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version 1.68, 2002/09/07 13:46:08

version 1.84, 2002/10/31 13:34:09

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</info> <text> <front> </front> <body> <chap> <pb/>

</info> <text> <front> <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.001.jpg"/><section>

<s>ARISTOTELIS</s>

<s id="id.000001">ARISTOTELIS<lb/>LOCA MATHEMATICA<lb/>Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/>& explicata.</s>

<s>LOCA MATHEMATICA</s>

<s id="id.000002"><emph type="italics"/>Aristotelicæ videlicet expo&longs;itionis complementum <lb/>hactenus de&longs;ideratum.<emph.end type="italics"/></s>

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

<s id="id.000003">Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/><expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s>

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

<s id="id.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>

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

<s id="id.000005">Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum<lb/>PETRVMFRANCISCVM MALASPINAM<lb/>Aedificiorum Marchionem, apud Cæ&longs;. Maie&longs;tatem <lb/>pro Sereni&longs;s. Parmen&longs;ium Duce Legatum.</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;. Maie&longs;tatem <lb/>pro Sereni&longs;s. </s>

<s id="id.000006">BONONIÆ M. D C. X V.</s>

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

<s>BONONIÆ M. D C. </s>

<s id="id.000007">Apud Bartholomæum Cochium. </s>

<s id="id.000008">Superiorum permi&longs;&longs;u.</s>

<s>Apud Bartholomæum Cochium. </s>

<s id="id.000009">Sumptibus Hieronymi Tamburini.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.002.jpg"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.003.jpg" pagenum="3"/>

</section>

<section><s id="id.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO<lb/>PETROFRANCISCO <lb/>MALASPINAE<lb/>ÆDIFICIORVM MARCHIONI.</s>

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

<s id="id.000011"><emph type="italics"/>En tandem Illustriß. 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="Mathematicor&utilde;">Mathematicorum</expan> 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>Sumptibus Hieronymi Tamburini.</s><pb pagenum="3"/><figure/>

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

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

<s id="id.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>ÆDIFICIORVM MARCHIONI.</s><figure/>

<s id="id.000013">cùm enim adiu&longs;tum <expan abbr="arbitr&utilde;">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><emph type="italics"/>En tandem Illustriß. 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 id="id.000014">tu enim cùm Phy&longs;iologiæ, ac Mathe<lb/>maticarum omnium Encyclopædiam mirum in modum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.004.jpg" 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 id="id.000015">Quanta por<lb/>rò in rebus agendis prudentia valeas, toti penè Europæ <lb/>innotuit, cùm pro no&longs;tris Sereniß. 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. Duce Ranutio <lb/>inter primarios de Rep. </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. 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 id="id.000016">Con&longs;iliorum Authores ad&longs;citus <lb/>fueris. </s>

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

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

<s id="id.000020">incolumem tibi, ac f&oelig;licem D. Opt. <lb/>Max. longæuitatem tueatur. <lb/></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/></s>

<s>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 id="id.000022"><emph type="italics"/>Parmæ Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/></s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.005.jpg" pagenum="5"/><section>

<s>longæuitatem tueatur. <lb/></s>

<s id="id.000023">Liber de &longs;e ip&longs;o.</s>

<s id="id.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"/></s>

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

<s id="id.000025">Ego Iordanus Ca&longs;&longs;ini Præpo&longs;itus Prouincialis Prouinciæ Venetæ Societatis <lb/>Ie&longs;u, ex auctoritate Adm. Reuer. P. nc&longs;tro Præpo&longs;iti Generalis P. Claudij <lb/>Aquæuiuæ, facultatem concedo, vt hoc opus P. 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>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/>

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

<s>P. nc&longs;tro Præpo&longs;iti Generalis P. 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. 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="id.000026">Parmæ die 15. Ianuarij 1615.</s>

<s>Parmæ die 15. Ianuarij 1615.</s>

<s id="id.000027"><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/>Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s>

<s><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/>Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s>

<s id="id.000028">& Reuerendi&longs;s. Archiepi&longs;c. Bonon.</s>

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

<s>Bonon</s>

<s id="id.000029">Imprimatur</s>

<s>Imprimatur</s>

<s id="id.000030">Fr. Hieronymus Onuphrius pro Reuerendi&longs;s. P. Inqui&longs;itore Bonon.</s>

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

<s>P. Inqui&longs;itore Bonon<gap/></s>

</section><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.006.jpg" pagenum="6"/><section>

<s>LECTORI.</s>

<s id="id.000031">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 id="id.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>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 id="id.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>

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

<s id="id.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>

<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 id="id.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>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 id="id.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 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>

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>

<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 id="id.000037">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, 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><pb pagenum="7"/>

ob&longs;curè dicta intelligunt.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.007.jpg" pagenum="7"/>

<s>Quarta. </s>

<s id="id.000038">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 id="id.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>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="id.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>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 id="id.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>

<s>Quinta. </s>

<s id="id.000042">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 id="id.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>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="id.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>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 id="id.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>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 id="id.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. </s>

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

<s id="id.000047">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 id="id.000049">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>Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. 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 id="id.000050">Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. 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/></s>

<s id="id.000051"><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/>It a voluntas antiqua ad effectum antiquum. <lb/></s>

<s>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 id="id.000052">Ergo permutatim, vt &longs;e habebit voluntas noua ad effectum <lb/>antiquum, ita 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 id="id.000053"><expan abbr="Spectat&utilde;">Spectatum</expan> admi&longs;&longs;i ri&longs;um 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 id="id.000054">nego, ait; qui&longs;piam con&longs;equen<pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.008.jpg" 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 id="id.000055">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 id="id.000056">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 id="id.000057">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 id="id.000058">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 id="id.000059">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 id="id.000060">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 id="id.000061">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 id="id.000062">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 id="id.000063">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 id="id.000064">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 id="id.000065">&longs;cilicet non intelligebat 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 id="id.000066">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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.009.jpg" 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 id="id.000067">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. & Scotus, <lb/>Hiomnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o<lb/>phantes excelluerint, nemo e&longs;t qui non nouerit. </s>

<s id="id.000068">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. & 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 id="id.000069">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>

<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 id="id.000070">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 id="id.000071">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 id="id.000072">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>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 id="id.000073">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>Tum fi<lb/>guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s>

<s id="id.000074">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 id="id.000075">Hocigitur

<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>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 id="id.000076">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>

<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 id="id.000077">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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.010.jpg" 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 id="id.000078">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 id="id.000079">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 id="id.000080">Fruere igitur amice Lector hoc no&longs;tro qualiquali 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"/>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>

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/></s>

<s id="id.000081">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.

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

<s id="id.000083">Pr&ecedil;cipua qu&ecedil;dam, aut noua, autre&longs;taurata,

<lb/>quæ obiter pertractantur.

<lb/><arrow.to.target n="table1"/></s><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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.012.jpg" pagenum="12"/><section>

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

<s id="id.000084"><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 id="id.000085"><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 id="id.000086">In Prædicamentis.</s>

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

<s id="id.000087"><emph type="italics"/>Gapite s. </s>

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

<s id="id.000088">de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s>

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

<s id="id.000089"><emph type="italics"/>Cap.

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

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

<s id="id.000090"><emph type="italics"/>Cap.

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

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

<s id="id.000091">In Primo Priorum Re&longs;olutoriorum.</s>

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

<s id="id.000092"><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s>

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

<s id="id.000093"><emph type="italics"/>Cap.

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

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

<s id="id.000094"><emph type="italics"/>Cap.

24. &longs;ecti 1. lib.

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

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

<s id="id.000095"><emph type="italics"/>Cap.

2. &longs;ect 2. lib.

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

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

<s id="id.000096"><emph type="italics"/>Cap.

3. &longs;ecti 2. lib.

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

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

<s id="id.000097"><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>

1. de eo, quod est, omnis triangulus habet tres angulos æquales

<lb/>æquales duobus rectis: Aequalitas Geometrica, quæ.<emph.end type="italics"/></s>

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

<s id="id.000098"><emph type="italics"/>Cap.

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

<s>In &longs;ecundo Priorum Re&longs;ol.<emph type="italics"/>Cap.

<s id="id.000099">In &longs;ecundo Priorum Re&longs;ol.<emph type="italics"/>Cap.

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

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

<s id="id.000100"><emph type="italics"/>Cap.

eodem. </s>

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

<s id="id.000101">de Paralellis, & de triangulo.<emph.end type="italics"/></s>

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

<s id="id.000102"><emph type="italics"/>Cap.

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

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

<s id="id.000103"><emph type="italics"/>Cap.

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

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

<s id="id.000104"><emph type="italics"/>Cap.

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

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

<s id="id.000105">In primo Po&longs;teriorum.</s>

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

<s id="id.000106"><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 id="id.000107"><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 id="id.000108"><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s>

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

<s id="id.000109">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 id="id.000110"><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 id="id.000111"><emph type="italics"/>T. 9. De Puncto, & linea. </s>

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

<s id="id.000112">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 id="id.000113">Item de numero pari, impari;

<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 id="id.000114"><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 id="id.000115"><emph type="italics"/>T. 13. De Parallelis. </s>

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

<s id="id.000116">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 id="id.000117">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 id="id.000118"><emph type="italics"/>T. 14. De ij&longs;dem cum præcedentibus.<emph.end type="italics"/></s>

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

<s id="id.000119"><emph type="italics"/>T. 20. Magnitudines euadunt numeri. </s>

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

<s id="id.000120">Item, quod non duo cubi cubus. </s>

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

<s id="id.000121">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 id="id.000122"><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/></s>

<s id="id.000123">Item per&longs;ectam illam e&longs;&longs;e Demon

<lb/>&longs;trationem, qua Geometræ o&longs;tendunt, quod Omnis triangulus habet tres, & c.

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

<s id="id.000124">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 id="id.000125"><emph type="italics"/>T. 24. De numero pari, impari, quodrangulo, cubo. </s>

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

<s id="id.000126">In Geometria quid irrationale,

<lb/>refrangi, concurrere. </s>

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

<s id="id.000127">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 id="id.000128"><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 id="id.000129"><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.013.jpg" pagenum="13"/>

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

<s id="id.000130"><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. </s>

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

<s id="id.000131">Item quid multiplicata propor

<s>Quid Cæneus dixerit. </s>

<s id="id.000132">Quid Cæneus dixerit. </s>

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

<s id="id.000133">Cur Affectiones <expan abbr="Mathematicor&utilde;">Mathematicor&utilde;</expan> maximè <expan abbr="conuertãtur">conuertantur</expan>.<emph.end type="italics"/></s>

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

<s id="id.000134"><emph type="italics"/>T. 30. De Lunæ &longs;phæricitate. </s>

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

<s id="id.000135">Quid &longs;tereometria. </s>

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

<s id="id.000136">& 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 id="id.000137">& 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 id="id.000138"><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 id="id.000139"><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 id="id.000140"><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 id="id.000141">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 id="id.000142"><emph type="italics"/>T. 43. Triangulum tres æquales, &c. </s>

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

<s id="id.000143">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 id="id.000144"><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 id="id.000145">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 id="id.000146"><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>

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

<s id="id.000147">In 2. Po&longs;teriorum.</s>

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

<s id="id.000148"><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 id="id.000149">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 id="id.000150">Item Quid con&longs;onantia.<emph.end type="italics"/></s>

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

<s id="id.000151"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &c. </s>

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

<s id="id.000152">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 id="id.000153"><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 id="id.000154"><emph type="italics"/>T. 11. Angulum in &longs;emicirculo rectum e&longs;&longs;e probari à Geometra per cau&longs;am materia

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

<s id="id.000155">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 id="id.000156"><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 id="id.000157"><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s>

<s>In primo lib. Topicorum.</s>

<s id="id.000158">In primo lib. Topicorum.</s>

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

<s id="id.000159"><emph type="italics"/>Cap.

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

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

<s id="id.000160">Vox acuta velox, cur. </s>

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

<s id="id.000162">Colores in

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

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

<s id="id.000163">tria genera veteris Mu&longs;icæ.<emph.end type="italics"/></s>

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

<s id="id.000164">In 4. libro.</s>

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

<s id="id.000165"><emph type="italics"/>Cap.

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

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

<s id="id.000166">In 6. libro.</s>

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

<s id="id.000167"><emph type="italics"/>Cap.

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

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

<s id="id.000168">In 8. libro.</s>

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

<s id="id.000169"><emph type="italics"/>Cap.

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

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

<s id="id.000170"><emph type="italics"/>Cap.

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

<s>In Elenchorum lib.

<s id="id.000171">In Elenchorum lib.

1.</s>

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

<s id="id.000172"><emph type="italics"/>Cap.

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

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

<s id="id.000173">Quadraturarur&longs;us Hippocratis, & Bry&longs;enis. </s>

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

<s id="id.000174">Mathe

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

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

<s id="id.000175">Quadratio Antiphontis.<emph.end type="italics"/></s>

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

<s id="id.000176">Ex 1. Phy&longs;ic.</s>

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

<s id="id.000177"><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, & Antiphontis.<emph.end type="italics"/></s>

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

<s id="id.000178">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 id="id.000179"><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 id="id.000180"><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 id="id.000181"><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 id="id.000182"><emph type="italics"/>T. 8. De nece&longs;&longs;ario, quod e&longs;t in Mathematicis. </s>

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

<s id="id.000183">& omnis triangulus habet tres an

<lb/>gulos, &c.<emph.end type="italics"/></s>

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

<s id="id.000184">Ex 3. Phy&longs;ic.</s>

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

<s id="id.000185"><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 id="id.000186"><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 id="id.000187"><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.014.jpg" pagenum="14"/>

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

<s id="id.000188">Ex 4. Phy&longs;ic.</s>

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

<s id="id.000189"><emph type="italics"/>T. 120. De commen&longs;urab. </s>

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

<s id="id.000190">& incommen&longs;.<emph.end type="italics"/></s>

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

<s id="id.000191">Ex 5. Phy&longs;ic.</s>

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

<s id="id.000192"><emph type="italics"/>T. 6. De chordis, graui, acuta; media, & vltima.<emph.end type="italics"/></s>

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

<s id="id.000193">Ex 8. Phy&longs;ic.</s>

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

<s id="id.000194"><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 id="id.000195">Ex 1. de C&oelig;lo.</s>

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

<s id="id.000196"><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 id="id.000197"><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. & incommen&longs;urab. </s>

<s id="id.000198"><emph type="italics"/>T. 48. Commen&longs;urab. & incommen&longs;urab. </s>

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

<s id="id.000200"><emph type="italics"/>T. 119. Omnis triangulus habet tres, &c. </s>

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

<s id="id.000201">Item de commen&longs;urabili.<emph.end type="italics"/></s>

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

<s id="id.000202">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 id="id.000203"><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 id="id.000204"><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 id="id.000205"><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 id="id.000206"><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s>

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

<s id="id.000207">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 id="id.000208"><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 id="id.000209"><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 id="id.000210"><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 id="id.000211">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 id="id.000212"><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 id="id.000214"><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 id="id.000215"><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 id="id.000216"><emph type="italics"/>T. 112. De quantitate Terræ.<emph.end type="italics"/></s>

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

<s id="id.000217">Ex 3. de C&oelig;lo.</s>

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

<s id="id.000218"><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 id="id.000219"><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 id="id.000220"><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 id="id.000221">Hinc de admirabili

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

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

<s id="id.000222"><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 id="id.000223">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 id="id.000224"><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 id="id.000225">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 id="id.000226"><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 id="id.000227"><emph type="italics"/>T. 44. & <expan abbr="&longs;eq.">&longs;eque</expan> Cur quædam grauiora quàm aqua, &longs;upernatent.<emph.end type="italics"/></s>

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

<s id="id.000228">Ex 2. de Generatione, & Corruptione.</s>

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

<s id="id.000229"><emph type="italics"/>Tex. 56. Cur Planetæ duobus motibus moueri dicantur.<emph.end type="italics"/></s>

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

<s id="id.000230">Ex 1. Meteororum.</s>

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

<s id="id.000231"><emph type="italics"/>Summa prima cap.

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

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

<s id="id.000232"><emph type="italics"/>Cap.

eodem. </s>

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

<s id="id.000233">De magnitudine A&longs;trorum.<emph.end type="italics"/></s>

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

<s id="id.000234"><emph type="italics"/>Cap.

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

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

<s id="id.000235"><emph type="italics"/>Summa 2. cap.

3. de Mercurij stella. </s>

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

<s id="id.000236">Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/></s>

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

<s id="id.000237"><emph type="italics"/>Cap.

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

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

<s id="id.000238"><emph type="italics"/>Cap.

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

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

<s id="id.000239"><emph type="italics"/>Cap.

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

6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde

<lb/>aperitur.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.015.jpg" pagenum="15"/>

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

<s id="id.000240"><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>

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

<s id="id.000241">Mare extraneum, quod. </s>

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

<s id="id.000242">Errata quæ

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

corriguntur. </s>

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

<s id="id.000243">Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s>

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

<s id="id.000244"><emph type="italics"/>Cap.

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 id="id.000245">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 id="id.000246">Ex 2. Meteororum.</s>

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

<s id="id.000247"><emph type="italics"/>Summa 1. cap.

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

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

<s id="id.000248"><emph type="italics"/>Summa 2. cap.

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

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

<s id="id.000249"><emph type="italics"/>Cap.

eodem, De Canicula. </s>

<s>De Zonis temperatis. </s>

<s id="id.000250">De Zonis temperatis. </s>

<s>Corona Ariadnæ. </s>

<s id="id.000251">Corona Ariadnæ. </s>

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

<s id="id.000252">Zonam torridam

<lb/>falsò putabant inho&longs;pitalem. </s>

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

<s id="id.000253">cur habitabilis.<emph.end type="italics"/></s>

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

<s id="id.000254"><emph type="italics"/>Cap.

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

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

<s id="id.000255">Ex 3. Meteor.</s>

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

<s id="id.000256"><emph type="italics"/>Summa 2. cap.

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

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

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

<s id="id.000257"><emph type="italics"/>Cap.

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

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

<s id="id.000258">Noua de eadem

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

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

<s id="id.000259"><emph type="italics"/>Cap.

5. De Parelio. </s>

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

<s id="id.000260">Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s>

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

<s id="id.000261">Ex 1. De Anima.</s>

<s><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>

<s id="id.000262"><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>

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

<s id="id.000263">& 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 id="id.000264"><emph type="italics"/>T. 13. Sphæra planum tangit in puncto.<emph.end type="italics"/></s>

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

<s id="id.000265">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 id="id.000266"><emph type="italics"/>T. 12. Definitioncm 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 id="id.000267"><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 id="id.000268"><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s>

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

<s id="id.000269">Ex 3. De Anima.</s>

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

<s id="id.000270"><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 id="id.000271"><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 id="id.000272"><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s>

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

<s id="id.000273">Ex lib. De Sen&longs;u.</s>

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

<s id="id.000274"><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/></s>

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

<s id="id.000275"><emph type="italics"/>Cap.

8. Nete. </s>

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

<s id="id.000276">Diapa&longs;on. </s>

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

<s id="id.000277">Diapen&longs;e.<emph.end type="italics"/></s>

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

<s id="id.000278">Ex lib. De Memoria, & Rem.</s>

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

<s id="id.000279"><emph type="italics"/>Cap.

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

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

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

<s id="id.000280"><emph type="italics"/>Cap.

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

<s>Ex lib. De Somnijs.</s>

<s id="id.000281">Ex lib. De Somnijs.</s>

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

<s id="id.000282"><emph type="italics"/>Cap.

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

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

<s id="id.000283"><emph type="italics"/>Cap.

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

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

<s id="id.000284">Ex 1. Methaphy&longs;.</s>

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

<s id="id.000285"><emph type="italics"/>Cap.

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

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

<s id="id.000286">Item, Automata,

<lb/>quæ &longs;olstitia. </s>

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

<s id="id.000287">Diameter incommen&longs;.<emph.end type="italics"/></s>

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

<s id="id.000288"><emph type="italics"/>Summa 2. cap.

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 id="id.000289"><emph type="italics"/>T. 47. Geometria habet &longs;uas præcognitiones.<emph.end type="italics"/></s>

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

<s id="id.000290">Ex 2. Methaphy&longs;.</s>

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

<s id="id.000291"><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s>

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

<s id="id.000292">Ex 3. Methaphy&longs;.</s>

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

<s id="id.000294">Mathematicas puras carere cau&longs;is efficiente, & finali. </s>

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

<s id="id.000295">Ari&longs;tippus, vt Mathe

<lb/>maticas &longs;ugillaret. </s>

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

<s id="id.000296">Tetragoni&longs;mus est inuentio mediæ.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.016.jpg" pagenum="16"/>

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

<s id="id.000297"><emph type="italics"/>Tex. 8. Geodæ&longs;ia quid.<emph.end type="italics"/></s>

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

<s id="id.000298">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 id="id.000299"><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 id="id.000300"><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s>

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

<s id="id.000301">Ex 5. Methaphy&longs;.</s>

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

<s id="id.000302"><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 id="id.000303">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 id="id.000304"><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 id="id.000305"><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 id="id.000306"><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 id="id.000307"><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>

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

<s id="id.000308">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 id="id.000309"><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>

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

<s id="id.000310">Ex 6. Methaphy&longs;.</s>

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

<s id="id.000311"><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 id="id.000312"><emph type="italics"/>T. 8. Diameter. </s>

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

<s id="id.000313">commen&longs;urab.<emph.end type="italics"/></s>

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

<s id="id.000314"><emph type="italics"/>T. 20. De&longs;criptiones. </s>

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

<s id="id.000315">Omnis triangulus habet tres, &c. </s>

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

<s id="id.000316">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 id="id.000317"><emph type="italics"/>T. 22. Omnis triangulus habet tres, &c.<emph.end type="italics"/></s>

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

<s id="id.000318">Ex 10. Methaphy&longs;.</s>

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

<s id="id.000319"><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>

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

<s id="id.000320">Die&longs;is.<emph.end type="italics"/></s>

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

<s id="id.000321"><emph type="italics"/>T. 11. Similes figuræ quæ. </s>

<s>Diuer&longs;um in Math. quid.<emph.end type="italics"/></s>

<s id="id.000322">Diuer&longs;um in Math. quid.<emph.end type="italics"/></s>

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

<s id="id.000323">Ex 11. Methaphy&longs;.</s>

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

<s id="id.000324"><emph type="italics"/>Cap.

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

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

<s id="id.000325">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 id="id.000326"><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 id="id.000327"><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 id="id.000328"><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 id="id.000329"><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 id="id.000330">Ex 13. Methaphy&longs;.</s>

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

<s id="id.000331"><emph type="italics"/>Cap.

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

3. Qua ratione Mathematici tractant de Bono.<emph.end type="italics"/></s>

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

<s id="id.000332">In Mechanicas Quæ&longs;tiones.</s>

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

<s id="id.000333"><emph type="italics"/>Cap.

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

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

<s id="id.000334"><emph type="italics"/>Cap.

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

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

<s id="id.000335"><emph type="italics"/>Quæ&longs;tio 1. De Libra. </s>

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

<s id="id.000336">cur maior, exactior. </s>

<s>inibi Ari&longs;t.

<s id="id.000337">inibi Ari&longs;t.

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

<s><emph type="italics"/>Quæ&longs;t. 2. Duplex Libra. </s>

<s id="id.000338"><emph type="italics"/>Quæ&longs;t. 2. Duplex Libra. </s>

<s>Piccolomineus reiectus.<emph.end type="italics"/></s>

<s id="id.000339">Piccolomineus reiectus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 3. De Vecte.<emph.end type="italics"/></s>

<s id="id.000340"><emph type="italics"/>Quæ&longs;t. 3. De Vecte.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 4. De Remo; Petri Nonÿ in Arist.

<s id="id.000341"><emph type="italics"/>Quæ&longs;t. 4. De Remo; Petri Nonÿ in Arist.

correctio.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 5. De Temone Nauis.<emph.end type="italics"/></s>

<s id="id.000342"><emph type="italics"/>Quæ&longs;t. 5. De Temone Nauis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 6. De Antenna.<emph.end type="italics"/></s>

<s id="id.000343"><emph type="italics"/>Quæ&longs;t. 6. De Antenna.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 8 De Rota.<emph.end type="italics"/></s>

<s id="id.000344"><emph type="italics"/>Quæ&longs;t. 8 De Rota.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 9. De Trochlea, & Scytali. </s>

<s id="id.000345"><emph type="italics"/>Quæ&longs;t. 9. De Trochlea, & Scytali. </s>

<s>figura antiquæ &longs;cytalis.<emph.end type="italics"/></s>

<s id="id.000346">figura antiquæ &longs;cytalis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s>

<s id="id.000347"><emph type="italics"/>Quæ&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s>

<s><emph type="italics"/>Qùæ&longs;t. 11. De Curru, & &longs;cytala.<emph.end type="italics"/></s>

<s id="id.000348"><emph type="italics"/>Qùæ&longs;t. 11. De Curru, & &longs;cytala.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 13. De lugo. </s>

<s id="id.000349"><emph type="italics"/>Quæ&longs;t. 13. De lugo. </s>

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

<s id="id.000350">De Succula.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s>

<s id="id.000351"><emph type="italics"/>Quæ&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s><pb pagenum="17"/>

<s id="id.000352"><emph type="italics"/>Quæ&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.017.jpg" pagenum="17"/>

<s><emph type="italics"/>Quæ&longs;t. 17. De Cuneo.<emph.end type="italics"/></s>

<s id="id.000353"><emph type="italics"/>Quæ&longs;t. 17. De Cuneo.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s>

<s id="id.000354"><emph type="italics"/>Quæ&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 19. De Securi. </s>

<s id="id.000355"><emph type="italics"/>Quæ&longs;t. 19. De Securi. </s>

<s>Securis veteris figura, & con&longs;tructio; vnà cum affectione <lb/>eius mirabili.<emph.end type="italics"/></s>

<s id="id.000356">Securis veteris figura, & con&longs;tructio; vnà cum affectione

<lb/>eius mirabili.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 20. De Statera. </s>

<s id="id.000357"><emph type="italics"/>Quæ&longs;t. 20. De Statera. </s>

<s>Veteris stateræ figura restaurata.<emph.end type="italics"/></s>

<s id="id.000358">Veteris stateræ figura restaurata.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/></s>

<s id="id.000359"><emph type="italics"/>Quæ&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 22. De Nucifrago.<emph.end type="italics"/></s>

<s id="id.000360"><emph type="italics"/>Quæ&longs;t. 22. De Nucifrago.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/></s>

<s id="id.000361"><emph type="italics"/>Quæ&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s>

<s id="id.000362"><emph type="italics"/>Quæ&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s>

<s id="id.000363"><emph type="italics"/>Quæ&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s>

<s id="id.000364"><emph type="italics"/>Quæ&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s>

<s id="id.000365"><emph type="italics"/>Quæ&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 28. De Tollenone.<emph.end type="italics"/></s>

<s id="id.000366"><emph type="italics"/>Quæ&longs;t. 28. De Tollenone.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 29. De onere à duobus phalanga ge&longs;iato.<emph.end type="italics"/></s>

<s id="id.000367"><emph type="italics"/>Quæ&longs;t. 29. De onere à duobus phalanga ge&longs;tato.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæ&longs;t. 30. De &longs;urgente à &longs;e&longs;&longs;ione.<emph.end type="italics"/></s>

<s id="id.000368"><emph type="italics"/>Quæ&longs;t. 30. De &longs;urgente à &longs;e&longs;&longs;ione.<emph.end type="italics"/></s>

<s>In libello De Mundo ad Alex.<emph type="italics"/>Cap.

<s id="id.000369">In libello De Mundo ad Alex.<emph type="italics"/>Cap.

2. Ordo Planetarum.<emph.end type="italics"/></s>

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

<s id="id.000370"><emph type="italics"/>Cap.

3. De Cometis.<emph.end type="italics"/></s>

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

<s id="id.000371"><emph type="italics"/>Cap.

5. De fluxu maris. </s>

<s>noua de maris æ&longs;tu &longs;ententia.<emph.end type="italics"/></s>

<s id="id.000372">noua de maris æ&longs;tu &longs;ententia.<emph.end type="italics"/></s>

<s>In libro De Admirandis audit.</s>

<s id="id.000373">In libro De Admirandis audit.</s>

<s>100. De <gap/>&longs;tro, error Ari&longs;t. & veterum Geographorum.<emph.end type="italics"/></s>

<s id="id.000376">100. De I&longs;tro, error Ari&longs;t. & veterum Geographorum.<emph.end type="italics"/></s>

<s>In libello De lineis in&longs;ecabilibus.</s>

<s id="id.000377">In libello De lineis in&longs;ecabilibus.</s>

<s><emph type="italics"/>Primus locus. </s>

<s id="id.000378"><emph type="italics"/>Primus locus. </s>

<s>De commen&longs;urabili, & incommen&longs;urabili.<emph.end type="italics"/></s>

<s id="id.000379">De commen&longs;urabili, & incommen&longs;urabili.<emph.end type="italics"/></s>

<s><emph type="italics"/>2. locus. </s>

<s id="id.000380"><emph type="italics"/>2. locus. </s>

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

<s id="id.000381">De figuris incommen&longs;.<emph.end type="italics"/></s>

<s><emph type="italics"/>3. locus. </s>

<s id="id.000382"><emph type="italics"/>3. locus. </s>

<s>Quæ linea rationalis, quæ irrationalis. </s>

<s id="id.000383">Quæ linea rationalis, quæ irrationalis. </s>

<s>Binomio, Apotome.<emph.end type="italics"/></s>

<s id="id.000384">Binomio, Apotome.<emph.end type="italics"/></s>

<s><emph type="italics"/>4. locus. </s>

<s id="id.000385"><emph type="italics"/>4. locus. </s>

<s>De communi men&longs;ura.<emph.end type="italics"/></s>

<s id="id.000386">De communi men&longs;ura.<emph.end type="italics"/></s>

<s><emph type="italics"/>5. locus. </s>

<s id="id.000387"><emph type="italics"/>5. locus. </s>

<s>Lineæ rectæ motus in &longs;emicirculum.<emph.end type="italics"/></s>

<s id="id.000388">Lineæ rectæ motus in &longs;emicirculum.<emph.end type="italics"/></s>

<s><emph type="italics"/>6. locus. </s>

<s id="id.000389"><emph type="italics"/>6. locus. </s>

<s>Circulorum æqualium ab inuicem motus.<emph.end type="italics"/></s>

<s id="id.000390">Circulorum æqualium ab inuicem motus.<emph.end type="italics"/></s>

<s><emph type="italics"/>7. locus. </s>

<s id="id.000391"><emph type="italics"/>7. locus. </s>

<s>Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/></s>

<s id="id.000392">Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/></s>

<s><emph type="italics"/>8. locus. </s>

<s id="id.000393"><emph type="italics"/>8. locus. </s>

<s>Si extarent indiuidua, omnes lineæ e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s>

<s id="id.000394">Si extarent indiuidua, omnes lineæ e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s>

<s><emph type="italics"/>9. locus. </s>

<s id="id.000395"><emph type="italics"/>9. locus. </s>

<s>Idem probat alite&racute;.<emph.end type="italics"/></s>

<s id="id.000396">Idem probat alite&racute;.<emph.end type="italics"/></s>

<s><emph type="italics"/>10. locus. </s>

<s id="id.000397"><emph type="italics"/>10. locus. </s>

<s>Idem ex triangulo.<emph.end type="italics"/></s>

<s id="id.000398">Idem ex triangulo.<emph.end type="italics"/></s>

<s><emph type="italics"/>11. locus. </s>

<s id="id.000399"><emph type="italics"/>11. locus. </s>

<s>Idem ex quadrato.<emph.end type="italics"/></s>

<s id="id.000400">Idem ex quadrato.<emph.end type="italics"/></s>

<s><emph type="italics"/>12. Ex diui&longs;ione lineæ idem confirmatur.<emph.end type="italics"/></s>

<s id="id.000401"><emph type="italics"/>12. Ex diui&longs;ione lineæ idem confirmatur.<emph.end type="italics"/></s>

<s><emph type="italics"/>13. Idem eodem ferè modo cum præcedenti.<emph.end type="italics"/></s>

<s id="id.000402"><emph type="italics"/>13. Idem eodem ferè modo cum præcedenti.<emph.end type="italics"/></s>

<s><emph type="italics"/>14. A quadrato cuiu&longs;uis lineæ.<emph.end type="italics"/></s>

<s id="id.000403"><emph type="italics"/>14. A quadrato cuiu&longs;uis lineæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>15. Idem probat ex &longs;uperficie, & ex corpore.<emph.end type="italics"/></s>

<s id="id.000404"><emph type="italics"/>15. Idem probat ex &longs;uperficie, & ex corpore.<emph.end type="italics"/></s>

<s><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s>

<s id="id.000405"><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s>

<s>Ex lib.

<s id="id.000406">Ex lib.

9. Hi&longs;toriæ Animalium.</s>

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

<s id="id.000407"><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>

<s>De Ince&longs;&longs;u Animal.</s>

<s id="id.000408">De Ince&longs;&longs;u Animal.</s>

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

<s id="id.000409"><emph type="italics"/>Cap.

7. qua ratione in gre&longs;&longs;u &longs;iat bypotenu&longs;a. </s>

7. qua ratione in gre&longs;&longs;u fiat bypotenu&longs;a. </s>

<s>& ea quid &longs;it.<emph.end type="italics"/></s>

<s id="id.000410">& ea quid &longs;it.<emph.end type="italics"/></s>

<s>De Motu Animal.</s>

<s id="id.000411">De Motu Animal.</s>

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

<s id="id.000412"><emph type="italics"/>Cap.

1. in flexuris animalium e&longs;&longs;e centrum, & circulum.<emph.end type="italics"/></s>

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

<s id="id.000413"><emph type="italics"/>Cap.

3. Automata.<emph.end type="italics"/></s><pb pagenum="18"/>

3. Automata.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.018.jpg" pagenum="18"/>

<s>De Generatione Animal.</s>

<s id="id.000414">De Generatione Animal.</s>

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

<s id="id.000415"><emph type="italics"/>Lib. 2. cap.

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

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

<s id="id.000416"><emph type="italics"/>Lib. 2. cap.

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

<s>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>

<s id="id.000417">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>

<s>In Ethicis ad Nicom.</s>

<s id="id.000418">In Ethicis ad Nicom.</s>

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

<s id="id.000419"><emph type="italics"/>Lib. 1. cap.

7. Faber, & Geometra diuersè con&longs;iderant angulum rectum.<emph.end type="italics"/></s>

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

<s id="id.000420"><emph type="italics"/>Lib. 2. cap.

6. De Arithmetica proportione.<emph.end type="italics"/></s>

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

<s id="id.000421"><emph type="italics"/>cap.

9. Centrum circuli reperire.<emph.end type="italics"/></s>

<s><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>

<s id="id.000422"><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>

<s><emph type="italics"/>Lib. 5. cap.

<s id="id.000423"><emph type="italics"/>Lib. 5. cap.

3. Vnitarius numerus. </s>

<s>Quid Proportionalitas. </s>

<s id="id.000424">Quid Proportionalitas. </s>

<s>Eam in 4. terminis con<lb/>&longs;i&longs;tere. </s>

<s id="id.000425">Eam in 4. terminis con

<lb/>&longs;i&longs;tere. </s>

<s>Item quid Permutata proportio. </s>

<s id="id.000426">Item quid Permutata proportio. </s>

<s>Item quid Geometrica proportio. </s>

<s id="id.000427">Item quid Geometrica proportio. </s>

<s>Propor<lb/>tio continuata, & di&longs;iuncta quid.<emph.end type="italics"/></s>

<s id="id.000428">Propor

<lb/>tio continuata, & di&longs;iuncta quid.<emph.end type="italics"/></s>

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

<s id="id.000429"><emph type="italics"/>cap.

6. Proportio Geometrica, & Arithmetica.<emph.end type="italics"/></s>

<s><emph type="italics"/>Lib. 6. cap.

<s id="id.000430"><emph type="italics"/>Lib. 6. cap.

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

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

<s id="id.000431"><emph type="italics"/>cap.

8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s>

<s><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/></s>

<s id="id.000432"><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/></s>

<s>Ex 1. Magnorum Moralium.</s>

<s id="id.000433">Ex 1. Magnorum Moralium.</s>

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

<s id="id.000434"><emph type="italics"/>Cap.

1. Numerus pariter par.<emph.end type="italics"/></s>

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

<s id="id.000435"><emph type="italics"/>Cap.

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

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

<s id="id.000436"><emph type="italics"/>Cap.

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

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

<s id="id.000437"><emph type="italics"/>Cap.

16. Quadratum quatuor rectis æquales habere.<emph.end type="italics"/></s>

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

<s id="id.000438"><emph type="italics"/>Cap.

30. Proportionale in quatuor terminis con&longs;i&longs;tit.<emph.end type="italics"/></s>

<s>Ex 1. lib. Moralium Eudemiorum.</s>

<s id="id.000439">Ex 1. lib. Moralium Eudemiorum.</s>

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

<s id="id.000440"><emph type="italics"/>Cap.

5. Duplum inter multiplices rationes primum tenet locum.<emph.end type="italics"/></s>

<s id="id.000441">Ex 1. lib. Mor. Eudemiorum.</s>

<s>Eudemiorum.</s>

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

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

<s id="id.000442"><emph type="italics"/>Cap.

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

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

<s id="id.000443"><emph type="italics"/>Cap.

10. Diametrum commen&longs;. </s>

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

<s id="id.000444">e&longs;&longs;e. </s>

<s>Circuli quadratio.<emph.end type="italics"/></s>

<s id="id.000445">Circuli quadratio.<emph.end type="italics"/></s>

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

<s id="id.000446"><emph type="italics"/>Cap.

12. Triangulus habet tres, &c.<emph.end type="italics"/></s>

<s id="id.000447">Ex 7. lib. Mor. Eudemiorum.</s>

<s>Eudemiorum.</s>

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

<s id="id.000448"><emph type="italics"/>Cap.

12. Diametralis oppo&longs;itio.<emph.end type="italics"/></s>

<s>Ex 3. lib. Politicorum.</s>

<s id="id.000449">Ex 3. lib. Politicorum.</s>

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

<s id="id.000450"><emph type="italics"/>Cap.

2. Modi Dorius, & Phrygius apud Mu&longs;icos, quì.<emph.end type="italics"/></s>

<s>Ex 4. lib. Polit.</s>

<s id="id.000451">Ex 4. lib. Polit.</s>

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

<s id="id.000452"><emph type="italics"/>Cap.

3. Modus Doricus, & Phrygius.<emph.end type="italics"/></s>

<s>Ex 5. lib. Polit.</s>

<s id="id.000453">Ex 5. lib. Polit.</s>

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

<s id="id.000454"><emph type="italics"/>Cap.

1. Aequitas Arithmetica, & quæ &longs;ecundum dignitatem.<emph.end type="italics"/></s>

<s>Ex 8. Polit.</s>

<s id="id.000455">Ex 8. Polit.</s>

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

<s id="id.000456"><emph type="italics"/>Cap.

5. Mu&longs;ica nuda, & cum melodia. </s>

<s>Rithmus quid.<emph.end type="italics"/></s>

<s id="id.000457">Rithmus quid.<emph.end type="italics"/></s>

<s><emph type="italics"/>Harmonia lydia. </s>

<s id="id.000458"><emph type="italics"/>Harmonia lydia. </s>

<s>Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s>

<s id="id.000459">Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s>

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

<s id="id.000460"><emph type="italics"/>Cap.

7. Harmoniæ, & Rithmi, vt in præcedenti.<emph.end type="italics"/></s>

<s>Ex Problematibus.</s>

<s id="id.000461">Ex Problematibus.</s>

<s><emph type="italics"/>Sectione 1. num. </s>

<s id="id.000462"><emph type="italics"/>Sectione 1. num. </s>

<s>3. De ortu &longs;yderum innerrantium: Succulæ, Hypades, Atlantides, <lb/>Virgiliæ, Pleiades. </s>

<s id="id.000463">3. De ortu &longs;yderum innerrantium: Succulæ, Hypades, Atlantides,

<lb/>Virgiliæ, Pleiades. </s>

<s>17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s>

<s id="id.000465">17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sectione 15. num. </s>

<s id="id.000466"><emph type="italics"/>Sectione 15. num. </s>

<s>1. Diametri ethymon.<emph.end type="italics"/></s>

<s id="id.000467">1. Diametri ethymon.<emph.end type="italics"/></s>

<s>2. Iterum Diametri ethymologia.<emph.end type="italics"/></s><pb pagenum="19"/>

<s id="id.000469">2. Iterum Diametri ethymologia.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.019.jpg" pagenum="19"/>

<s>3. Denarius numerus cur perfectus. </s>

<s id="id.000471">3. Denarius numerus cur perfectus. </s>

<s>eius dignitates. </s>

<s id="id.000472">eius dignitates. </s>

<s>Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s>

<s id="id.000473">Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s>

<s><emph type="italics"/>4. De inæquali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s>

<s id="id.000474"><emph type="italics"/>4. De inæquali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s>

<s><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotundæ, quamuis per angulo&longs;a foramina ingre<lb/>diantur.<emph.end type="italics"/></s>

<s id="id.000475"><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotundæ, quamuis per angulo&longs;a foramina ingre

<lb/>diantur.<emph.end type="italics"/></s>

<s><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s>

<s id="id.000476"><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s>

<s>vbi de illuminatione Lunæ, <lb/>quæ experientia docetur.<emph.end type="italics"/></s>

<s id="id.000477">vbi de illuminatione Lunæ,

<lb/>quæ experientia docetur.<emph.end type="italics"/></s>

<s><emph type="italics"/>7. Cur Sol, & Luna videantur plana?<emph.end type="italics"/></s>

<s id="id.000478"><emph type="italics"/>7. Cur Sol, & Luna videantur plana?<emph.end type="italics"/></s>

<s><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s>

<s id="id.000479"><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s>

<s><emph type="italics"/>9. Cur Lunæ, quàm Solis minores vmbræ?<emph.end type="italics"/></s>

<s id="id.000480"><emph type="italics"/>9. Cur Lunæ, quàm Solis minores vmbræ?<emph.end type="italics"/></s>

<s><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiuæ &longs;unt? </s>

<s id="id.000481"><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiuæ &longs;unt? </s>

<s>modus commodè <lb/>videndi eclyp&longs;im Solis.<emph.end type="italics"/></s>

<s id="id.000482">modus commodè

<lb/>videndi eclyp&longs;im Solis.<emph.end type="italics"/></s>

<s>1. Cur ba&longs;es bullarum in aquis &longs;unt albæ?<emph.end type="italics"/></s>

<s id="id.000484">1. Cur ba&longs;es bullarum in aquis &longs;unt albæ?<emph.end type="italics"/></s>

<s><emph type="italics"/>3. Opp lumbati tali.<emph.end type="italics"/></s>

<s id="id.000485"><emph type="italics"/>3. Opplumbati tali.<emph.end type="italics"/></s>

<s><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s>

<s id="id.000486"><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s>

<s><emph type="italics"/>5. Cur conus, & cylindrus diuersè moueantur.<emph.end type="italics"/></s>

<s id="id.000487"><emph type="italics"/>5. Cur conus, & cylindrus diuersè moueantur.<emph.end type="italics"/></s>

<s><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s>

<s id="id.000488"><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s>

<s><emph type="italics"/>12. Idem cum præcedenti 3.<emph.end type="italics"/></s>

<s id="id.000489"><emph type="italics"/>12. Idem cum præcedenti 3.<emph.end type="italics"/></s>

<s><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>

<s id="id.000490"><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>

<s>reflexio radior&ubreve; pulchrè comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s>

<s id="id.000491">reflexio radior&ubreve; pulchrè comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s>

<s>Ex &longs;ectione 19. De Mu&longs;ica.</s>

<s id="id.000492">Ex &longs;ectione 19. De Mu&longs;ica.</s>

<s>2. Lineæ duplæ quadratum quadruplum. </s>

<s id="id.000494">2. Lineæ duplæ quadratum quadruplum. </s>

<s>Hoc loco &longs;equentium probl. </s>

<s id="id.000495">Hoc loco &longs;equentium probl. </s>

<s>cau&longs;a, <lb/>præmittitur totius Mu&longs;icæ ortus breuis tractatio.<emph.end type="italics"/></s>

<s id="id.000496">cau&longs;a,

<lb/>præmittitur totius Mu&longs;icæ ortus breuis tractatio.<emph.end type="italics"/></s>

<s><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s>

<s id="id.000497"><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s>

<s><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s>

<s id="id.000498"><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s>

<s><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s>

<s id="id.000499"><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s>

<s><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s>

<s id="id.000500"><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s>

<s><emph type="italics"/>8. Cur grauis &longs;onum potest acutæ?<emph.end type="italics"/></s>

<s id="id.000501"><emph type="italics"/>8. Cur grauis &longs;onum potest acutæ?<emph.end type="italics"/></s>

<s><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s>

<s id="id.000502"><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s>

<s><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s>

<s id="id.000503"><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s>

<s><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s>

<s id="id.000504"><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s>

<s><emph type="italics"/>12. Grauior è fidibus contilenam &longs;u&longs;cipit.<emph.end type="italics"/></s>

<s id="id.000505"><emph type="italics"/>12. Grauior è fidibus contilenam &longs;u&longs;cipit.<emph.end type="italics"/></s>

<s><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s>

<s id="id.000506"><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s>

<s><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s>

<s id="id.000507"><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s>

<s>Punicum quid.<emph.end type="italics"/></s>

<s id="id.000508">Punicum quid.<emph.end type="italics"/></s>

<s><emph type="italics"/>15. Leges Mu&longs;icæ, quæ. </s>

<s id="id.000509"><emph type="italics"/>15. Leges Mu&longs;icæ, quæ. </s>

<s>Genera, Diatonicum, Chromaticum, Encharmonium. <lb/></s>

<s id="id.000510">Genera, Diatonicum, Chromaticum, Encharmonium.

<s>Tetrachorda quæ.<emph.end type="italics"/></s>

<s id="id.000511">Tetrachorda quæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s>

<s id="id.000512"><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s>

<s><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s>

<s id="id.000513"><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s>

<s>Magadis quid. </s>

<s id="id.000514">Magadis quid. </s>

<s>Magadare.<emph.end type="italics"/></s>

<s id="id.000515">Magadare.<emph.end type="italics"/></s>

<s><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s>

<s id="id.000516"><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s>

<s><emph type="italics"/>19. Cur Diapente, & Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s>

<s id="id.000517"><emph type="italics"/>19. Cur Diapente, & Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s>

<s><emph type="italics"/>20. Me&longs;e &longs;ola di&longs;&longs;onante, totum de&longs;&longs;onat p&longs;alterium.<emph.end type="italics"/></s>

<s id="id.000518"><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>

<s><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s>

<s id="id.000519"><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s>

<s><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s>

<s id="id.000520"><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s>

<s><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s>

<s id="id.000521"><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s>

<s><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s>

<s id="id.000522"><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s>

<s><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s>

<s id="id.000523"><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s>

<s>Rithmus quid.<emph.end type="italics"/></s>

<s id="id.000524">Rithmus quid.<emph.end type="italics"/></s>

<s><emph type="italics"/>28. Cur cantilenæ quædam leges de cebantur?<emph.end type="italics"/></s>

<s id="id.000525"><emph type="italics"/>28. Cur cantilenæ quædam leges de cebantur?<emph.end type="italics"/></s>

<s><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s><pb pagenum="20"/>

<s id="id.000526"><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.020.jpg" pagenum="20"/>

<s><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melopæos.<emph.end type="italics"/></s>

<s id="id.000527"><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melopæos.<emph.end type="italics"/></s>

<s><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s>

<s id="id.000528"><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s>

<s><emph type="italics"/>33. Cur aptè de acuto in graue, non è contra canitur?<emph.end type="italics"/></s>

<s id="id.000529"><emph type="italics"/>33. Cur aptè de acuto in graue, non è contra canitur?<emph.end type="italics"/></s>

<s><emph type="italics"/>34. Cur bi&longs;diapente, aut bi&longs;diate&longs;&longs;aron con&longs;onantia non e&longs;t.<emph.end type="italics"/></s>

<s id="id.000530"><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>

<s><emph type="italics"/>35. Cur diapa&longs;on omnium pulcherrima e&longs;t con&longs;onantia?<emph.end type="italics"/></s>

<s id="id.000531"><emph type="italics"/>35. Cur diapa&longs;on omnium pulcherrima e&longs;t con&longs;onantia?<emph.end type="italics"/></s>

<s><emph type="italics"/>36. Me&longs;e &longs;ola di&longs;&longs;onante, tota perit harmonia.<emph.end type="italics"/></s>

<s id="id.000532"><emph type="italics"/>36. Me&longs;e &longs;ola di&longs;&longs;onante, tota perit harmonia.<emph.end type="italics"/></s>

<s><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s>

<s id="id.000533"><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s>

<s><emph type="italics"/>38. Cur Rythmo, & harmonij omnes gaudent?<emph.end type="italics"/></s>

<s id="id.000534"><emph type="italics"/>38. Cur Rythmo, & harmonij omnes gaudent?<emph.end type="italics"/></s>

<s><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s>

<s id="id.000535"><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s>

<s><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s>

<s id="id.000536"><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s>

<s><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>

<s id="id.000539"><emph type="italics"/>43. Idem cum 24. Iugum in lyra veteri quodnam fuerit, vna cum figura vete

<s><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s>

<s id="id.000540"><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s>

<s><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s>

<s id="id.000541"><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s>

<s><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s>

<s id="id.000544"><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s>

<s><emph type="italics"/>49. Idem cum 30. In choris trag&oelig;diarum, nec &longs;ubdorius, nec &longs;ubphrygius modus <lb/>erat in v&longs;u.<emph.end type="italics"/></s>

<s id="id.000545"><emph type="italics"/>49. Idem cum 30. In choris trag&oelig;diarum, nec &longs;ubdorius, nec &longs;ubphrygius modus

<lb/>erat in v&longs;u.<emph.end type="italics"/></s>

<s><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s>

<s id="id.000546"><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s>

<s><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>

<s id="id.000547"><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>

<s>Ex &longs;ectione 23.</s>

<s id="id.000548">Ex &longs;ectione 23.</s>

<s><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s>

<s id="id.000549"><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s>

<s>Ex &longs;ectione 30.</s>

<s id="id.000550">Ex &longs;ectione 30.</s>

<s><emph type="italics"/>6. Omnis triangulus habet tres æquales, &c.<emph.end type="italics"/></s>

<s id="id.000551"><emph type="italics"/>6. Omnis triangulus habet tres æquales, &c.<emph.end type="italics"/></s>

<s>Ex &longs;ectione 31.</s>

<s id="id.000552">Ex &longs;ectione 31.</s>

<s><emph type="italics"/>7. Cur o culos, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla vi, ab inuicem di&longs;&longs;ociari nequimus?<emph.end type="italics"/></s>

<s id="id.000553"><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>

<s><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s>

<s id="id.000554"><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s>

<s>Cur aliquando rei vi&longs;æ gemina<lb/>tio accidat.<emph.end type="italics"/></s>

<s id="id.000555">Cur aliquando rei vi&longs;æ gemina

<lb/>tio accidat.<emph.end type="italics"/></s>

<s><emph type="italics"/>11. Cur di&longs;tractis oculis res vna duæ apparent?<emph.end type="italics"/></s>

<s id="id.000556"><emph type="italics"/>11. Cur di&longs;tractis oculis res vna duæ apparent?<emph.end type="italics"/></s>

<s><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s>

<s id="id.000557"><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s>

<s><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s>

<s id="id.000558"><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s>

<s>Auctarium De Oculi Pupilla.</s>

<s id="id.000559">Auctarium De Oculi Pupilla.</s>

<s><emph type="italics"/>Oculi fabrica præmittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s>

<s id="id.000560"><emph type="italics"/>Oculi fabrica præmittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s>

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

<s id="id.000561"><emph type="italics"/>Primo. </s>

<s>De pupillæ voce.<emph.end type="italics"/></s>

<s id="id.000562">De pupillæ voce.<emph.end type="italics"/></s>

<s><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s>

<s id="id.000563"><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s>

<s><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s>

<s id="id.000564"><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s>

<s><emph type="italics"/>4. Pupillæ definitio.<emph.end type="italics"/></s>

<s id="id.000565"><emph type="italics"/>4. Pupillæ definitio.<emph.end type="italics"/></s>

<s><emph type="italics"/>5. Cur mgra in omnibus hominibus.<emph.end type="italics"/></s>

<s id="id.000566"><emph type="italics"/>5. Cur mgra in omnibus hominibus.<emph.end type="italics"/></s>

<s><emph type="italics"/>6. Cur in Sole euane&longs; cat.<emph.end type="italics"/></s>

<s id="id.000567"><emph type="italics"/>6. Cur in Sole euane&longs; cat.<emph.end type="italics"/></s>

<s><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s>

<s id="id.000568"><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s>

<s><emph type="italics"/>8. Cur modo maior, modo minor videatur, & cui&longs;dam lepida deceptio.<emph.end type="italics"/></s><pb pagenum="21"/>

<s id="id.000569"><emph type="italics"/>8. Cur modo maior, modo minor videatur, & cui&longs;dam lepida deceptio.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.021.jpg" pagenum="21"/>

<s>Additamentum de natura Mathematicarum di&longs;ciplinarum.</s>

<s id="id.000570">Additamentum de natura Mathematicarum di&longs;ciplinarum.</s>

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

<s id="id.000571"><emph type="italics"/>Primo. </s>

<s>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>

<s id="id.000572">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>

<s>2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s>

<s id="id.000573">2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s>

<s>3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumniæ diluuntur.<emph.end type="italics"/></s>

<s id="id.000574">3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumniæ diluuntur.<emph.end type="italics"/></s>

<s>4. <emph type="italics"/>De præstantia cognitionis, quam Geometria, & Arithmetica gignunt.<emph.end type="italics"/></s>

<s id="id.000575">4. <emph type="italics"/>De præstantia cognitionis, quam Geometria, & Arithmetica gignunt.<emph.end type="italics"/></s>

<s>5. <emph type="italics"/>De 4. Mathematicis medijs: A&longs;tronomia, Per&longs;pectiua, Mu&longs;ica, Mechanica.<emph.end type="italics"/></s>

<s id="id.000576">5. <emph type="italics"/>De 4. Mathematicis medijs: A&longs;tronomia, Per&longs;pectiua, Mu&longs;ica, Mechanica.<emph.end type="italics"/></s>

<s>6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/></s>

<s id="id.000577">6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/></s>

<s>7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s>

<s id="id.000578">7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s>

<s><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s><figure/><pb pagenum="22"/>

<s id="id.000579"><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.022.jpg" pagenum="22"/><section>

<s><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s>

<s id="id.000580"><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s>

<s><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>

<s id="id.000581"><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>

<s><emph type="italics"/>In Primo Elem.

<s id="id.000582"><emph type="italics"/>In Primo Elem.

Euclidis.<emph.end type="italics"/></s>

<s>Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. 4. quinti <lb/>Methaph.</s>

<s id="id.000583">Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. 4. quinti

<lb/>Methaph.</s>

<s>Ad principia primi elementorum, vide infra tex. 5. pri. </s>

<s id="id.000584">Ad principia primi elementorum, vide infra tex. 5. pri. Po&longs;ter.</s>

<s>Po&longs;ter.</s>

<s>Ad definitionem 10. pri. pro angulo recto, vide 30. quæ&longs;t. </s>

<s id="id.000585">Ad definitionem 10. pri. pro angulo recto, vide 30. quæ&longs;t. </s>

<s>Mecha<lb/>nic. & cap.

<s id="id.000586">Mecha

<lb/>nic. & cap.

7. lib.

Line 1474

Line 1548

<s>Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="quãdam">quandam</expan> inter Philo&longs;ophos valdè difficilem, <lb/>facile di&longs;&longs;olui. </s>

<s id="id.000587">Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim

<lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="quãdam">quandam</expan> inter Philo&longs;ophos valdè difficilem,

<lb/>facile di&longs;&longs;olui. </s>

<s>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="id.000588">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>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>

<s id="id.000589">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>

<s>Ad Calcem axiomatum primi accommodetur tex. 1. primi Po&longs;ter.</s>

<s id="id.000590">Ad Calcem axiomatum primi accommodetur tex. 1. primi Po&longs;ter.</s>

<s>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.

<s id="id.000591">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. 4. quinti Methaph. </s>

24. &longs;ecti primi, libri primi Priorum, &

<lb/>tex. 4. quinti Methaph. & tex. 20. &longs;exti Methaph. & cap.

3. lib.

3. Ethic.

<s>& tex. 20. &longs;exti Methaph. </s>

<s>& cap.

3. lib.

3. Ethic. <lb/></s>

<s>Item ad primam primi, vide tex. 7. &longs;ecundi Po&longs;ter. loco 2.</s>

<s id="id.000592">Item ad primam primi, vide tex. 7. &longs;ecundi Po&longs;ter. loco 2.</s>

<s>Ad 5. primi, vide cap.

<s id="id.000593">Ad 5. primi, vide cap.

24. &longs;ecti 1 lib.

1. Priorum.</s>

<s>Ad 21. primi, vide tex. 20. primi Po&longs;ter. </s>

<s id="id.000594">Ad 21. primi, vide tex. 20. primi Po&longs;ter. loco 2.</s>

<s>Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s>

<s id="id.000595">Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s>

<s>Ad 28. primi, vide cap.

<s id="id.000596">Ad 28. primi, vide cap.

21. & cap.

Line 1528

Line 1616

<s>Ad 32. primi, vide cap.

<s id="id.000597">Ad 32. primi, vide cap.

1. &longs;ecti 3. lib.

1. Prior. & cap.

26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, & tex. </s>

26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, & tex. 2.

<lb/>primi Po&longs;ter. loco 4. & tex. 23. primi Po&longs;ter. vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam

<lb/><expan abbr="demõ&longs;trationem">demon&longs;trationem</expan>. </s>

<s>2. <lb/>primi Po&longs;ter. loco 4. & tex. 23. primi Po&longs;ter. </s>

<s>vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam <lb/><expan abbr="demõ&longs;trationem">demon&longs;trationem</expan>. </s>

<s>& tex. 37. primi Po&longs;ter. & tex. </s>

<s id="id.000598">& tex. 37. primi Po&longs;ter. & tex. 39. primi Po&longs;ter. </s>

<s>39. primi Po&longs;ter. </s>

<s>Ibidem <lb/>loco 4. & tex. 43. primi Po&longs;ter. </s>

<s>& tex. 2. &longs;ecundi Po&longs;ter. </s>

<s id="id.000599">Ibidem

<lb/>loco 4. & tex. 43. primi Po&longs;ter. & tex. 2. &longs;ecundi Po&longs;ter. bis. </s>

<s>& tex. 89. &longs;e<lb/>cundi Phy&longs;. & tex. </s>

<s>15. octaui Phy&longs;. & tex. </s>

<s id="id.000600">& tex. 89. &longs;e

<lb/>cundi Phy&longs;. & tex. 15. octaui Phy&longs;. & tex. 119. primi de C&oelig;lo. </s>

<s>119. primi de C&oelig;lo. </s>

<s>& tex. 25. <lb/>&longs;ecundi de C&oelig;lo. </s>

<s>tex 11. primi de Anima. & cap.

1. de mem. </s>

<s id="id.000601">& tex. 25.

<lb/>&longs;ecundi de C&oelig;lo. </s>

<s>& remini&longs;c. <lb/></s>

<s>& tex. 35. quinti Methaphy&longs;. & tex. </s>

<s id="id.000602">tex 11. primi de Anima. & cap.

1. de mem. </s>

<s>20. &longs;exti Methaphy&longs;. & tex. </s>

<s id="id.000603">& remini&longs;c.

<s>22. &longs;exti <lb/>Methaphy&longs;. & cap.

<s id="id.000604">& tex. 35. quinti Methaphy&longs;. & tex. 20. &longs;exti Methaphy&longs;. & tex. 22. &longs;exti

<lb/>Methaphy&longs;. & cap.

4. lib.

2. de Generat. </s>

2. de Generat. animal. </s>

<s>animal. </s>

<s>& cap.

<s id="id.000605">& cap.

5. lib.

6. Ethic. & <lb/>cap.

6. Ethic. &

<lb/>cap.

2. Magnorum Moral. & cap.

10. Mag. Moral. & cap. 16. Mag. Moral. <lb/></s>

10. Mag. Moral. & cap. 16. Mag. Moral.

<lb/>& cap. 7. &longs;ecundi Eudem. & cap. 12. &longs;ecundi Eudem. & problema 6. &longs;ectio<pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.023.jpg" pagenum="23"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica hæc Euclidis Demon&longs;tratio.</s>

<s>& cap. 7. &longs;ecundi Eudem. & cap. </s>

<s>12. &longs;ecundi Eudem. & problema 6. &longs;ectio<pb pagenum="23"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica hæc Euclidis Demon&longs;tratio.</s>

<s>Ad &longs;cholion præcedentis 32. primi, vide tex. 39. primi Po&longs;ter. loco 3. Item <lb/>tex. </s>

<s id="id.000606">Ad &longs;cholion præcedentis 32. primi, vide tex. 39. primi Po&longs;ter. loco 3. Item

<lb/>tex. 25. &longs;ecundi Po&longs;ter. loco vlt.</s>

<s>25. &longs;ecundi Po&longs;ter. loco vlt.</s>

<s>Ad 45. primi, vide locum 9. de lineis in&longs;ecabilibus.</s>

<s id="id.000607">Ad 45. primi, vide locum 9. de lineis in&longs;ecabilibus.</s>

<s>Ad 46. primi, vide locum 11. de lineis in&longs;ecabilibus.</s>

<s id="id.000608">Ad 46. primi, vide locum 11. de lineis in&longs;ecabilibus.</s>

<s>Ad 47. primi, vide locum 11. de lineis in&longs;ecab. </s>

<s id="id.000609">Ad 47. primi, vide locum 11. de lineis in&longs;ecab. </s>

<s>Item locum 14. de ij&longs;dem.</s>

<s id="id.000610">Item locum 14. de ij&longs;dem.</s>

<s><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/></s>

<s id="id.000611"><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/></s>

<s>Ad 2. definitionem 2. Gnomonis, vide cap.

<s id="id.000612">Ad 2. definitionem 2. Gnomonis, vide cap.

de Motu in Po&longs;tprædicam. </s>

<s>Qua<lb/>dratum augetur Gnomone circumpo&longs;ito.</s>

<s id="id.000613">Qua

<lb/>dratum augetur Gnomone circumpo&longs;ito.</s>

<s>Ad 14. propo&longs;. </s>

<s id="id.000614">Ad 14. propo&longs;. </s>

<s>2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>vide igitur cap.

<s id="id.000615">2. opportunum e&longs;t Auditores de Quadratura circuli erudire,

<lb/>vide igitur cap.

de relatione in prædicam. </s>

<s>& cap.

<s id="id.000616">& cap.

31. &longs;ecundi Priorum, & <lb/>tex. 23. primi Po&longs;ter. & finem 1. cap. primi Elenchorum. </s>

31. &longs;ecundi Priorum, &

<lb/>tex. 23. primi Po&longs;ter. & finem 1. cap. primi Elenchorum. </s>

<s>lege primam Ar<lb/>chimedis de dimen&longs;ione circuli.</s>

<s id="id.000617">lege primam Ar

<lb/>chimedis de dimen&longs;ione circuli.</s>

<s><emph type="italics"/>In tertio Elem.<emph.end type="italics"/></s>

<s id="id.000618"><emph type="italics"/>In tertio Elem.<emph.end type="italics"/></s>

<s>Ad primam 3. vide cap.

<s id="id.000619">Ad primam 3. vide cap.

9. lib.

2. Ethycorum.</s>

<s>Ad 2. tertij, vide tex. 13. lib.

<s id="id.000620">Ad 2. tertij, vide tex. 13. lib.

1. de Anima. </s>

1. de Anima. & locum 16. de lineis in&longs;ecab.</s>

<s>& locum 16. de lineis in&longs;ecab.</s>

<s id="id.000621">Ad 31. tertij, vide tex. 11. &longs;ecundi Po&longs;ter. & tex. 20. &longs;exti Methaph. loco 2.</s>

<s>Ad 31. tertij, vide tex. 11. &longs;ecundi Po&longs;ter. & tex. </s>

<s>20. &longs;exti Methaph. loco 2.</s>

<s><emph type="italics"/>In quarto.<emph.end type="italics"/></s>

<s id="id.000622"><emph type="italics"/>In quarto.<emph.end type="italics"/></s>

<s>Ad commentarium P. Clauij extremum lib.

<s id="id.000623">Ad commentarium P. Clauij extremum lib.

4. elementorum. </s>

<s>lege tex. 66. <lb/>tertij de C&oelig;lo.</s>

<s id="id.000624">lege tex. 66.

<lb/>tertij de C&oelig;lo.</s>

<s><emph type="italics"/>In quinto.<emph.end type="italics"/></s>

<s id="id.000625"><emph type="italics"/>In quinto.<emph.end type="italics"/></s>

<s>Ad 4. definitionem 5. vide cap.

<s id="id.000626">Ad 4. definitionem 5. vide cap.

3. lib.

2. Ethyc.</s>

<s>Ad 9. definitionem 5. vide cap.

<s id="id.000627">Ad 9. definitionem 5. vide cap.

3. lib.

5. Ethyc. loco 4. & cap. 31. primi Ma<lb/>gnorum Moralium.</s>

5. Ethyc. loco 4. & cap. 31. primi Ma

<lb/>gnorum Moralium.</s>

<s>Ad 10. definitionem 5. vide tex. 29. primi Po&longs;ter. loco 2.</s>

<s id="id.000628">Ad 10. definitionem 5. vide tex. 29. primi Po&longs;ter. loco 2.</s>

<s>Ad 12. definitionem 5. vide tex. 13. primi Po&longs;ter. </s>

<s id="id.000629">Ad 12. definitionem 5. vide tex. 13. primi Po&longs;ter. loco 3. & tex. 25. &longs;ecundi

<lb/>Po&longs;ter. & tex. 32. tertij de Anima. & cap.

3. lib.

5. Ethyc. loco 4.</s>

<s>loco 3. & tex. 25. &longs;ecundi <lb/>Po&longs;ter. </s>

<s>& tex. 32. tertij de Anima. </s>

<s>& cap.

3. lib.

5. Ethyc. loco 4.</s>

<s>Ad 16. propo&longs;. </s>

<s id="id.000630">Ad 16. propo&longs;. </s>

<s id="id.000631">5. vide tex. 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/>comm. 15. &longs;cilicet.</s>

<s>5. vide tex. 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/></s>

<s>comm. 15. &longs;cilicet.</s>

<s>Vt &longs;e habet voluntas antiqua ad antiquum effectum, <lb/>Ita &longs;e habet etiam voluntas noua ad effectum nouum: <lb/>Ergo permutando, ita &longs;e habebit voluntas antiqua ad effectum nouum. <lb/></s>

<s id="id.000632">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.

<s>Quemadmodum voluntas noua ad effectum antiquum.</s>

<s id="id.000633">Quemadmodum voluntas noua ad effectum antiquum.</s>

<s>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>

<s id="id.000634">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>

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

<s id="id.000635"><emph type="italics"/>In &longs;exto.<emph.end type="italics"/></s>

<s>Ad 2. propo&longs;it. </s>

<s id="id.000636">Ad 2. propo&longs;it. </s>

<s>6. vide cap.

<s id="id.000637">6. vide cap.

2. lib.

8. Topicorum loco 41.</s>

<s>Ad 13. &longs;exti, vide tex. 12. &longs;ecundi de Anima, & tex. </s>

<s id="id.000638">Ad 13. &longs;exti, vide tex. 12. &longs;ecundi de Anima, & tex. 3. tertij Methaphy&longs;.<emph type="italics"/>In &longs;eptimo.<emph.end type="italics"/></s>

<s>3. tertij Methaphy&longs;.<emph type="italics"/>In &longs;eptimo.<emph.end type="italics"/></s>

<s>Ad primam definitionem 7. vide tex. 5. primi Po&longs;ter.</s>

<s id="id.000639">Ad primam definitionem 7. vide tex. 5. primi Po&longs;ter.</s>

<s>Ad 8. definitionem 7. vide cap.

<s id="id.000640">Ad 8. definitionem 7. vide cap.

1. lib.

1. Magnorum Moral.</s>

<s><emph type="italics"/>In octauo.<emph.end type="italics"/></s>

<s id="id.000641"><emph type="italics"/>In octauo.<emph.end type="italics"/></s>

<s>Ad 4. propo&longs;. </s>

<s id="id.000642">Ad 4. propo&longs;. </s>

<s>9. vide tex. 20. primi Po&longs;ter. loco 2.</s>

<s id="id.000643">9. vide tex. 20. primi Po&longs;ter. loco 2.</s>

<s>Ad 8. propo&longs;. </s>

<s id="id.000644">Ad 8. propo&longs;. </s>

<s>9. vide problem. </s>

<s id="id.000645">9. vide problem. </s>

<s>3. &longs;ectionis 15. loco 4.</s><pb pagenum="24"/>

<s id="id.000646">3. &longs;ectionis 15. loco 4.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.024.jpg" pagenum="24"/>

<s><emph type="italics"/>In decimo.<emph.end type="italics"/></s>

<s id="id.000647"><emph type="italics"/>In decimo.<emph.end type="italics"/></s>

<s>Ad primam definitionem 10. vide cap.

<s id="id.000648">Ad primam definitionem 10. vide cap.

23. &longs;ecti 1. primi Priorum. </s>

<s>& tex. 48. <lb/>primi de C&oelig;lo.</s>

<s id="id.000649">& tex. 48.

<lb/>primi de C&oelig;lo.</s>

<s>Ad 118. decimi, vide cap.

<s id="id.000650">Ad 118. decimi, vide cap.

23. &longs;ecti 1. libri 1. Priorum. </s>

<s>& &longs;ecto 2. cap.

<s id="id.000651">& &longs;ecto 2. cap.

23. li<lb/>bri 1. Priorum. </s>

23. li

<lb/>bri 1. Priorum. </s>

<s>& cap. 22. lib.

<s id="id.000652">& cap. 22. lib.

2. Priorum. </s>

<s>& tex. 5. primi Po&longs;ter. & tex. </s>

<s id="id.000653">& tex. 5. primi Po&longs;ter. & tex. 44.

<lb/>primi Po&longs;ter. & cap.

15. primi Po&longs;ter. & tex. 119. primi de C&oelig;lo. </s>

<s>44. <lb/>primi Po&longs;ter. & cap.

15. primi Po&longs;ter. </s>

<s>& tex. 119. primi de C&oelig;lo. </s>

<s>& tex. <lb/>120. quarti Phy&longs;. & tex. </s>

<s id="id.000654">& tex.

<lb/>120. quarti Phy&longs;. & tex. 21. tertij de Anima. & cap.

<s>21. tertij de Anima. & cap.

1. primi Methaphy&longs;.

<lb/>& tex. 28. quarti Met. & tex. 34. quinti Met. & tex. 8. &longs;exti Met. & cap.

1. primi Methaphy&longs;. <lb/></s>

<lb/>lib.

2. de Generat. animal. </s>

<s>& tex. 28. quarti Met. </s>

<s>& tex. 34. quinti Met. </s>

<s>& tex. 8. &longs;exti Met. </s>

<s>& cap.

4. <lb/>lib.

2. de Generat. animal. </s>

<s>& lib.

3. cap.

3. Ethyc. & cap. 10. &longs;ecundi Eu<lb/>dem. </s>

<s>tot Ari&longs;t.

loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s>

<s><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s>

<s id="id.000655">& lib.

<s>Ad primam propo&longs;. </s>

3. cap.

<s>13. &longs;ecundum editionem Commandini, aut Zamberti. <lb/></s>

3. Ethyc. & cap. 10. &longs;ecundi Eu

<s>vide initio Priorum, in verbum (Re&longs;olutio)</s>

<s>Atqne hæc &longs;unt, quæ ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit, <lb/>quæque nos infra explicabimus.</s>

<s><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s>

<s id="id.000656">tot Ari&longs;t.

<s>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><figure/><pb pagenum="25"/>

loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s>

<s><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s>

<s id="id.000657"><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s>

<s><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/><lb/><arrow.to.target n="table2"/></s><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"/>Antipbonæ 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 numer are &longs;oliti.<emph.end type="italics"/></cell><cell>340</cell></row><row><cell><emph type="italics"/>Bry&longs;onis quadratura circuli.<emph.end type="italics"/></cell><cell>35</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Calippi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell><cell>236</cell></row><row><cell><emph type="italics"/>Cantilenam notam &longs;uauius, quam ignotam audimus.<emph.end type="italics"/></cell><cell>362</cell></row><row><cell><emph type="italics"/>Centrum circuli reperire. 303. Centrum mundi 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"/>C&oelig;lorum ordinem petendum ex A&longs;tronomis 109. item numerum<emph.end type="italics"/></cell><cell>233</cell></row><row><cell><emph type="italics"/>Colores in mu&longs;ica 78. Colores oculorum vnde.<emph.end type="italics"/></cell><cell>408</cell></row><row><cell><emph type="italics"/>Cometarum tractatiuncula ex recentioribus, qui eas in C&oelig;lo collocant. 136. e&longs;&longs;e &longs;u-pra aerem longi&longs;&longs;imo &longs;altem interuallo o&longs;tenditur 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"/><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 denari&ubreve; omnes <expan abbr="g&etilde;tes">gentes</expan> <expan abbr="numer&etilde;t">numerent</expan>.<emph.end type="italics"/></cell><cell>339. 8. <emph type="italics"/>&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 pulcberrima.<emph.end type="italics"/></cell><cell>388</cell></row><row><cell><emph type="italics"/>Diapa&longs;on diapente.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Diapente con&longs;onantia, 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 C&oelig;lorum.<emph.end type="italics"/></cell><cell>234</cell></row><row><cell><emph type="italics"/>Exempla mathematicorum, qualia. 11. non e&longs;&longs;e fal&longs;a.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>Exemplorum veritas, & conformitas, quatenus requirantur.<emph.end type="italics"/></cell><cell>36</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Figuram omnem planam habere &longs;uos angulos externos <expan abbr="quotc&ubreve;q;">quotc&ubreve;que</expan> 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 rratum aperitur.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Figuratio lucis.<emph.end type="italics"/></cell><cell>345</cell></row><row><cell><emph type="italics"/>Figurationes pro demonftrationibus Mathem.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Filum Araneorum, ex qua parte corporis exeat, & 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"/>Fu<gap/>ium l<gap/>ctorum 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"/><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, ei&queacute; aptaretur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Grauiden&longs;um, quid.<emph.end type="italics"/></cell><cell>399</cell></row><row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Halonis demonfiratio.<emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>Hippocratis chij quadratura circuli. 17. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> quadratura 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"/>Li<gap/>ea, 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"/>Mater<gap/>a intelligibilis. fusè verò. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Mathema<gap/>icæ 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"/>Mathematic<gap/>s 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"/><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"/>Monochordiux<gap/>.<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 c&oelig;lestium motuum.<emph.end type="italics"/></cell><cell>225</cell></row><row><cell><emph type="italics"/>Mu&longs;ici recentiores reprehen&longs;i. 331. & 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"/><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 dignita<gap/>em, 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 bominibus. probl.<emph.end type="italics"/> 5.</cell><cell/></row><row><cell><emph type="italics"/>Cur in Sole euane&longs;<gap/>at. 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, eas&queacute; ceteris &longs;cientijs præponeb&abreve;t.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Qv adra<gap/>ura 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 conctet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis mathematicis.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Remi problema.<emph.end type="italics"/></cell><cell>245</cell></row><row><cell><emph type="italics"/>Re&longs;olutio logica, & 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<gap/>antiquæ &longs;<gap/>uris 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 C&oelig;li paruam valde. 115. e&longs;&longs;e cubum cur Plato voluerit.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>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"/><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"/>Tunic<gap/> oculi. 408. in tractatu de Pupi<gap/>la.<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>

<s id="id.000658">Ad primam propo&longs;. </s>

<s>Finis Tertij Indicis.</s><figure/><pb pagenum="31"/>

<s id="id.000659">13. &longs;ecundum editionem Commandini, aut Zamberti.

<s>Vi&longs;um e&longs;t etiam opportunum Lectori fore, ea &longs;imul in vnum <lb/>loca colligere, in quibus Ari&longs;toteles mihi vi&longs;us e&longs;t in Ma<lb/>thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&ecedil;&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><pb pagenum="33"/><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 demonctratione ostenditur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>147<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Tanaim, & 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 inhabit abilem exi&longs;timat.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>164<emph.end type="italics"/></cell><cell><emph type="italics"/>Putat Iridis angulos non po&longs;&longs;e vnum &longs;upra alterum collocari, &longs;ed tantummodo in orbem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>182<emph.end type="italics"/></cell><cell><emph type="italics"/>Rationes, quas in Parelij dubitationibus affert, videntur inanes.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>236<emph.end type="italics"/></cell><cell><emph type="italics"/>In &longs;ubducendo c&oelig;le&longs;tium orbium numero, memoria labitur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>243<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait lineam O L, &longs;uperare lineam L R, quantitate P L, vt in figura.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>245<emph.end type="italics"/></cell><cell><emph type="italics"/>Remum ad vectem primi generis reducit.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>246<emph.end type="italics"/></cell><cell><emph type="italics"/>Temonem nauis reducit ad vectem primi generis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>247<emph.end type="italics"/></cell><cell><emph type="italics"/>In motu Remi collato cum motu Nauigij, 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><figure/>

<s id="id.000660">vide initio Priorum, in verbum (Re&longs;olutio)</s>

<s id="id.000661">Atqne hæc &longs;unt, quæ ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit,

<lb/>quæque nos infra explicabimus.</s>

<s>MATHEMATICA</s>

<s id="id.000662"><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s>

<s>EX LIBRO</s>

<s id="id.000663">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></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.025.jpg" pagenum="25"/><section>

<s>PRÆDICAMENTORVM</s>

<s id="id.000664"><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s>

<s>Per ordinem declarata.</s><figure/>

<s id="id.000665"><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/>

<lb/><arrow.to.target n="table2"/></s><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"/>Antipbonæ 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 numer are &longs;oliti.<emph.end type="italics"/></cell><cell>340</cell></row><row><cell><emph type="italics"/>Bry&longs;onis quadratura circuli.<emph.end type="italics"/></cell><cell>35</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Calippi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell><cell>236</cell></row><row><cell><emph type="italics"/>Cantilenam notam &longs;uauius, quam ignotam audimus.<emph.end type="italics"/></cell><cell>362</cell></row><row><cell><emph type="italics"/>Centrum circuli reperire. 303. Centrum mundi 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"/>C&oelig;lorum ordinem petendum ex A&longs;tronomis 109. item numerum<emph.end type="italics"/></cell><cell>233</cell></row><row><cell><emph type="italics"/>Colores in mu&longs;ica 78. Colores oculorum vnde.<emph.end type="italics"/></cell><cell>408</cell></row><row><cell><emph type="italics"/>Cometarum tractatiuncula ex recentioribus, qui eas in C&oelig;lo collocant. 136. e&longs;&longs;e &longs;u-pra aerem longi&longs;&longs;imo &longs;altem interuallo o&longs;tenditur 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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.026.jpg" pagenum="26"/><row><cell><emph type="italics"/>Cubus numerus. duo cubi cubus, quid &longs;ignificet.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell><emph type="italics"/>Curru problema.<emph.end type="italics"/></cell><cell>252</cell></row><row><cell><emph type="italics"/>Cunei problema.<emph.end type="italics"/></cell><cell>256</cell></row><row><cell><emph type="italics"/>Cylindri, & 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 denari&ubreve; omnes <expan abbr="g&etilde;tes">gentes</expan> <expan abbr="numer&etilde;t">numerent</expan>.<emph.end type="italics"/></cell><cell>339. 8. <emph type="italics"/>&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 pulcberrima.<emph.end type="italics"/></cell><cell>388</cell></row><row><cell><emph type="italics"/>Diapa&longs;on diapente.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Diapente con&longs;onantia, 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 C&oelig;lorum.<emph.end type="italics"/></cell><cell>234</cell></row><row><cell><emph type="italics"/>Exempla mathematicorum, qualia. 11. non e&longs;&longs;e fal&longs;a.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>Exemplorum veritas, & conformitas, quatenus requirantur.<emph.end type="italics"/></cell><cell>36</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Figuram omnem planam habere &longs;uos angulos externos <expan abbr="quotc&ubreve;q;">quotc&ubreve;que</expan> 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 rratum aperitur.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Figuratio lucis.<emph.end type="italics"/></cell><cell>345</cell></row><row><cell><emph type="italics"/>Figurationes pro demonftrationibus Mathem.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Filum Araneorum, ex qua parte corporis exeat, & 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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.027.jpg" pagenum="27"/><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 demonfiratio.<emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>Hippocratis chij quadratura circuli. 17. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> quadratura 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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.028.jpg" pagenum="28"/><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 c&oelig;lestium motuum.<emph.end type="italics"/></cell><cell>225</cell></row><row><cell><emph type="italics"/>Mu&longs;ici recentiores reprehen&longs;i. 331. & 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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.029.jpg" pagenum="29"/><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 præponeb&abreve;t.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Qvadratura circuli. vide circulus. de quadratura figurarum rectangularum, & quadraturæ duplex definitio cau&longs;alis, & formalis.<emph.end type="italics"/></cell><cell>185</cell></row><row><cell><emph type="italics"/>Quantitas an conctet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis mathematicis.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Remi problema.<emph.end type="italics"/></cell><cell>245</cell></row><row><cell><emph type="italics"/>Re&longs;olutio logica, & 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;euris 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 C&oelig;li paruam valde. 115. e&longs;&longs;e cubum cur Plato voluerit.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.030.jpg" pagenum="30"/><row><cell><emph type="italics"/>Teretizare, quid.<emph.end type="italics"/></cell><cell>366</cell></row><row><cell><emph type="italics"/>Tetrachordon, quid.<emph.end type="italics"/></cell><cell>386</cell></row><row><cell><emph type="italics"/>Tollenonis problema.<emph.end type="italics"/></cell><cell>267</cell></row><row><cell><emph type="italics"/>Tonus mu&longs;icus, qui; vnde oriatur.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>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><s id="id.000666">Finis Tertij Indicis.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.031.jpg" pagenum="31"/>

</section><section>

<s id="id.000667">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&ecedil;&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><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 demonctratione ostenditur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>147<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Tanaim, & 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 inhabit abilem exi&longs;timat.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>164<emph.end type="italics"/></cell><cell><emph type="italics"/>Putat Iridis angulos non po&longs;&longs;e vnum &longs;upra alterum collocari, &longs;ed tantummodo in orbem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>182<emph.end type="italics"/></cell><cell><emph type="italics"/>Rationes, quas in Parelij dubitationibus affert, videntur inanes.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>236<emph.end type="italics"/></cell><cell><emph type="italics"/>In &longs;ubducendo c&oelig;le&longs;tium orbium numero, memoria labitur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>243<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait lineam O L, &longs;uperare lineam L R, quantitate P L, vt in figura.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>245<emph.end type="italics"/></cell><cell><emph type="italics"/>Remum ad vectem primi generis reducit.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>246<emph.end type="italics"/></cell><cell><emph type="italics"/>Temonem nauis reducit ad vectem primi generis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>247<emph.end type="italics"/></cell><cell><emph type="italics"/>In motu Remi collato cum motu Nauigij, 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="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.032.jpg"/></section></front><body><chap> <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.033.jpg" pagenum="33"/>

<s id="id.000668">LOCA

<lb/>MATHEMATICA

<lb/>EX LIBRO

<lb/>PRÆDICAMENTORVM

<lb/>Per ordinem declarata.</s>

<s>Ex c. 3. De his, quæ ad aliquid. </s>

<s id="id.000671">Ex c. 3. De his, quæ ad aliquid. </s>

<s>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.

<s id="id.000672">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/>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>

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>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="id.000673">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>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="id.000674">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>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>

<s id="id.000675">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>

<s>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 fseri expo&longs;cit)<emph.end type="italics"/> neutrum a<gap/> t<gap/>m tem<lb/>pore Ari&longs;t.

<s id="id.000676">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<gap/> m ducen<lb/>tis circiter annis ab Archimede: problema verò nondum à quoquam per<lb/>fectè potuit reperiri. </s>

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>qua di&longs;tinctione &longs;aluari po&longs;&longs;unt nonnulli, vt Boetius <lb/>hocloco, qui aiunt, &longs;e vidi&longs;&longs;e Demon&longs;trationem quadraturæ huius, &longs;i nimi<lb/>rum intelligant theorema. </s>

<s id="id.000677">qua di&longs;tinctione &longs;aluari po&longs;&longs;unt nonnulli, vt Boetius

<lb/>hocloco, qui aiunt, &longs;e vidi&longs;&longs;e Demon&longs;trationem quadraturæ huius, &longs;i nimi

<lb/>rum intelligant theorema. </s>

<s>& 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"/>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="id.000678">& 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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.034.jpg" pagenum="34"/>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>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><figure/>

<s id="id.000679">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><figure id="id.009.01.034.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/009-01-figures/009.01.034.1.jpg" place="text"/>

<s>Sit, v.g. datus circulus, cuius &longs;emidiameter A B; & fit trian gulum 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="id.000680">Sit, v.g. datus circulus, cuius &longs;emidiameter A B; & fit trian gulum 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>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="id.000681">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.

<s>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. po&longs;&longs;imus triangulo huic quadratum æquale con&longs;truere, quod <lb/>con&longs;equenter dato circulo æquale erit. </s>

<s id="id.000682">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. po&longs;&longs;imus triangulo huic quadratum æquale con&longs;truere, quod

<lb/>con&longs;equenter dato circulo æquale erit. </s>

<s>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="id.000683">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>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.

<s id="id.000684">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>

<lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematicè, non tamen problematicè inue

<lb/>&longs;tigauit. </s>

<s>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="id.000685">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>tu ip&longs;um con&longs;ule, <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s>

<s id="id.000686">tu ip&longs;um con&longs;ule,

<lb/>&longs;i admirandarum rerum contemplatione delectaris. </s>

<s>Multa hac de re Pap<lb/>pus Alexandrinus lib.

<s id="id.000687">Multa hac de re Pap

<lb/>pus Alexandrinus lib.

4. Math. coll. </s>

<s>& 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="id.000688">& 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>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="quar&utilde;">quarum</expan> &longs;æpe meminit Ari&longs;t. & alij. </s>

<s id="id.000689">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="quar&utilde;">quarum</expan> &longs;æpe meminit Ari&longs;t. & alij. </s>

<s>&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="id.000690">&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>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="id.000691">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>Quod &longs;i po<lb/>te&longs;t fieri, quare non etiam demon&longs;trari? </s>

<s id="id.000692">Quod &longs;i po

<lb/>te&longs;t fieri, quare non etiam demon&longs;trari? </s>

<s>pr&ecedil;fertim cum videamus ab Archi<lb/>mede iam inuentam e&longs;&longs;e, quatenus Theorema e&longs;t. </s>

<s id="id.000693">pr&ecedil;fertim cum videamus ab Archi

<lb/>mede iam inuentam e&longs;&longs;e, quatenus Theorema e&longs;t. </s>

<s>& præterea con&longs;tet<gap/> Hip<lb/>pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, & Archimedem in libel<pb pagenum="35"/>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>

<s id="id.000694">& præterea con&longs;tet, Hip

<lb/>pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, & Archimedem in libel<pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.035.jpg" pagenum="35"/>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>

<s>Ex cap.

<s id="id.000697">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>

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>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/xei.</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, optim è <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="id.000698">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/xei.</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, optim è <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>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>

<s id="id.000699">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>

<s>Ex cap.

<s id="id.000702">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="fig2"/><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>

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/>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

<s>& 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.</s>

<s id="id.000703">& 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.</s>

<s>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="id.000704">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>addito numero impari. <lb/></s>

<s id="id.000706">addito numero impari.

<s>quemadmodum infra 3. Phy&longs;. tex. 26. fusè explicabimus.</s>

<s id="id.000707">quemadmodum infra 3. Phy&longs;. tex. 26. fusè explicabimus.</s>

<s><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s>

<s id="id.000708"><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s>

</chap><chap>

<s>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="id.000711">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>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="id.000712">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>Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>Alex. initio &longs;eptimi Mathem. collect. </s>

<s id="id.000713">Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus

<lb/>Alex. initio &longs;eptimi Mathem. collect. </s>

<s>antiqui&longs;&longs;imos videlicet Geometras, <lb/>Euclidem, Apollonium Pergæum, & Ari&longs;t&ecedil;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="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s>

<s id="id.000714">antiqui&longs;&longs;imos videlicet Geometras,

<lb/>Euclidem, Apollonium Pergæum, & Ari&longs;t&ecedil;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="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.036.jpg" pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s>

<s>Porrò Diogenes Laert. 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="id.000715">Porrò Diogenes Laert. 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>definitio <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s>

<s id="id.000716">definitio

<lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s>

<s>13. Elem. iuxta tran&longs;latio<lb/>nem Zamb<gap/>rti, & 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="id.000717">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>&longs;unt præterea fre<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, & Pap<lb/>pi. </s>

<s id="id.000718">&longs;unt præterea fre

<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, & Pap

<s>extat adhuc liber Datorum Euclidis, qui geometricis re&longs;olutionibus in<lb/>&longs;eruiebat. </s>

<s id="id.000719">extat adhuc liber Datorum Euclidis, qui geometricis re&longs;olutionibus in

<lb/>&longs;eruiebat. </s>

<s>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 exip&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="id.000720">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 exip&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>Quod quidem erat fignum euidens, quæ&longs;itum quoque verum <lb/>e&longs;&longs;e. </s>

<s id="id.000721">Quod quidem erat fignum euidens, quæ&longs;itum quoque verum

<lb/>e&longs;&longs;e. </s>

<s>eadem omnino habet Proclus in comm. ad &longs;extam primi elem. </s>

<s id="id.000722">eadem omnino habet Proclus in comm. ad &longs;extam primi elem. </s>

<s>Quod <lb/>porrò Ari&longs;t.

<s id="id.000723">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. 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>

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. 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="id.000724">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>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.

<s id="id.000725">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>

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="id.000726">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>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="id.000727">maximè

<lb/>verò, quia &longs;i horum lib.

<s>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>

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.

<s>maximè <lb/>verò, quia &longs;i horum lib.

<s id="id.000728">at verò vbinam docuit hanc re&longs;olutionem? </s>

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="id.000729">profecto nullibi. </s>

<s>at verò vbinam docuit hanc re&longs;olutionem? </s>

<s id="id.000730">quid opus e&longs;t

<lb/>iam factum &longs;yllogi&longs;mum re&longs;oluere? </s>

<s>profecto nullibi. </s>

<s id="id.000731">at verò propo&longs;itam quæ&longs;tionem re&longs;ol

<lb/>uere veterum mathematicorum more, hoc opus, hic labor e&longs;t.</s>

<s>quid opus e&longs;t <lb/>iam factum &longs;yllogi&longs;mum re&longs;oluere? </s>

<s id="id.000732">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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.037.jpg" pagenum="37"/>bus vltimis, non prætereundum. </s>

<s>at verò propo&longs;itam quæ&longs;tionem re&longs;ol<lb/>uere veterum mathematicorum more, hoc opus, hic labor e&longs;t.</s>

<s id="id.000733">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>

<s>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"/>bus vltimis, non prætereundum. </s>

<s>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>

<s id="id.000736">Ex cap.

23. &longs;ecti primi lib.

<s>Ex cap.

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;ur abilis. </s>

23. &longs;ecti primi lib.

<s id="id.000737">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>

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;ur abilis. </s>

<s id="id.000738">definit, quæ nam &longs;int magnitudines

<lb/>commen&longs;. </s>

<s>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="id.000739">& quæ incommen&longs;. </s>

<s>definit, quæ nam &longs;int magnitudines <lb/>commen&longs;. </s>

<s id="id.000740">&longs;ic; commen&longs;. </s>

<s>& quæ incommen&longs;. </s>

<s id="id.000741">magnitudines dicuntur, quas

<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. 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. 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/>rum, A, B, nunquam po&longs;&longs;et reperiri aliqua men&longs;u

<lb/>ra, quæ <expan abbr="vtranq;">vtranque</expan> adæquatè metiretur, v. g. &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>&longs;ic; commen&longs;. </s>

<s>magnitudines dicuntur, quas <lb/><figure id="fig3"/><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. 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. </s>

<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="fig4"/><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. g. </s>

<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>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="id.000742">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>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="id.000743">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>Quapropter <lb/>non immeritò diuinus ille Plato lib.

<s id="id.000744">Quapropter

<lb/>non immeritò diuinus ille Plato lib.

7. de legib. </s>

<s>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="id.000745">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>inter lineas incommen&longs;. </s>

<s id="id.000746">inter lineas incommen&longs;. </s>

<s>&longs;unt diameter, & latus eiu&longs;<lb/>dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti <lb/><figure id="fig5"/><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. g. <lb/></s>

<s id="id.000747">&longs;unt diameter, & latus eiu&longs;

<lb/>dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti

<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. g.

<lb/>latus B C, præcisè omnino metiatur. </s>

<s>latus B C, præcisè omnino metiatur. </s>

<s>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"/>propo&longs;itionis, quæfal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito prædictas lineas e&longs;&longs;e comm. <lb/>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="id.000748">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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.038.jpg" pagenum="38"/>propo&longs;itionis, quæfal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito prædictas lineas e&longs;&longs;e comm.

<lb/>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>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. & proinde altera pars con<lb/>tradictionis, quæ e&longs;t, e&longs;&longs;e incomm. </s>

<s id="id.000749">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. & proinde altera pars con

<lb/>tradictionis, quæ e&longs;t, e&longs;&longs;e incomm. vera a&longs;truitur. </s>

<s>vera a&longs;truitur. </s>

<s>ex quibus &longs;atis videtur ex<lb/>plicari hic locus. </s>

<s>videas igitur, quàm leuiter nonnulli no&longs;træ tempe&longs;tatis <lb/>ageometreti i&longs;tud exponant, dicentes diametrum e&longs;&longs;e incomm. co&longs;tæ, nihil <lb/>aliud &longs;igni&longs;icare, quam diametrum e&longs;&longs;e longiorem co&longs;ta, qua expo&longs;itione <lb/>nihil ineptius. </s>

<s id="id.000750">ex quibus &longs;atis videtur ex

<lb/>plicari hic locus. </s>

<s id="id.000751">videas igitur, quàm leuiter nonnulli no&longs;træ tempe&longs;tatis

<lb/>ageometreti i&longs;tud exponant, dicentes diametrum e&longs;&longs;e incomm. co&longs;tæ, nihil

<lb/>aliud &longs;igni&longs;icare, quam diametrum e&longs;&longs;e longiorem co&longs;ta, qua expo&longs;itione

<lb/>nihil ineptius. </s>

<s>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>

<s id="id.000752">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>

<s>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 ex. </s>

<s>&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="id.000755">Et cap.

<s>amplius ab æqualibus existentibus totis angulis, & ablatorum æquales e&longs;&longs;e re<lb/>tiquos 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>

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 ex. </s>

<s>Secundo, per de&longs;criptiones <lb/>Ari&longs;t.

<s id="id.000756">&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

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="id.000757">amplius ab æqualibus existentibus totis angulis, & ablatorum æquales e&longs;&longs;e re

<lb/>tiquos 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>In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t.

<s id="id.000758">Secundo, per de&longs;criptiones

<lb/>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>

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>e&longs;t au<lb/>tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="rè&longs;t&imacr;tuendam">rè&longs;tintuendam</expan> e&longs;&longs;e <lb/>ex quodam græco codice, qui characteres hoc modo appo&longs;uerat. </s>

<s id="id.000759">In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t.

<s>&longs;it I&longs;o&longs;ce<lb/><figure id="fig6"/><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>

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>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="id.000760">e&longs;t au

<lb/>tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="rè&longs;t&imacr;tuendam">rè&longs;tintuendam</expan> e&longs;&longs;e

<lb/>ex quodam græco codice, qui characteres hoc modo appo&longs;uerat. </s>

<s>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="id.000761">&longs;it I&longs;o&longs;ce

<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>Præte<lb/>rea cùm anguli ciu&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="angulor&utilde;">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="id.000762">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>hinc Ari&longs;t.

<s id="id.000763">omnes anguli &longs;emicirculi &longs;unt æquales in

<lb/>ter &longs;e, ergo anguli A C G, A B D, &longs;unt æquales. </s>

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="id.000764">Præte

<lb/>rea cùm anguli ciu&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="angulor&utilde;">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>Quænam vero &longs;it æqualitas, quam <lb/>Geometræ con&longs;iderant, infra cap.

<s id="id.000765">hinc Ari&longs;t.

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

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="id.000766">Quænam vero &longs;it æqualitas, quam

<lb/>Geometræ con&longs;iderant, infra cap. 1. &longs;ecti 3. explicabicur.</s>

<s>Ex cap.

<s id="id.000769">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;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39"/>ine&longs;&longs;e; &longs;ic græcè, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/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 diale cticos 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>

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;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.039.jpg" pagenum="39"/>ine&longs;&longs;e; &longs;ic græcè, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/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 diale cticos 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>

<s id="id.000772">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;eientijs

<lb/>po&longs;&longs;e probari, aut demou&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="id.000773">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="id.000774">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="id.000775">dies naturales e&longs;&longs;e inuicem inæquales, &c. </s>

<s id="id.000776">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>

<s>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;eientijs <lb/>po&longs;&longs;e probari, aut demou&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="id.000779">Ex cap.

<s>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>

3. &longs;ecti 2. lib.

<s>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>

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.

<s>dies naturales e&longs;&longs;e inuicem inæquales, &c. </s>

23. &longs;ecti 1. huius libri; quæ &longs;i repetantur, optimè hunc <expan abbr="loc&utilde;">locum</expan> declarant.</s>

<s>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>

<s id="id.000782">Ex cap.

<s>Ex cap.

1. &longs;ecti 3. lib.

3. &longs;ecti 2. 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 in clinatio

<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="ill&utilde;">illum</expan>, quem

<lb/>duæ lineæ non in directum con&longs;titutæ faciunt, vt duarum linearum A B, A C,

<lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro,

<lb/>e&longs;t ratio anguli. </s>

<s id="id.000783">&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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.040.jpg" pagenum="40"/><expan abbr="linear&utilde;">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. </s>

<s id="id.000784">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.

<s id="id.000785">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="n&utilde;quam">nunquam</expan> tamen licet dicere angulum A C B,

<s id="id.000786">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/>angulus B A C, diuidatur in duos angulos à linea A D. tunc enim duo angu

<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

<s id="id.000787">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/>niilli, quem con&longs;tituerent alij duo anguli, quibus illi tres

<lb/>&longs;unt pares, v.g. &longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti,

<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 fimul &longs;umpti, & vniti ad punctum

<lb/>E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum

<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. &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-qu&utilde;">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/>rectorú, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G,

<lb/>con&longs;tituant. </s>

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="loc&utilde;">locum</expan> declarant.</s>

<s>Ex cap.

<s id="id.000788">habet igitur omne triangulum &longs;iue &ecedil;quilaterum, &longs;iue &longs;calenum,

<lb/>&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian

<lb/>guli &longs;int æquales duobus rectis angulis. </s>

<s id="id.000789">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="id.000790">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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.041.jpg" pagenum="41"/>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/>ce&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam,

<lb/>quæ &longs;cilicet faciat, cum illa duos angulos rectos. </s>

<s id="id.000791">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 punctnm 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="id.000792">Hoc autem experiri poteris in diuer&longs;is admodum

<lb/>triangulis Scalenis, Rectangulis, I&longs;o&longs;celibus, Aequilateris, &c. </s>

<s id="id.000793">non &longs;ine de

<lb/>lectatione, atque hic e&longs;t &longs;en&longs;us illorum verborum, omnis triangulus habet

<lb/>tres &ecedil;quales duobus rectis. </s>

<s id="id.000794">Ab&longs;tineo à demon&longs;trationibus geometricis, quo

<lb/>niam ij, qui Mathematicis &longs;unt imbuti, no&longs;tra hac opera parum indigent.

<s id="id.000795">&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. </s>

<s id="id.000796">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="id.000797">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.

1. &longs;ecti 3. lib.

textum percipere. </s>

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.

<s id="id.000798">&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>

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 in clinatio<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="ill&utilde;">illum</expan>, quem <lb/>duæ lineæ non in directum con&longs;titutæ faciunt, vt duarum linearum A B, A C, <lb/><figure id="fig7"/><lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>e&longs;t ratio anguli. </s>

<s id="id.000799">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="triangul&utilde;">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 crit

<lb/>medium ip&longs;ius A, quia prædicta pa&longs;&longs;io. </s>

<s>&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"/><expan abbr="linear&utilde;">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. </s>

<s id="id.000800">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>

<s>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/></s>

<s>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="n&utilde;quam">nunquam</expan> tamen licet dicere angulum A C B, <lb/>vel C B A. </s>

<s>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/>angulus B A C, diuidatur in duos angulos à linea A D. tunc enim duo angu<lb/><figure id="fig8"/><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="id.000803">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="id.000804">&longs;ed &longs;icut

<lb/>Geometra pedalem, & rectam hanc, & &longs;ine latitudine dicit, quæ non &longs;unt. </s>

<s id="id.000805">verum

<lb/>non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t.

<s>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/>niilli, quem con&longs;tituerent alij duo anguli, quibus illi tres <lb/>&longs;unt pares, v.g. &longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti, <lb/><figure id="fig9"/><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 fimul &longs;umpti, & vniti ad punctum <lb/>E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum <lb/><figure id="fig10"/><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. </s>

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="id.000806">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. 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>&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-qu&utilde;">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/>rectorú, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G, <lb/>con&longs;tituant. </s>

<s>habet igitur omne triangulum &longs;iue &ecedil;quilaterum, &longs;iue &longs;calenum, <lb/>&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian<lb/>guli &longs;int æquales duobus rectis angulis. </s>

<s>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="id.000807">idem dicen

<lb/>dum e&longs;t de &longs;uperficiebus, necnon de corporibus, quæ ijdem Goometræ de

<lb/>&longs;cribunt, vt per ea, de verè mathematicis di&longs;currant.</s></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.042.jpg" pagenum="42"/>

<chap>

<s id="id.000808"><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s>

<s>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"/>æqualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>vitare ob &longs;ui imperfectione<gap/>on licet: vnde inter eæ, quæ mathematicè <lb/>&longs;unt æqualia, nullus intellectus aliquam valeat reper<gap/>re differentiam) &longs;umat <lb/>inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po<lb/>ce&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/>quæ &longs;cilicet faciat, cum illa duos angulos rectos. </s>

<s>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 punctnm 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>Hoc autem experiri poteris in diuer&longs;is admodum <lb/>triangulis Scalenis, Rectangulis, I&longs;o&longs;celibus, Aequilateris, &c. </s>

<s id="id.000811">Ex cap.

<s>non &longs;ine de<lb/>lectatione, atque hic e&longs;t &longs;en&longs;us illorum verborum, omnis triangulus habet <lb/>tres &ecedil;quales duobus rectis. </s>

21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;i

<lb/>&longs;e ip&longs;os talia accip entes, quæ non est po&longs;&longs;ibile monstrare uon exi&longs;tentibus

<s>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>

<lb/>coalternis)<emph.end type="italics"/> Vult Ari&longs;t.

<s>&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. </s>

exemplo mathematico explicare, quid &longs;it pe

<lb/>titio principij. </s>

<s>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.

<s id="id.000812">vbi per coalternas intelligit parallelas lineas, vox

<lb/>enim græca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, & coalternus. </s>

velle &longs;ignifi<lb/>care, quàm omnem triangulum habere tres angulos, quod inquiunt, noti&longs;<lb/>&longs;imum e&longs;t. </s>

<s id="id.000813">quoad

<lb/>exempli explicationem vtor figura textibus apponi &longs;olita, quæ e&longs;t præ&longs;ens.

<lb/>probat Euclides in 28. primi Elem.

<s>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.

quod &longs;i

<lb/>linea recta quædam, vti E F, cadens &longs;uper

<lb/>duas rectas, vti &longs;unt A B, C D, fe cerit angu

<lb/>los alternos &ecedil;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H,

<lb/>G H D, ij enim dicuntur alterni; &longs;iue alios

<lb/>dnos, nimirum B G H, G H C, hi enim &longs;unt

<lb/><expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li

<lb/>neas A B, C D, e&longs;&longs;e inuicem parallelas. </s>

textum percipere. </s>

<s id="id.000814">Iam &longs;i quis vellet probare, &longs;e duas

<lb/>parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet fa ciunt 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="proband&utilde;">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>&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="id.000815">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>

<s>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="triangul&utilde;">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 crit <lb/>medium ip&longs;ius A, quia prædicta pa&longs;&longs;io. </s>

<s>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>

<s id="id.000818">Ex cap.

22. lib.

<s>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>

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.

<s>&longs;ed &longs;icut <lb/>Geometra pedalem, & rectam hanc, & &longs;ine latitudine dicit, quæ non &longs;unt. </s>

<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 vtramq, quantitatem men&longs;urare, debet in men&longs;urando

<lb/>infinitas partes pertran&longs;ire, uimirum medietates medietatum in in&longs;initum,

<lb/>e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, & 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.

<s>verum <lb/>non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t.

non cau&longs;am pro cau&longs;a.</s>

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>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. 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="id.000821">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="id.000822">per coalternas intellige lineas æquidi&longs;tantes, &longs;eu pa

<lb/>rallelas, vt in &longs;uperiori cap.

monuimus. </s>

<s>idem dicen<lb/>dum e&longs;t de &longs;uperficiebus, necnon de corporibus, quæ ijdem Goometræ de<lb/>&longs;cribunt, vt per ea, de verè mathematicis di&longs;currant.</s><pb pagenum="42"/>

<s id="id.000823">Cæterum Euclides propo&longs;. </s>

<s><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s>

<s id="id.000824">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. g. 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>Ex cap.

21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;<gap/><lb/>&longs;e ip&longs;os talia accip entes, quæ non est po&longs;&longs;ibile monstrare uon exiftentibus <lb/><gap/>o lternis)<emph.end type="italics"/> Vult Ari&longs;t.

exemplo mathematico explicare, quid &longs;it pe<lb/>titio principij. </s>

<s>vbi per coalternas intelligit parallelas lineas, vox <lb/>enim græca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, & coalternus. </s>

<s id="id.000825">& pro

<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.043.jpg" pagenum="43"/>G H D, appo&longs;ito <expan abbr="vtiq;">vtique</expan> communi angulo B G H, erant primum, duo anguli

<lb/>E G B, B G H, maiores, quam &longs;int duo B G H, G H D, quia &longs;i 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>quoad <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, quæ e&longs;t præ&longs;ens. <lb/><figure id="fig11"/><lb/>probat Euclides in 28. primi Elem.

<s id="id.000826">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.

quod &longs;i <lb/>linea recta quædam, vti E F, cadens &longs;uper <lb/>duas rectas, vti &longs;unt A B, C D, fe cerit angu<lb/>los alternos &ecedil;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H, <lb/>G H D, ij enim dicuntur alterni; &longs;iue alios <lb/>dnos, nimirum B G H, G H C, hi enim &longs;unt <lb/><expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li<lb/>neas A B, C D, e&longs;&longs;e inuicem parallelas. </s>

<s id="id.000827">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="angulor&utilde;">angulorum</expan>. </s>

<s>Iam &longs;i quis vellet probare, &longs;e duas <lb/>parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet fa ciunt 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="proband&utilde;">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="id.000828">quod

<lb/>P. Clauius luculenti, & hactenus de&longs;iderata demon&longs;tratione ad 28. primi

<lb/>demon&longs;trauit. </s>

<s>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>

<s id="id.000829"><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>

<s>Ex cap.

<s id="id.000830">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/>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

22. lib.

<s id="id.000831">ergo totus i&longs;te angulus B C D, &longs;imul cum reliquo <expan abbr="triãguli">trianguli</expan> angulo B. con

<lb/>flabit 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>

2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom<lb/>men&longs;. </s>

<s id="id.000832">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>argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib.

<s id="id.000833">& &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio

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 vtramq, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, uimirum medietates medietatum in in&longs;initum, <lb/>e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, & 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.

<s id="id.000834">ex quibus textus Ari&longs;t.

non cau&longs;am pro cau&longs;a.</s>

videtur &longs;atis clarus.</s>

<s>Ex eodem cap. <emph type="italics"/>(Quoniam idem <expan abbr="vtiq;">vtique</expan> fal&longs;um per plures petitiones accidere <lb/>nihil forta&longs;&longs;e inconueniens, veluti coalternas coincidere; & &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="id.000837">Ex cap.

<s>per coalternas intellige lineas æquidi&longs;tantes, &longs;eu pa<lb/>rallelas, vt in &longs;uperiori cap.

26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C,

<lb/>&longs;en&longs;ibuis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis

<lb/>triangulus habet duos rectos: quare &longs;imul no&longs;cet, & ignorabit idem. </s>

monuimus. </s>

<s id="id.000838">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>Cæterum Euclides propo&longs;. </s>

<s id="id.000839">&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.

<s>28. pri<lb/>mi Elem.

1. &longs;ecto 3. cap.

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. g. </s>

1. ex quibus quidquid Ma

<lb/>thematicum e&longs;t hic, clarum redditur. </s>

<s id="id.000840">reliqua verò, quæ ad Logicum &longs;pe

<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s>

<s id="id.000841">In cap.

<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>

31. de Abductione.</s>

<s>& pro<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb pagenum="43"/>G H D, appo&longs;ito vtiq<gap/> 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>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>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="angulor&utilde;">angulorum</expan>. </s>

<s id="id.000844">Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc

<lb/>cap.

<s>quod <lb/>P. Clauius luculenti, & hactenus de&longs;iderata demon&longs;tratione ad 28. primi <lb/>demon&longs;trauit. </s>

agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</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="id.000845">e&longs;&longs;e <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.044.jpg" pagenum="44"/>autem terminum mathematicum colligitur manife&longs;tè ex Proelo, qui lib.

<s><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>

<lb/>in comm. Elem.

<s>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="fig12"/><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>

Euclidis ad primam propo&longs;itionem primi Elementi, pag.

<s>ergo totus i&longs;te angulus B C D, &longs;imul cum reliquo <expan abbr="triãguli">trianguli</expan> angulo B. con<lb/>flabit 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>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>& &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio<lb/>ne. </s>

<s id="id.000846">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>ex quibus textus Ari&longs;t.

<s id="id.000847">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>

videtur &longs;atis clarus.</s>

<s id="id.000848">Primum autem dicunt Hippocra

<lb/>tem Chium pr&ecedil;dictorum titulorum, Abductionem feci&longs;&longs;e, qui & lunulæ qua

<lb/>dratum fecit æquale, & alia multa in Geometria inuenit. </s>

<s id="id.000849">hæc Proclus. </s>

<s id="id.000850">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>

<s>Ex cap.

<s id="id.000851">Notandum præterea Hippoetatem 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>

26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C, <lb/>&longs;en&longs;ibuis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis <lb/>triangulus habet duos rectos: quare &longs;imul no&longs;cet, & ignorabit idem. </s>

<s id="id.000852">&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>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="id.000853">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="Alexandrin&utilde;">Alexandrinum</expan>, & apud P. Cla

<lb/>uium in fine &longs;exti Elem.

<s>&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.

& alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio

<lb/>circa probationem minoris, in qua adhuc Mathematici verfantur; quæ pro

<lb/>batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro

<lb/>blema, nimirum circulus quadraretur; vide quæ &longs;crip&longs;imus in cap.

1. &longs;ecto 3. cap.

3. Præ

<lb/>dicam. de hac re, quia plurimum hunc conferunt. </s>

1. ex quibus quidquid Ma<lb/>thematicum e&longs;t hic, clarum redditur. </s>

<s>reliqua verò, quæ ad Logicum &longs;pe<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s>

<s>In cap.

31. de Abductione.</s>

<s id="id.000854">&longs;ed iam ad textus expli

<lb/>cationem veniamus.</s>

<s>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;">camque</expan>; Ari&longs;t.

<s id="id.000857">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. 11. primi Phy&longs;ic. 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 cius 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="diametr&utilde;">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 xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.045.jpg" pagenum="45"/><figure id="id.009.01.045.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/009-01-figures/009.01.045.1.jpg" place="text"/>

<lb/>angulo recto C, ergo quadratum eius ex eorol

<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>

quemadmodum multa <lb/>alia à Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s>

<s>e&longs;&longs;e <pb pagenum="44"/>autem terminum mathematicum colligitur manife&longs;tè ex Proelo, qui lib.

3. <lb/>in comm. Elem.

Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s>

<s id="id.000858"><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be

<lb/>nè procedit Hippocrates. </s>

<s id="id.000859">&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/>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>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="id.000860">& <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="diametror&utilde;">diametrorum</expan> B C, L Q, Q S,

<lb/>S M, erit &longs;emicirculus L O M, &ecedil;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> detrapezio 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>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="id.000861">&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;egment&utilde;">&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>Primum autem dicunt Hippocra<lb/>tem Chium pr&ecedil;dictorum titulorum, Abductionem feci&longs;&longs;e, qui & lunulæ qua<lb/>dratum fecit æquale, & alia multa in Geometria inuenit. </s>

<s id="id.000862">mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunulæ

<lb/>quadratio. </s>

<s>hæc Proclus. </s>

<s id="id.000863">Ex quibus &longs;atis clara e&longs;&longs;e po&longs;&longs;unt ea, quæ ad <expan abbr="Mathematic&utilde;">Mathematicum</expan> per

<lb/>tinent, ad locum hunc de Abductione declarandum. </s>

<s>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>

<s id="id.000864">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>Notandum præterea Hippoetatem 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 Abductioni<gap/><lb/>Mathematicæ. </s>

<s id="id.000865">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>&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="id.000866">Hippocrates i&longs;te Chius e&longs;t alter <pb xlink:href="http://archimedes.fas.harvard.edu/images/009-01-pageimg/009.01.046.jpg" pagenum="46"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre

<lb/>Aphrod. in Primum Meteororum de Cometis.</s>

<s>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="Alexandrin&utilde;">Alexandrinum</expan>, & apud P. Cla<lb/>uium in fine &longs;exti Elem.

</chap><chap>

& alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio <lb/>circa probationem minoris, in qua adhuc Mathematici verfantur; quæ pro<lb/>batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro<lb/>blema, nimirum circulus quadraretur; vide quæ &longs;crip&longs;<gap/>mus in cap.

<s id="id.000867"><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s>

3. Præ<lb/>dicam. </s>

<s id="id.000870">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>de hac re, quia plurimum hunc conferunt. </s>

<s id="id.000871">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&ecedil;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>&longs;ed iam ad textus expli<lb/>cationem veniamus.</s>

<s id="id.000872">Tertium

<lb/>Axiomata, &longs;eu communes omnium conceptiones, & &longs;ententias, ex quibus

<lb/>tanquam ex vberrimis, & chri&longs;taltinis fontibus Demon&longs;trationes Geome

<lb/>tricæ deriuantur. </s>

<s id="id.000873">Idem vìdere licet in operibus aliorum Geometrarum,

<lb/>Archimedis, Apollonij, Pappi, & cæterorum. </s>

<s id="id.000874">Aliæ &longs;iniliter 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.

<s>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. 11. primi Phy&longs;ic. </s>

<s id="id.000875">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="typ&utilde;">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>

<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 cius 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="diametr&utilde;">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"/><figure id="fig13"/><lb/>angulo recto C, ergo quadratum eius ex eorol<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="id.000878">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. &longs;ecto 3. cap.

<s><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be<lb/>nè procedit Hippocrates. </s>

1. explicaui de angulis

<lb/>trianguli. </s>

<s>&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="fig14"/><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>& <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="diametror&utilde;">diametrorum</expan> B C, L Q, Q S, <lb/>S M, erit &longs;emicirculus L O M, &ecedil;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> detrapezio 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>&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;egment&utilde;">&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="id.000879">deinde &longs;cias, quod quando Ari&longs;t.

<s>mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunulæ <lb/>quadratio. </s>

ait, hoc, quod e&longs;t in &longs;emicir cu

<lb/>lo triangulum, &c. </s>

<s>Ex quibus &longs;atis clara e&longs;&longs;e po&longs;&longs;unt ea, quæ ad <expan abbr="Mathematic&utilde;">Mathematicum</expan> per<lb/>tinent, ad locum hunc de Abductione declarandum. </s>

<s id="id.000880">alludit ad demon&longs;trationem quandam, quam ip&longs;e infe

<lb/>rius in exemplum adducet, & quæ e&longs;t in 3. Elem.

<s>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>

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/>micirculo. </s>

<s>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="id.000881">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 paricer in

<lb/>circumferentia con&longs;tituant, quibus pr&ecedil;mi&longs;sis

<lb/>&longs;ic textum explicaueris: quod enim omne

<lb/>triangulum habet tres angulos 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>

<s>Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>Aphrod. in Primum Meteororum de Cometis.</s>