mare, <lb/> quod inter Africam, & Arabiam &longs;e in&longs;inuat, e&longs;t quidam &longs;inus, quem nunc <lb/> communiter omnes Rubrum mare appellant. </s> <s id="s.001763">de illo inquam meritò intel­<lb/> ligit Alexander, non de hoc Aegyptiaco, cum ex a&longs;pectu illius à monte Pa­<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> <s id="s.001764">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"> <s id="s.001765"><arrow.to.target n="marg147"/></s> </p> <p type="margin"> <s id="s.001766"><margin.target id="marg147"/>147</s> </p> <p type="main"> <s id="s.001767">Ibidem <emph type="italics"/>(Ex hoc igitur fluunt & alij fluuij, & Bactrus, & Choa&longs;pes, & Ara­<lb/> xes. </s> <s id="s.001768">ab hoc autem ab&longs;cinditur Tanais pars exi&longs;tens in Meotidem paludem fluit au­<lb/> tem, & Indus ex ip&longs;o, omnium fluuiorum fluxio maxima)<emph.end type="italics"/> hæc omnia &longs;unt fal&longs;a, <lb/> & impo&longs;&longs;ibilia; nam cum Bactrus Bactrianam regionem irriget, quæ e&longs;t vl­<lb/> tra Per&longs;iam, Choa&longs;pes verò Per&longs;iam ip&longs;am, Indus <expan abbr="deniq;">denique</expan> in India oriatur: <lb/> quì fieri pote&longs;t, vt in Regionibus adeò inuicem di&longs;&longs;itis orti fluuij ab eodem <lb/> <expan abbr="quoq;">quoque</expan> Paropame&longs;&longs;o monte ortum ducant. </s> <s id="s.001769">nec minus fal&longs;um e&longs;t illud de Ta­<lb/> nai, quod &longs;it qua&longs;i ip&longs;ius Araxis ramus quidam, Tanais enim ex Riphæis <lb/> <expan abbr="mõtibus">montibus</expan> Scythiæ delabitur in Meotidem paludem longè longius ab Araxi. <lb/> <!-- KEEP S--></s> <s id="s.001770"><expan abbr="eum&qacute;">eumque</expan>; terminum inter Europam, & A&longs;iam Geographi con&longs;tituunt, vnde <lb/> Diony&longs;ius Afer &longs;ic cecinit:</s> </p> <p type="main"> <s id="s.001771"><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"> <s id="s.001772">verùm huiu&longs;modi errata Ari&longs;t. <!-- REMOVE S--><expan abbr="atq;">atque</expan> adeò Geographis illius temporis con­<lb/> donanda &longs;unt, cum nondum Geographia &longs;atis exculta e&longs;&longs;et.</s> </p> <p type="head"> <s id="s.001773"><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001774"><arrow.to.target n="marg148"/></s> </p> <p type="margin"> <s id="s.001775"><margin.target id="marg148"/>148</s> </p> <p type="main"> <s id="s.001776">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> æ&longs;tiua­<lb/> lem, & multitudine, & altitudine &longs;igna autem altitudinis quidem, quia <lb/> videtur & à vocatis Profundis, & à nauigantibus in Stagnum in&longs;uper il­<lb/> lu&longs;trantur à Sole ip&longs;ius &longs;ummitates, v&longs;que ad tertiam partem nocte, & ab <lb/> aurora, & iterum a ve&longs;pera)<emph.end type="italics"/> Cauca&longs;us mons &longs;itus e&longs;t inter mare Euxinum, & <lb/> Ca&longs;pium, &longs;upra Cholchidem, & Iberiam regiones, vbi polus eleuatur 47. <lb/> circiter grad. <!-- REMOVE S-->ac re&longs;pectu Græciæ, & maris Euxini vergit ad eam mundi pla­<lb/> gam, vnde illis æ&longs;tiuo tempore Sol oritur. </s> <s id="s.001777">ait Ari&longs;t. eum e&longs;&longs;e omnium mon­<lb/> tium illius plagæ alti&longs;&longs;imum, quod probat primò, quia admodum à longè <lb/> cernitur, <expan abbr="nimirũ">nimirum</expan> ab illo Euxini loco, qui Profunda vocatur, eò quòd à Nau­<lb/> tis nu&longs;quam ibi fundus reperiatur. </s> <s id="s.001778">& præterea à Nauigantibus in Stagnum, <lb/> &longs;iue in Meotidem paludem, quæ quidem loca minimùm di&longs;tant a Cauca&longs;o <lb/> 560. milliaribus. </s> <s id="s.001779">Secundò, probat il ius altitudinem ex eo, quòd &longs;ummi­<lb/> tates ip&longs;ius <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam partem nocte, & ve&longs;peri à Sole illu&longs;trentur. </s> <s id="s.001780">Lo­<lb/> cum hunc fusè pertractat eruditi&longs;&longs;imus Iacobus Mazonius &longs;ectione 3. & 4. <lb/> de Comparatione Platonis, & Ari&longs;t. quo in opere plurima habet ex Mathe­<lb/> maticis de&longs;umpta, quibus naturalem Philo&longs;ophiam mirificè illu&longs;trat, <expan abbr="mani-fe&longs;tum&qacute;">mani­<lb/> fe&longs;tumque</expan>; reddit, quàm nece&longs;&longs;ariæ &longs;int Mathematicæ ad philo&longs;ophicæ veri­ <pb pagenum="99" xlink:href="009/01/099.jpg"/>tatis in&longs;pectionem. </s> <s id="s.001781">Is igitur &longs;ect. </s> <s id="s.001782">3. cap. 5. de hoc Ari&longs;t. loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="tũ">tum</expan> quia <lb/> multis an&longs;am dedit reprehendendi Ari&longs;t. tanquam puerilia effutientem. </s> <s id="s.001783">tex­<lb/> tus <expan abbr="itaq;">itaque</expan> Ari&longs;t. duplicem habet &longs;en&longs;um; alter à quo non abhorret <expan abbr="Alexãder">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 hæc Mazonij expo&longs;itio nulla e&longs;t, cuiu&longs;libet enim montis etiam medio­<lb/> cris altitudinis Sol illu&longs;trat non &longs;olum tertiam partem, &longs;ed & dimidium, & <lb/> duas tertias, & ferè totum, antequam ad planam illius ba&longs;im de&longs;cendat. <lb/> </s> <s id="s.001784">Ego &longs;ic exponendum cen&longs;eo, vt Ari&longs;t. dicat, mane, ide&longs;t initio Crepu&longs;culi <lb/> matutini, & ve&longs;pere, ide&longs;t, in fine Crepu&longs;culi ve&longs;pertini ip&longs;ius tertiam par­<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;ariò re&longs;pectu Cauca&longs;i &longs;unt occidentales, <lb/> quì manè hoc vident, vti &longs;unt ij, qui in Euxino, &longs;eu Ponto, & Meotide naui­<lb/> gant, vel loca proxima inhabitant: illi verò, qui in fine Crepu&longs;culi ve&longs;per­<lb/> tini hoc cernunt, nece&longs;&longs;ariò re&longs;pectu Cauca&longs;i erunt orientales. </s> <s id="s.001785">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 manè. </s> <s id="s.001786">v. <!-- REMOVE S-->g. <!-- REMOVE S-->initio tertiæ, & vltimæ noctis <lb/> parte, cacumen Cauca&longs;i illuminetur. </s> <s id="s.001787">hæc ille. </s> <s id="s.001788">vbi animaduertendum expo­<lb/> &longs;itionem <expan abbr="hãc">hanc</expan> parùm differre à no&longs;tra modò allata, cùm <expan abbr="vtraq;">vtraque</expan> in idem tem­<lb/> pus recidat; nam &longs;i dixerimus initio Crepu&longs;culi matutini illuminari ter­<lb/> tiam partem Cauca&longs;i, tempus hoc coincidit cum initio tertiæ partis noctis, <lb/> quantitas enim Crepu&longs;culi in poli eleuatione 47. grad. <!-- REMOVE S-->qualem habet Cau­<lb/> ca&longs;us, per totam æ&longs;tatem tres horas plus minus continet, vt patet ex tabu­<lb/> la quantitatis Crepu&longs;culi, quæ e&longs;t apud Nonium, & apud Clauium in &longs;phæ­<lb/> ra vltimæ editionis; quæ quantitas reperiri geometrico calculo pote&longs;t, vt <lb/> docent Nonius, Clauius, & Maginus lib. 10. primi mob. </s> <s id="s.001789">quod quidem trium <lb/> circiter horarum tempus e&longs;t tertia ferè 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 tertiæ partis noctis, erit idem tempus, trium &longs;cilicet horarum. <lb/> </s> <s id="s.001790">&longs;i ergo, inquit Mazonius, &longs;equamur priorem declarationem, nece&longs;&longs;arium <lb/> e&longs;t dicere, quod ea tertia pars montis, quæ initio auroræ Solis lumine per­<lb/> funditur, &longs;it ea montis altitudo, qua ip&longs;e exuperat illam aeris regionem, <lb/> vnde Crepu&longs;culum incipit apparere. </s> <s id="s.001791">quo po&longs;ito aptè, ac &longs;agaciter altitudi­<lb/> nem Cauca&longs;i inue&longs;tigat hoc pacto. </s> <s id="s.001792">præmittit autem &longs;eptem propo&longs;itiones <lb/> apud Mathematicos manife&longs;tas, quas ego mi&longs;&longs;as facio cum non mihi nece&longs;­<lb/> &longs;ariæ videantur. </s> <s id="s.001793">po&longs;tea &longs;ic di&longs;currit; His ergo ita &longs;e habentibus, dico nos in­<lb/> uenire po&longs;&longs;e viam, qua &longs;altem rudi Minerua, montis altitudinem comper­<lb/> tam habeamus. </s> <s id="s.001794">&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/>videtur tertiam illam partem &longs;upra eam regionem collocari, ex qua Cre­<lb/> pu&longs;culum in planitie apparere incipit, &longs;ed illa regio ex Alhazino, & Vitell. <lb/> <!-- REMOVE S-->de Crepu&longs;culis milliaribus 52. à terra recedit, ergo duæ tertiæ montis par­<lb/> tes, quæ Solem initio auroræ non vident, &longs;unt 52. milliaria ad perpendicu­<lb/> lum, & 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 papè in quos acu­ <pb pagenum="100" xlink:href="009/01/100.jpg"/>leos imprudens me conieci? </s> <s id="s.001795">rident enim hoc Ari&longs;t. dictum Mathematici, <lb/> putant enim eum pueriliter lap&longs;um e&longs;&longs;e. </s> <s id="s.001796">Cæterum ego pro præceptoris tu­<lb/>tela, dico eum &longs;equutum e&longs;&longs;e famam. </s> <s id="s.001797">hæc Mazonius, quorum nonnulla in­<lb/> digent con&longs;ideratione cuiu&longs;modi, &longs;unt illa, quando dicit, nece&longs;&longs;arium vi­<lb/> detur, quod ea pars &longs;upra eam regionem attollatur, vnde Crepu&longs;culum in <lb/>planitie apparere incipit. </s> <s id="s.001798">videtur enim his verbis velle dicere, quod quan­<lb/> do habitantibus planitiem, quæ e&longs;t ad pedem montis Cauca&longs;i, vel horizon­<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<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 geometricè demon&longs;trabo. </s> <s id="s.001799">de&longs;cribatur enim figura <lb/> <figure id="id.009.01.100.1.jpg" place="text" xlink:href="009/01/100/1.jpg"/> <pb pagenum="101" xlink:href="009/01/101.jpg"/>illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/> & Clauius, in qua terræ globus e&longs;t F L G E, regiò vaporum, & exhalatio­<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, vnà cum. <lb/> </s> <s id="s.001800">Cauca&longs;o F V. <!-- KEEP S--></s> <s id="s.001801">Sol A B C, qui initio Crepu&longs;culi infra horizontem O P, depri­<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> <s id="s.001802">Cæterùm prædicti autho­<lb/> res po&longs;t longam ratiocinationem ex calculo planorum <expan abbr="triangulorũ">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 terræ, quæ e&longs;t milliar. 3579. reliqua L K, &longs;um­<lb/>ma halituum eleuatio relinquatur 52. milliar. </s> <s id="s.001803">quibus ab ip&longs;is demon&longs;tra­<lb/> tis, &longs;i H F, terræ &longs;emidiameter, quæ continet milliar. 3579. ponatur &longs;inus <lb/> totus 100000. & latus F K, ponatur tangens anguli ad H, quem pr&etail;dicti au­<lb/> thores probant e&longs;&longs;e grad. <!-- REMOVE S-->8. 54. erit F K, tangens partium 15659. fiat igi­<lb/> tur per 2. pro. </s> <s id="s.001804">trjang. </s> <s id="s.001805">rectil. </s> <s id="s.001806">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"> <s id="s.001807">& inueniemus per auream regulam latus F K, continere milliar. </s> <s id="s.001808">560. quan­<lb/> ta &longs;cilicet e&longs;t di&longs;tantia ab oculo no&longs;tro ad exhalationes Crepu&longs;culi initium <lb/> efficientes. </s> <s id="s.001809">Con&longs;ideremus iam triangulum F K V, vt ip&longs;ius latus F V, quæ <lb/> e&longs;t Cauca&longs;i altitudo, in milliaribus innote&longs;cat. </s> <s id="s.001810">iam ip&longs;ius latus F K, inno­<lb/> tuit, angulus verò 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 æquales 4. rectis ex 32. primi. </s> <s id="s.001811">duo <lb/> autem F, & I, &longs;unt recti ex 18. 3. ergo reliqui duo H, & K, æquales erunt duo­<lb/> bus rectis, quorum alter H, e&longs;t gr. <!-- REMOVE S-->17. 48. vt præditi 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> <s id="s.001812">qui &longs;i detra­<lb/> hatur à 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 verò F V, tangens anguli noti, erit ip&longs;a 32100. fiat igitur,<lb/> <arrow.to.target n="table5"/></s> </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"> <s id="s.001813"><expan abbr="inueniemus&qacute;">inueniemusque</expan>; latus F V, continere milliar. </s> <s id="s.001814">180. cuius pars F X, quæ e&longs;t in­<lb/> fra habituum altitudinem continet milliar. </s> <s id="s.001815">52. quibus detractis ex 180. re­<lb/> manent 128. pro tota X V, quæ tota e&longs;t &longs;upra vapores, nondum tamen illu­<lb/> minata. </s> <s id="s.001816">vnde patet Mazonium erra&longs;&longs;e in colligenda hoc modo Cauca&longs;i al­<lb/> titudine, ex prima Crepu&longs;culi illuminatione in horizonte Cauca&longs;i facta, <lb/> cum ex præmi&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 multò regionem vaporum, contrà quàm <lb/> ip&longs;e putabat, &longs;uperat enim eam milliar. </s> <s id="s.001817">128. quare duæ tertiæ montis erunt <lb/> non 52. mill. <!-- REMOVE S-->vt ip&longs;e ait, &longs;ed mill. <!-- REMOVE S-->180. & proinde tota altitudo erit mill. <!-- REMOVE S-->270. <lb/> quod &longs;anè ridiculum e&longs;t, cum nullius montis altitudo &longs;e&longs;quimilliare tran­<lb/> &longs;cendat. </s> <s id="s.001818">Quod &longs;i &longs;equamur alteram expo&longs;itionem, vt nimirum Ari&longs;tot. <!-- REMOVE S-->lo­<lb/> quatur non de tertia montis parte, &longs;ed noctis, ita vt dicat, circa initium <lb/> tertiæ partis noctis apicem montis illu&longs;trari, altitudo eius erit tantum­ <pb pagenum="102" xlink:href="009/01/102.jpg"/>modo 180. quot continet latus F V. vt vidimus, quæ quamuis illa minor &longs;it, <lb/> adhuc tamen ab&longs;urda e&longs;t.</s> </p> <p type="main"> <s id="s.001819">Si verò dixerimus Ari&longs;t. intelligere hæc 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<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. intelligatur de tertia montis par­<lb/> te; e&longs;t enim L K, altitudo habituum 52. mill. <!-- REMOVE S-->& duæ tertiæ montis, quare <lb/> totus mons erit 78. &longs;i autem intelligatur circa tertiam noctis partem, mon­<lb/>tis apicem illuminatum videri ab habitatore F, &longs;ic altitudo eius erit tan­<lb/> tummodo 52. mill. <!-- REMOVE S-->quæ tamen adhuc omnem veritatem nimium &longs;uperat. <lb/> </s> <s id="s.001820">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> <s id="s.001821">Verumenimuerò &longs;apientiores iudicent num rectè philo&longs;ophus, cuius e&longs;t re­<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"> <s id="s.001822">Tandem monendus mihi Lector e&longs;t, in demon&longs;tratione Magini, quæ e&longs;t <lb/> apud Mazonium &longs;ect. </s> <s id="s.001823">4. citati operis; a&longs;&longs;umi radium Solis tangentem terræ <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 à centro Solis ad centrum terræ 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 verò 276. vbi etiam, &longs;icut & nos a&longs;&longs;umit horizon­<lb/> tem Cauca&longs;i.</s> </p> <p type="main"> <s id="s.001824">Aduertendum tandem Mazonium admodum aduer&longs;antia loquutum e&longs;&longs;e, <lb/> &longs;ect. </s> <s id="s.001825">enim 3. demon&longs;tratinè concludit altitudinem 76. mill. <!-- REMOVE S-->&longs;ect. </s> <s id="s.001826">verò 4. &longs;i­<lb/> mul <expan abbr="cũ">cum</expan> Magino demon&longs;tratiuè pariter colligit altitudinem eiu&longs;dem 276. m. <lb/> </s> <s id="s.001827">quæ nimis ab inuicem di&longs;crepant, cum tamen <expan abbr="vtrobiq;">vtrobique</expan> demon&longs;tret, & ve­<lb/> ritas &longs;it vna. </s> <s id="s.001828">At verò cau&longs;a huius di&longs;crepantiæ e&longs;t, quòd &longs;ect. </s> <s id="s.001829">3. accipit Cre­<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> <s id="s.001830">vt &longs;upra o&longs;tendimus. </s> <s id="s.001831">&longs;ect. </s> <s id="s.001832">verò 4. accipit horizontem ip&longs;ius Cauca&longs;i, vt ex <lb/> figura illic de&longs;cripta videre e&longs;t. </s> <s id="s.001833">ex hac igitur horizontum varia &longs;uppo&longs;itio­<lb/> ne, varia etiam altitudo colligitur, quamuis <expan abbr="vtrobiq;">vtrobique</expan> ex <expan abbr="vtraq;">vtraque</expan> &longs;uppo&longs;itio­<lb/> ne <expan abbr="vtramq;">vtramque</expan> altitudinem rectè concludat. </s> <s id="s.001834"><expan abbr="Atq;">Atque</expan> hæc de Cauca&longs;o &longs;ufficiant.</s> </p> <p type="main"> <s id="s.001835"><arrow.to.target n="marg149"/></s> </p> <p type="margin"> <s id="s.001836"><margin.target id="marg149"/>149</s> </p> <p type="main"> <s id="s.001837">Eodem cap. <emph type="italics"/>(Ex Pyreneo autem, hic autem est mons ad occidentem æquino­<lb/>ctialem in Gallia, fluunt i&longs;ter, & Tarte&longs;&longs;us, iste quidem extra columnas, I&longs;ter au­<lb/>tem per totam Europam in Pontum Euxinum)<emph.end type="italics"/> Ari&longs;t. fortè &longs;equutus e&longs;t Herodo­<lb/>tum, qui falsò tradit I&longs;trum, &longs;ine Dannbium ex Pyreneis defluere, nam Iu­<lb/> ce clarius con&longs;tat ip&longs;um ex ijs Alpibus, quæ Heluetiorum montes dicuntur, <lb/> propè Ba&longs;ileam ex Adula monte ortum ducere. </s> <s id="s.001838"><expan abbr="neq;">neque</expan> verum e&longs;t Tarte&longs;&longs;um, <lb/> quem & Bœtim alij nominant ex Pyreneis de&longs;cendere. </s> <s id="s.001839">Tarte&longs;&longs;um hunc Ma­<lb/> ginus putat e&longs;&longs;e Tagum, cui fauet vocabulorum quali&longs;cunque &longs;imilitudo. <lb/> </s> <s id="s.001840">extra tamen columnas Herculis qui&longs;quis &longs;it in Oceanum occidentale illa­<lb/> bitur. </s> <s id="s.001841">Igno&longs;cenda &longs;unt i&longs;ta Ari&longs;t. tunc enim Geographia <expan abbr="nondũ">nondum</expan> adoleuerat.</s> </p> <p type="main"> <s id="s.001842"><arrow.to.target n="marg150"/></s> </p> <p type="margin"> <s id="s.001843"><margin.target id="marg150"/>150</s> </p> <p type="main"> <s id="s.001844">Ad finem eiu&longs;dem cap. <emph type="italics"/>(Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/> quidam fluuius, & iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompertũ">incompertum</expan> & hoc <pb pagenum="103" xlink:href="009/01/103.jpg"/>Ari&longs;t. vt &longs;uperiora, ob Geographiæ illius &longs;eculi imperfectionem, nu&longs;quam <lb/> enim in tota Liguria quidpiam tale reperitur.</s> </p> <p type="head"> <s id="s.001845"><emph type="italics"/>De Terræ rotunditate.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001846"><arrow.to.target n="marg151"/></s> </p> <p type="margin"> <s id="s.001847"><margin.target id="marg151"/>151</s> </p> <p type="main"> <s id="s.001848">Svmma 4. cap. 2. quod e&longs;t de permutatione, & vici&longs;&longs;itudine aquarum, <lb/> & continentis. </s> <s id="s.001849">Pergratum Lectori fore exi&longs;timaui, nec alienum ab <lb/> in&longs;tituto, &longs;i occa&longs;ione huius permutationis maris, ac terræ, rem ex­<lb/>po&longs;uero &longs;citu digni&longs;&longs;imam, quam pridem ob&longs;eruare cœpi, ac in dies <lb/> ob&longs;eruo, præ&longs;ertim cum nullus præteritorum &longs;criptorum, quod &longs;ciam, eam <lb/> literis mandauerit: Terræ &longs;cilicet totius molem paulatim reduci ad perfe­<lb/> ctam &longs;phæricitatem, ita vt aliquando nece&longs;&longs;e &longs;it futurum ip&longs;am à mari inun­<lb/> dari, <expan abbr="atq;">atque</expan> omninò inhabitabilem reddi. </s> <s id="s.001850">Primum igitur illud ex &longs;acris lite­<lb/> ris &longs;tatuendum, orbem terræ in &longs;uo primordio fui&longs;&longs;e ab opifice rerum om­<lb/> nium, figura &longs;phærica donatum, hoc e&longs;t <expan abbr="ab&longs;q;">ab&longs;que</expan> montium eminentijs, atque <lb/> vallium depre&longs;&longs;ionibus. </s> <s id="s.001851">quod patet ex eo, quia <expan abbr="tũc">tunc</expan> tota Mari obtegebatur, <lb/> ita vt minimè apta e&longs;&longs;et animantibus ad inhabitandum. </s> <s id="s.001852">redditam verò ha­<lb/> bitabilem, cum ip&longs;ius conditor <expan abbr="quãdam">quandam</expan> ip&longs;ius partem humiliorem, & quan­<lb/> dam eminentiorem effeci&longs;&longs;et; transferendo nimirum maximam terræ por­<lb/> tionem ex vno loco in alium, vnde illic maris concauitas, i&longs;tic verò mon­<lb/> tium &longs;ublimitas emer&longs;it. </s> <s id="s.001853">quo facto aquæ omnes in loca illa decliuiora &longs;ua <lb/> &longs;pontè rece&longs;&longs;erunt, quæ aquarum congregatio Mare appellatum e&longs;t. </s> <s id="s.001854">Hine <lb/> nonnulli auctores graui&longs;&longs;imi a&longs;&longs;erere non dubitarunt, montes <expan abbr="cõflatos">conflatos</expan> fui&longs;­<lb/> &longs;e ex terra illa, quæ locum illum occupabat, quem po&longs;tea maria inua&longs;erunt. <lb/> </s> <s id="s.001855">quæ cum ita &longs;int. </s> <s id="s.001856">&longs;equitur terram <expan abbr="nũc">nunc</expan> e&longs;&longs;e extra naturalem &longs;uam figuram, & <lb/> propterea in quodam &longs;tatu violento, <expan abbr="viol&etilde;tum">violentum</expan> autem <expan abbr="nullũ">nullum</expan> <expan abbr="perpetuũ">perpetuum</expan>. </s> <s id="s.001857">præ­<lb/> terea cum terra &longs;it grauior quàm aqua, nulla ratione deberent terræ partes <lb/> &longs;uperiores a quæ &longs;uperficiem &longs;uperare, cuius tamen <expan abbr="contrariũ">contrarium</expan> accidit, nam <lb/> &longs;uperficies ip&longs;a terræ, & multò magis <expan abbr="mõtana">montana</expan> loca &longs;uperficiem maris cuiu&longs;­<lb/> uis non parum &longs;uperant; quæ altera violentia terræ, & aquæ ine&longs;t, & ideò <lb/> minimè mirum e&longs;t, imò <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> naturæ valdè 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 primæuam recuperaturam e&longs;&longs;e figuram. </s> <s id="s.001858">cau&longs;am au­<lb/> tem re&longs;tauratricem huius terrenæ <expan abbr="rotũditatis">rotunditatis</expan> e&longs;&longs;e aquas tum pluuiales, tum <lb/> fluuiales iamdiù ob&longs;eruauimus, vt ex &longs;equentibus ob&longs;eruationibus patebit.</s> </p> <p type="main"> <s id="s.001859">Primò, 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&etail;­<lb/> cipitia, <expan abbr="atq;">atque</expan> hinc inde prærupti appareant montes, vt meritò legamus apud <lb/>Iob cap. 14. alluuione paulatim terra con&longs;umitur. </s> <s id="s.001860">humum porrò illam ex <lb/> montibus delap&longs;am &longs;emper ad loca humiliora fluuij &longs;ecum detrahunt. </s> <s id="s.001861">Ex <lb/> continua etiam hac inter montes corro&longs;ione facta manife&longs;tè apparet, flumi­<lb/> num alueos in montanis modò e&longs;&longs;e humiliores quàm olim, quamuis contra­<lb/>rium accidat alueis fluuiorum per plana decurrentium, qui modò altiores <lb/> &longs;unt <expan abbr="quã">quam</expan> exordio mundi, vt paulò po&longs;t <expan abbr="o&longs;t&etilde;dam">o&longs;tendam</expan>. </s> <s id="s.001862">Illud autem liquidò apparet <lb/> ex &longs;ignis, &longs;eu &longs;ymbolis, &longs;eu ex &longs;imilitudine terræ, aut lapidis, quæ in alti&longs;&longs;imis <lb/> fluminum ripis hinc inde pa&longs;&longs;im <expan abbr="vid&etilde;tur">videntur</expan>, quæ indicio &longs;unt montes illos iam <pb pagenum="104" xlink:href="009/01/104.jpg"/>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 Ciliciæ amne ob&longs;eruauit Strabo, <lb/> dum libro 12. de illius ripis hæc tradit, mira præterea e&longs;t montis cæ&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<lb/> nentias, vt coniungi po&longs;&longs;int: &longs;ic videre e&longs;t imminentes flumini petras vtrin­<lb/> que ferè <expan abbr="v&longs;q;">v&longs;que</expan> ad montis &longs;umma pertendentes duorum, triumuè iugerum <lb/> &longs;patio concauitates qua&longs;dam eminentijs oppo&longs;itas habere. </s> <s id="s.001863">hæc Strabo de <lb/> vno, quod nos in pluribus ob&longs;eruauimus. </s> <s id="s.001864">Pr&etail;terea videmus quotidie pluuias <lb/> aquas, idem quantum po&longs;&longs;unt efficere, &longs;uperficies montium, eorum maxi­<lb/> mè, qui coluntur, perpetuò ab&longs;umentes, <expan abbr="atq;">atque</expan> ad loca conuallium deducen­<lb/> tes. </s> <s id="s.001865">hinc videre e&longs;t, montes cæteris duriores, vt &longs;unt lapido&longs;i, cæteris altio­<lb/> res reman&longs;i&longs;&longs;e; quippe qui magis & pluuijs, & fluuialibus aquis &longs;ua duritie <lb/> ob&longs;titerunt. </s> <s id="s.001866">idem montani incolæ 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, turremuè in vlteriore mon­<lb/> te &longs;itam con&longs;picerent, quam deinde plures po&longs;t annos intermedio monte <lb/> depre&longs;&longs;o, commodè videbant. </s> <s id="s.001867">Ad hæc; antiqua in montium verticibus con­<lb/> &longs;tituta ædeficia, propterea intercidunt, quia terra hinc, & inde ab aquis <lb/>paulatim con&longs;umpta, <expan abbr="deor&longs;um&qacute;">deor&longs;umque</expan>; delap&longs;a, fundamenta ip&longs;orum nuda primò <lb/> relinquit; deindé terra etiam ip&longs;a, qua fundamenta innitebatur &longs;en&longs;im de­<lb/> lap&longs;a, ip&longs;a <expan abbr="quoq;">quoque</expan> fundamenta vnà cum toto ædeficio nece&longs;&longs;e e&longs;t collabi, hu­<lb/> ius &longs;igna infinita propemodum videri po&longs;&longs;unt; vnum tamen, quod toti orbi <lb/>con&longs;picuum e&longs;t, non ommittam; Capitolium videlicet Romanum, cuius <lb/> modo fundamenta tota extant, quæ olim altè &longs;ub terram de&longs;cendebant. </s> <s id="s.001868">vi­<lb/> de pulcherrimam hac de re tractationem apud Georgium Agricolam lib. 3. <lb/> cap. 1. qui amplius addit illud, quod & mihi maximè probatur; flumina ni­<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/> quædam terræ 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 terræ eminens <lb/> quidem, &longs;ed nullis vallibus in tot particulares colles, aut montes di&longs;&longs;ectum; <lb/> &longs;ed po&longs;tquam flumina à &longs;ummitate ip&longs;ius deor&longs;um fluere cœperunt; paula­<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>; plurimos totus Apenninus diui&longs;us e&longs;t. </s> <s id="s.001869">hæc de <lb/> montibus &longs;ufficiant, nunc ad plana de&longs;cendamus.</s> </p> <p type="main"> <s id="s.001870">Contrarium igitur omninò accidere videmus in planis, quoniam eædem <lb/> aquæ, quæ ex montibus quotidie terram &longs;ecum deducunt, eam ad humilio­<lb/> ra loca, vt &longs;unt plana, & campe&longs;tria, &longs;iue ibi &longs;int maria, &longs;iue arida, compor­<lb/> tant, <expan abbr="eam&qacute;">eamque</expan>; ibidem deponunt. </s> <s id="s.001871">hinc videmus antiqua ædeficia in planis locis <lb/> ex&longs;tructa, e&longs;&longs;e iam penè tota &longs;epulta, contra quam in montanis, cuius exem­<lb/> plum habes etiam Romæ propè ip&longs;um Capitolium, in Arcu triumphali Sep­<lb/> timij, qui iam ferè totus ruino&longs;a vndique terra obruitur. </s> <s id="s.001872">&longs;ic Pantheon. </s> <s id="s.001873">&longs;ic <lb/> etiam templa Epi&longs;copalia, quæ <expan abbr="plerunq;">plerunque</expan> &longs;atis peruetu&longs;ta &longs;unt, admodum <lb/> infra terram con&longs;piciuntur. </s> <s id="s.001874">Idem affirmant cœmentarij, & architectores <pb pagenum="105" xlink:href="009/01/105.jpg"/>omnes, quibus <expan abbr="vbiq;">vbique</expan> terrarum, dum in planis ædeficiorum fundamenta ex­<lb/> canant, occurrit primò terra quædam, quam ip&longs;i motam appellant, quæ li­<lb/> gnis, ruderibus, ferramentis, numi&longs;matis, &longs;epulturis, <expan abbr="varijs&qacute;">varijsque</expan>; rebus per­<lb/> mixta e&longs;t; qua eruta, reperitur terra alia, quam nunquam fui&longs;&longs;e motam, ap­<lb/> paret, ex eo quod &longs;olida, ac benè compacta &longs;it, neque vllis externis rebus, <lb/> præ&longs;ertim artificiatis admixta, terra illa, quam motam dicunt, variam va­<lb/> rijs in locis &longs;ortita e&longs;t altitudinem, prout aquæ plurimum, vel minimum <lb/> montanæ terræ huc, vel illuc comportarunt: alicubi vt hic Parmæ erit &longs;ex <lb/> vlnarum, alibi viginti, vt Mutinæ; alibi triginta, vt Romæ, nonnullis in lo­<lb/> cis. </s> <s id="s.001875">Comprobatur tandem hæc no&longs;tra ob&longs;eruatio ex arte illa, qua per ea&longs;­<lb/> dem fluuiales aquas &longs;olent, tam loca depre&longs;&longs;iora per aggerationem paula­<lb/> tim replere, <expan abbr="atq;">atque</expan> eleuare: quàm etiam altiora per aquarum earumdem cor­<lb/> ro&longs;ionem deprimere. </s> <s id="s.001876">qua in arte exercitati&longs;&longs;imum P. <!-- REMOVE S-->Augu&longs;tinum Spernac­<lb/> ciatum no&longs;træ Societatis videmus modo de mandato Summi Pontificis Pa­<lb/> dum, ac Renum Bononien&longs;em ob aggerationem &longs;tagnantes in mari emitte­<lb/> re; cui totus hic no&longs;ter di&longs;cur&longs;us maximè probatur. </s> <s id="s.001877">Ex quibus omnibus &longs;e­<lb/> quitur &longs;uperficiem terræ tam montium, quam planorum quotidie variari. <lb/> </s> <s id="s.001878">illam nimirum deprimi, hanc attolli. </s> <s id="s.001879">vnde aliud maximum notandum &longs;e­<lb/> quitur, videlicet hac tempe&longs;tate non e&longs;&longs;e eandem agrorum &longs;uperficiem, quæ <lb/> erat antiquitus, cum in montanis agris &longs;it multò humilior, in campe&longs;tribus <lb/> verò altior, quàm antiqua illa, ac primigenia; quapropter mirum videri <lb/> non debet, &longs;i quorumdam locorum adeò immutata natura e&longs;t, vt quæ olim <lb/> genero&longs;a vina ferebant, vel quouis alio e&longs;&longs;ent prædita munere, adeò dege­<lb/> nerauerint, vt & vina, & alia nullius modò valoris, vel in parua copia pro­<lb/> ferant. </s> <s id="s.001880">Quod verò ad marium aggerationem &longs;pectat, dicimus ij&longs;dem aquis <lb/>magnam arenarum copiam perpetuò importantibus, fieri aggerationem, <lb/> hoc e&longs;t littora quotidie magis cre&longs;cere, &longs;eu in mare ingredi, & con&longs;equen­<lb/> ter mare recedere. </s> <s id="s.001881">quod primò Ari&longs;t. te&longs;timonio in hoc cap. comprobatur, <lb/> cum quo pariter &longs;entiunt veteres Geographi, & Hi&longs;torici omnes. </s> <s id="s.001882">Ari&longs;t. igi­<lb/> tur in comprobationem huius adducit primò magnam Aegypti aggeratio­<lb/> nem; pars enim illa Aegypti, quæ Delta, <expan abbr="Nili&qacute;">Nilique</expan>; donum appellatur ab He­<lb/> rodoto, ex arenis, & limo, ex Aethyopiæ 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<lb/> nas importante &longs;it facta. </s> <s id="s.001883">&longs;ecundum, Ari&longs;t. exemplum e&longs;t Ammonia Regio, <lb/> cuius humiliora loca. </s> <s id="s.001884">f. </s> <s id="s.001885">maritima, palam e&longs;t, inquit, quod aggeratione facta, <lb/> fiunt &longs;tagna, & continens: &longs;uccedente autem tempore, &longs;tagnans aqua ob <lb/> nouam aggerationem de&longs;iccata e&longs;t, & iam annihilata. </s> <s id="s.001886">tertium e&longs;t Meotidis <lb/> Paludis; At verò, ait, & quæ &longs;unt circa Meotidem Paludem creuerunt allu­<lb/> uione fluuiorum tantum, vt multò minores magnitudine naues, nunc innare <lb/> po&longs;&longs;int, quàm anno ab hinc &longs;exage&longs;imo. </s> <s id="s.001887">quare ex hoc facilè e&longs;t ratiocinari, <lb/> quod & primò, vt multa &longs;tagnorum, ita & hoc opus e&longs;t fluuiorum, & tan­<lb/> dem nece&longs;&longs;e e&longs;t totum fieri &longs;iccum. </s> <s id="s.001888"><expan abbr="quartũ">quartum</expan> e&longs;t illi Bo&longs;phorus Tracius; quod <lb/> vnà cum præcedentibus &longs;atius e&longs;t apud ip&longs;um, vel potius apud eius expo&longs;i­<lb/> torem Vicomercatum videre, vt breuitati con&longs;ulatur. </s> <s id="s.001889">Accedit & Plinij te­<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;ed <pb pagenum="106" xlink:href="009/01/106.jpg"/>etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraciæ portu 10. millia pa&longs;&longs;uum; ab <lb/> Athenarum verò <expan abbr="quinq;">quinque</expan> millia, & alijs in locis plus minu&longs;uè rece&longs;&longs;i&longs;&longs;e &longs;cri­<lb/> bit. </s> <s id="s.001890">Huc facit locus quidam Strabonis ex lib. 12. de Pyramo Ciliciæ fluuio: <lb/> &longs;ic; montes verò egre&longs;&longs;us tantum limum in mare deducit, partim ex Ca­<lb/>taonia, partim ex Ciliciæ campis, vt huiu&longs;modi de eo oraculum feratur;</s> </p> <p type="main"> <s id="s.001891"><emph type="italics"/>Tempus erit rapidis olim cum Pyramus vndis <lb/>In &longs;acram veniet conge&longs;to litore, Cyprum:<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001892">hic enim fluuius è regione Cypri in&longs;ulæ in mari influit, &c. </s> <s id="s.001893">hæc Strabo.</s> </p> <p type="main"> <s id="s.001894">Verùm recentiora non de&longs;unt exempla. </s> <s id="s.001895">Rauenna olim erat in extremo <lb/> littore &longs;ita, nunc paulatim aggeratione aucto litore, mare multum ab ea <lb/> rece&longs;&longs;it. </s> <s id="s.001896">Patauium pariter, vt fertur mare alluebat, quod modo 25. pa&longs;&longs;uum <lb/> millibus ab eo di&longs;tat. </s> <s id="s.001897">Aæ&longs;tuarium ip&longs;um Venetum, ob arenas à varijs flu­<lb/> minibus in ip&longs;um immi&longs;&longs;as adeò fundum extulit, vt vix amplius nauigatio­<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> <s id="s.001898">demum exemplum &longs;it Bononien&longs;ium Renus, qui quamuis exi­<lb/> guus &longs;it torrens, paucis tamen annis Padum ip&longs;um, in quem immi&longs;&longs;us fue­<lb/> rat arena ita repleuit, vt & &longs;ibi, & Pado magno vicinorum agrorum damno <lb/> viam in mare ob&longs;truxerit. </s> <s id="s.001899">Cum igitur mare ob hanc ad aggerationem co­<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> elatior, 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, & aliquando futurum, vt exundare incipiat. </s> <s id="s.001900">quod <lb/> iam <expan abbr="pleri&longs;q;">pleri&longs;que</expan> in locis accidit, vt in littore Baltico, Danico, & Hollandico, <lb/> quibus in locis &longs;unt hac tempe&longs;tate extructi prælongi, ac præalti aggeres <lb/> contra maritimas innundationes: quibus antiquitus minimè fui&longs;&longs;e opus hi­<lb/> &longs;toricorum, ac <expan abbr="Geographorũ">Geographorum</expan> &longs;ilentium comprobat. </s> <s id="s.001901">Hoc igitur modo ter­<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, terræ &longs;uperfi­<lb/> ciei &longs;uperfundatur, <expan abbr="terra&qacute;">terraque</expan>; iterum, quemadmodum exordio mundi inhabi­<lb/>tabilis reddatur: quod tunc maximè accidet cum aquæ tam fluuiales, quàm <lb/> pluuiæ, &longs;uper faciem terræ perpetuò 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<lb/> tuerint; tunc terra erit iterum rotunda, & &longs;phærica, hoc e&longs;t &longs;uæ primigeniæ <lb/> iterum figuræ re&longs;tituetur: quapropter mare etiam rur&longs;us &longs;icut initio mundi <lb/> totam terræ faciem <expan abbr="circumquaq;">circumquaque</expan> innundabit, quod probare volebam.</s> </p> <p type="main"> <s id="s.001902"><emph type="italics"/>Tantum æui mutare potest longæua vetu&longs;tas.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001903">Hinc nonnulla colligi po&longs;&longs;unt non minus notatu, ac &longs;citu, quàm præceden­<lb/> tia digni&longs;&longs;ima, quibus Ethnicorum Philo&longs;ophorum error redarguatur, &longs;ides <lb/> verò no&longs;tra magis roboretur: mundum nimirum ab æterno neutiquam ex­<lb/> titi&longs;&longs;e, vel &longs;altem terram ab æterno non fui&longs;&longs;e hac figura præditam, qua nunc <lb/>videmus, nec mundum perpetuò duraturum. </s> <s id="s.001904">nam &longs;i hæc montuo&longs;a illi figu­<lb/> ra ab æterno ine&longs;&longs;et, iampridem tota illa montium tubero&longs;itas fui&longs;&longs;et ab <lb/> aquis exæ&longs;a, & con&longs;umpta: <expan abbr="neq;">neque</expan> æterna erit, quia &longs;ucce&longs;&longs;u temporis, vt pro­<lb/> bauimus, reducetur ad rotunditatem, <expan abbr="atq;">atque</expan> à mari innundabitur, & idcircò <lb/> inhabitabilis, vnde nece&longs;&longs;ariò mortalium genus interibit. </s> <s id="s.001905">Quapropter ni&longs;i <lb/> igne illo, quem &longs;acræ literæ innuunt catacly&longs;mus ille præueniatur, aqua <lb/> mundus interiturus e&longs;&longs;et. </s> <s id="s.001906">&longs;ed de his hactenus.</s> </p> <pb pagenum="107" xlink:href="009/01/107.jpg"/> <p type="main"> <s id="s.001907">Quoad magnum illud Diluuium, quod Ari&longs;t. 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="cõchiliorum">conchiliorum</expan> genera, quæ tùm in Apennino mon­<lb/> te, tùm in Alpibus ob&longs;eruaui; <expan abbr="Ìdem&qacute;">Ìdemque</expan>; in alijs mundi partibus inueniri pu­<lb/> to; præ&longs;ertim in tam immen&longs;a copia, <expan abbr="atq;">atque</expan> intra vi&longs;cera montium colloca­<lb/>ta, quæ nulla vis humana illuc contuli&longs;&longs;et, ni&longs;i temporibus catacly&longs;mi ebul­<lb/> lientibus aquis maris &longs;uper terram facta fui&longs;&longs;et hæc varia rerum maritima­<lb/> rum cum terre&longs;tribus commixtio: quæ quidem optimè ex Pomponio Mela <lb/> comprobantur, qui libro 1. de Numidia &longs;ic narrat: interius, & longè &longs;atis <lb/> à litore, &longs;i fides res capit, mirum admodum, &longs;pinæ pi&longs;cium, <expan abbr="Muricũ">Muricum</expan>, <expan abbr="O&longs;treo-rum&qacute;">O&longs;treo­<lb/> rumque</expan>; fragmenta, &longs;axi atritu, vti &longs;olent fluctibus, & non differentia mari­<lb/> nis, infixæ cautibus anchoræ, <expan abbr="alia&qacute;">aliaque</expan>; huiu&longs;modi &longs;igna, & 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> <s id="s.001908">neque locus ille Ouid. <!-- REMOVE S-->Met. <!-- REMOVE S-->15. extra rem:</s> </p> <p type="main"> <s id="s.001909"><emph type="italics"/>Vidi ego, quod fuerat olim &longs;olidi&longs;&longs;ima petra <lb/>E&longs;&longs;e fretum, vidi factas ex æquore terras: <lb/> Et procul à Pelago conchæ iacuere marinæ, <lb/> Et vetus inuenta e&longs;t in montibus anchora &longs;ummis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001910">Nos autem Chri&longs;tiani ad Noemi Diluuium i&longs;ta referre debemus.</s> </p> </chap> <chap> <p type="head"> <s id="s.001911"><emph type="italics"/>Ex Secundo Meteororum.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001912"><arrow.to.target n="marg152"/></s> </p> <p type="margin"> <s id="s.001913"><margin.target id="marg152"/>152</s> </p> <p type="main"> <s id="s.001914">Cap. 1. ait multa e&longs;&longs;e maria, quæ ad inuicem non communicant. <lb/> </s> <s id="s.001915">Eorum rubrum mare vnum e&longs;&longs;e; quod cum Oceano <expan abbr="Atlãtico">Atlantico</expan>, qui <lb/> e&longs;t extra Herculeum fretum ad occidentem parum videtur com­<lb/> mi&longs;ceri &longs;iue Ari&longs;t. 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> <s id="s.001916">&longs;ed meritò hoc <lb/> Ari&longs;tot. condonandum, cum tunc temporis nondum tota Africa e&longs;&longs;et certò <lb/> circumlu&longs;trata, <expan abbr="neq;">neque</expan> iter ab Hi&longs;pania ad Indos maritimum, adeo nunc fre­<lb/> quens, patefactum e&longs;&longs;et.</s> </p> <p type="main"> <s id="s.001917"><arrow.to.target n="marg153"/></s> </p> <p type="margin"> <s id="s.001918"><margin.target id="marg153"/>153</s> </p> <p type="main"> <s id="s.001919">Summæ 2. cap. 2. <emph type="italics"/>(Quapropter & circa Orionis ortum maximè fit tranquilli­<lb/> tas)<emph.end type="italics"/> quando Medici, Philo&longs;ophi, Poetæ, ac reliqui auctores loquuntur de <lb/> ortu a&longs;trorum fixorum, aut con&longs;tellationum, quæ &longs;unt in firmamento, vti <lb/> e&longs;t Orion (& 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 paulò ante <lb/> Solem emergunt, ita vt videantur à nobis; qui ortus dicitur Co&longs;micus, tunc <lb/> propriè, quando &longs;imul a&longs;trum cum Sole oritur; quando autem incipit appa­<lb/>rere mane ante Solem, dicitur ortus Heliacus. </s> <s id="s.001920">i. </s> <s id="s.001921">&longs;olaris, quia oritur quodam­<lb/> modo ex radijs Solis, &longs;ub quibus antea latebat. </s> <s id="s.001922">A&longs;tra verò inerrantia, & <lb/> planetæ Sole tardiores oriuntur <expan abbr="vtroq;">vtroque</expan> modo. </s> <s id="s.001923">nam cùm ip&longs;a Sol, quippe il­<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<lb/> rum heliacus: cum verò eadem præterierit, ac po&longs;t &longs;e reliquerit fit, vt mo­<lb/> tu diurno toto cœlo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliacè <lb/>oriantur: & cum quotidie magis Sol ab illis recedat, ip&longs;aque magis à Sole <pb pagenum="108" xlink:href="009/01/108.jpg"/>elongentur, fit, vt quotidie magis ortum Solis anticipent, & citius mane au­<lb/> te Solem videantur. </s> <s id="s.001924"><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 paulò ante occa&longs;um Solis. <!-- KEEP S--></s> <s id="s.001925">de­<lb/> mum cum fuerint Soli oppo&longs;ita, occidente Sole oriantur, qui ortus dicitur <lb/> Ve&longs;pertinus, vel Acronicus. </s> <s id="s.001926">po&longs;tea oriuntur &longs;emper in die ante Solis occa­<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<lb/> liacè occidere; & mox cum ip&longs;o Sole occumbant, quod Acronicè e&longs;t occi­<lb/> dere. </s> <s id="s.001927">Totum porrò illud tempus, quo per diem oriuntur, non eorum ortui, <lb/> &longs;ed occa&longs;ui deputatur, eò quod non cernuntur oriri, vt &longs;equenti loco expli­<lb/> cabitur. </s> <s id="s.001928">Quæ omnia adhibito Globo a&longs;tronomico, in quo con&longs;tellationes <lb/> omnes depictæ &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<lb/>diatur, & interim diurno motu globus conuertatur, ad &longs;en&longs;um manife&longs;ta <lb/> apparebunt. </s> <s id="s.001929">In &longs;umma auctores intelligunt de ortu, qui mane fit ante So­<lb/> lem, quia tunc primum po&longs;t diuturnas latebras incipit apparere. </s> <s id="s.001930"><expan abbr="nõ">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> <s id="s.001931">fit au­<lb/> tem ortus hic Orionis, heliacus, & matutinus, de quo Ari&longs;t. hoc loco, & alij <lb/> auctores, no&longs;tra hac tempe&longs;tate paulò ante Solis ingre&longs;&longs;um in Cancrum, &longs;i­<lb/> ue ante &longs;ol&longs;titium æ&longs;tiuum circa 22. Iunij.<!-- REMOVE S--><arrow.to.target n="marg154"/></s> </p> <p type="margin"> <s id="s.001932"><margin.target id="marg154"/>154</s> </p> <p type="main"> <s id="s.001933">Eodem cap. <emph type="italics"/>(Incertus autem, & mole&longs;tus Orion e&longs;&longs;e videtur & occumbens, & <lb/> oriens, quia in tran&longs;mutatione temporis accidit occa&longs;us, & ortus, a&longs;tate, aut hye­<lb/> me, & propter magnitudinem a&longs;tri dierum &longs;it aliqua pluralitas)<emph.end type="italics"/> hoc loco Vico­<lb/> mercatus ex &longs;ententia a&longs;tronomorum occa&longs;um Orionis fieri autumni tem­<lb/> pore, Sole Scorpionem ob&longs;idente docet, quod & verba Ari&longs;t. clarè &longs;ignifi­<lb/> cant, cum dicat ortum ip&longs;ius fieri æ&longs;tate; in tran&longs;mutatione verò temporis, <lb/> videlicet in autumno fieri occa&longs;um. </s> <s id="s.001934">Porrò 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, & infra orizontem cadit: deinde paulò ante Solis or­<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, & tandem cum Sole ip&longs;o heliacè euane­<lb/> &longs;cat. </s> <s id="s.001935">Scriptores autem ferè &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> <s id="s.001936">affixa <expan abbr="namq;">namque</expan> &longs;ydera per &longs;ex fermè men­<lb/> &longs;es noctu oriuntur, <expan abbr="oriri&qacute;">oririque</expan>; ea con&longs;picimus, & propterea totum illud tem­<lb/> pus, ortui ip&longs;orum deputamus: Reliquum verò <expan abbr="t&etilde;pus">tempus</expan>, quo per diem oriun­<lb/> tur, & idcircò ortus illorum minimè apparet, nulla ratione ortui debuit <lb/> a&longs;cribi: totum verò tempus, quo noctu occidunt, & occidere cernuntur, oc­<lb/> ca&longs;ui illorum meritò attribuitur. </s> <s id="s.001937">& <expan abbr="quemadmodũ">quemadmodum</expan> temporis illius initium, <lb/> quo primo de nocte apparere incipiunt, dicitur ab&longs;olutè ortus cuiu&longs;uis &longs;y­<lb/> deris; &longs;ic etiam initium temporis illius, quo primum per noctem ea occide­<lb/> re videmus, &longs;impliciter occa&longs;um appellamus.</s> </p> <p type="main"> <s id="s.001938"><arrow.to.target n="marg155"/></s> </p> <p type="margin"> <s id="s.001939"><margin.target id="marg155"/>155</s> </p> <p type="main"> <s id="s.001940">Eodem cap. <emph type="italics"/>(Ete&longs;iæ autem flant post ver&longs;iones, & Canis ortum)<emph.end type="italics"/> per ver&longs;io­<lb/> nes intelligit tropicos, quod & tropici etymon confirmat, <expan abbr="cũ">cum</expan> tropicus idem <lb/> valeat, ac conuer&longs;iuus. </s> <s id="s.001941">circa Canis ortum eadem &longs;unt notanda, quæ &longs;upra <lb/>de ortu Orionis annotaui; intelligit enim eum Canis ortum, qui mane fiat <pb pagenum="109" xlink:href="009/01/109.jpg"/>primum paulò ante Solis ortum, cum &longs;cilicet incipit apparere.</s> </p> <p type="main"> <s id="s.001942">Cum porrò in c&etail;lo &longs;it Canis maior, & Canis minor, qui & Procyon, ide&longs;t <lb/> Anticanis dicitur, exi&longs;timo Canem maiorem e&longs;&longs;e eum, qui vulgò Canicula <lb/> nominatur, <expan abbr="&longs;olet&qacute;">&longs;oletque</expan>; vehementes, ac noxios calores excitare. </s> <s id="s.001943">de quo etiam <lb/> putò Ari&longs;t. intelligere. </s> <s id="s.001944">eius porrò ortus in no&longs;tra poli eleuatione quadra­<lb/> ginta quinque graduum, circa diem tertium Augu&longs;ti contingit, Sole autem <lb/> 10. gradum Leonis occupante. </s> <s id="s.001945">Ex Magini tabulis ante ephemerides.</s> </p> <p type="main"> <s id="s.001946"><arrow.to.target n="marg156"/></s> </p> <p type="margin"> <s id="s.001947"><margin.target id="marg156"/>156</s> </p> <p type="main"> <s id="s.001948">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, & ad meridiem: <lb/> <expan abbr="ea&qacute;">eaque</expan>, tympani &longs;peciem habeant, talem enim figuram terræ excidunt ex centro ip&longs;ius <lb/>ductæ lineæ, & faciunt duos conos, hunc quidem habentem ba&longs;im tropicum, alte­<lb/> rum autem habentem ba&longs;im circulum &longs;emper manifestum, verticem autem in me­<lb/> dio terræ. </s> <s id="s.001949">eodem autem modo ad inferiorem polum alij duo coni terræ &longs;egmenta fa­<lb/> ciunt)<emph.end type="italics"/> vt benè duas ha&longs;ce terræ portiones, quas &longs;olas habitabiles putat Ari­<lb/> &longs;tot. concipias, <expan abbr="reliquaq;">reliquaque</expan> huius loci intelligas, in&longs;pice &longs;equentem figuram. <lb/> <figure id="id.009.01.109.1.jpg" place="text" xlink:href="009/01/109/1.jpg"/><lb/> Maior circulus &longs;it cœlum, in quo polus L, articus; M, antarticus, ille eleua­<lb/> tus &longs;upra no&longs;trum horizontem S N, 45. gradibus, i&longs;te verò totidem infra <lb/> depre&longs;&longs;us. </s> <s id="s.001950"><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb pagenum="110" xlink:href="009/01/110.jpg"/>diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/> X O, Capricorni, vt vides in figura. </s> <s id="s.001951">Terra &longs;it A B C H G F E D Z K. à cu­<lb/> ius centro Z, educantur primo duæ lineæ rectæ Z R, Z S. ad circulum &longs;em­<lb/> per apparentium maximum, quæ in terra tran&longs;eant per puncta B, K. & iun­<lb/> gatur linea B K: iam vides conum S R Z, cuius ba&longs;is e&longs;t circulus &longs;emper ap­<lb/> parens S R, vertex autem Z, in centro terræ, vt ait Ari&longs;tot. <!-- KEEP S--></s> <s id="s.001952">educantur nunc <lb/> duæ aliæ rectæ ad tropicum Cancri Z T, Z Q, quæ 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<lb/> &longs;is e&longs;t circulus Cancri, vertex verò centrum terræ Z. con&longs;idera iam figuram <lb/> B K I C, inter duas rectas B K, I C, & duos circuli terræ arcus contentam; <lb/> hanc Ari&longs;t. appellat tympanum vnum terræ habitabile, quod e&longs;t ad Vr&longs;am, <lb/> ide&longs;t in &longs;eptentrionali plaga, in qua &longs;umus nos: quæ quidem portio &longs;i con&longs;i­<lb/> deretur vt &longs;olida, & à reliqua terra præci&longs;a, erit corpus rotundum, <expan abbr="vtrinq;">vtrinque</expan> <lb/> tamen duobus planis circulis ad in&longs;tar tympani terminatum: Ductis dein­<lb/> de &longs;imiliter alijs quattuor lineis à centro Z, ver&longs;us polum antarticum fit al­<lb/> terum tympanum H D E G, au&longs;tralis terræ habitabilis, vt in figura manife­<lb/> &longs;tum e&longs;t. </s> <s id="s.001953">fui&longs;&longs;e autem huiu&longs;modi habitabilis terræ &longs;egmenta figuræ tympa­<lb/> ni &longs;imilia, optimè declarant veteres figuræ geographicæ Ptol&etail;mei, & patet <lb/> etiam ex longitudine, & latitudine, vt benè ait Ari&longs;t. quas Geographi por­<lb/> tioni terræ habitabili attribuebant, longitudinem enim dixerunt eius di­<lb/> men&longs;ionem ab occa&longs;u ad ortum: latitudinem autem à &longs;eptentrione in meri­<lb/> diem, eò quòd illa multò hac longior e&longs;&longs;et. </s> <s id="s.001954">Ex quibus apparet habitatam <lb/> fui&longs;&longs;e veluti Zonam, terram ab occa&longs;u ad ortum præcingentem. </s> <s id="s.001955">quæ Zona <lb/> &longs;i &longs;umatur cum &longs;oliditate, quam ambit, ab Ari&longs;t. tympano a&longs;&longs;imilatur.</s> </p> <p type="main"> <s id="s.001956"><arrow.to.target n="marg157"/></s> </p> <p type="margin"> <s id="s.001957"><margin.target id="marg157"/>157</s> </p> <p type="main"> <s id="s.001958">Eodem cap. <emph type="italics"/>(Hæ autem habitari &longs;olæ po&longs;&longs;ibiles: & <expan abbr="neq;">neque</expan> vltra ver&longs;iones; vm­<lb/> bra enim non <expan abbr="vtiq;">vtique</expan> e&longs;&longs;et ad Vr&longs;am: nunc autem inhabitabilia prius fiunt loca, quàm <lb/> &longs;ubdeficiat, aut permutetur vmbra ad meridiem. </s> <s id="s.001959">Quæ autem &longs;ub Vr&longs;a, è 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 plurimæ regiones <lb/> tam veteris, quam noui orbis, &longs;uperiori &longs;eculo patefactæ, in quibus magna <lb/> in amœnitate, ac fertilitate, <expan abbr="&longs;ummis&qacute;">&longs;ummisque</expan>; delicijs viuitur. </s> <s id="s.001960">Quoad vmbram il­<lb/> lam, intellige meridianam. </s> <s id="s.001961">i. </s> <s id="s.001962">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> <s id="s.001963">Quod &longs;i ad meridiem <lb/> perrexerimus, occurret inhabitabilis (vt falsò putat) terra, prius quam. <lb/> </s> <s id="s.001964">vmbra meridiana in Boream vergens deficiat. </s> <s id="s.001965">quæ &longs;igna &longs;unt no&longs;tram habi­<lb/> tationem e&longs;&longs;e citra Zonam torridam, in Boreali parte. </s> <s id="s.001966">Quæ autem &longs;ub Vr­<lb/> &longs;a, ide&longs;t &longs;ub polo arctico, ob nimium frigus inho&longs;pita omninò habetur, nam</s> </p> <p type="main"> <s id="s.001967"><emph type="italics"/>Quod latus mundi nebulæ, <expan abbr="malus&qacute;">malusque</expan>; <lb/> Iupiter vrget.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001968">Verumtamen, quæ &longs;ub <expan abbr="vtroq;">vtroque</expan> polo partes &longs;unt adhuc incognitæ manent.</s> </p> <p type="main"> <s id="s.001969"><arrow.to.target n="marg158"/></s> </p> <p type="margin"> <s id="s.001970"><margin.target id="marg158"/>158</s> </p> <p type="main"> <s id="s.001971">Eodem cap: <emph type="italics"/>(Fertur autem, & corona &longs;ecundam hunc locum, videtur enim &longs;u­<lb/>per caput e&longs;&longs;e nobis, cum fuerit &longs;ecundum meridianum)<emph.end type="italics"/> con&longs;tellatio videlicet, <lb/> quæ corona Ariadnæ dicitur, hæc cum in cœlo manife&longs;tè &longs;it Borealis, <expan abbr="no-&longs;tro&qacute;">no­<lb/> &longs;troque</expan>; vertici noctu, quando meridianum pertran&longs;it, incumbat: clarè indi­<lb/> cat nos <expan abbr="quoq;">quoque</expan> e&longs;&longs;e Boreales.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001972"><arrow.to.target n="marg159"/></s> </p> <p type="margin"> <s id="s.001973"><margin.target id="marg159"/>159</s> </p> <p type="main"> <s id="s.001974">Eodem cap. <emph type="italics"/>(Et quidem ad latitudinem <expan abbr="v&longs;q;">v&longs;que</expan> ad inhabitabilia &longs;cimus habita-<emph.end type="italics"/> <pb pagenum="111" xlink:href="009/01/111.jpg"/><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter æ&longs;tum)<emph.end type="italics"/><lb/> illic autem, ide&longs;t &longs;ub Zona torrida, compertum autem e&longs;t nunc totam ferè <lb/> torridam Zonam, & quidem alicubi percommodè habitari, cuius cau&longs;æ &longs;unt <lb/> quatuor, quæ ip&longs;um latuerunt. </s> <s id="s.001975">prima <expan abbr="ea&qacute;">eaque</expan>; toti Zonæ torridæ communis, <lb/> e&longs;t perpetuum æquinoctium, quo Sol tantum &longs;upra, quantum infra terram <lb/> immoratur. </s> <s id="s.001976">accedit, quòd Sol nocturno tempore maximè ad imum cœli fe­<lb/> ratur, <expan abbr="plurimum&qacute;">plurimumque</expan>; ab horizonte, <expan abbr="&longs;upero&qacute;">&longs;uperoque</expan>; hemi&longs;pherio recedat. </s> <s id="s.001977">atque ob <lb/> hanc &longs;olam rationem Campanus in &longs;ua &longs;phæra Zonam hanc putat maximè <lb/> e&longs;&longs;e habitabilem: quamuis hæc &longs;ola cau&longs;a, vt quotidiana docet experientia, <lb/> non &longs;ufficiat. </s> <s id="s.001978">&longs;ecunda &longs;unt pluuiæ, quæ alicubi quotidie &longs;tata hora decidunt. <lb/> </s> <s id="s.001979">tertia venti, qui veluti flabella quædam aerem agitant. </s> <s id="s.001980">quarta præalti mon­<lb/> tes perpetuis niuibus ob&longs;iti. </s> <s id="s.001981">quæ quatuor torridam hanc pa&longs;&longs;im refrigerant, <lb/> atque habitabilem reddunt.</s> </p> <p type="main"> <s id="s.001982"><arrow.to.target n="marg160"/></s> </p> <p type="margin"> <s id="s.001983"><margin.target id="marg160"/>160.a</s> </p> <p type="main"> <s id="s.001984">Summæ 2. cap. 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<lb/> qua, vt in &longs;equenti con&longs;iderare; &longs;olet enim Ari&longs;t. figuras, imò demon&longs;tratio­<lb/> nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;æpius in Logicis <lb/> monuimus.</s> </p> <p type="main"> <s id="s.001985"><emph type="italics"/>De&longs;criptus &longs;it igitur, vt clarior res euadat horizontis circulus quapropter, & <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 id="id.009.01.111.1.jpg" place="text" xlink:href="009/01/111/1.jpg"/> <pb pagenum="112" xlink:href="009/01/112.jpg"/> <p type="main"> <s id="s.001986"><emph type="italics"/>Oportet autem ip&longs;ius alteram portionem intelligere, quæ nobis habitatur; quæ <lb/> eodem modo diuidi poterit)<emph.end type="italics"/> ide&longs;t oportet intelligere ip&longs;ius horizontis, vel ter­<lb/> ræ habitatæ partem, quæ quamuis rotunda non &longs;it, poterit tamen, ac &longs;i ro­<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"> <s id="s.001987"><emph type="italics"/>Supponatur autem primò 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> <s id="s.001988">plurimum autem di&longs;tant &longs;ecundum locum, quæ per diametrum opponuntur, <lb/> &longs;it igitur vbi A, occidens æquinoctionalis, contrarius autem huic locus vltimus B, <lb/> ortus æquinoctionalis)<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 æquinoctialis, qui fit Sole exi&longs;tente in <lb/> alterutro æquinoctio; huic igitur per diametrum opponatur ortus æquino­<lb/> ctialis in B. qui pariter contingit tempore æquinoctiorum: linea autem B A, <lb/> refert ip&longs;um æquatorem.</s> </p> <p type="main"> <s id="s.001989"><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"/> hæc dia­<lb/> meter erit ip&longs;a linea meridiana. </s> <s id="s.001990">pro Vr&longs;a verò intelligit &longs;eptentrionem, <lb/> quod ibi &longs;it Vr&longs;æ con&longs;tellatio.</s> </p> <p type="main"> <s id="s.001991"><emph type="italics"/>Id autem, in quo F, ortus æ&longs;tiualis; in quo verò E, occidens æ&longs;tiualis)<emph.end type="italics"/> quæ duo <lb/> puncta iunguntur linea F E, quæ refert &longs;ectionem tropici, Cancri cum ho­<lb/> rizonte: ortus enim, & occa&longs;us æ&longs;tiualis contingunt Sole Cancri tropicum <lb/> percurrente.</s> </p> <p type="main"> <s id="s.001992"><emph type="italics"/>Id autem, in quo D, oriens hyemalis; vbi verò C, occidens hyemalis)<emph.end type="italics"/> linea au­<lb/> tem D C, erit &longs;ectio tropici Capricorni, & horizontis; Sole enim hunc tro­<lb/> picum attingente ortus, & occa&longs;us hybernus fiunt.</s> </p> <p type="main"> <s id="s.001993"><emph type="italics"/>Ab F, autem ducatur diameter ad C, & à D, ad E. quoniam igitur plurimum <lb/> di&longs;tantia &longs;ecundum locum, contraria &longs;unt &longs;ecundum locum: plurimum autem di­<lb/> stantia, quæ &longs;ecundum diametrum; nece&longs;&longs;arium e&longs;t, & flatuum hos inuicem con­<lb/> trarios e&longs;&longs;e, <expan abbr="quicunq;">quicunque</expan> &longs;ecundum diametrum exi&longs;tunt. </s> <s id="s.001994">vocantur autem &longs;ecundum po­<lb/> &longs;itionem locorum venti &longs;ic; Zephyrus quidem ab A, hoc enim e&longs;t occidens æquino­<lb/> ctialis. </s> <s id="s.001995">Boreas autem, & Aparetias à G. hic enim Vr&longs;a, contrarius autem huic <lb/> Notus ab H. <!-- KEEP S--></s> <s id="s.001996">Meridies enim e&longs;t hic, à quo flat, & H, ip&longs;i G, contrarium e&longs;t; &longs;ecun­<lb/> dum enim diametrum &longs;unt. </s> <s id="s.001997">Ab F, autem Cæcias; hic enim oriens æ&longs;tiuus e&longs;t; cui <lb/> contrarius est, non qui flat ab E, &longs;ed qui à 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> <s id="s.001998">Qui verò à D, <lb/> Eurus, i&longs;te enim ab horiente hyberno flat, vicinus existens Noto, vnde & &longs;æpè Eu­<lb/> ronoti flare dicuntur: <expan abbr="cõtrarius">contrarius</expan> autem huic, non qui à C. Libs, &longs;ed qui ab E, quem <lb/> vocant, hi quidem Arge&longs;ten, hi autem Olympium, alij verò Scironem; iste enim ab <lb/> occidente æ&longs;tiuo flat, & &longs;ecundum diametrum ip&longs;i &longs;olus opponitur. </s> <s id="s.001999">Venti igitur, qui <lb/> &longs;ecundum diametrum po&longs;iti &longs;unt, & quibus alij aduer&longs;antur, ij &longs;unt. </s> <s id="s.002000">Alij autem <lb/> &longs;unt, &longs;ecundum quos non &longs;unt contrarij venti, ab I, quem vocant Tra&longs;ciam, qui me­<lb/>dius e&longs;t inter Argesten, & Apparitiam, à K, autem, quem vocant Me&longs;en, Medius <lb/> enim e&longs;t Cæciæ, & Aparetiæ. </s> <s id="s.002001">Diameter autem K I, iuxta circulum &longs;emper con&longs;pi­<lb/> cuum e&longs;&longs;e &longs;olet, non tamen exactè)<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 ferè <lb/>&longs;ub diametro illius, in qualibet enim &longs;phæra obliqua, ide&longs;t, in qua polus ele­<pb pagenum="113" xlink:href="009/01/113.jpg"/>uatur, intelligunt A&longs;tronomi circulum quendam &longs;emper apparentium ma­<lb/>ximum, quem de&longs;cribunt ex ip&longs;o polo, tanquam centro, & interuallo 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> <s id="s.002002">huius igitur dia­<lb/> metrum vult Ari&longs;t. per lineam, quæ à K, in I, duceretur (quamuis non exa­<lb/> ctè) repre&longs;entari.</s> </p> <p type="main"> <s id="s.002003"><emph type="italics"/>Contrarij autem non &longs;unt his &longs;tatibus, <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> Trafciæ ab N, enim, <lb/> quod punctum per diametrum aduer&longs;um illi e&longs;t, &longs;piraret. </s> <s id="s.002004">Ni&longs;i ab eo veniat, qui ta­<lb/> men non longè progreditur ventus quidam, quem accolæ Phæniciam vocant. </s> <s id="s.002005">maxi­<lb/> mè igitur præcipui, & definiti venti hi &longs;unt: <expan abbr="hoc&qacute;">hocque</expan>, modo di&longs;po&longs;iti)<emph.end type="italics"/> &longs;upradicta por­<lb/> rò omnia ex &longs;equenti figura optimè poterunt intelligi, quam diligenti ope­<lb/> ra ad mentem Ari&longs;t. ex græcis codicibus re&longs;tituere conatus &longs;um, cum ani­<lb/>maduerterem figuras valdè deprauatas pa&longs;&longs;im apud <expan abbr="cõmentatores">commentatores</expan> reperiri. <lb/> </s> <s id="s.002006">Porrò ad literam M, in figura &longs;crip&longs;i ventum Libonotum, quem Ari&longs;t. qui­<lb/> dem non ponit propter ip&longs;ius paruitatem; imò apertè 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"> <s id="s.002007"><emph type="italics"/>Ex Tertio Meteororum.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.002008"><arrow.to.target n="marg161"/></s> </p> <p type="margin"> <s id="s.002009"><margin.target id="marg161"/>160.b</s> </p> <p type="main"> <s id="s.002010">Antequam textuum explicationem aggrediar, illud animaduerten-<lb/> dum e&longs;t, <expan abbr="vbicunq;">vbicunque</expan> interpretatio antiqua vtitur verbis, refractio, <lb/> & refrangere; ibi Vicomercatum in &longs;ua interpretatione meritò, <lb/> & propriè v&longs;um e&longs;&longs;e verbis; reflexio, & reflecti: differunt enim <lb/> valdè apud Opticos refractio, & reflexio, vt etiam refrangere, & reflectere. <lb/> </s> <s id="s.002011">propterea optimè hoc loco Olympiodorus di&longs;tinguit inter <foreign lang="greek">anaklasin, kai <lb/>diaklasin,</foreign> reflexionem, & refractionem. </s> <s id="s.002012">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 propriè per&longs;pectiuis reflecti, vnde reflexio. </s> <s id="s.002013">Re­<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<lb/> pre&longs;entatiua non tendit recta ad oculum, &longs;ed in confinio aquæ, & aeris fran­<lb/> gitur, dicitur fieri refractio, & refrangi, in refractione igitur requiruntur <lb/>duo media, per quæ fiat vi&longs;io, quæ &longs;int diuer&longs;æ den&longs;itatis, vt &longs;unt aqua, & <lb/> aer: vapor, exhalatio, & aer: vitrum, & aer, &c. </s> <s id="s.002014">quando igitur videmus <lb/> Solem, aut Lunam per vapores, aut exhalationes fit refractio, quia den&longs;ior <lb/> e&longs;t vapor, & exhalatio, quam aer.</s> </p> <p type="main"> <s id="s.002015">Notandum etiam Aream, de qua mox dicam explicari po&longs;&longs;e tam per re­<lb/> flexionem, quàm per refractionem: per reflexionem, quia &longs;upponunt Philo­<lb/>&longs;ophi e&longs;&longs;e in acre rorido innumera &longs;pecula parua inuicem valdè proxima, <lb/>ide&longs;t guttulas, per quas reflectatur ad oculum no&longs;trum &longs;pecies &longs;yderis. </s> <s id="s.002016">per <lb/>refractionem verò, vt vult Vitellio, quia &longs;umit totum illum aerem humi­<lb/> dum magis den&longs;um e&longs;&longs;e aere paro, qui e&longs;t circa oculos no&longs;tros, & hoc modo <lb/>con&longs;tituit diuer&longs;a media in den&longs;itate, per quam fiat vi&longs;io; corpus inquam <pb pagenum="114" xlink:href="009/01/114.jpg"/>illud humidum den&longs;ius, & aerem deinde circa oculum rarius. </s> <s id="s.002017">Vicomerca­<lb/> tus igitur quamuis vtatur voce reflexionis in Halone, non tamen ex prædi­<lb/>ctis videtur reprehendendus.</s> </p> <p type="main"> <s id="s.002018"><arrow.to.target n="marg162"/></s> </p> <p type="margin"> <s id="s.002019"><margin.target id="marg162"/>161</s> </p> <p type="main"> <s id="s.002020">Summæ 2. cap. 2. De Areæ figura <emph type="italics"/>(Refrangitur autem à 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> <s id="s.002021"><expan abbr="Vn-diq;">Vn­<lb/> dique</expan> autem &longs;imiliter refracto, nece&longs;&longs;e e&longs;t circulum e&longs;&longs;e, aut circuli partem. </s> <s id="s.002022">ab co­<lb/> dem enim &longs;igno ad idem &longs;ignum æquales frangentur &longs;uper circuli lineam &longs;emper. </s> <s id="s.002023">&longs;it <emph.end type="italics"/><lb/> <figure id="id.009.01.114.1.jpg" place="text" xlink:href="009/01/114/1.jpg"/><lb/> <emph type="italics"/>enim à puncto, in quo A, ad B, fracta, & ea, quæ est <lb/> A C B, & quæ A F B, & quæ A D B, æquales autem <lb/>& hæ A C, A F, A D, inuicem. </s> <s id="s.002024">& quæ ad B, inui­<lb/> cem &longs;cilicet C B, E B, D B. & protrahatur A E B, <lb/> quare trianguli æquales, etenim &longs;uper æqualem, quæ <lb/> e&longs;t A E B, ducantur autem <expan abbr="perp&etilde;diculares">perpendiculares</expan> ad A E B, <lb/> ex angulis; à C, quidem, quæ e&longs;t C E; ab F, autem, <lb/> quæ e&longs;t F E; à D, autem, quæ e&longs;t D E, æquales itaque <lb/>hæ, in æqualibus enim triăngulis, & in vno plano om­<lb/>nes, ad rectum enim omnes ei, quæ e&longs;t A E B. & 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, quæ autem e&longs;t circa C D F, circun­<lb/> ferentia nubes, à qua refrangitur vi&longs;us ad Solem)<emph.end type="italics"/><lb/> quia &longs;uppono Aream, &longs;iue Halonem fieri per re­<lb/> fractionem, vt vult etiam Vitellio, propterea <lb/> <expan abbr="præmitt&etilde;dum">præmittendum</expan> e&longs;t principium quoddam, quo tra­<lb/> ctatio de refractione innititur; e&longs;t autem huiu&longs;­<lb/> modi; ea, quæ <expan abbr="vid&etilde;tur">videntur</expan> per refractionem, &longs;iue &longs;ub <lb/> aliquo refractionis angulo, manentibus nobis & <lb/> a&longs;tro, & medio ij&longs;dem in locis, non po&longs;&longs;unt vide­<lb/> ri &longs;ub diuer&longs;o angulo à priori, nec per con&longs;e<expan abbr="qu&etilde;s">quens</expan> <lb/> alibi apparere. </s> <s id="s.002025">v. <!-- REMOVE S-->g. <!-- REMOVE S-->Sol (vt in præ&longs;enti figura) <lb/> videatur ab oculo A, media nube C D F, &longs;ub an­<lb/> gulo refractionis B C A, vel B F A, & alijs &longs;imilibus angulis in eadem nube; <lb/> manente igitur oculo A, & a&longs;tro B, necnon nube C D E. eodem in loco, im­<lb/> po&longs;&longs;ibile e&longs;t Solem videri ab eodem oculo &longs;ub diuer&longs;o angulo à priori, nec <lb/> con&longs;equenter alibi apparere, quam in B. <!-- KEEP S--></s> <s id="s.002026">Nunc ad textus declarationem, in <lb/> quo continetur Geometrica demon&longs;tratio rotunditatis Areæ, quam &longs;ic bre­<lb/> uiter prius veteres excogitarunt: Viderunt primò Solem in Area apparere <lb/> in orbem, & con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/> con&longs;imiles, &longs;iue æquales 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 æquales refractionis an­<lb/> gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="cõ&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun­<lb/> ditatis huius, e&longs;t angulorum refractionis æqualitas. </s> <s id="s.002027">Sed iam textum Ari&longs;t. <lb/>qui geometricam huius rei continet demon&longs;trationem, explicemus. </s> <s id="s.002028">Suppo­<lb/> nit igitur primò Ari&longs;t. lineas vi&longs;uales à &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<lb/> dique</expan> circa Solem, Lunamuè facere angulos refractionis æquales. </s> <s id="s.002029">quod etiam <pb pagenum="115" xlink:href="009/01/115.jpg"/>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<lb/> tes con&longs;imilem refractionem, ide&longs;t angulos refractos B C A, B D A, B E A, <lb/> æquales in punctis C, D, F: <expan abbr="atq;">atque</expan> hoc e&longs;t con&longs;imilem facere refractionem. <lb/> </s> <s id="s.002030">Supponit &longs;ecundò lineas à &longs;ydere ad nubem, v&longs;que exten&longs;as e&longs;&longs;e æquales, vt <lb/> &longs;unt B C, B D, B F: &longs;imiliter reliquas tres à 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 omninò æqualia, & &longs;imilia, cum duo latera vnius <lb/> &longs;int æqualia duobus alterius <expan abbr="vtrunq;">vtrunque</expan> vtrique, & angulus angulo, & præterea <lb/> ba&longs;is &longs;it communis; ideò per quartam primi &longs;unt omninò æqualia. </s> <s id="s.002031">ducan­<lb/> tur nunc ex angulis C, D, F, tres perpendiculares ad rectam A B, quæ &longs;int <lb/> C E, D E, F E, in figura; quæ tres nece&longs;&longs;ariò erunt æquales, cum &longs;int ductæ <lb/> ab angulis æqualibus æqualium triangulorum ad communem ba&longs;im, & di­<lb/> uident nece&longs;&longs;ariò ba&longs;im in eodem puncto E, cum diuidant triangula æqua­<lb/> lia proportionaliter; <expan abbr="erunt&qacute;">eruntque</expan>; propterea hæ tres rectæ 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 æqualium C E, D E, F E, de­<lb/> &longs;criptus erit circulus per 9. tertij, cuius circumferentia C D F. <!-- KEEP S--></s> <s id="s.002032">Ex quibus <lb/> patet tria illa puncta C, D, E, per quæ Sol tran&longs;paret e&longs;&longs;e in orbem di&longs;po&longs;i­<lb/> ta. </s> <s id="s.002033">cau&longs;a igitur rotunditatis Areæ, 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;ariò <lb/> in orbem con&longs;tituuntur, vt o&longs;ten&longs;um e&longs;t. </s> <s id="s.002034">Eadem ratione omnia alia puncta <lb/> eiu&longs;dem <expan abbr="circũferentiæ">circunferentiæ</expan> &longs;unt puncta, per quæ Sol videtur refractè; & hoc mo­<lb/> do ad &longs;imilitudinem trium linearum A C B, A D B, A F B, refractarum, in­<lb/> finitæ <expan abbr="vndiq;">vndique</expan> intelligendæ &longs;unt, quarum aliæ refrangantur in circunferentia <lb/> prædicta, aliæ verò in alia periphæria maiori, aliæ etiam in minori, ita vt <lb/> ex tota nube fiant refractiones circulares plurimæ, ex quibus in nube area <lb/> con&longs;tituatur. </s> <s id="s.002035"><expan abbr="Atq;">Atque</expan> hæc cur Halonis figura orbicularis videatur, rationem <lb/> reddunt, <expan abbr="vna&qacute;">vnaque</expan>; textui lucem afferunt.</s> </p> <p type="head"> <s id="s.002036"><emph type="italics"/>Summæ 2. cap. 4. De Iridis figura.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002037"><arrow.to.target n="marg163"/></s> </p> <p type="margin"> <s id="s.002038"><margin.target id="marg163"/>162</s> </p> <p type="main"> <s id="s.002039"><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<lb/> culo portionem, & 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;æpius monui Ari&longs;t. 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<lb/> ptionem appellat, Iridis figuræ accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/> circularis, nunquam tamen circulus integer, imò <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/> maior, &longs;ed tamen &longs;emicirculo minor.</s> </p> <p type="main"> <s id="s.002040"><arrow.to.target n="marg164"/></s> </p> <p type="margin"> <s id="s.002041"><margin.target id="marg164"/>163</s> </p> <p type="main"> <s id="s.002042">Ibidem <emph type="italics"/>(Hemi&longs;phærio enim exi&longs;tente &longs;uper horizontis circulum in quo A. cen­<lb/> tro autem K, alio autem quodam oriente puncto, in quo G, &longs;i lineæ, quæ à K, &longs;ecun­<lb/> dum conum excidentes faciant velut axem lineam in qua G K, & à K. ad M, co­<lb/> pulatæ refrangantur ab hemi&longs;phærio ad G, &longs;uper maiorem angulum, circuli circun­<lb/> ferentiam incident lineæ, quæ à K, & &longs;i quidem in ortu, aut in occa&longs;u a&longs;tri reflexio <lb/> fiat, &longs;emicirculus ab <expan abbr="horizõte">horizonte</expan> a&longs;&longs;umetur &longs;uper terram factus. </s> <s id="s.002043">&longs;i autem &longs;upra, minor<emph.end type="italics"/> <pb pagenum="116" xlink:href="009/01/116.jpg"/><figure id="id.009.01.116.1.jpg" place="text" xlink:href="009/01/116/1.jpg"/><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<lb/> tinendam</expan> vocem reflexionis, <expan abbr="quã-uis">quam­<lb/> uis</expan> in antiqua tran&longs;latione lega­<lb/> tur refractio, e&longs;t enim apud om­<lb/> nes in confe&longs;&longs;o Iridem fieri per <lb/> reflexionem. </s> <s id="s.002044">E&longs;t igitur in &longs;upe­<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;phærium no&longs;trum in arcu G A M O, repræ&longs;entatum, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; nubes rori­<lb/> da, in qua Iris appareat, vbi M, quod punctum M, nubem referens, in figu­<lb/> ra ponitur in hemi&longs;phærij ambitu, quod cœlum repræ&longs;entat, cum tamen <lb/>nubes parum à terra &longs;ubuehatur; id enim ad demon&longs;trationem ferè perinde <lb/> e&longs;t. </s> <s id="s.002045">in oriente G, &longs;it a&longs;trum. </s> <s id="s.002046">&longs;i ergò lineæ vi&longs;uales à K, ad M, nubem tenden­<lb/> tes reflectantur &longs;uper maiorem angulum M K G, ad G, erit reflexarum vna <lb/> veluti M G. <!-- KEEP S--></s> <s id="s.002047">Porro omnes lineæ vi&longs;uales, quæ ad nubem M, incidunt, nece&longs;­<lb/> &longs;ariò, vt probabo, cadent in ambitum circularem. </s> <s id="s.002048">debemus enim innume­<lb/>ras lineas imaginari à K, in coni figuram excidentes, cuius vertex &longs;it in K, <lb/> & axis G K O, quas omnes repræ&longs;entat vna K M, <expan abbr="melius&qacute;">meliusque</expan>; repræ&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> <s id="s.002049">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 illæ con­<lb/> formare debebant. </s> <s id="s.002050">In prædicta autem axis volutatione, extremum M, li­<lb/> neæ K M, nece&longs;&longs;ariò de&longs;cribit circulum, qui e&longs;t circulus Iridis, & e&longs;t ba&longs;is <lb/> memorati coni.</s> </p> <p type="main"> <s id="s.002051">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&etail;dicti (quem horizon bifariam diuidit) quæ &longs;upra ter­<lb/> ram extabit. </s> <s id="s.002052">&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="cũ">cum</expan> a&longs;trum <lb/> <expan abbr="meridianũ">meridianum</expan> <expan abbr="circulũ">circulum</expan> occupauerit. </s> <s id="s.002053">h&etail;c tria &longs;unt, quæ deinceps <expan abbr="probãda">probanda</expan> recipit.</s> </p> <p type="main"> <s id="s.002054"><arrow.to.target n="marg165"/></s> </p> <p type="margin"> <s id="s.002055"><margin.target id="marg165"/>264</s> </p> <figure id="id.009.01.116.2.jpg" place="text" xlink:href="009/01/116/2.jpg"/> <p type="main"> <s id="s.002056">Ibidem <emph type="italics"/>(Sit enim in <expan abbr="ori&etilde;te">oriente</expan> pri­<lb/> mum vbi G, & refracta &longs;it K M, <lb/> ad G, & planum erectum &longs;it in quo <lb/> A, à triangulo in quo G K M, cir­<lb/> culus igitur erit &longs;ectio &longs;phæræ, qui <lb/> maximus &longs;it in quo A, differet enim <lb/>nihil &longs;i quod<expan abbr="cŭq;">cŭque</expan> eorum, quæ &longs;uper <lb/> G K, &longs;ecundum triangulŭ K M G, <lb/> erectum fuerit planum. </s> <s id="s.002057">lineæ igitur <lb/>ab ijs, quæ G, K, ductæ in hac ratio­<lb/>ne non con&longs;tituentur ad aliud, & <lb/> aliud punctum, quàm &longs;emicirculi <lb/> in quo A. <!-- KEEP S--></s> <s id="s.002058">Quoniam enim puncta <lb/> G, K, data &longs;unt, & quæ K M, vtique data erit; & quæ M G, ad M K; datam igi­<lb/> tur circunferentiam tanget M, fit <expan abbr="itaq;">itaque</expan> hæc in qua M N, quare &longs;ectio circunferen-<emph.end type="italics"/> <pb pagenum="117" xlink:href="009/01/117.jpg"/><emph type="italics"/>tiarum data e&longs;t. </s> <s id="s.002059">apud autem aliud punctum, quam ip&longs;ius M N, circunferentiæ, ab <lb/> ij&longs;dem punctis, eadem ratio in eodem plano non con&longs;i&longs;tit)<emph.end type="italics"/> eorum omnium, quæ <lb/> demon&longs;tranda &longs;unt, præmittenda &longs;unt duo nece&longs;&longs;aria fundamenta. </s> <s id="s.002060">Primum <lb/> e&longs;t; ea, quæ videmus per reflexionem &longs;ub quopiam angulo, manentibus no­<lb/> bis &longs;peculo, & 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> <s id="s.002061">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, & nube in M. ex qua ra­<lb/>dius Solis G M, reflectatur ad vi&longs;um in K, per <expan abbr="lineã">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<lb/> &longs;o angulo à priori, nec alibi apparere. </s> <s id="s.002062">Alterum e&longs;t apud Opticos vulga­<lb/> tum; ea &longs;cilicet, quæ per reflexionem (de quorum numero e&longs;t Iris) viden­<lb/> tur, videri, tunc &longs;olum, quando angulus incidentiæ fuerit æqualis angulo <lb/> reflexionis, quia tunc breui&longs;&longs;imis lineis fit vi&longs;io; quibus &longs;oli, natura (&longs;i fieri <lb/> <figure id="id.009.01.117.1.jpg" place="text" xlink:href="009/01/117/1.jpg"/><lb/> pote&longs;t) vtitur. </s> <s id="s.002063">v. <!-- REMOVE S-->g. <!-- REMOVE S-->in figura præ&longs;enti &longs;it &longs;pe­<lb/> culum C D E, obiectum A, oculus B, linea in­<lb/> cidentiæ e&longs;t A D, & angulus pariter inciden­<lb/> tiæ e&longs;t A D C. linea verò D B, e&longs;t linea refle­<lb/> xionis, & angulus pariter reflexionis e&longs;t B D­<lb/> E, qui duo anguli ni&longs;i fuerint æquales, nun­<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, à nobis pariter ante <lb/> &longs;peculum con&longs;titutis, videri nequit, quia &longs;ci­<lb/> licet in tali po&longs;itione &longs;peculi, obiecti, & no&longs;tri, nulla linea incidentiæ, ide&longs;t, <lb/> quæ ab obiecto in &longs;peculum tendit, facere pote&longs;t angulum cum &longs;peculo, qui <lb/> dicitur angulus incidentiæ, æqualem angulo illi, quem facit linea eadem re­<lb/>flexa à &longs;peculo ad oculum, quem dicunt angulum reflexionis. </s> <s id="s.002064">Cum ergo in <lb/> Iride videamus colorem Solis per reflexionem, tunc &longs;olum apparebit Iris, <lb/> quando Sol, nubes, & oculus fuerint in ea con&longs;titutione, qua radius <expan abbr="incid&etilde;s">incidens</expan> <lb/> nubi, & radius à nube repercu&longs;&longs;us faciant pares angulos. </s> <s id="s.002065">Et quia quando <lb/>nubes ro&longs;cida perpendiculariter opponitur Soli, & nobis, po&longs;&longs;unt fieri præ­<lb/> dicti anguli æquales non in vno loco nubis, &longs;ed in pluribus, con&longs;titutis ta­<lb/> men in circuli periphæria, hinc fit, quod Solis color reflectatur ex pluribus <lb/> locis in orbem con&longs;titutis, quæ reflexio e&longs;t ip&longs;ius Iridis arcus. </s> <s id="s.002066">ex Vitellion <lb/> 63. 10. Totam autem figuræ Iridis demon&longs;trationem &longs;ic breuiter puto ad­<lb/> inuentam e&longs;&longs;e. </s> <s id="s.002067">cum Sol in Iride videatur in orbem, <expan abbr="atq;">atque</expan> con&longs;imiliter, ne ce&longs;­<lb/> &longs;e e&longs;t id prouenire ex angulis reflexionum con&longs;imilibus, &longs;iue æqualibus: di&longs;­<lb/> &longs;imiles enim anguli, di&longs;&longs;imilem <expan abbr="vtiq;">vtique</expan> efficiunt Solis <expan abbr="appar&etilde;tiam">apparentiam</expan>. </s> <s id="s.002068">atqui con­<lb/> &longs;imiles anguli, &longs;iue æquales, non ni&longs;i in orbem po&longs;&longs;unt con&longs;titui; igitur an­<lb/> gulorum æqualitas cau&longs;a erit rotundationis arcus. </s> <s id="s.002069">h&etail;c e&longs;t &longs;umma totius di­<lb/> &longs;cur&longs;us, quem pluribus, & nimis ob&longs;curè Ari&longs;t. explicat.</s> </p> <p type="main"> <s id="s.002070">Inquit igitur Ari&longs;t. &longs;it enim in oriente, &c. </s> <s id="s.002071">vbi aggreditur probare vnum <lb/> ex tribus illis, quæ &longs;upra propo&longs;uit, nimirum tunc Iridem e&longs;&longs;e &longs;emicircu­<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="planũ">planum</expan> exten&longs;um, in quo A, in figura, adeo <lb/> magnum, vt totum &longs;ecet hemi&longs;phærium, faciet in &longs;uperficie hemi&longs;phærij &longs;e­ <pb pagenum="118" xlink:href="009/01/118.jpg"/>ctionem, quæ erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e­<lb/> cans hemi&longs;phærium, tran&longs;eat per <expan abbr="centrũ">centrum</expan> ip&longs;ius, quæ &longs;ectio, &longs;iue circuli por­<lb/>tio repræ&longs;entatur in figura, per &longs;emicirculum in quo A, &longs;iue in quo G A M­ <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> <s id="s.002072">Præmitten­<lb/> dum præterea non po&longs;&longs;e in &longs;emicirculo &longs;uperiori, quod e&longs;t planum, & &longs;ectio <lb/> trianguli G K M, poni alias duas lineas. </s> <s id="s.002073">v. <!-- REMOVE S-->g. <!-- REMOVE S-->G R, K R, ad aliud punctum, <lb/> vti e&longs;t R, quæ habeant eandem inuicem proportionem, quam habent prio­<lb/> res duæ 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. & tamen deberet e&longs;&longs;e æqualis illi; quemadmo­<lb/> dum K M, e&longs;t æqualis alteri K R; nequeunt autem duæ lineæ inæquales inui­<lb/> cem, habere eandem rationem ad duas inuicem æquales: ergo non habent <lb/> eandem rationem G M, & K M, quam habent G R, & K R. quod &longs;i punctum <lb/> R, &longs;umatur &longs;upra M, erit &longs;imilis <expan abbr="demõ&longs;tratio">demon&longs;tratio</expan>, &longs;i literæ M, & R, loca permu­<lb/> tent. </s> <s id="s.002074">his po&longs;itis, ait <emph type="italics"/>(Quoniam enim G, K, puncta data &longs;unt, & c.)<emph.end type="italics"/> ide&longs;t data <lb/> &longs;unt po&longs;itione, cum notum &longs;it vbi &longs;int. </s> <s id="s.002075">G, enim e&longs;t in ortu. </s> <s id="s.002076">K, verò in centro <lb/>horizontis, &longs;equitur, quod etiam linea G K, cuius ip&longs;a &longs;unt extrema, data <lb/> &longs;it, & po&longs;itione, & magnitudine, per 26. Datorum Euclidis. <!-- KEEP S--></s> <s id="s.002077">eadem quoque <lb/> ratione data erit K M, linea; &longs;iue quia e&longs;t æqualis ip&longs;i G K, &longs;iue quia per <lb/> a&longs;trolabium po&longs;&longs;umus ip&longs;ius longitudinem, & po&longs;itionem inue&longs;tigare; qua­<lb/> re & punctum M, datum erit per 27. Datorum, quare & linea G M, data <lb/> erit quoad &longs;itum, & magnitudinem per 26. Datorum. <!-- KEEP S--></s> <s id="s.002078">Quare per primam <lb/> Datorum erit data proportio linearum G M, M K, punctum <expan abbr="itaq;">itaque</expan> M, tanget <lb/> ambitum datum, qui ba&longs;is e&longs;t coni, quem linea K M, de&longs;cribit in reuolutio­<lb/> ne axis G K O, &longs;uper polis G, O. cum enim data &longs;it K M, po&longs;itu, & magni­<lb/> tudine, <expan abbr="ea&qacute;">eaque</expan>; &longs;it latus prædicti coni, &longs;equitur periphæriam, vel ambitum ba­<lb/> &longs;is coni e&longs;&longs;e datum per &longs;imilem definitionem 5. definitioni Datorum. <!-- KEEP S--></s> <s id="s.002079">&longs;it <expan abbr="au-t&etilde;">au­<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/> falsò pingitur in figura; &longs;ed debemus ip&longs;um concipere tanquam erectum ad <lb/> angulos rectos cum prædicto &longs;emicirculo, necnon cum horizonte G K O. <lb/> <!-- KEEP S--></s> <s id="s.002080">Iam &longs;i <expan abbr="triãgulum">triangulum</expan> G M K, prioris figuræ circumuoluatur circa axem G K O, <lb/> punctum ip&longs;ius M, de&longs;cribit prædictum ambitum L M N. hunc ambitum <lb/>inquit Ari&longs;tot. <!-- REMOVE S-->linea K M, attinget, <expan abbr="erit&qacute;">eritque</expan>; hic ambitus datus, vt dictum e&longs;t. <lb/> <figure id="id.009.01.118.1.jpg" place="text" xlink:href="009/01/118/1.jpg"/><lb/> Erit præterea &longs;ectio circunferentiarum ho­<lb/>rizontis, & huius ambitus data, cuius extre­<lb/> ma puncta e&longs;&longs;ent L, & N. &longs;i enim <expan abbr="cõcipiamus">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, & N, <lb/>vt in præ&longs;enti de&longs;criptione melius intellige­<lb/> tur, in qua horizon G N O L, & ambitus <lb/> prædictus e&longs;t L M N, qui debet intelligi ele­<lb/> uatus &longs;upra horizontem perpendiculariter) <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb pagenum="119" xlink:href="009/01/119.jpg"/>linea N P L, cuius extrema puncta &longs;unt L, N, quæ data erunt, cum &longs;int ex­<lb/> trema lineæ K M, circumlatæ; & quemadmodum dabatur &longs;uperius punctum <lb/> M. eadem ratione ex Datis, dabitur punctum N, & L. quare etiam &longs;ectio <lb/> N P L, quæ inter data puncta continetur, data erit ex 26. Datorum.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002081">Illud nunc in memoriam <expan abbr="reuocãdum">reuocandum</expan>, quod paulò ante probaui, nimirum <lb/> proportionem linearum G M, K M, non po&longs;&longs;e &longs;eruari in alijs lineis, quæ &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, quæ cadant in prædictum ambitum, &longs;iue <expan abbr="cir-cunfer&etilde;tiam">cir­<lb/> cunferentiam</expan> L M N, <expan abbr="quæ&qacute;">quæque</expan>; &longs;int in alio plano, <expan abbr="quã">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> <s id="s.002082">Verumenimuerò ad quid probatio hæc? </s> <s id="s.002083">non po&longs;&longs;e duas <lb/> alias lineas in eodem plano, &c.? exi&longs;timo Ari&longs;t. idcircò hoc proba&longs;&longs;e, quia <lb/> &longs;i aliæ duæ lineæ habentes eandem rationem, po&longs;&longs;ent collocari in eodem <lb/> plano; e&longs;&longs;ent <expan abbr="permutãdo">permutando</expan> illæ duæ (in priori figura) G R, R K. <expan abbr="vtraq;">vtraque</expan> <expan abbr="vtriq;">vtrique</expan> <lb/> æquales prioribus G M, M K, per quas videtur Iris, cum enim K R, &longs;it æqua­<lb/> lis ip&longs;i K M, erit, & G M, æqualis ip&longs;i G R, per 7. 5. & in eius &longs;cholio. </s> <s id="s.002084">qua­<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 per has etiam Iris videri po&longs;&longs;et. </s> <s id="s.002085">cum ergò con&longs;tet non po&longs;&longs;e has <lb/> e&longs;&longs;e prioribus proportionales, &longs;ed maiorem, vel minorem, alteram illarum, <lb/> quàm &longs;it G M, &longs;equitur, quod non faciunt angulum æqualem angulo G M K, <lb/> &longs;ub quo videtur Iris, <expan abbr="nimirũ">nimirum</expan> angulum G R K, qui &longs;it æqualis angulo G M K; <lb/> habet enim Iris hunc angulum determinatum, ita vt &longs;ub maiori, vel mino­<lb/> ri videri nequeat; ex 10. Bapti&longs;ta Porta. </s> <s id="s.002086">&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 verò &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 hæc tractatio. </s> <s id="s.002087">Fortè etiam addi pote&longs;t, quod alibi exi&longs;ten­<lb/> te puncto R, quàm in M, non po&longs;&longs;ent anguli incidentiæ, & reflexionis e&longs;&longs;e <lb/> æquales, quæ cau&longs;a e&longs;&longs;et cur &longs;ub alio angulo, quam prædicto G M K, Iris <lb/> non appareret.</s> </p> <p type="main"> <s id="s.002088">Prædicta omnia &longs;unt &longs;ecundum Ari&longs;tot. di&longs;cur&longs;um, & figurationem dicta, <lb/> nam &longs;ecundum veritatem po&longs;&longs;unt in eadem nube con&longs;titui plures anguli <lb/> æquales, nec tamen in eodem orbe, &longs;ed vnus &longs;upra <expan abbr="alterũ">alterum</expan>; vt in figura præ­<lb/> <figure id="id.009.01.119.1.jpg" place="text" xlink:href="009/01/119/1.jpg"/><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, æ­<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="illorũ">illorum</expan> vtrun­<lb/> que Sol Iridem efficere. </s> <s id="s.002089">atque <lb/> animaduer&longs;io h&etail;c videtur ma­<lb/> gni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;&longs;e, ad Iridis <expan abbr="de-mon&longs;tration&etilde;">de­<lb/> mon&longs;trationem</expan> con&longs;tituendam: <lb/> cum hinc v&longs;itatæ demon&longs;tra­<lb/> tiones infringatur. </s> <s id="s.002090">Fortè confugiendum e&longs;t ad illud, quod Maurolycus, & <lb/> 10. Bapti&longs;ta Porta ob&longs;eruarunt; debere <expan abbr="nimirũ">nimirum</expan> di&longs;tantiam ab oculo ad cen­<lb/> trum Iridis e&longs;&longs;e æqualem altitudini, &longs;iue &longs;emidiametro Iridis. </s> <s id="s.002091">Ita vt non &longs;o­ <pb pagenum="120" xlink:href="009/01/120.jpg"/>lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="quãta">quanta</expan> requi­<lb/> ritur vt angulus in orbem con&longs;tituatur, ex quo Iris po&longs;&longs;it apparere. </s> <s id="s.002092">hæc à <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) præ&longs;tabimus.<lb/> <arrow.to.target n="marg166"/></s> </p> <p type="margin"> <s id="s.002093"><margin.target id="marg166"/>165</s> </p> <p type="main"> <s id="s.002094">Ibidem <emph type="italics"/>(Extraponatur igitur quædam linea, quæ D B, & &longs;eindatur vt M G, ad <lb/> M K, &longs;ic quæ D, ad B, maior autem quæ M G, ea quàm M K, quoniam &longs;uper ma­<lb/> iorem angulum reflexio coni, maiori enim angulo &longs;ubtenditur trianguli M K G. <lb/> <!-- KEEP S--></s> <s id="s.002095">Maior igitur e&longs;t & ip&longs;a D, ip&longs;a B. addatur igitur ad eam, quæ B, ea in qua F, vt <lb/> &longs;it quod D, ad B, quæ B F, ad D. <!-- KEEP S--></s> <s id="s.002096">Deinde quod F, ad K G, quæ B, ad aliam fiat, <lb/> quæ K P. & à P, ad M, copuletur quæ P M, erit igitur P. polus circuli, ad quem <lb/> lineæ, quæ à 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<lb/> ctum in Iridis periphæriam, pergit deinceps inue&longs;tigare polum, & po&longs;tea <lb/> centrum eiu&longs;dem ambitus, vtraque autem exi&longs;tere in horizonte reperit, vt <lb/> hinc inferat Iridis portionem illam, quæ oriente Sole &longs;upra horizontem ap­<lb/> paret, e&longs;&longs;e &longs;emicirculum, vt propo&longs;uerat. </s> <s id="s.002097">Differt autem polus circuli à cen­<lb/> tro eiu&longs;dem circuli. </s> <s id="s.002098">polus e&longs;t punctum extra planum circuli, ex quo tamen <lb/> vt <expan abbr="c&etilde;tro">centro</expan> adhibito circino circuli periphæria de&longs;cribi pote&longs;t; &longs;ic polus æqua­<lb/> toris e&longs;t idem, qui polus mundi: <expan abbr="centrũ">centrum</expan> verò e&longs;t in plano &longs;ui cir culi, &longs;ic cen­<lb/> trum æquatoris e&longs;t idem cum centro mundi, cum æquator per illud incedat.</s> </p> <p type="main"> <s id="s.002099">Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t. cum data &longs;it proportio linearum K M, & M G, in &longs;upe­<lb/> riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex­<lb/> <figure id="id.009.01.120.1.jpg" place="text" xlink:href="009/01/120/1.jpg"/><lb/> ponatur alia linea recta B D. quæ diui­<lb/> datur in partes B, & D. proportionales <lb/> cum lineis K M, G M, per 10. 6. cum <lb/> ergo K M, &longs;it minor quàm G M, per 19. <lb/> primi, quia in triangulo G M K, oppo­<lb/> nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor quàm D, addatur iam ip&longs;i B. linea <lb/> nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, & D, per 11. 6. <lb/> hoc ordine, vt F B, ad D. ita D, ad B. <!-- KEEP S--></s> <s id="s.002100">Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/> B, ad aliam, quæ &longs;it K P, in eadem figura per 12. 6. & à puncto P, ad M, iun­<lb/> gatur recta P M. <!-- KEEP S--></s> <s id="s.002101">Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, & in quem li­<lb/> neæ à K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/> in &longs;equentibus.</s> </p> <p type="main"> <s id="s.002102"><arrow.to.target n="marg167"/></s> </p> <p type="margin"> <s id="s.002103"><margin.target id="marg167"/>166</s> </p> <p type="main"> <s id="s.002104">Ibidem <emph type="italics"/>(Erit etiam, quod quæ F, ad K G. & quæ B, ad K P. & quæ D, ad P M. <lb/>non enim &longs;it, &longs;ed aut ad minorem, aut ad maiorem ea, quæ P M, nihil enim differet. <lb/> </s> <s id="s.002105">&longs;it enim ad P R. eandem ergo rationem G K, & K P, & P R, inuicem habebunt, <lb/> quam quæ F, B, D: quæ autem F, B, D, proportionales crant, quod quidem D, ad <lb/> B. quæ F B, ad D: quare quod quæ P G, ad P R, quæ P R, ad eam, quæ P K. &longs;i igi­<lb/> tur ab ijs, quæ K G, quæ G R, & K R, ad R, coniungantur, coniunctæ hæ eandem <lb/> habebunt rationem, quam quæ G P, ad eam, quæ P R, circa eundem enim angulum <lb/> P, proportion aliter, & quæ trianguli G P R, & eius, qui K R P. quare & quæ G R, <lb/> ad eam quæ K R, eandem rationem habebit, quam & quæ G P, ad eam quæ P R, <lb/> habet autem & quæ M G, ad M K, eam rationem, quam quæ D, ad eam quæ B, <lb/>quare ambæ à punctis G K, non &longs;olum ad circunferentiam M N, con&longs;tituentur ean­<lb/>dem habentes rationem, &longs;ed & alibi, quod quidem impo&longs;&longs;ibile)<emph.end type="italics"/> incipit, vt dixi, <pb pagenum="121" xlink:href="009/01/121.jpg"/>probare P, e&longs;&longs;e polum prædicti ambitus, &longs;ic. </s> <s id="s.002106">Primò enim &longs;ciendum in præ­<lb/> mi&longs;&longs;a con&longs;tructione e&longs;&longs;e, vt F, ad G K, & B, ad K P, ita D, ad P M. nam &longs;i non <lb/> &longs;it eadem ratio D, ad P M, cum alijs prædictis, erit eadem ratio eiu&longs;dem D, <lb/>ad aliam maiorem, vel minorem ip&longs;a 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<lb/> neæ 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<lb/> tur à punctis G, & K, figuræ nu. </s> <s id="s.002107">164. <expan abbr="iungãtur">iungantur</expan> lineæ ad R, quæ &longs;int G R, K R, <lb/> erit vt G R, ad K R, ita G P, ad P R. quia orta <expan abbr="sũt">sunt</expan> duo <expan abbr="triãgula">triangula</expan> G P R, K P R, <lb/> quæ habent eundem angulum ad P. & latera proportionalia circa dictum <lb/> angulum. </s> <s id="s.002108">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 æquian­<lb/> gula; ergò per 4. 6. erunt latera circum æquales 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. & ita etiam G P, ad P R; ergò per 11. 5. vt K M, ad M G. ita K R, <lb/> ad R G, intra eandem circunferentiam, & in eodem plano: quod e&longs;&longs;e im­<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; & B, ad K P, ita D, ad P M.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002109"><arrow.to.target n="marg168"/></s> </p> <p type="margin"> <s id="s.002110"><margin.target id="marg168"/>167</s> </p> <p type="main"> <s id="s.002111">Ibidem <emph type="italics"/>(Quoniăm igitur quæ D, <expan abbr="neq;">neque</expan> ad minorem ea, quæ P M, <expan abbr="neq;">neque</expan> ad maiorem <lb/>(&longs;imiliter enim demon&longs;trabimus) palam e&longs;t, quod ad ip&longs;am <expan abbr="vtiq;">vtique</expan> erit, in qua P M, <lb/> quare erit, quod quæ M P, ad P K, quæ P G, ad M P. <!-- KEEP S--></s> <s id="s.002112">Si igitur eo in quo P, polo <lb/>vtens, di&longs;tantia autem ea, in qua P M, circulus de&longs;cribatur, omnes angulos attin­<lb/> get, quos reflexæ faciunt, quæ à K, G. &longs;i autem non, &longs;imiliter o&longs;tendentur eandem <lb/> babere rationem, quæ 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<lb/> iorem quam P M, habet eam rationem, quæ 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> <s id="s.002113">palàm e&longs;t, quoniam <lb/> erit D, ad P M, vt prædictæ ad prædictas: quare componendo, & permu­<lb/> tando, erunt tandem vt G P, ad P M, ita P M, ad P K, & 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, & D, ad <lb/> B. quare cum &longs;it vt G M, ad M K, ita F B, ad D. & G P, ad P M. & P M, ad <lb/> K P; erunt per 11. 5. vt G M, ad M K. ita G P, ad P M. & P M, ad P K. &longs;i quis <lb/> igitur vtens puncto P, tanquam polo, & interuallo P M, circulum de&longs;cribat, <lb/> omnes angulos reflexionis attinget, quos faciunt lineæ productæ à K, & re­<lb/> flexæ ab M, ad G. harum enim infinitam multitudinem debemus imaginari <lb/> à K, ad infinita puncta M, produci in ambitu illo con&longs;tituta, <expan abbr="re&longs;lecti&qacute;">reflectique</expan>; ad G. <lb/> &longs;i enim non attingat omnes illos angulos, &longs;equitur, vt &longs;upra, in eodem &longs;emi­<lb/> circulo <expan abbr="cõ&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> <s id="s.002114">Porrò &longs;ub angulo G M K, linearum G M, M K, Iris <lb/> apparet: quare apparebit etiam &longs;ub alijs omnibus, quæ à punctis G K, duci <lb/> po&longs;&longs;unt ad extremum lineæ P M, quia erunt in eadem ratione cum illis; cum <lb/> non de&longs;inant in eundem <expan abbr="&longs;emicirculũ">&longs;emicirculum</expan>, &longs;ed in ambitum Iridis M N, in quo M, <lb/> punctum imaginamur circumduci. </s> <s id="s.002115">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" xlink:href="009/01/122.jpg"/> <p type="main"> <s id="s.002116"><arrow.to.target n="marg169"/></s> </p> <p type="margin"> <s id="s.002117"><margin.target id="marg169"/>168</s> </p> <p type="main"> <s id="s.002118">Ibidem <emph type="italics"/>(Si igitur circumducas &longs;emicirculŭm, in quo A, circa diametrum in qua <lb/> G K P, que à G, K, reflexæ ad id in quo M; in omnibus planis &longs;imiliter &longs;e habebunt, <lb/>& æqualem facient angulum, qui K M G, & quem etiam facient angulum, quæ <lb/> K P, & P M, &longs;uper eam, quæ G P, &longs;emper æqualis erit. </s> <s id="s.002119">Trianguli igitur &longs;uper eam, <lb/> quæ G P, æquales ei, qui G M P. con&longs;i&longs;tunt. </s> <s id="s.002120">horum autem perpendiculares ad idem <lb/> &longs;ignum cadent eius, quæ G P, & æquales erunt, cadunt ad <foreign lang="greek">w,</foreign> centrum ergò 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 vltima <lb/> textus parte concludit Iridis portionem &longs;upra horizontem a&longs;tro <expan abbr="ori&etilde;te">oriente</expan> exi­<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<lb/> uolutione duæ lineæ G M, M K, in omnibus planis con&longs;titui po&longs;&longs;ibilibus cir­<lb/> ca prædictam diametrum, quæ &longs;upra etiam fieri à triangulis infinitis dixi­<lb/> mus, &longs;ucce&longs;&longs;iuè erunt; &longs;iue percurrent &longs;imiliter omnia illa plana, & facient <lb/> vbique angulum Iridis K M G, eundem: pariter duæ lineæ K P, P M, facient <lb/> vndique eundem angulum K P M. quare omnia triangula in predictis planis <lb/> imaginata, & <expan abbr="cõ&longs;tituta">con&longs;tituta</expan> &longs;uper linea G P, &longs;imilia ip&longs;i G M P, & æqualia erunt; <lb/> &longs;i igitur ab angulis ip&longs;orum, in quibus M, ductæ &longs;int perpendiculares ad la­<lb/> tus G P, omnes cadent in idem punctum <foreign lang="greek">w,</foreign> vt in figura; <expan abbr="quarũ">quarum</expan> vna erit M <foreign lang="greek">w,</foreign><lb/> quæ tamen cæteras 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 æquales, quandoquidem &longs;unt trian­<lb/> gulorum æqualium. </s> <s id="s.002121"><expan abbr="erunt&qacute;">eruntque</expan>; in eodem eiu&longs;dem circuli plano, & punctum <foreign lang="greek">w,</foreign><lb/> erit centrum ip&longs;ius. </s> <s id="s.002122">&longs;imilia dicta &longs;unt in Halone. </s> <s id="s.002123">Cum ergò ip&longs;ius centrum <lb/> <foreign lang="greek">w</foreign>, &longs;it in diametro horizontis G K <foreign lang="greek">w</foreign> P O, manife&longs;tum fit portionem eius, quæ <lb/> &longs;upra horizontem eminet, e&longs;&longs;e &longs;emicirculum, qui in figura notatur lineis <lb/> L M N. <!-- KEEP S--></s> <s id="s.002124">Atque hoc accidit Sole, vel Luna in horizonte exi&longs;tentibus; quod <lb/> erat primo loco demon&longs;trandum.</s> </p> <p type="main"> <s id="s.002125">Porrò &longs;ciendum po&longs;&longs;e nos breuius polum prædictum inuenire, &longs;i nimirum <lb/> <figure id="id.009.01.122.1.jpg" place="text" xlink:href="009/01/122/1.jpg"/><lb/> ad M, ducatur M P, faciens angulum K P M, æqua­<lb/> lem angulo G M K, per 23. primi, erunt enim duo <lb/> triangula <expan abbr="æquiãgula">æquiangula</expan> G P M, K P M, angulus enim <lb/> P, e&longs;t communis, angulus verò M K P, e&longs;t æqualis <lb/> duobus G, & G M K, per 32. primi, ergo etiam <lb/> duobus ad M, &longs;iue toti G M P, & reliquus K M P, <lb/> reliquo, quare per 4.6. latera circa angulos æqua­<lb/> les proportionalia erunt, & omologa G M, ad M K, ita G P, ad P M, quæ <lb/>æqualibus angulis &longs;ubtenduntur. </s> <s id="s.002126"><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habebant etiam <lb/> triangula Ari&longs;t. in figura, de qua paulò ante dicebam. </s> <s id="s.002127">Verba illa <emph type="italics"/>(Quæ ali­<lb/>bi quam in &longs;emicirculo constituuntur)<emph.end type="italics"/> &longs;unt perperam in antiqua tran&longs;latione <lb/> tran&longs;lata, nam Græcè &longs;ic, <foreign lang="greek">ai alloqi toá¿¡ hmikoklnou/ sunistamenai,</foreign> transferenda <lb/> e&longs;&longs;ent, quæ in alio circuli loco concurrunt.</s> </p> <p type="main"> <s id="s.002128"><arrow.to.target n="marg170"/></s> </p> <p type="margin"> <s id="s.002129"><margin.target id="marg170"/>169</s> </p> <p type="main"> <s id="s.002130">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> <s id="s.002131">Alia igitur omnia &longs;imiliter o&longs;tendentur vt & prius. <lb/> </s> <s id="s.002132">Polus autem circuli, in quo P, erit &longs;ub horizonte eo, in quo A C, eleuato puncto, <lb/> in quo G. in eadem autem & polus, & centrum circuli, & terminantis nunc ortum, <lb/> e&longs;t enim i&longs;te, in quo G P. <!-- KEEP S--></s> <s id="s.002133">Quoniam autem &longs;upra diametrum, quæ 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" xlink:href="009/01/123.jpg"/><figure id="id.009.01.123.1.jpg" place="text" xlink:href="009/01/123/1.jpg"/><lb/> <emph type="italics"/>Quare minor erit &longs;uperior &longs;ectio &longs;emicir­<lb/> culo, in qua S T, (nam Q S T, &longs;emicir­<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<lb/> tionem &longs;ecundam nimirum Sole &longs;upra <lb/>horizontem eleuato, ambitum Iridis <lb/> e&longs;&longs;e minorem circuli portionem, &longs;iue <lb/> &longs;emicirculo minorem. </s> <s id="s.002134">&longs;it igitur in fi­<lb/> gura &longs;uperiori, quam textui <expan abbr="cõgruen-tem">congruen­<lb/> tem</expan> re&longs;tituimus, linea A C, horizon­<lb/> talis, &longs;upra quam Sol &longs;it eleuatus in <lb/> circulo altitudinis in loco G, axis au­<lb/> rem coni, quem reflexè faciunt &longs;it <lb/> G K <foreign lang="greek">w</foreign> P. alia igitur omnia, quæ &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<lb/> les, & æquales lineis G M, M K, quia Iris videri nequit, ni&longs;i in tali, ac deter­<lb/> minata reflexione, & angulo, vt initio &longs;uppo&longs;ui; & quia lineæ illis propor­<lb/> tionales non po&longs;&longs;unt alibi con&longs;titui, quam in ambitu circulari, & 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, & <lb/> centrum <foreign lang="greek">w,</foreign> inueniemus &longs;imiliter in axe G K <foreign lang="greek">w</foreign> P, & quia axis hic &longs;ecat hori­<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> & P, exi&longs;tunt, infra horizontem deprimi. <lb/> </s> <s id="s.002135">& quia (vt pater ex 64. 10. Vitell.) & P, polus, & centrum <foreign lang="greek">w,</foreign> Iridis, & cen­<lb/>trum K, circuli horizontis, cuius &longs;cilicet diameter e&longs;&longs;et A K S, & 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<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<lb/> tenta inter duos arcus Q S, & T R, e&longs;t infra horizontem. </s> <s id="s.002136">debemus autem <lb/> hunc &longs;emicirculum, & hanc portionem ip&longs;ius S L T, extantem &longs;upra hori­<lb/> zontem imaginari erectam e&longs;&longs;e, vt planum ip&longs;ius circuli faciat angulos re­<lb/> ctos &longs;iue &longs;it perpendiculare cum axe G K P; & <expan abbr="circulũ">circulum</expan> altitudinis A G M N, <lb/> modo fungi vice horizontis. </s> <s id="s.002137">&longs;ic enim &longs;ola portio S L T, appareret nobis, <expan abbr="e&longs;-&longs;et&qacute;">e&longs;­<lb/> &longs;etque</expan>; rationabiliter con&longs;tituta. </s> <s id="s.002138">Ex quibus 2. Ari&longs;t. propo&longs;itio manife&longs;ta e&longs;t.</s> </p> <p type="main"> <s id="s.002139"><arrow.to.target n="marg171"/></s> </p> <p type="margin"> <s id="s.002140"><margin.target id="marg171"/>180</s> </p> <p type="main"> <s id="s.002141">Ibidem <emph type="italics"/>(Minima autem cum in meridie, quanto enim &longs;uperius G, tanto infe­<lb/> rius & polus, & centrum circuli erit)<emph.end type="italics"/> probat tertiam propo&longs;itionem, nimi­<lb/> rum Sole exi&longs;tente in meridie minimam <expan abbr="omniũ">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, & <lb/> con&longs;equenter <foreign lang="greek">w;</foreign> centrum Iridis e&longs;t depre&longs;si&longs;&longs;imum, quare tunc maxima cir­<lb/> culi Iridis portio ab&longs;condetur, & proinde minima apparebit, quod erat vl­<lb/> timo <expan abbr="demõ&longs;trandum">demon&longs;trandum</expan>. </s> <s id="s.002142">Non me latet has Ari&longs;t. figurationes e&longs;&longs;e apud Olym­<lb/> piodorum nonnullis obiectionibus obnoxias, &longs;ed cum facilè dilui po&longs;&longs;int, & <lb/> etiam &longs;i non diluantur, &longs;aluetur tamen veritas Ari&longs;totelicæ demon&longs;tratio­<lb/> nis, breuitati &longs;tudens, con&longs;ultò eas prætermitto.</s> </p> <p type="main"> <s id="s.002143">Aduertendum præterea Vicomercatum inordinatè citare librum Dato­<lb/> rum Euclidis, & <expan abbr="quandoq;">quandoque</expan> etiam malè citare Euclidem ip&longs;um. </s> <s id="s.002144">peius verò <pb pagenum="124" xlink:href="009/01/124.jpg"/>faciunt ij, qui has demon&longs;trationes <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla libri Datorum mentione ex­<lb/> plicare conantur, cum manife&longs;tè illo innitantur.</s> </p> <p type="main"> <s id="s.002145">Cæterum &longs;i quis breues, ac dilucidas harum rerum demon&longs;trationes re­<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> <s id="s.002146">ego enim longiorem hanc, <expan abbr="atq;">atque</expan> impeditam Ari&longs;t. tra­<lb/> ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e­<lb/> quutus &longs;um.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002147"><arrow.to.target n="marg17