texts/archimedes/xml/bianc_locam_01_la_1615.xml - Colored diff

Main History Search Repository tree

Return to bianc_locam_01_la_1615.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/Attic/bianc_locam_01_la_1615.xml between version 1.4 and 1.5

version 1.4, 2002/06/27 17:26:40

version 1.5, 2002/06/28 13:03:24

Line 1

<?xml version="1.0"?>

<!DOCTYPE archimedes [

<!-- footnotes and margnotes get yanked out of their

s, repl. by <arrow>, -->

<!ELEMENT foot.target

Line 210

Line 213

id ID #IMPLIED

n CDATA #IMPLIED>

<!-- <lb> occurs at

<s> level and at level -->

<!-- <lb> at end of

<s> must be placed after </s> -->

Line 254

Line 261

<!-- pb can occur inside

<s> etc. and inside and inside <chap> -->

Line 448

Line 457

]><archimedes> <info> <author>Bianchini, Giuseppe</author> <title>Aristotelis loca mathematica</title> <date>1615</date> <place>Bologna</place> <editor></editor> <publisher></publisher> <translator></translator> <lang>la</lang> <chunk unit="page*">page</chunk><locator>0000000009</locator> </info> <text> <front> </front> <body> <chap> <pb/>

<s>ARISTOTELIS</s>

<s>LOCA MATHEMATICA</s>

<s>Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/>& explicata.</s>

<s><emph type="italics"/>Aristotelicæ videlicet expo&longs;itionis complementum <lb/>hactenus de&longs;ideratum.<emph.end type="italics"/></s>

<s>Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/><expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s>

<s><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>

<s>Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum</s>

<s>PETRVMFRANCISCVM MALASPINAM</s>

<s>Aedificiorum Marchionem, apud Cæ&longs;. </s>

<s>Maie&longs;tatem <lb/>pro Sereni&longs;s. </s>

<s>Parmen&longs;ium Duce Legatum.</s><figure></figure>

<s>BONONIÆ M. </s>

<s>Apud Bartholomæum Cochium. </s>

<s>Superiorum permi&longs;&longs;u.</s>

<s>Sumptibus Hieronymi Tamburini.</s><pb pagenum="3"/><figure></figure>

<s>ILLVSTRISSIMO <lb/>AC NOBILISSIMO</s>

<s>PETROFRANCISCO <lb/>MALASPINAE</s>

<s>ÆDIFICIORVM MARCHIONI.</s><figure></figure>

<s><emph type="italics"/>En tandem Illustriß. </s>

<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 Mathematicor&ubreve; Chronologia; <lb/>quod tibi Mec&oelig;nati meo munificenti&longs;simo iure meritò <lb/>dicare, ac &longs;ub clarißimi tui nominis patrocinio in lucem <lb/>dare con&longs;titui. </s>

<s>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>cùm enim adiu&longs;tum arbitr&ubreve; 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>tu enim cùm Phy&longs;iologiæ, ac Mathe<lb/>maticarum omnium Encyclopædiam mirum in modum<emph.end type="italics"/><pb pagenum="4"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>per&longs;ua&longs;i&longs;ti, vt Archimedis, & Apollonij admirandis, ac <lb/>&longs;ubtilißimis Demon&longs;trationibus detinearis. </s>

<s>Quanta por<lb/>rò in rebus agendis prudentia valeas, toti penè Europæ <lb/>innotuit, cùm pro no&longs;tris Sereniß. </s>

<s>Ducibus, non &longs;olùm ad <lb/>omnes ferè Italiæ, atque Germaniæ Principes, verùm etiam <lb/>ad Cæ&longs;aream Maie&longs;tatem rebus f&oelig;liciter ge&longs;tis Legatus <lb/>decimùm extiteris; ac demùm à Sereniß. </s>

<s>Duce Ranutio <lb/>inter primarios de Rep. </s>

<s>Con&longs;iliorum Authores ad&longs;citus <lb/>fueris. </s>

<s>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>Complectere <lb/>igitur ea benignitate, atque clementia, qua &longs;oles no&longs;tra stu<lb/>dia promouere, mea hæc quantulacumque munu&longs;cula. <lb/>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>incolumem tibi, ac f&oelig;licem D. Opt. <lb/>Max. </s>

<s>longæuitatem tueatur. <lb/>Vale.<emph.end type="italics"/></s>

<s><emph type="italics"/>Parmæ Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/><figure id="fig1"></figure></s><pb pagenum="5"/><figure></figure>

<s>Liber de &longs;e ip&longs;o.</s>

<s><emph type="italics"/>Nec di&longs;cet Lector me &longs;olo interprete totum, <lb/>Nec &longs;ine me totum di&longs;cet Aristotelem.<emph.end type="italics"/></s><figure></figure>

<s>Ego Iordanus Ca&longs;&longs;ini Præpo&longs;itus Prouincialis Prouinciæ Venetæ Societatis <lb/>Ie&longs;u, ex auctoritate Adm. </s>

<s>Reuer. </s>

<s>P. nc&longs;tro Præpo&longs;iti Generalis P. </s>

<s>Claudij <lb/>Aquæuiuæ, facultatem concedo, vt hoc opus P. </s>

<s>Io&longs;ephi Blancani eiu&longs;dem <lb/>Societatis, quod in&longs;cribitur, Ari&longs;t. </s>

<s>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>Parmæ die 15. Ianuarij 1615.</s>

<s><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/></s>

<s>Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s>

<s>& Reuerendi&longs;s. </s>

<s>Archiepi&longs;c. </s>

<s>Bonon</s>

<s>Imprimatur</s>

<s>Hieronymus Onuphrius pro Reuerendi&longs;s. </s>

<s>Inqui&longs;itore Bonon<gap/></s><pb pagenum="6"/>

<s>LECTORI.</s>

<s>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>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>

<s>Prima &longs;it, quod hæc Ari&longs;t. </s>

<s>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>

<s>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>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">ag aiome/trhtos <lb/>ud<gap/>i/s <gap/>i/to</foreign>; & in quibus Mathematicæ di&longs;ciplinæ rudes, & imperiti, quem <lb/>&longs;equuntur ducem Ari&longs;t. </s>

<s>eum &longs;æpe de&longs;erere non &longs;ine turpi dedecoris no<lb/>ta coguntur; quo fit vt exempla illa Mathematica luc<gap/>m rebus aliquan<lb/>do allatura, t<gap/>n<gap/>bras cimmerijs, vt aiunt vmbris cra&longs;&longs;iores ij&longs;dem <lb/>obducant.</s>

<s>Tertia, quia Græcieorumdem locorum commentatores breuiter, & <lb/>ob&longs;curè admodum ea, quæ ad Mathematicum &longs;pectant, attingunt, hoc <lb/>enim ab ip&longs;is <expan abbr="cert&utilde;">certum</expan> ponitur, I ectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/>Philo &longs;ophorum, Mathematicis imbutum; at 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. </s>

<s>ob&longs;curè dicta intelligunt.</s><pb pagenum="7"/>

<s>Quarta. </s>

<s>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>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>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>

<s>Quinta. </s>

<s>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. </s>

<s>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>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>quod &longs;i dicat, omnis triangulus habet tres æquales duo<lb/>busrectis: 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>Nec mi<lb/>nus elegans illa altera expo&longs;itio; Diametrum e&longs;le incommen&longs;urabilem <lb/>co&longs;tæ; quod &longs;æpe apud Ari&longs;t. </s>

<s>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. </s>

<s>7. non hominum, &longs;ed &longs;uum, <expan abbr="peco-rumq;">peco<lb/>rumque</expan> appellare non dubitauit. </s>

<s>cum Ari&longs;t. </s>

<s>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/>Auerroes ip&longs;e tantus vir 5. Phy&longs;. </s>

<s>commen. </s>

<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>

<s><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/>It a voluntas antiqua ad effectum antiquum. <lb/>Ergo permutatim, vt &longs;e habebit voluntas noua ad effectum <lb/>antiquum, <gap/>ta voluntas antiqua ad effectum nouum.<emph.end type="italics"/></s>

<s><expan abbr="Spectat&utilde;">Spectatum</expan> admi&longs;&longs;i rilum teneatis amici? </s>

<s>nego, ait; qui&longs;piam con&longs;equen<pb pagenum="8"/>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>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>

<s>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>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>

<s>Alij ex altera parte contra A&longs;tronomos in &longs;urgunt, eccentricos, <expan abbr="atq;">atque</expan> <lb/>epiciclos omnes de c&oelig;lo detrahere cupientes. </s>

<s>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 C&oelig;lorum fabricam a&longs;&longs;erere, non autem &longs;upponere: <lb/>&longs;ed a&longs;tronomi illam &longs;upponunt, <expan abbr="eam&qacute;">eamque</expan>; propterea hypothe&longs;im <expan abbr="appellãt">appellant</expan>, <lb/>non a&longs;&longs;erunt. </s>

<s>Quod &longs;i aliqua probabili ratione id facerent, vti nonnulli <lb/>ex recentioribus, quorum Ticho Coripheus e&longs;t, laudandi potius, quam <lb/>vituperandi e&longs;&longs;ent. </s>

<s>Impugnant <expan abbr="itaq;">itaque</expan> a&longs;tronomachi i&longs;ti hypothe&longs;im pro <lb/>a&longs;&longs;ertione; <expan abbr="tales&qacute;">talesque</expan>; &longs;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>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>Sed exi&longs;timandum <lb/>e&longs;t <expan abbr="i&longs;t&utilde;">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>

<s>Quid tandem <expan abbr="dic&etilde;dum">dicendum</expan> de quodam magni nominis Philo&longs;opho, om<lb/>nium tamen <expan abbr="Mathematicar&utilde;">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>&longs;cilicet non intellig<gap/>bat ma<lb/>thematicum tantummodo tractare de Quantitate finita, ac terminata, <lb/>in qua axioma prædictum ab omnibus conceditur. </s>

<s>Neque vero hic <lb/>nonnullorum infen&longs;us in Mathematicas animus quieuit, verum etiam <lb/>cò progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien<pb pagenum="9"/>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>Verum enim verò optimè &longs;cio, ea, <lb/>qu&ecedil; 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>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. </s>

<s>& Scotus, <lb/>Hiomnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o<lb/>phantes excelluerint, nemo e&longs;t qui non nouerit. </s>

<s>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. </s>

<s>de <lb/>demon&longs;tratione &longs;ententiam a&longs;&longs;equi po&longs;&longs;et.</s>

<s>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>

<s>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>Quapr<gap/>p<lb/><gap/>er loca hæc mathematica num rectè e&longs;&longs;ent è græco in latinum tran&longs;lata <lb/>diligenter prius expendi. </s>

<s>Deinde claritate, quàm potui max ma 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>Tum fi<lb/>guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s>

<s>Hocigitur <lb/>mo&longs;tro qualicunque labore poterit qui&longs;que omnia illa facile intelligere, <lb/><expan abbr="atq;">atque</expan> enumerata incommoda euitare, vnum tantummodo à L<gap/>ctore 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 ommbus &longs;int obuia; <lb/>cætera ego explicanda recipio. </s>

<s>Obiter etiam auctaria nonnulla partim <lb/>mathematica, partim naturalia in&longs;erui, quæ ob nouitatem, ac pulchri<lb/>cudinem grata Lectori, atque iucunda fore exi&longs;timaui.</s>

<s>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><pb pagenum="10"/>

<s>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&ecedil;q;">vnaqu&ecedil;que</expan> <lb/>debeat, & ex illis de cæteris iudicium fiat. </s>

<s>Tandem in gratiam etiam <lb/>Mathematicorum tertiam appendicem appendi, qua omnia loca Ari&longs;t. <lb/>Geometrica ad Euclidis ordinem referuntur; vnde & ip&longs;i ad &longs;uas pr&ecedil;le<lb/>ctiones exornandas aliquid &longs;ubinde depromere queant.</s>

<s>Fruere igitur amice Lector hoc no&longs;tro qualiquali labore, quo ad ple<lb/>nam totius Ari&longs;t. </s>

<s>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"/>Aristot elicæ 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>

<s>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/>Vale.</s><figure></figure><pb pagenum="11"/>

<s>Pr&ecedil;cipua qu&ecedil;dam, aut noua, autre&longs;taurata, <lb/>quæ obiter pertractantur.<lb/><arrow.to.target n="table1"></arrow.to.target></s><table><table.target id="table1"></table.target><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><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"/>S<gap/>ytala 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></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></cell></row></table><figure></figure><pb pagenum="12"/>

<s><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/></s>

<s><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>

<s>In Prædicamentis.</s>

<s><emph type="italics"/>Gapite s. </s>

<s>de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s>

<s>de Priori, vbi de Principijs Mathematicarum,<emph.end type="italics"/></s>

<s>de Motu, vbi de Gnomone.<emph.end type="italics"/></s>

<s>In Primo Priorum Re&longs;olutoriorum.</s>

<s><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s>

<s>23. &longs;ect 1. libri 1. de Incommen &longs;ur abilibus.<emph.end type="italics"/></s>

<s>24. &longs;ecti 1. lib. </s>

<s>1. de De&longs;criptionibus.<emph.end type="italics"/></s>

<s>2. &longs;ect 2. lib. </s>

<s>1. de De&longs;criptionibus.<emph.end type="italics"/></s>

<s>3. &longs;ecti 2. lib. </s>

<s>1. de Incommen&longs;urabili.<emph.end type="italics"/></s>

<s>1. &longs;ecti 3. lib. </s>

<s>1. de eo, quod est, omnis triangulus habet tres angulos æquales <lb/>æquales duobus rectis: Aequalitas Geometrica, quæ.<emph.end type="italics"/></s>

<s>eodem, de exemplis, quibus vtuntar Geometræ.<emph.end type="italics"/></s>

<s>In &longs;ecundo Priorum Re&longs;ol.</s>

<s>21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s>

<s>eodem. </s>

<s>de Paralellis, & de triangulo.<emph.end type="italics"/></s>

<s>26. Quod omnis triangulus habet tres, & c.<emph.end type="italics"/></s>

<s>31. de Abductione.<emph.end type="italics"/></s>

<s>codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/></s>

<s>In primo Po&longs;teriorum.</s>

<s><emph type="italics"/>Textu primo, De Præcognitis Mathematicarum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 2. Omnis triangulus habet tres, & c.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s>

<s>Item De Mathematicarum Principijs.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. eodem, De Indiui&longs;ibilitate vnitatis.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 9. De Puncto, & linea. </s>

<s>Item de recto, & circulari. </s>

<s>Item de numero pari; impari<gap/><lb/>primo, & compo&longs;ito; æquilatero, & altera parte longiore.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 11. Lineæ punctum inest per &longs;e, & c.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 13. De Parallelis. </s>

<s>De I&longs;o&longs;cele. </s>

<s>De Alterna Proportione, <lb/>Item quod omnis triangulus habet tres, & c.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 14. De ij&longs;aem cum præcedentibus.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 20. Magnitudines euadun<gap/> numeri. </s>

<s>Item, quod non duo cubi cubus. </s>

<s>Item de <lb/>Mathematicis &longs;ubalternatis.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 23. Quadratura circuli &longs;ecundum Bry&longs;onem. </s>

<s>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/>Per&longs;pectinam, & Mechanicam &longs;ubalternari Geometriæ, Mu&longs;icam, Arithmeticæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 24. De numero pari, impari, quodrangulo, cubo. </s>

<s>In Geometria quid irrationale, <lb/>refrangi, concurrere. </s>

<s>Quid Astronomia con&longs;ideret.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/></s><pb pagenum="13"/>

<s><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. </s>

<s>Item quid multiplicata propor<lb/>tio. </s>

<s>Quid Cæneus dixerit. </s>

<s>Cur Affectiones Mathematicor&ubreve; maximè <expan abbr="conuertãtur">conuertantur</expan>.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 30. De Lunæ &longs;phæricitate. </s>

<s>Quid &longs;tereometria. </s>

<s>& De &longs;ubalternatione, &c. </s>

<s>& Ma<lb/>thematicorum e&longs;t &longs;cire Propter quid: &longs;en&longs;itiuorum verò &longs;cire Quod.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 37. I&longs;o&longs;celes, & Scalenum habere tres æquales, &c.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 39. Habere tres angulos æquales, &c. </s>

<s>Item, quod omnis figura habet &longs;uos angu<lb/>los externos æquales quatuor tantum rectis.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 43. Triangulum tres æquales, &c. </s>

<s>De Eclyp&longs;i.<emph.end type="italics"/></s>

<s><emph type="italics"/>De combu&longs;tione per refractionem ex &longs;phæra vitrea. </s>

<s>De principijs &longs;cientiarum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>

<s>In 2. Po&longs;teriorum.</s>

<s><emph type="italics"/>T. 1. Aequalitas, & inæqualitas. </s>

<s>Terram e&longs;&longs;e in medio mundi ab A&longs;tronomis per<lb/>fectè demon&longs;tratur. </s>

<s>Item Quid con&longs;onantia.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &c. </s>

<s>Item de Definitionibus Mathematicarum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 7. Geometra, quædam accipit, quædam demon&longs;trat.<emph.end type="italics"/></s>

<s><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>Zabarella correctus.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 24. Echo, Imago è &longs;peculo, Iris.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s>

<s>In primo lib. </s>

<s>Topicorum.</s>

<s>13. Diameter est incommen&longs;urabilis. </s>

<s>Vox acuta velox, cur. </s>

<s>Colores in <lb/>Mu&longs;ica, qui. </s>

<s>tria genera veteris Mu&longs;icæ.<emph.end type="italics"/></s>

<s>In 4. libro.</s>

<s>1. loco 1. lineæ in&longs;ecabiles.<emph.end type="italics"/></s>

<s>In 6. libro.</s>

<s>2. loco 32. Definitio lineæ.<emph.end type="italics"/></s>

<s>In 8. libro.</s>

<s>2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/></s>

<s>4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s>

<s>In Elenchorum lib. </s>

<s>10. Quid P&longs;eudographia. </s>

<s>Quadraturarur&longs;us Hippocratis, & Bry&longs;enis. </s>

<s>Mathe<lb/>maticæ non contentio&longs;æ. </s>

<s>Quadratio Antiphontis.<emph.end type="italics"/></s>

<s>Ex 1. Phy&longs;ic.</s>

<s><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, & Antiphontis.<emph.end type="italics"/></s>

<s>Ex 2. Phy&longs;ic.</s>

<s><emph type="italics"/>T. 20. Quatenus Per&longs;pectmus con&longs;ideret lineam.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes babere cau&longs;am, quæ reducitur ad defini<lb/>tionem.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 8. Denece&longs;&longs;ari<gap/>, quod e&longs;t in Mathematicis. </s>

<s>& omnis triangulus habet tres an<lb/>gulos, &c.<emph.end type="italics"/></s>

<s>Ex 3. Phy&longs;ic.</s>

<s><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/></s><pb pagenum="14"/>

<s>Ex 4. Phy&longs;ic.</s>

<s><emph type="italics"/>T. 120. De commen&longs;urab. </s>

<s>& incommen&longs;.<emph.end type="italics"/></s>

<s>Ex 5. Phy&longs;ic.</s>

<s><emph type="italics"/>T. 6. De chordis, graui, acuta; media, & vltima.<emph.end type="italics"/></s>

<s>Ex 8. Phy&longs;ic.</s>

<s><emph type="italics"/>T. 15. Omnis triangulus habet tres æquales, &c.<emph.end type="italics"/></s>

<s>Ex 1. de C&oelig;lo.</s>

<s><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 36. Ratione vtitur lineari; vt probet mundum e&longs;&longs;e finitum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 48. Commen&longs;urab. </s>

<s>& incommen&longs;urab. </s>

<s><emph type="italics"/>T. 119. Omnis triangulus habet tres, &c. </s>

<s>Item de commen&longs;urabili.<emph.end type="italics"/></s>

<s>Ex 2. de C&oelig;lo.</s>

<s><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, quì.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 25. Ordo figurarum planarum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 31. Aquæ &longs;uperficiem e&longs;&longs;e &longs;phæricam.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s>

<s>Recentiorum ob&longs;eruationes.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 57. De ordine C&oelig;lorum ex &longs;ententia A&longs;tronomorum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 59. De rotunditate Lunæ, bis.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 107. Centrum duplex grauit: & molis. </s>

<s>Qua ratione grauia ad mundi centrum <lb/>aptarentur.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 109. Terram e&longs;&longs;e rotundam. </s>

<s><emph type="italics"/>T. 110. Terram e&longs;&longs;e paruam re&longs;pectu C&oelig;li.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 112. De quantitate Terræ.<emph.end type="italics"/></s>

<s>Ex 3. de C&oelig;lo.</s>

<s><emph type="italics"/>T. 40. Vt componatur &longs;phæra.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 66. Omne corpus diui&longs;ibile.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 66. Quænam planarum figurarum totum &longs;patium repleant. </s>

<s>Hinc de admirabili <lb/>Apum mgenio.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. eodem. </s>

<s>Num plures Pyramides locum replere valeant, vbi Ari&longs;totiles, & omnes <lb/>expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s>

<s>Ex 4. de C&oelig;lo.</s>

<s><emph type="italics"/>T. 33. Extare centrum Mundi, quò grauia tendunt, à quo leuia abeant.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 44. & <expan abbr="&longs;eq.">&longs;eque</expan> Cur quædam grautora quàm aqua, &longs;upernatent.<emph.end type="italics"/></s>

<s>Ex 2. de Generatione, & Corruptione.</s>

<s>56. Cur Planetæ duobus motibus moueri dicantur.<emph.end type="italics"/></s>

<s>Ex 1. Meteororum.</s>

<s><emph type="italics"/>Summa prima cap. </s>

<s>3. De magnitudine Terræ ad a&longs;tra, & &longs;olem collata.<emph.end type="italics"/></s>

<s>eodem. </s>

<s>De magnitudine A&longs;trorum.<emph.end type="italics"/></s>

<s>4. De ordine Luminarium Solis, & Lunæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>Summa 2. cap. </s>

<s>3. de Mercurij stella. </s>

<s>Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/></s>

<s>5. De Magnitudine Solis, & de vmbra Terræ.<emph.end type="italics"/></s>

<s>5. De Glaxia.<emph.end type="italics"/></s>

<s>6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde <lb/>aperitur.<emph.end type="italics"/></s><pb pagenum="15"/>

<s><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>

<s>Mare extraneum, quod. </s>

<s>Errata quæ<lb/>dam veterum Geographorum, & Ari&longs;t. </s>

<s>corriguntur. </s>

<s>Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s>

<s>2. De permutatione Aquarum, & continentis. </s>

<s>Noua ob&longs;eruatio de rotundi<lb/>tate Terræ, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s>

<s>Ex 2. Meteororum.</s>

<s><emph type="italics"/>Summa 1. cap. </s>

<s>1. De Marirubro.<emph.end type="italics"/></s>

<s><emph type="italics"/>Summa 2. cap. </s>

<s>2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s>

<s>eodem, De Canicula. </s>

<s>De Zonis temperatis. </s>

<s>Corona Ariadnæ. </s>

<s>Zonam torrid<gap/>m <lb/>falsò putabant inho&longs;pitalem. </s>

<s>cur habitabilis.<emph.end type="italics"/></s>

<s>3. De Ventorum&longs;itu.<emph.end type="italics"/></s>

<s>Ex 3. Meteor.</s>

<s><emph type="italics"/>Summa 2. cap. </s>

<s>2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;iratio.<emph.end type="italics"/></s>

<s>4. De Iridis figura Mathematica demon&longs;tratio, &longs;ed deficiens. </s>

<s>Noua de eadem <lb/>tractatio.<emph.end type="italics"/></s>

<s>5. De Parelio. </s>

<s>Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s>

<s>Ex 1. De Anima.</s>

<s>11. Quid rectum, quid obliquum. </s>

<s>& omnis triangulus babet tres, &c.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 13. Sphæra planum tangit in puncto.<emph.end type="italics"/></s>

<s>Ex 2. De Anima.</s>

<s><emph type="italics"/>T. 12. D finitioncm formalem, & cau&longs;alem explicat exemplo Quadrationis Geo<lb/>metricæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 86. Acutum, & Graue, vt differant.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s>

<s>Ex 3. De Anima.</s>

<s><emph type="italics"/>T. 21. Incommen&longs;urabile.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 25. Indiui&longs;ibilia e&longs;&longs;e priuationes.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s>

<s>De Sen&longs;u.</s>

<s><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/></s>

<s>Diapa&longs;on. </s>

<s>Diapen&longs;e.<emph.end type="italics"/></s>

<s>De Memoria, & Rem.</s>

<s>1. Omnis triangulus babet tres, &c.<emph.end type="italics"/></s>

<s>3. Mathemata facile remini&longs;cibilia.<emph.end type="italics"/></s>

<s>De Somnijs.</s>

<s>2. Terra, cur nauigantibus moueri videatur.<emph.end type="italics"/></s>

<s>3. Cur Oculus digito dimotus res geminatas videat.<emph.end type="italics"/></s>

<s>Ex 1. Methaphy&longs;.</s>

<s>1. Initium Mathematicarum ab Aegyptiorum Saterdotibus. </s>

<s>Item, Automata, <lb/>quæ &longs;olstitia. </s>

<s>Diameter incommen&longs;.<emph.end type="italics"/></s>

<s><emph type="italics"/>Summa 2. cap. </s>

<s>3. Pythagorei Mathematicas cæteris præferebant.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 47. Geometria habet &longs;uas præcognitiones.<emph.end type="italics"/></s>

<s>Ex 2. Methaphy&longs;.</s>

<s><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s>

<s>Ex 3. Methaphy&longs;.</s>

<s>Mathematicas puras carere cau&longs;is efficiente, & finali. </s>

<s>Ariftippus, vt Mathe<lb/>maticas &longs;ugillaret. </s>

<s>Tetragoni&longs;mus est inuentio mediæ.<emph.end type="italics"/></s><pb pagenum="16"/>

<s>8. Geodæ&longs;ia quid.<emph.end type="italics"/></s>

<s>Ex 4. Methaphy&longs;.</s>

<s><emph type="italics"/>T. 4. Quæ &longs;int primæ, & quæ &longs;ecundæ inter Mathematicas.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s>

<s>Ex 5. Methaphy&longs;.</s>

<s><emph type="italics"/>T. 2. Exemplum cau&longs;æ formalis ex Diapa&longs;on. </s>

<s>Quæ &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 3. Quæ &longs;it Materia in Mathematicis.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>

<s>Quid potentia vnius lineæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>

<s>Ex 6. Methaphy&longs;.</s>

<s><emph type="italics"/>T. 1. Principia, elementa, & cau&longs;æ in Mathem.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 8. Diameter. </s>

<s>commen&longs;urab.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 20. De&longs;criptiones. </s>

<s>Omnis triangulus habet tres, &c. </s>

<s>Cur Angulus in &longs;emicir<lb/>culo rectus.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 22. Omnis triangulus habet tres, &c.<emph.end type="italics"/></s>

<s>Ex 10. Methaphy&longs;.</s>

<s><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>

<s>Die&longs;is.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 11. Similes figuræ quæ. </s>

<s>Diuer&longs;um in Math. </s>

<s>Ex 11. Methaphy&longs;.</s>

<s>2. Ortus punctorum, linearum, &longs;uperficierum.<emph.end type="italics"/></s>

<s>Ex 12. Methaphy&longs;.</s>

<s><emph type="italics"/>T. 44. Peculiari&longs;&longs;imam Philo&longs;ophiam, Mathematicorum videlicet, A&longs;tronomiam <lb/>pluralitatem C&oelig;lorum docere.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 45. Numerus orbium c&oelig;le&longs;t ium &longs;ecundum Eudoxum.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 46. Itidem ex Eudoxo.<emph.end type="italics"/></s>

<s><emph type="italics"/>T. 47. Orbium c&oelig;le&longs;tium numerus, & fabrica ex Calippo.<emph.end type="italics"/></s>

<s>Ex 13. Methaphy&longs;.</s>

<s>3. Quaratione Mathematici tractant de Bo<gap/>o.<emph.end type="italics"/></s>

<s>In Mechanicas Quæ&longs;tiones.</s>

<s>1. Quæ &longs;it Mechanica facultas.<emph.end type="italics"/></s>

<s>2. De Admirandis circuli.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;tio 1. De Libra. </s>

<s>cur maior, exactior. </s>

<s>inibi Ari&longs;t. </s>

<s>lap&longs;us.<emph.end type="italics"/></s>