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version 1.8, 2002/07/31 14:04:00

version 1.14, 2002/08/06 17:19:52

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<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Bianchini, Giuseppe</author> <title>Aristotelis loca mathematica</title> <date>1615</date>

<place>Bologna</place> <editor></editor> <publisher></publisher> <translator></translator> <lang>la</lang> <chunk unit="page*">page</chunk><locator>0000000009</locator> </info> <text> <front> </front> <body> <chap> <pb/>

<place>Bologna</place> <translator></translator> <lang>la</lang> <cvs_file>bianc_locam_01_la_1615.xml</cvs_file><cvs_version>1.13</cvs_version><locator>0000000009</locator> </info> <text> <front> </front> <body> <chap> <pb/>

<s>ARISTOTELIS</s>

Line 122

<s>Vt autem huius operis nece&longs;&longs;itas, <expan abbr="variæ&qacute;">variæque</expan>; vtilitates pla<lb/>nius cogno&longs;cantur operæpretium erit initio illius cau&longs;as exponere; quæ <lb/>me poti&longs;&longs;imum ad illud con&longs;cribendum compulerunt, quarum</s>

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

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

<s>loca Mathematica, quæ quidem ferè 408. <lb/>numerantur, pe&longs;&longs;imè latinis literis con&longs;ignata &longs;unt v&longs;que adeò, vt Ari<lb/>&longs;totelem ip&longs;um, vel inuitum (quod po&longs;tea multis in locis planum fiet) in <lb/>ab&longs;urdi&longs;&longs;ima errata &longs;æpi&longs;&longs;imè compellant.</s>

loca Mathematica, quæ quidem ferè 408. <lb/>numerantur, pe&longs;&longs;imè latinis literis con&longs;ignata &longs;unt v&longs;que adeò, vt Ari<lb/>&longs;totelem ip&longs;um, vel inuitum (quod po&longs;tea multis in locis planum fiet) in <lb/>ab&longs;urdi&longs;&longs;ima errata &longs;æpi&longs;&longs;imè compellant.</s>

<s>Secunda, quòd plurima huiu&longs;modi loca à nemine, quod &longs;ciam, adhuc <lb/>declarata in tenebris magno no&longs;trorum malo delite&longs;cunt: cuiu&longs;modi <lb/>&longs;unt ad &longs;exaginta problemata, libellus de lineis in &longs;ecabilibus, libellus <lb/>de mundo, &longs;i tamen Ari&longs;totelis e&longs;t, & Mechanicæ quæ&longs;tiones, quamuis <lb/>enim Picolomineus in eas paraphra&longs;im ediderit, loca tamen earum dif<lb/>ficiliora non &longs;atis illu&longs;trauit. </s>

<s>Vt autem dixi 408. in vniuer&longs;um loca mi<lb/>nimùm numerantur, quibus illud Platonis in&longs;criptum e&longs;t <foreign lang="greek">ag aiome/trhtos <lb/>ud<gap/>i/s <gap/>i/to</foreign>; & in quibus Mathematicæ di&longs;ciplinæ rudes, & imperiti, quem <lb/>&longs;equuntur ducem Ari&longs;t. </s>

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

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

<s>Tertia, quia Græcieorumdem locorum commentatores breuiter, & <lb/>ob&longs;curè admodum ea, quæ ad Mathematicum &longs;pectant, attingunt, hoc <lb/>enim ab ip&longs;is <expan abbr="cert&utilde;">certum</expan> ponitur, I ectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/>Philo &longs;ophorum, Mathematicis imbutum; at verò no&longs;tra ætate magna <lb/>cum Philo&longs;ophiæ iactura, quamplurimi earumdem di&longs;ciplinarum de&longs;ti<lb/>tuti præ&longs;idijs, ne Græcorum quidem Interpretum explanationes, ne<lb/>dum Ari&longs;t. </s>

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

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

<s>Quarta. </s>

Line 146

<s>Quinta. </s>

<s>Ex his omnibus in aliud incommodum, vel maximum Phi<lb/>lo&longs;ophi quidam incidebant; aut enim horum locorum expo&longs;itionem ta<lb/>citi declinabant: aut eam minime nece&longs;&longs;ariam ad Ari&longs;t. </s>

<s>percipiendam <lb/>&longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;<lb/>&longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s>

percipiendam <lb/>&longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;<lb/>&longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s>

<s>Eorum verò nonnulli eorumdem <lb/>locorum expo&longs;itionem audacter nimis aggrediebantur, <expan abbr="atq;">atque</expan> hinc pueri<lb/>les illæ, ac ridiculæ expo&longs;itiones pa&longs;&longs;im auditæ, cuiu&longs;modi e&longs;t illa, quan<lb/>do Ari&longs;toteles ait, quod illi frequenti&longs;&longs;imum e&longs;t, omnis triangulus ha<lb/>bet tres; nihil aliud &longs;ignificari volunt, quàm omnem triangulum habe<lb/>re tres angulos. </s>

<s>quod &longs;i dicat, omnis triangulus habet tres æquales duo<lb/>busrectis: hic hærent, hinc anguntur: <expan abbr="cumq;">cumque</expan> ex his angu&longs;tijs, ac tricis <lb/>&longs;e minimè expedire valeant, aurea verba illa, quibus ingentes &longs;apientiæ <lb/>the&longs;auri continentur, alto &longs;ilentij velo contegere Mathematicarum eos <lb/>cogit in&longs;citia: vnde illud, quod Græcæ linguæ imperitis mutata oratio<lb/>ne acclamandum illis foret, Mathematicum e&longs;t, non legitur. </s>

<s>Nec mi<lb/>nus elegans illa altera expo&longs;itio; Diametrum e&longs;le incommen&longs;urabilem <lb/>co&longs;tæ; quod &longs;æpe apud Ari&longs;t. </s>

<s>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>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>

legentibus occurrit, nihil aliud &longs;ibi velle, <lb/>quam Diametrum e&longs;&longs;e longiorem co&longs;ta, quam quidem a&longs;ymetriæ huius <lb/>ignorantiam Plato de legibus dial. </s>

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

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

<s>cum Ari&longs;t.

<s>ait duo cubi, cu<lb/>bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in<lb/>uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/></s>

ait duo cubi, cu<lb/>bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in<lb/>uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/></s>

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

Line 210

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

<s>Illud hoc loco minimè <lb/>tacendum, Iacobum Zabarellam in &longs;uis logicæ commentarijs te&longs;tari &longs;e <lb/>bis &longs;umma diligentia totum Euclidem perlegi&longs;&longs;e, vt perfectè Ari&longs;t. </s>

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

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>

Line 236

<s>Geometrica ad Euclidis ordinem referuntur; vnde & ip&longs;i ad &longs;uas pr&ecedil;le<lb/>ctiones exornandas aliquid &longs;ubinde depromere queant.</s>

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

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

<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>

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>

Line 256

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>eodem. </s>

eodem. </s>

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

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

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

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

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

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

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

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

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

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

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

Line 434

<s>Topicorum.</s>

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

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

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

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

Line 448

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>In Elenchorum lib. </s>

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

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

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

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

Line 600

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

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

<s>eodem. </s>

eodem. </s>

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

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

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

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

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

Line 616

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

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

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

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

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

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

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

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

<s>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 pagenum="15"/>

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

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

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

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

<s>corriguntur. </s>

corriguntur. </s>

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

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

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

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

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

Line 654

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

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

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

eodem, De Canicula. </s>

<s>De Zonis temperatis. </s>

Line 666

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

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

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

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

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

Line 676

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

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

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

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

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

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

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

5. De Parelio. </s>

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

Line 720

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

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

8. Nete. </s>

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

Line 732

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

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

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

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

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

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

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

<s>De Somnijs.</s>

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

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

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

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

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

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

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

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

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

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

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

Line 840

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

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

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

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

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

Line 856

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>inibi Ari&longs;t.

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

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

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

Line 890

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

<s>4. De Remo; Petri Nonÿ in Arist. </s>

<s>4. De Remo; Petri Nonÿ in Arist.

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

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

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

Line 996

<s>In libello De Mundo ad Alex.</s>

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

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

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

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

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

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

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

<s>5. De fluxu maris. </s>

5. De fluxu maris. </s>

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

Line 1084

<s>9. Hi&longs;toriæ Animalium.</s>

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

<s>39. error Ari&longs;t. </s>

39. error Ari&longs;t. </s>

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

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

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

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

<s>De Motu Animal.</s>

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

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

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

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

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

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

<s>De Generatione Animal.</s>

Line 1186

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Moralium Eudemiorum.</s>

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

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

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

Line 1220

<s>Eudemiorum.</s>

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

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

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

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

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

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

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

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

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

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

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

Line 1242

<s>Eudemiorum.</s>

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

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

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

<s>Politicorum.</s>

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

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

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

<s>Polit.</s>

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

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

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

<s>Polit.</s>

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

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

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

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

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

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

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

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

Line 1282

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

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

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

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

<s>Ex Problematibus.</s>

Line 1998

<s>10. &longs;ecundi Eu<lb/>dem. </s>

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

<s>tot Ari&longs;t.

<s>loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s>

loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s>

<s><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s>

Line 2042

<s>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>

<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>

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>

Line 2052

<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>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>

<s>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<gap/> m 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>

Line 2180

<s>ad &longs;extam primi elem. </s>

<s>Quod <lb/>porrò Ari&longs;t. </s>

<s>Quod <lb/>porrò Ari&longs;t.

<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. </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. </s>

Line 2190

<s>vbi &longs;ic ait <emph type="italics"/>(Qui enim <lb/>con&longs;ultat, quærere videtur, & re&longs;oluere prædicto modo, quemadmodum de&longs;igna<lb/>tiones)<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt <lb/>&longs;upra innuimus, & infra probabimus; cum ergo con&longs;ultatio nihil aliud &longs;it, <lb/>quam medij idonei ad finem in rebus agendis inqui&longs;itio, eamque dicat e&longs;&longs;e <lb/>&longs;imilem re&longs;olutioni Geometricæ, manife&longs;tum e&longs;t, ip&longs;am <expan abbr="quoq;">quoque</expan> re&longs;olutionem <lb/>e&longs;&longs;e medij in rebus &longs;peculatiuis idonei perue&longs;tigationem. </s>

<s>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>

<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>

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>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>

Line 2266

<s>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/></s>

<s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t. </s>

<s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.

<s>fal&longs;um ratiocinatur, quod &longs;ci<lb/>licet idem numerus e&longs;&longs;et par, & impar, quod Ari&longs;t. </s>

fal&longs;um ratiocinatur, quod &longs;ci<lb/>licet idem numerus e&longs;&longs;et par, & impar, quod Ari&longs;t. </s>

<s>&longs;ignificat, quando ait, <lb/>imparia æqualia paribus fiunt. </s>

Line 2298

<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>

<s>Secundo, per de&longs;criptiones <lb/>Ari&longs;t. </s>

<s>Secundo, per de&longs;criptiones <lb/>Ari&longs;t.

<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>

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>In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t. </s>

<s>In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t.

<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>

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>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>

Line 2316

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

<s>hinc Ari&longs;t.

<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>

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>Quænam vero &longs;it æqualitas, quam <lb/>Geometræ con&longs;iderant, infra cap. </s>

Line 2408

<s>&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. </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>

<s>velle &longs;ignifi<lb/>care, quàm omnem triangulum habere tres angulos, quod inquiunt, noti&longs;<lb/>&longs;imum e&longs;t. </s>

velle &longs;ignifi<lb/>care, quàm omnem triangulum habere tres angulos, quod inquiunt, noti&longs;<lb/>&longs;imum e&longs;t. </s>

<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. </s>

<s>textum percipere. </s>

textum percipere. </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>

Line 2432

<s>&longs;ed &longs;icut <lb/>Geometra pedalem, & rectam hanc, & &longs;ine latitudine dicit, quæ non &longs;unt. </s>

<s>verum <lb/>non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t. </s>

<s>verum <lb/>non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t.

<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. </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.

<s>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>

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. </s>

Line 2452

<s>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. </s>

<s>exemplo mathematico explicare, quid &longs;it pe<lb/>titio principij. </s>

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>

Line 2478

<s>argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. </s>

<s>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>

<s>non cau&longs;am pro cau&longs;a.</s>

non cau&longs;am pro cau&longs;a.</s>

Line 2522

<s>& &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio<lb/>ne. </s>

<s>ex quibus textus Ari&longs;t. </s>

<s>ex quibus textus Ari&longs;t.

<s>videtur &longs;atis clarus.</s>

videtur &longs;atis clarus.</s>

Line 2554

<s>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap. </s>

<s>agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t. </s>

<s>agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t.

<s>quemadmodum multa <lb/>alia à Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </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. </s>

Line 2654

<s>1. explicaui de angulis <lb/>trianguli. </s>

<s>deinde &longs;cias, quod quando Ari&longs;t. </s>

<s>deinde &longs;cias, quod quando Ari&longs;t.

<s>ait, hoc, quod e&longs;t in &longs;emicir cu<lb/>lo triangulum, &c. </s>

ait, hoc, quod e&longs;t in &longs;emicir cu<lb/>lo triangulum, &c. </s>

<s>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe<lb/>rius in exemplum adducet, & quæ e&longs;t in 3. Elem. </s>

Line 2814

<s>hoc <lb/>loco di&longs;ce&longs;&longs;imus à Zabarella, qui putat i&longs;tud e&longs;&longs;e exemplum primi erroris, <lb/>cum verba textus adeo clara &longs;int, vt expo&longs;itionem illius nullo modo admit<lb/>tant. </s>

<s>&longs;unt autem hæc textus verba <emph type="italics"/>(Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o<lb/>&longs;celes, &longs;ecundum quod I&longs;o&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e)<emph.end type="italics"/> quibus verbis manife&longs;tè <lb/>apparet Ari&longs;t. </s>

<s>accipere pro &longs;ubiecto vniuer&longs;ali non indiuiduum vnum, vt in <lb/>primo errore contingit, &longs;ed &longs;peciem loco generis, &longs;cilicet I&longs;o&longs;celes, quod <lb/>e&longs;t &longs;pecies trianguli pro genere ip&longs;o, nimirum pro Triangulo. </s>

accipere pro &longs;ubiecto vniuer&longs;ali non indiuiduum vnum, vt in <lb/>primo errore contingit, &longs;ed &longs;peciem loco generis, &longs;cilicet I&longs;o&longs;celes, quod <lb/>e&longs;t &longs;pecies trianguli pro genere ip&longs;o, nimirum pro Triangulo. </s>

<s>ait enim, &longs;i <lb/>non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quod I&longs;o&longs;celes: quibus verbis cla<lb/>rè &longs;peciem, non indiuiduum, &longs;igni&longs;icat, ex his duobus exemplis manife&longs;tus <lb/>e&longs;t tertius error, qui erat, quando erat <emph type="italics"/>(vt in parte totum)<emph.end type="italics"/> <expan abbr="quod&qacute;">quodque</expan>; illis verbis <lb/>expo&longs;uerat <emph type="italics"/>(vei contingit etiam, vt in parte totum, in quo mon&longs;tratur: ijs emm, <lb/>quæ &longs;unt in parte inerit quidem demon&longs;tratio, & erit de omni, &longs;ed tamen non erit <lb/>buius primi vniuer&longs;aliter demon&longs;tratio. </s>

Line 2840

<s>vt 6. ad 3. ita &longs;int 4. ad <lb/>2. &longs;i igitur argumentemur &longs;ic, vt 6. ad 3. ita 4. ad 2. ergo al<lb/>ternatim erit, vt 6. ad 4. ita 3. ad 2. &longs;iue dixerimus, vt pri<lb/>mum ad &longs;ecundum, ita tertium ad quartum, igitur alterna<lb/>tim erit, vt primum ad tertium, ita &longs;ecundum ad quartum: valebit con&longs;e<lb/>quentia; quæ quidem probatur deinde propo&longs;itione 16. quinti de magnitu<lb/>dinibus, hoc e&longs;t in vniuer&longs;um de lineis, &longs;uperficiebus, & &longs;olidis. </s>

<s>quando igi<lb/>tur Ari&longs;t. </s>

<s>quando igi<lb/>tur Ari&longs;t.

<s>ait, mon&longs;tramus proportionale, ide&longs;t, qua&longs;uis quatuor quantita<lb/>tes proportionales, habere hanc proprietatem, vt &longs;int etiam alternatim <lb/>proportionales, & non mon&longs;tramus vnica demon&longs;tratione de omni quouis <lb/>proportionali, &longs;ed &longs;eparatim de magnitudinibus in 16. quinti, de numeris <lb/>in 13. &longs;eptimi, & &longs;eor&longs;um de temporibus in a&longs;tronomia, vel phy&longs;ica; hoc <lb/>modo non o&longs;tendimus vniuer&longs;aliter de primo &longs;ubiecto, quia talis affectio <lb/>conuenit &longs;ingulis, non vt numeri, aut ma gnitudines, aut tempora &longs;unt, &longs;ed <lb/>&longs;ecundum quandam naturam illis omnibus communem, cui primò illa pa&longs;<lb/>&longs;io debetur; quæ quidem natura communis nomine caret, & propterea e&longs;t <lb/>cau&longs;a erroris.</s>

ait, mon&longs;tramus proportionale, ide&longs;t, qua&longs;uis quatuor quantita<lb/>tes proportionales, habere hanc proprietatem, vt &longs;int etiam alternatim <lb/>proportionales, & non mon&longs;tramus vnica demon&longs;tratione de omni quouis <lb/>proportionali, &longs;ed &longs;eparatim de magnitudinibus in 16. quinti, de numeris <lb/>in 13. &longs;eptimi, & &longs;eor&longs;um de temporibus in a&longs;tronomia, vel phy&longs;ica; hoc <lb/>modo non o&longs;tendimus vniuer&longs;aliter de primo &longs;ubiecto, quia talis affectio <lb/>conuenit &longs;ingulis, non vt numeri, aut ma gnitudines, aut tempora &longs;unt, &longs;ed <lb/>&longs;ecundum quandam naturam illis omnibus communem, cui primò illa pa&longs;<lb/>&longs;io debetur; quæ quidem natura communis nomine caret, & propterea e&longs;t <lb/>cau&longs;a erroris.</s>

Line 2870

<s>hoc autem e&longs;&longs;e exemplum primi erroris manife&longs;tè conuincitnr, <lb/>tum ex verbis illis, quando nihil &longs;it &longs;uperius, præter &longs;ingulare, tum ex hu<lb/>ius textus verbis illis <emph type="italics"/>(Singulum triangulum)<emph.end type="italics"/> & ex illis <emph type="italics"/>(Ni&longs;i &longs;ecundum nume<lb/>rum)<emph.end type="italics"/> ide&longs;t, ni&longs;i de vno, quod &longs;it vnum numero. </s>

<s>propterea nos de &longs;in gulari <lb/>triangulo omi&longs;&longs;a Zabarellæ &longs;ententia explicauimus tandem in confirma<lb/>tionem no&longs;træ expo&longs;itionis in hæc tria errata illud non omittendum, &longs;atiu<gap/><lb/>e&longs;&longs;e dicere, Ari&longs;t. </s>

<s>attuli&longs;&longs;e pro tribus erratis tria exempla ordine retrogra<lb/>do, quàm, quod facit Zabarella, primum e&longs;&longs;e pro tertio, &longs;ecundum pro pri<lb/>mo, tertium verò pro &longs;ecundo; eo enim modo, Ari&longs;t. </s>

attuli&longs;&longs;e pro tribus erratis tria exempla ordine retrogra<lb/>do, quàm, quod facit Zabarella, primum e&longs;&longs;e pro tertio, &longs;ecundum pro pri<lb/>mo, tertium verò pro &longs;ecundo; eo enim modo, Ari&longs;t.

<s>confu&longs;ionem nulla ra<lb/>tione, imò contra omnem rationem imponimus.</s>

confu&longs;ionem nulla ra<lb/>tione, imò contra omnem rationem imponimus.</s>

Line 2898

<s>Ibidem <emph type="italics"/>(Propter hoc Geometriæ non licet mon&longs;trare, quod contrariorum vna <lb/>e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus)<emph.end type="italics"/> quo ad verba illa, duo cubi cubus<gap/><lb/>quæ ad nos pertinent, vult Ari&longs;t. </s>

<s>docere<gap/>, quod non debet Geometra o&longs;ten<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometricè o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem. </s>

docere<gap/>, quod non debet Geometra o&longs;ten<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometricè o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem. </s>

<s>&longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>multiplicauerit, productus numerus erit pariter cubus. </s>

Line 2970

<s>In codem textu <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus, non &longs;ecundum accidens, quando <lb/>&longs;ecundum illud cogno&longs;camus, &longs;ecundum quod ine&longs;t ex principijs illius, &longs;ecundam <lb/>quod illud; vt duobus rectis æquales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/><pb pagenum="55"/><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, quæ non <lb/>ex communibus, vt præcedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>affectionem de &longs;ubiecto proprio. </s>

<s>E&longs;t autem illud exemplum toties decan<lb/>tatum de triangulo habente tres angulos æquales duobus rectis angulis; id<lb/>circo operæpretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli<lb/>dis, quæ i&longs;tud ex proprijs principijs demon&longs;trat, & quam hoc loco Ari&longs;to<lb/>teles innuit, hoc enim modo ip&longs;ius Ari&longs;t. </s>

<s>mentem probè penetrare poteri<lb/><figure id="fig27"></figure><lb/>mus. </s>

mentem probè penetrare poteri<lb/><figure id="fig27"></figure><lb/>mus. </s>

<s>&longs;it ergo <expan abbr="triãgulum">triangulum</expan> A B C. </s>

Line 3000

<s>Hinc videas eos magnopere decipi, qui pu<lb/>tant, hanc demon&longs;trationem e&longs;&longs;e per extrin&longs;eca, eò quod ad demon&longs;tran<lb/>dum producatur linea B C, in D, putantes lineam illam productam C D, <lb/>e&longs;&longs;e demon&longs;trationis medium; lineæ <expan abbr="namq;">namque</expan> huiu&longs;modi, quæ in demon&longs;tra<lb/>tionibus geometricis con&longs;truuntur, nunquam &longs;unt media propria demon<lb/>&longs;trationum, &longs;ed tantummodo a&longs;&longs;umuntur ad probandum medium iam ex<lb/>cogitatum e&longs;&longs;e veram cau&longs;am conclu&longs;ionis. </s>

<s>Hinc etiam manife&longs;tè colligas <pb pagenum="56"/>Mathematicas facultates habere demon&longs;trationes perfecti&longs;&longs;imas, quod <lb/>ageometreti negare &longs;olent, &longs;ed audacter aiunt exempla Ari&longs;t. </s>

<s>non e&longs;&longs;e vera: <lb/><expan abbr="neq;">neque</expan> requiri veritatem exemplorum; in <expan abbr="quor&utilde;">quorum</expan> <expan abbr="vtroq;">vtroque</expan> peccant, nam dictum <lb/>illud v&longs;urpari &longs;olet, & debet de exemplis moralibus. </s>

non e&longs;&longs;e vera: <lb/><expan abbr="neq;">neque</expan> requiri veritatem exemplorum; in <expan abbr="quor&utilde;">quorum</expan> <expan abbr="vtroq;">vtroque</expan> peccant, nam dictum <lb/>illud v&longs;urpari &longs;olet, & debet de exemplis moralibus. </s>

<s>at vero requiri confor<lb/>mitatem exemplorum cum regulis traditis, nemo &longs;anæ mentis dubitabit. <lb/></s>

Line 3014

<s>narratur ab <lb/>Ari&longs;t. </s>

<s>narratur ab <lb/>Ari&longs;t.

<s>de quodam filio, qui patrem crudeliter traxerat, qui po&longs;tea grandior <lb/>factus, cum filium procrea&longs;&longs;et, ab eodem pariter raptatus e&longs;t ip&longs;e, v&longs;que ad <lb/>eundem locum, quo ip&longs;e patrem &longs;uum impiè raptauerat. </s>

de quodam filio, qui patrem crudeliter traxerat, qui po&longs;tea grandior <lb/>factus, cum filium procrea&longs;&longs;et, ab eodem pariter raptatus e&longs;t ip&longs;e, v&longs;que ad <lb/>eundem locum, quo ip&longs;e patrem &longs;uum impiè raptauerat. </s>

<s>non e&longs;t nece&longs;&longs;e, ta<lb/>lem extiti&longs;&longs;e filium, <expan abbr="neq;">neque</expan> patrem. </s>

Line 3026

<s>re<lb/>quiritur igitur &longs;emper in omni exemplo conformitas cum eo, quod doce<lb/>tur; in moralibus tamen non &longs;emper requiritur veritas, vti diximus; Alij <lb/>verò dicunt non requiri in exemplis determinatam veritatem, &longs;ed &longs;atis e&longs;&longs;e, <lb/>&longs;i exemplum verum &longs;it &longs;ecundum opinionem aliquorum: <expan abbr="quor&utilde;">quorum</expan> &longs;ententiam <lb/>non improbamus. </s>

<s>Exempla igitur ab Ari&longs;t. </s>

<s>Exempla igitur ab Ari&longs;t.

<s>pa&longs;&longs;im ex mathem aticis allata, <lb/>congrua, <expan abbr="conformia&qacute;">conformiaque</expan>; omninò &longs;unt ip&longs;ius doctrinæ, aliter ip&longs;um perpetuò <lb/>mentientem facimus. </s>

pa&longs;&longs;im ex mathem aticis allata, <lb/>congrua, <expan abbr="conformia&qacute;">conformiaque</expan>; omninò &longs;unt ip&longs;ius doctrinæ, aliter ip&longs;um perpetuò <lb/>mentientem facimus. </s>

<s>Po&longs;tremò illud etiam e&longs;t aduertendum, fortè Ari&longs;t. </s>

<s>Po&longs;tremò illud etiam e&longs;t aduertendum, fortè Ari&longs;t.

<s>in <lb/>præ&longs;enti textu &longs;pecta&longs;&longs;e <expan abbr="nõ">non</expan> ad hanc Euclidianam demon&longs;trationem, &longs;ed po<lb/>tius ad Pithagoricam. </s>

in <lb/>præ&longs;enti textu &longs;pecta&longs;&longs;e <expan abbr="nõ">non</expan> ad hanc Euclidianam demon&longs;trationem, &longs;ed po<lb/>tius ad Pithagoricam. </s>

<s>Pithagorei enim eam aliter, quamuis per idem me<lb/>dium, &longs;cilicet à cau&longs;a materiali, demon&longs;trabant; con&longs;truebant enim aliter, <lb/><expan abbr="neq;">neque</expan> vlla vtebantur diui&longs;ione. </s>

Line 3056

<s>Ibidem <emph type="italics"/>(Demon&longs;tratio autem non computatur in aliud genus; m&longs;i, vt dictum <lb/>e&longs;t geometricæ demon&longs;trationes in Per&longs;pectiuas, aut Mcchamcas, & arithmeticæ in <lb/>harmonicas)<emph.end type="italics"/> exempla &longs;ubalternationis Per&longs;pectiuæ, & Mu&longs;icæ in tex. </s>

<s>20. at<lb/>tulimus; nunc Mechanicæ &longs;ubalternationis, quam hic Ari&longs;t. </s>

<s>20. at<lb/>tulimus; nunc Mechanicæ &longs;ubalternationis, quam hic Ari&longs;t.

<s>in&longs;inuat, exem<lb/>plum &longs;it illud, quod Archimedes prop. </s>

in&longs;inuat, exem<lb/>plum &longs;it illud, quod Archimedes prop. </s>

<s>14. primi Aequep. </s>

Line 3090

<s>Ibidem <emph type="italics"/>(Geometrica verò quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/>verbum, irrationale, non videtur Ari&longs;t. </s>

<s>Ibidem <emph type="italics"/>(Geometrica verò quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/>verbum, irrationale, non videtur Ari&longs;t.

<s>intellexi&longs;&longs;e proprietatem illam duo<lb/>rum linearum incommen&longs;urabilium longitudine, & potentia, quia v&longs;us fui&longs;<lb/>&longs;et verbo, <foreign lang="greek">a/rrpton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio<lb/>ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latinè redditur improportionale.</s>

intellexi&longs;&longs;e proprietatem illam duo<lb/>rum linearum incommen&longs;urabilium longitudine, & potentia, quia v&longs;us fui&longs;<lb/>&longs;et verbo, <foreign lang="greek">a/rrpton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio<lb/>ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latinè redditur improportionale.</s>

Line 3106

<s>Ibidem <emph type="italics"/>(Et Astrologia &longs;imiliter)<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t. </s>

<s>Ibidem <emph type="italics"/>(Et Astrologia &longs;imiliter)<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t.

<s>non iu<lb/>diciariam, quamuis à recentioribus hoc nomine vocetur, &longs;ed quam hodie <lb/>dicunt A&longs;tronomiam, <expan abbr="ait&qacute;">aitque</expan>; ip&longs;am con&longs;iderare quantitatem, figuram, mo<lb/>tum, & locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt C&oelig;li, <lb/>& Elementa.</s>

non iu<lb/>diciariam, quamuis à recentioribus hoc nomine vocetur, &longs;ed quam hodie <lb/>dicunt A&longs;tronomiam, <expan abbr="ait&qacute;">aitque</expan>; ip&longs;am con&longs;iderare quantitatem, figuram, mo<lb/>tum, & locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt C&oelig;li, <lb/>& Elementa.</s>

Line 3270

<s>alicuius effectus in Per&longs;pectiua cau&longs;a inqui<lb/>ritur, & inuenitur ope Geometriæ, cuiilla &longs;ubiacet. </s>

<s>Hic obiter notandum, <lb/>Ari&longs;t. </s>

<s>Hic obiter notandum, <lb/>Ari&longs;t.

<s>fateri manife&longs;tè Mathematicas &longs;ubalternatas, &longs;eu medias o&longs;tendere <lb/>per cau&longs;as, quas &longs;ubalternantium ope perue&longs;tigant.</s>

fateri manife&longs;tè Mathematicas &longs;ubalternatas, &longs;eu medias o&longs;tendere <lb/>per cau&longs;as, quas &longs;ubalternantium ope perue&longs;tigant.</s>

Line 3318

<s>igitur interual<lb/>lum i&longs;tud minimum dictum e&longs;t die&longs;is, quod &longs;it quædam diui&longs;io, &longs;eu &longs;egmen<lb/>turn Toni (<emph type="italics"/>Quemadmodum in pondere mina<emph.end type="italics"/>) qui de ponderibus antiquis tra<lb/>ctant, a&longs;&longs;erunt, Minam fui&longs;&longs;e maiorem libra per &longs;emunciam, æquipondera<lb/>bat enim centum drachmis: quæ refragantur huic loco. </s>

<s>&longs;ed fortè <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/>Ari&longs;t. </s>

<s>&longs;ed fortè <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/>Ari&longs;t.

<s>con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>principium, cum &longs;ex millia minarum in Attico talento continerentur.</s><figure></figure>

con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>principium, cum &longs;ex millia minarum in Attico talento continerentur.</s><figure></figure>

Line 3366

<s>Ex quo fit, vt an<lb/>guli externi cuiu &longs;uis figuræ &longs;int æquales angulis omnibus externis alterius <lb/>cuiu&longs;libet figuræ. </s>

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

<s>Ari&longs;t.

<s>igitur inquit, quando cogno&longs;cimus, quod quatuor <lb/>angulis rectis &longs;unt æquales exteriores omnes anguli alicuius figuræ, quo<lb/>niam figura illa e&longs;t triangulum &longs;calenum, adhuc talis cognitio e&longs;t defecti<lb/>ua, quia non illi competit illa pa&longs;&longs;io, quia &longs;it triangulum &longs;calenum, neque <lb/>competit &longs;caleno, quia &longs;it triangulum; &longs;ed his omnibus competit, quia &longs;unt <lb/>figuræ rectilineæ, cui hæc proprietas ine&longs;t primo, & vniuer&longs;aliter: qui igi<lb/>tur &longs;cit, &longs;calenum habere prædictam affectionem, ex eo, quod &longs;it figura re<lb/>ctilinea, perfectius &longs;cit, quia nihil amplius quæri pote&longs;t, quia illa figura re<lb/>ctilinea illud vniuer&longs;ale e&longs;t, cui primo competit; reliquis autem per illam. <lb/></s>

igitur inquit, quando cogno&longs;cimus, quod quatuor <lb/>angulis rectis &longs;unt æquales exteriores omnes anguli alicuius figuræ, quo<lb/>niam figura illa e&longs;t triangulum &longs;calenum, adhuc talis cognitio e&longs;t defecti<lb/>ua, quia non illi competit illa pa&longs;&longs;io, quia &longs;it triangulum &longs;calenum, neque <lb/>competit &longs;caleno, quia &longs;it triangulum; &longs;ed his omnibus competit, quia &longs;unt <lb/>figuræ rectilineæ, cui hæc proprietas ine&longs;t primo, & vniuer&longs;aliter: qui igi<lb/>tur &longs;cit, &longs;calenum habere prædictam affectionem, ex eo, quod &longs;it figura re<lb/>ctilinea, perfectius &longs;cit, quia nihil amplius quæri pote&longs;t, quia illa figura re<lb/>ctilinea illud vniuer&longs;ale e&longs;t, cui primo competit; reliquis autem per illam. <lb/></s>

<s>qui igitur vniuer&longs;ale &longs;cit, perfectius &longs;cit; quod volebat Ari&longs;t. </s>

<s>qui igitur vniuer&longs;ale &longs;cit, perfectius &longs;cit; quod volebat Ari&longs;t.

<s>demon&longs;trare.</s>

demon&longs;trare.</s>

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<s>vt in appo&longs;ita figura cer<lb/>nere facile e&longs;t; in qua radij à Sole <lb/>manentes, &longs;phæram vitream perua<pb pagenum="63"/>dunt, <expan abbr="atq;">atque</expan> in exitu ita refraguntur, vt ad A, punctum coaceruati, ibi po&longs;<lb/>&longs;int, &longs;i quid combu&longs;tibile occurrat, comburere. </s>

<s>Si igitur, inquit Ari&longs;t. </s>

<s>Si igitur, inquit Ari&longs;t.

<s>vide<lb/>remus illos radios &longs;ic permeare, & refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro<lb/>pter quid incendant.<lb/><arrow.to.target n="marg61"></arrow.to.target></s>

vide<lb/>remus illos radios &longs;ic permeare, & refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro<lb/>pter quid incendant.<lb/><arrow.to.target n="marg61"></arrow.to.target></s>

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<s>1. Priorum &longs;ecto 1. cap. </s>

<s>23. ait igitur Ari&longs;t. </s>

<s>23. ait igitur Ari&longs;t.

<s>ab&longs;urdum e&longs;&longs;e opinari dia<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;tæ, &longs;eu lateri eiu&longs;dem quadrati, reli<lb/>qua &longs;unt Logica.</s>

ab&longs;urdum e&longs;&longs;e opinari dia<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;tæ, &longs;eu lateri eiu&longs;dem quadrati, reli<lb/>qua &longs;unt Logica.</s>

<s><emph type="italics"/>Ex Secundo Posteriorum.<emph.end type="italics"/></s>

Line 3482

<s>Ibidem <emph type="italics"/>(Quid e&longs;t con&longs;onantia? </s>

<s>ratio numerorum in acuto, & graui, &c)<emph.end type="italics"/> tan<lb/>git breuiter Ari&longs;t. </s>

<s>ratio numerorum in acuto, & graui, &c)<emph.end type="italics"/> tan<lb/>git breuiter Ari&longs;t.

<s>cau&longs;am formalem con&longs;onantiæ, & con&longs;equenter defini<lb/>tionem ip&longs;ius. </s>

cau&longs;am formalem con&longs;onantiæ, & con&longs;equenter defini<lb/>tionem ip&longs;ius. </s>

<s>definiunt igitur Mu&longs;ici con&longs;onantiam hoc modo; Con&longs;onan<lb/>tia e&longs;t compo&longs;itio &longs;oni grauis, & acuti, quæ &longs;uauiter auribus accidit; & quo<lb/>rum &longs;onorum proportio ad inuicem &longs;it &longs;icuti proportio numerorum, qui <lb/>quaternario includuntur: vt e&longs;t proportio 2. ad 1. vel 3. ad 1. vel 4. ad 1. <lb/>vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs;eunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64"/>ex <expan abbr="quinq;">quinque</expan> prædictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnue <lb/>tantum &longs;onus efficiatur; &longs;onus ille erit concordans, & auribus gratus. </s>

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<s>vbi ip&longs;e o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum. </s>

<s>Vbi aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t. </s>

<s>Vbi aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t.

<s>cui a&longs;cripta e&longs;t figura &longs;imilis huic no&longs;træ; <lb/>in editione Clauiana. </s>

cui a&longs;cripta e&longs;t figura &longs;imilis huic no&longs;træ; <lb/>in editione Clauiana. </s>

<s>quod fortè non benè aduertens Iacobus Zabarella, <lb/>alioquin in his &longs;atis oculatus incidit in errorem, dicens, &longs;e nullo pacto vi<lb/>dere medium Euclidianæ demon&longs;trationis e&longs;&longs;e cau&longs;am materialem; quod <lb/>tamen nos mox aperiemus. </s>

<s>per angulum in &longs;emicirculo intelligas eum, qui <lb/>fit à lineis ductis ab extremitatibus diametri, & &longs;imul in quoduis punctum <lb/><figure id="fig30"></figure><lb/>circumferentiæ coeuntibus, vt in figura <lb/>præ&longs;enti vides lineas A C, B C, ad C, pun<lb/>ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/>A C B, qui dicitur angulus in &longs;emicircu<lb/>lo, quia de&longs;criptus e&longs;t in &longs;emicirculo A<lb/>C B. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;anè mirabilis hæc &longs;emicirculi <lb/>proprietas, cum <expan abbr="vbicunq;">vbicunque</expan> punctum C, in <lb/>periphæria &longs;umptum fuerit, &longs;emper ta<lb/>men angulus A C B, fiat rectus. </s>

<s>quod Euclides eodem pror&longs;us medio, quod <lb/>Ari&longs;t. </s>

<s>quod Euclides eodem pror&longs;us medio, quod <lb/>Ari&longs;t.

<s>hic innuit, hoc modo demon&longs;trat. </s>

hic innuit, hoc modo demon&longs;trat. </s>

<s>ducta enim recta D C, à centro D, <lb/>ad punctum C, exurgunt duo l&longs;o&longs;celia triangula A D C, C D B, ergo per <lb/>5. primi, anguli D C A, D A C, &longs;unt æquales: pariter anguli D C B, D B C, <lb/>æquales &longs;unt. </s>

Line 3584

<s>Sequitur igitur, angulum A C B, in &longs;emicirculo e&longs;&longs;e dimidium duorum re<lb/>ctorum; & quia omnes recti &longs;unt æquales, &longs;equitur dimidium duorum re<lb/>ctorum, nihil aliud e&longs;&longs;e, quam vnum rectum angulum, ergo angulus in &longs;e<lb/>micirculo, cum &longs;it &longs;emi&longs;&longs;is duorum <expan abbr="rector&utilde;">rectorum</expan>, erit vnus rectus angules; quod <lb/>erat probandum. </s>

<s>ex quibus vides medium illud, quod Ari&longs;t. </s>

<s>ex quibus vides medium illud, quod Ari&longs;t.

<s>a&longs;&longs;ump&longs;it, e&longs;&longs;e <lb/>omnino idem cum eo, quo Euclides vtitur, &longs;cilicet, e&longs;&longs;e dimidium duorum <lb/>rectorum, & propterea e&longs;&longs;e rectum: quod etiam medium in toto demon<lb/>&longs;trationis decur&longs;u e&longs;t vltimum, & principale, quod proximè conclu&longs;ionem <lb/>attingit, & propterea dici meretur e&longs;&longs;e medium huius demon&longs;trationis. <lb/></s>

a&longs;&longs;ump&longs;it, e&longs;&longs;e <lb/>omnino idem cum eo, quo Euclides vtitur, &longs;cilicet, e&longs;&longs;e dimidium duorum <lb/>rectorum, & propterea e&longs;&longs;e rectum: quod etiam medium in toto demon<lb/>&longs;trationis decur&longs;u e&longs;t vltimum, & principale, quod proximè conclu&longs;ionem <lb/>attingit, & propterea dici meretur e&longs;&longs;e medium huius demon&longs;trationis. <lb/></s>

<s>Cæterum, quod medium i&longs;tud &longs;it in genere cau&longs;æ materialis, patet ex co, <lb/>quod e&longs;t, e&longs;&longs;e dimidium; nam e&longs;&longs;e dimidium, vel e&longs;&longs;e tertiam partem, & &longs;i<lb/>milia, nihil aliud e&longs;t, quam e&longs;&longs;e partem; e&longs;&longs;e autem partem e&longs;t e&longs;&longs;e materiam <lb/>totius, etiam ex &longs;ententia ip&longs;ius Ari&longs;t. </s>

<s>ex hac præterea materia conflatur <lb/>definitio minoris extremi, vel &longs;ubiecti; d<gap/>m dicitur, angulus in &longs;emicircu<lb/>lo e&longs;t dimidium duorum rectorum. </s>

ex hac præterea materia conflatur <lb/>definitio minoris extremi, vel &longs;ubiecti; d<gap/>m dicitur, angulus in &longs;emicircu<lb/>lo e&longs;t dimidium duorum rectorum. </s>

<s>&longs;yllogi&longs;mus enim reducitur tandem ad <pb pagenum="66"/>hanc formam, dimidium duorum rectorum e&longs;t rectus, angulus in &longs;emicir<lb/>culo e&longs;t dimidium duorum <expan abbr="rector&utilde;">rectorum</expan>, ergo angulus in &longs;emicirculo e&longs;t rectus. <lb/></s>

Line 3678

<s>13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;tæ incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>quæ de hac re &longs;crip&longs;i lib. </s>

<s>Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;tæ incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>quæ de hac re &longs;crip&longs;i lib. </s>

<s>1. Priorum &longs;ecto 1. cap. </s>

Line 3730

<s>quia in vno continebantur plures toni, vt in Diato<lb/>nico; in alio plures die&longs;es, vt in Enharmonico; in tertio verò plura &longs;emito<lb/>nia, vt in Chromatico: quæ vox deducitur à chroma, græco, quod latinis <lb/>e&longs;t color; quare Chromaticum latinè redditur coloratum. </s>

<s>Hic e&longs;t igitur <lb/>color ille, quem hic Ari&longs;t. </s>

<s>Hic e&longs;t igitur <lb/>color ille, quem hic Ari&longs;t.

<s>innuit. </s>

innuit. </s>

<s>quod genus for&longs;itan à calore denomina<lb/>batur, quòd ip&longs;ius notæ mu&longs;icales e&longs;&longs;ent coloratæ, vt hoc modo ab alijs ge<lb/>neribus digno&longs;eeretur<gap/> quam con&longs;uetudinem exi&longs;timat Zarlinus cap. </s>

Line 3744

<s>1. loco 10. (<emph type="italics"/>Si quis in&longs;ecabiles ponens lineas<emph.end type="italics"/>) nonnulli antiquorum <lb/>Philo&longs;ophorum putarunt omnia ex indiui&longs;ibilibus componi, vt Demo<lb/>critus, & Leucippus, & propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam ade ò paruis, quæ omnino e&longs;ient in&longs;ecabiles, &longs;eu indiui&longs;ibiles: de <lb/>quibus plura in libello de line is in&longs;ecabilibus.</s>

<s>Cap. 1. loco 10. (<emph type="italics"/>Si quis in&longs;ecabiles ponens lineas<emph.end type="italics"/>) nonnulli antiquorum <lb/>Philo&longs;ophorum putarunt omnia ex indiui&longs;ibilibus componi, vt Demo<lb/>critus, & Leucippus, & propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam ade ò paruis, quæ omnino e&longs;ient in&longs;ecabiles, &longs;eu indiui&longs;ibiles: de <lb/>quibus plura in libello de line is in&longs;ecabilibus.</s>

<s><emph type="italics"/>Libro Sexio.<emph.end type="italics"/></s>

Line 3754

<s>2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudmem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem. </s>

<s>Cap. 2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudmem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem. </s>

<s>in<lb/>ter quas d<gap/>f<gap/>nitio lineæ e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">cademque</expan>; cum hac Ari&longs;totelis.</s>

Line 3766

<s>2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis quædam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt & quoniam, quæ ad latus &longs;e<lb/>cat planum linea, &longs;imiliter diuidit & lineam, & locum: definitione autem dicta, <lb/>fi <gap/>m man fe&longs;tu<gap/>t&longs;t, quod dicitur, nam eandem ablationem habent lota, & <gap/>inea, <lb/><gap/>se latus planæ figuræ, est autem definitio eiu&longs;dem proportionis hæc<emph.end type="italics"/>) mendosè <lb/>lugitur à nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis hæc<emph.end type="italics"/>) quos puto de<lb/>ceptos ab æquiuoco <foreign lang="greek">lsgous</foreign> quod & orationem, & rationem, &longs;iue proportio<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani<lb/>fe&longs;tat. </s>

<s>Cap. 2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis quædam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt & quoniam, quæ ad latus &longs;e<lb/>cat planum linea, &longs;imiliter diuidit & lineam, & locum: definitione autem dicta, <lb/>fi <gap/>m man fe&longs;tu<gap/>t&longs;t, quod dicitur, nam eandem ablationem habent lota, & <gap/>inea, <lb/><gap/>se latus planæ figuræ, est autem definitio eiu&longs;dem proportionis hæc<emph.end type="italics"/>) mendosè <lb/>lugitur à nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis hæc<emph.end type="italics"/>) quos puto de<lb/>ceptos ab æquiuoco <foreign lang="greek">lsgous</foreign> quod & orationem, & rationem, &longs;iue proportio<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani<lb/>fe&longs;tat. </s>

<s>Notandum po&longs;tea cum Alexandro (quod & &longs;uperius alias commo<lb/>nui in cap. </s>

<s>de Priori, & alibi) per verbum (De&longs;cribi) fignificari hoc loco <lb/>geometricè demon&longs;trare, quoniam Geometræ <expan abbr="nõ">non</expan> ni&longs;i adhibit is de&longs;criptio<lb/>nibus, &longs;<gap/>u figutis demon&longs;trant. </s>

<s>Vult autem Ari&longs;t. </s>

<s>Vult autem Ari&longs;t.

<s>exemplo mathematico <lb/>o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <gap/> <expan abbr="rgum&etilde;tari">rgumentari</expan>, ni&longs;i prius rectè a&longs;&longs;ignetur <pb pagenum="69"/>definitio illius rei, de qua di&longs;&longs;eritur. </s>

exemplo mathematico <lb/>o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <gap/> <expan abbr="rgum&etilde;tari">rgumentari</expan>, ni&longs;i prius rectè a&longs;&longs;ignetur <pb pagenum="69"/>definitio illius rei, de qua di&longs;&longs;eritur. </s>

<s>Porrò exemplum mathematicum hic <lb/>allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro<lb/>po&longs;itionem; &longs;i linea ducta fuerit æquidi&longs;tans lateri vnius plani trianguli, &longs;e<lb/>cabit & latera, & locum, ideft &longs;uperficiem illam triangularem &longs;imiliter, ide &longs;t <lb/><figure id="fig32"></figure><lb/>in eadem proportione, vt in triangulo A B C, <lb/>linea D E, parallela ba&longs;i B C, &longs;ecat latera A B, <lb/>& A C, in punctis D, & E, in eadem ratione, <lb/>in qua etiam fecat totum triangulum, ita vt <lb/>eadem &longs;it proportio lineæ A D, ad D B, & lineæ <lb/>A E, ad E C, quæ e&longs;t partium totalis trianguli <lb/>A B C, &longs;eilicet quæ e&longs;t partis A D E, ad partem <lb/>E D C, fiue ad partem D E B. quod con&longs;tat ex <lb/>&longs;ecunda 6. Elem. </s>

Line 3784

<s>Si quis <lb/>vellet hoc demon&longs;trare nondum præmi&longs;&longs;a defi<lb/>nitione eorum, quæ habent eandem rationem, &longs;iue nondum definitione al<lb/>lata quantitatum proportionalium, hic difficile id valeret o&longs;tendere: at ve<lb/>rò allata prins definitione quantitatum proportionalium facile demon&longs;tra<lb/>bit. </s>

<s>Subdit verò Ari&longs;t. </s>

<s>Subdit verò Ari&longs;t.

<s>dictam definitionem, dicens, tunc quantitates e&longs;&longs;e <lb/>proportionales, quando habent eandem ablationem, ide&longs;t, eandem diui&longs;io<lb/>nem, ide&longs;t, eadem diui&longs;io ne tantum proportionaliter de vna, quantum de <lb/>altera magnitudine re&longs;ecatur: Quemadmodum etiam Euclides loco cita<lb/>to probat, latera illius trianguli, & &longs;uperficiem e&longs;&longs;e &longs;imiliter diui&longs;a, ex quo <lb/>&longs;equitur e&longs;&longs;e proportionalia. </s>

dictam definitionem, dicens, tunc quantitates e&longs;&longs;e <lb/>proportionales, quando habent eandem ablationem, ide&longs;t, eandem diui&longs;io<lb/>nem, ide&longs;t, eadem diui&longs;io ne tantum proportionaliter de vna, quantum de <lb/>altera magnitudine re&longs;ecatur: Quemadmodum etiam Euclides loco cita<lb/>to probat, latera illius trianguli, & &longs;uperficiem e&longs;&longs;e &longs;imiliter diui&longs;a, ex quo <lb/>&longs;equitur e&longs;&longs;e proportionalia. </s>

<s>Porrò Euclides definit. </s>

Line 3802

<s>4. loco 86. <emph type="italics"/>(Tentandum autem, & ea, in quæ &longs;æpi&longs;&longs;imè incidunt di&longs;puta<lb/>tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer<lb/>citatum e&longs;&longs;e, & in numeris circa capitales promptè &longs;e habere, & multum refert ad <lb/>boc, & alium numerum cogno&longs;cere multiplicatum)<emph.end type="italics"/> Elementa vocabant antiqui <lb/>demon&longs;trationes faciliores, & &longs;impliciores, quales propriè &longs;unt omnes, quæ <lb/>&longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele<lb/>mentis ab&longs;tru&longs;iores, & difficiliores demon&longs;trationes deducebant. </s>

<s>Cap. 4. loco 86. <emph type="italics"/>(Tentandum autem, & ea, in quæ &longs;æpi&longs;&longs;imè incidunt di&longs;puta<lb/>tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer<lb/>citatum e&longs;&longs;e, & in numeris circa capitales promptè &longs;e habere, & multum refert ad <lb/>boc, & alium numerum cogno&longs;cere multiplicatum)<emph.end type="italics"/> Elementa vocabant antiqui <lb/>demon&longs;trationes faciliores, & &longs;impliciores, quales propriè &longs;unt omnes, quæ <lb/>&longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele<lb/>mentis ab&longs;tru&longs;iores, & difficiliores demon&longs;trationes deducebant. </s>

<s><expan abbr="atq;">atque</expan> hæc <lb/>e&longs;t ratio, cur Euclides &longs;uos libr<gap/>s elementa nuncupauerit. </s>

Line 3820

<s>10. <emph type="italics"/>(Nam p&longs;eudograpbiæ non contentio&longs;æ (&longs;ecundum enim ea, quæ <lb/>&longs;ub arte &longs;unt, captio&longs;æ &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra<lb/>phia circa verum, vt Hippocratis quadratura, quæ per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; & tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere æquale tentauerit, explicatum e&longs;t abundè in 2. Priorum cap. </s>

<s>Cap. 10. <emph type="italics"/>(Nam p&longs;eudograpbiæ non contentio&longs;æ (&longs;ecundum enim ea, quæ <lb/>&longs;ub arte &longs;unt, captio&longs;æ &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra<lb/>phia circa verum, vt Hippocratis quadratura, quæ per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; & tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere æquale tentauerit, explicatum e&longs;t abundè in 2. Priorum cap. </s>

<s>31. <lb/>& quo itidem modo Bry&longs;&longs;o lib. </s>

Line 3864

<s>Ad &longs;inem cap. <emph type="italics"/>(Aut vt Antiphon quadra<lb/>uit)<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon<lb/>tem in orbe quadrando, ac Hippocratem, <lb/>Ari&longs;t. </s>

<s>his verbis videtur &longs;ignificare, ide&longs;t, <lb/>ip&longs;um, quamuis ex proprijs Geometriæ, <lb/>fal&longs;is tamen ratiocinatum e&longs;&longs;e. </s>

his verbis videtur &longs;ignificare, ide&longs;t, <lb/>ip&longs;um, quamuis ex proprijs Geometriæ, <lb/>fal&longs;is tamen ratiocinatum e&longs;&longs;e. </s>

<s>Cæterum <lb/>Antiphontem in hunc modum orbem ad <lb/>quadrum redigere tenta&longs;&longs;e, tradit Simpli<lb/>cius. </s>

Line 3922

<s>20. (<emph type="italics"/>Geometria enim de phy&longs;ica linea con&longs;iderat, &longs;ed non quatenus <lb/>e&longs;t phy&longs;ici: Per&longs;pectiua autem ma<gap/> hematicam quidem imcam, &longs;ed non <lb/>quatenus phy&longs;ica e&longs;t<emph.end type="italics"/>) quamuis textus hic non pertineat ad Mathe<lb/>maticum, libuit tamen illum in ordin<gap/>m no&longs;trum recen&longs;ere, ope<lb/>ræpretium etenim e&longs;t ea, quæ in ip&longs;o continentur à nonnullis recentioribus <lb/>rectè intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab<lb/>&longs;tineant, ac tandem ex Ari&longs;t. </s>

<s>lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picuè videant. </s>

lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picuè videant. </s>

<s>cætera, quæ in præcedentibus locis Ari&longs;t. </s>

<s>cætera, quæ in præcedentibus locis Ari&longs;t.

<s>de Natura Ma<lb/>thematicarum habet, &longs;unt præter no&longs;trum in&longs;titutum.</s>

de Natura Ma<lb/>thematicarum habet, &longs;unt præter no&longs;trum in&longs;titutum.</s>

Line 3964

<s>deinde, quia <lb/>etiam græci in exemplo mathematico enodando, vel malè, vt Simplicius; <lb/>vel ob&longs;curè nimis, vt reliqui; Latini verò vel nihil, vel peius multò loquun<lb/>tur, ideò &longs;ic ego exponendum cen&longs;ui. </s>

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

<s>cum velit Ari&longs;t.

<s>o&longs;tendere nece&longs;&longs;ita<lb/>tem, quæ in &longs;cientijs inter præmi&longs;&longs;as, &longs;cu medium, & conclu&longs;ionem reperi<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos æqua<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap. </s>

o&longs;tendere nece&longs;&longs;ita<lb/>tem, quæ in &longs;cientijs inter præmi&longs;&longs;as, &longs;cu medium, & conclu&longs;ionem reperi<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos æqua<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap. </s>

<s>1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s>

<s>pro medio autem <lb/>huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/><emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/><figure id="fig33"></figure><lb/>A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, & pro<lb/>ducatur B C, in D; tunc triangulum A B C, <lb/>habere tres angulos, A, B, & A C B, æquales <lb/>duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>&longs;it perpendiculare (quod Ari&longs;t. </s>

<s>dicit, cum <expan abbr="re-ct&utilde;">re<lb/>ctum</expan> hoc &longs;it) erunt duo anguli deinceps A C B, <lb/>A C D, recti, ex definitione lineæ perpendicu<lb/>laris, cum ergo duo anguli A, & B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int æquales per <lb/>32. primi, & reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu<lb/>li, & angulus vnus lineæ perpendicularis, & ideò rectus; manife&longs;tè apparet, <lb/>tres angulos A, B, A C B, e&longs;&longs;e æquales nece&longs;&longs;ariò duobus rectis, ex po&longs;itio<lb/>ne illius recti, &longs;iue lateris perpendicularis, quia ex verò, verum nece&longs;&longs;ariò <lb/>&longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/>tres angulos æquales duobus rectis, nece&longs;&longs;ariò &longs;equitur illud e&longs;&longs;e rectum, <lb/>idelt latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/>&longs;equi pote&longs;t ex verò, & falsò. </s>

dicit, cum <expan abbr="re-ct&utilde;">re<lb/>ctum</expan> hoc &longs;it) erunt duo anguli deinceps A C B, <lb/>A C D, recti, ex definitione lineæ perpendicu<lb/>laris, cum ergo duo anguli A, & B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int æquales per <lb/>32. primi, & reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu<lb/>li, & angulus vnus lineæ perpendicularis, & ideò rectus; manife&longs;tè apparet, <lb/>tres angulos A, B, A C B, e&longs;&longs;e æquales nece&longs;&longs;ariò duobus rectis, ex po&longs;itio<lb/>ne illius recti, &longs;iue lateris perpendicularis, quia ex verò, verum nece&longs;&longs;ariò <lb/>&longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/>tres angulos æquales duobus rectis, nece&longs;&longs;ariò &longs;equitur illud e&longs;&longs;e rectum, <lb/>idelt latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/>&longs;equi pote&longs;t ex verò, & falsò. </s>

<s>valebit tamen hæc con&longs;e quen<lb/>tia, &longs;i triangulum non habet hanc proprietatem, ne<lb/>que illud rectum e&longs;t, ide&longs;t, <expan abbr="neq;">neque</expan> latus prædi<lb/>ctum crit <expan abbr="perp&etilde;diculare">perpendiculare</expan>, quia fal&longs;um <lb/>non, ni&longs;i exfal&longs;o &longs;equitur.</s><pb pagenum="74"/>

Line 3990

<s>de Motu in po&longs;t prædicamentis &longs;crip&longs;i de Gnomone, ad <lb/>&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu<lb/>meris Gnomones Arithmetici. </s>

<s>Pythagorici enim (à quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t. </s>

<s>Pythagorici enim (à quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t.

<s>numeros impares &longs;olos appellabant Gnomones, eò quod in for<lb/>mam normæ æquilateræ, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/><figure id="fig34"></figure><lb/>nimirum in ternario, quinario, &longs;eptenario, & &longs;ic de <lb/>reliquis imparibus. </s>

numeros impares &longs;olos appellabant Gnomones, eò quod in for<lb/>mam normæ æquilateræ, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/><figure id="fig34"></figure><lb/>nimirum in ternario, quinario, &longs;eptenario, & &longs;ic de <lb/>reliquis imparibus. </s>

<s>pares autem numeri, quia ne<lb/>queunt in figuram normæ æquilateræ di&longs;poni, cum <lb/>non habeant vnitatem pro angulo, & paria po&longs;tea la<lb/>tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di<lb/>&longs;ponatur &longs;ic <figure id="fig35"></figure> non refert Gnomonem, quia lateribus in&ecedil;qualibus con<lb/>&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="fig36"></figure> quia dee&longs;t huic figuræ angularis vnitas, quæ <lb/>illi nece&longs;iaria e&longs;t. </s>

Line 4144

<s>in qua quidem, quamuis duæ lineæ infinitæ &longs;upponantur, vna <lb/>ad alteram <expan abbr="tãtum">tantum</expan> partem in qua E: altera verò ad <expan abbr="vtramq;">vtramque</expan> partem <foreign lang="greek">b,</foreign> & B, <pb pagenum="77"/>non potuerunt tamen de&longs;cribi, ni&longs;i finitæ; appo&longs;itæ idcircò &longs;unt ad partes <lb/>illas, ad quas deberent e&longs;&longs;e infinitæ lineolæ quædam infinitatem indicantes. <lb/></s>

<s>debemus po&longs;tea, vt mentem Ari&longs;t. </s>

<s>debemus po&longs;tea, vt mentem Ari&longs;t.

<s>percipiamus concipere lineam A G E, <lb/>moueri circulariter facto centro in G. quæ quia infinita &longs;upponitur ad par<lb/>tem E, &longs;ecabit nece&longs;&longs;ariò alteram <expan abbr="vtrinq;">vtrinque</expan> infinitam <foreign lang="greek">b</foreign> B, <expan abbr="illam&qacute;">illamque</expan>; nece&longs;&longs;ariò <lb/>finito tempore percurret, finito enim tempore tota mundi circulatio per<lb/>agitur, &longs;patio videlicet viginti quatuor horarum. </s>

percipiamus concipere lineam A G E, <lb/>moueri circulariter facto centro in G. quæ quia infinita &longs;upponitur ad par<lb/>tem E, &longs;ecabit nece&longs;&longs;ariò alteram <expan abbr="vtrinq;">vtrinque</expan> infinitam <foreign lang="greek">b</foreign> B, <expan abbr="illam&qacute;">illamque</expan>; nece&longs;&longs;ariò <lb/>finito tempore percurret, finito enim tempore tota mundi circulatio per<lb/>agitur, &longs;patio videlicet viginti quatuor horarum. </s>

<s>ex quo Ari&longs;t. </s>

<s>ex quo Ari&longs;t.

<s>infert mun<lb/>dum non po&longs;&longs;e e&longs;&longs;e infinitæ magnitudinis; quia &longs;i mundus e&longs;&longs;et infinitus; &. <lb/></s>

infert mun<lb/>dum non po&longs;&longs;e e&longs;&longs;e infinitæ magnitudinis; quia &longs;i mundus e&longs;&longs;et infinitus; &. <lb/></s>

<s>duæ lineæ infinitæ, quales &longs;unt prædictæ in ip&longs;o, <expan abbr="atq;">atque</expan> cum ip&longs;o moueri alte<lb/>ra earum A E, intelligatur, alteram <foreign lang="greek">b</foreign> B, manentem in tempore finito, ide&longs;t, <lb/>in diurna conuer&longs;ione pertran&longs;ibit: fieri autem nequit, vt infinita magni<lb/>tudo finito tempore percurratur; quare dicendum e&longs;t, mundum e&longs;&longs;e finita <lb/>magnitudine præditum.</s>

Line 4184

<s>&longs;i in triangulo pag. </s>

<s>73. producto late<lb/>re A C, in D. &longs;i &longs;upponatur externus angulus B C D, non e&longs;&longs;e æqualis duobus <lb/>internis, & oppofitis A, & B, nunquam poterimus eo modo, quo Euclides, <lb/>demon&longs;trare pa&longs;&longs;ionem prædictam de triangulo A B C. huiu&longs;modi impo&longs;&longs;i<lb/>bile, cuius oppo&longs;itum non &longs;olum po&longs;&longs;ibile, &longs;ed etiam nece&longs;&longs;arium e&longs;t, vocat <lb/>Ari&longs;t. </s>

<s>impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo<lb/>dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an<lb/>gulos æquales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up<lb/>po&longs;itione, impo&longs;&longs;ibile oua&longs;it.</s>

impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo<lb/>dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an<lb/>gulos æquales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up<lb/>po&longs;itione, impo&longs;&longs;ibile oua&longs;it.</s>

Line 4272

<s>Verumtamen &longs;i circuli <lb/>ambo &longs;imul moueantur, maior circulus æquali tem<lb/>pore maius illud &longs;patium D E, & minor minus B C, <lb/>pertran&longs;ibit: idem igitur de c&oelig;le&longs;tibus orbibus di<lb/>cendum, qui quamuis omnes diurnum &longs;imul motum <lb/>ab&longs;oluunt, maiores tamen celerius conuertuntur: quo fit, vt &longs;tellæ maiori<lb/>bus circulis infixæ, <expan abbr="atq;">atque</expan> delatæ, maiori celeritate &longs;uos cur&longs;us peragant, ne<lb/>que oportet eas, dum mouentur c&oelig;lum di&longs;&longs;ecare, quod accideret, &longs;i pro<lb/>prio motu veluti pri&longs;ces per aquam progrederentur.</s>

<s>Hæc quidem Ari&longs;t. </s>

<s>Hæc quidem Ari&longs;t.

<s>con&longs;entanea ob&longs;eruationibus veterum A&longs;tronomo<lb/>rum; at verò illis no&longs;træ ætatis ob&longs;eruationes repugnant; præ&longs;ertim illæ, <lb/>quæ fiunt circa &longs;tellas errantes: ex quibus fatendum e&longs;&longs;e videtur, C&oelig;lum, <lb/>qua parte Planetas continet, liquidum e&longs;&longs;e, ac per illud Planetas proprio <lb/>motu, ceu pi&longs;ces in aqua progredi. </s>

con&longs;entanea ob&longs;eruationibus veterum A&longs;tronomo<lb/>rum; at verò illis no&longs;træ ætatis ob&longs;eruationes repugnant; præ&longs;ertim illæ, <lb/>quæ fiunt circa &longs;tellas errantes: ex quibus fatendum e&longs;&longs;e videtur, C&oelig;lum, <lb/>qua parte Planetas continet, liquidum e&longs;&longs;e, ac per illud Planetas proprio <lb/>motu, ceu pi&longs;ces in aqua progredi. </s>

<s>Tycho <expan abbr="namq;">namque</expan> Brahe, <expan abbr="alij&qacute;">alijque</expan>; plures exactè <lb/>demon&longs;trant Cometas in regione Planetarum e&longs;&longs;e, <expan abbr="eos&qacute;">eosque</expan>; motu quodam in <lb/>tran&longs;uer&longs;um moueri, quo nece&longs;&longs;ario C&ecedil;lú deberent perforare; ijdem o&longs;ten<lb/>dunt nonnullos Planetas, Martem præ&longs;ertim, ac Venerem modo &longs;upra So<lb/>lem, modo infra a&longs;cendere, & de&longs;cendere. </s>

Line 4294

<s>Dicit igi<lb/>tur ordinem c&oelig;lorum, ac &longs;yderum, item &longs;itum, & proportiones magnitu<lb/>dinum corundem, cum per naturalis &longs;cientiæ princip ia &longs;ciri nequeant, ex <lb/>rationibus A&longs;tronomorum petenda e&longs;&longs;e, apud quos i&longs;ta &longs;ufficienter <expan abbr="demon-&longs;tr&etilde;tur">demon<lb/>&longs;trentur</expan>. </s>

<s>& meritò quidem hæc dicuntur; po&longs;teriores enim ab Ari&longs;t. </s>

<s>& meritò quidem hæc dicuntur; po&longs;teriores enim ab Ari&longs;t.

<s>ordines, <lb/>&longs;itus, ac magnitudines tam c&oelig;lorum, quam &longs;yderum firmis rationibus, <expan abbr="atq;">atque</expan> <lb/>inuentu peracutis demon&longs;trarunt. </s>

ordines, <lb/>&longs;itus, ac magnitudines tam c&oelig;lorum, quam &longs;yderum firmis rationibus, <expan abbr="atq;">atque</expan> <lb/>inuentu peracutis demon&longs;trarunt. </s>

<s>quorum princeps fuit ptolæmeus; no&longs;tra <lb/>tamen ætate Tycho Brahe, qui certis ob&longs;eruationibus, quas maximo labo<lb/>re, ac &longs;umptu exantlauit, in nonnullis à Ptolæmeo, ac reliquis di&longs;&longs;entjt: &longs;tan<lb/>dum autem e&longs;&longs;e recentioribus ob&longs;eruationibus apud A&longs;tronomiæ peritos in <lb/>confe&longs;&longs;o e&longs;t.</s>

Line 4342

<s>In corporibus deinde irregularibus, etiam&longs;i <lb/>&longs;int vniformis ponderis, aliud tamen e&longs;&longs;e pote&longs;t centrum molis à <expan abbr="c&etilde;tro">centro</expan> gra<lb/>uitatis, vt in corpore oblongo, cuius alterum extremum &longs;it reliquis parti<lb/>bus multò maius, vti e&longs;t claua: vbi centrum molis erit in medio longitudi<lb/>nis clauæ; centrum verò grauitatis, erit propinquius capiti clauæ. </s>

<s>quando <lb/>igitur Ari&longs;t. </s>

<s>quando <lb/>igitur Ari&longs;t.

<s>ait, graue de&longs;cen&longs;urum, donec ip&longs;ius medium, &longs;iue centrum, <lb/>mundi centrum attingat; benè dicit, &longs;i de medio grauitatis intelligat; ma<lb/>lè autem &longs;i de medio molis. </s>

ait, graue de&longs;cen&longs;urum, donec ip&longs;ius medium, &longs;iue centrum, <lb/>mundi centrum attingat; benè dicit, &longs;i de medio grauitatis intelligat; ma<lb/>lè autem &longs;i de medio molis. </s>

<s>quia grauia omnia ratione centri grauitatis <lb/>ponderant, <expan abbr="neq;">neque</expan> manent; ni&longs;i ip&longs;um maneat: quare ni&longs;i ip&longs;um <expan abbr="attingãt">attingant</expan> cen<lb/>trum mundi &longs;emper grauitabunt, & mouebuntur. </s>

Line 4442

<s>ex quibus &longs;e<lb/>ctionibus tota &longs;phæra in octo partes diuiditur, quibus &longs;phæram componi <lb/>vult Ari&longs;toteles. </s>

<s>aduerte tamen hanc &longs;phæræ compo&longs;itionem nullo modo <lb/>habere partes actu, cum &longs;phæra &longs;it vnica &longs;implici &longs;uperficie terminata; &longs;ed <lb/>quæ tantum &longs;int à prædictis imaginatis circulis de&longs;ignatæ: at verò aliæ fi<lb/>guræ, quæ pluribus planis terminantur, vt cubus, octaedrum, & &longs;imilia, quæ <lb/>Ari&longs;t. </s>

<s>vocat rectiliheas, quia terminantur &longs;uperficiebus rectilineis actu di<lb/>&longs;tinctis ab inuicem ex natura &longs;ua, non per no&longs;tram de&longs;ignationem, ideò re<lb/>ctè dicuntur componi ex pyramidibus, v. </s>

vocat rectiliheas, quia terminantur &longs;uperficiebus rectilineis actu di<lb/>&longs;tinctis ab inuicem ex natura &longs;ua, non per no&longs;tram de&longs;ignationem, ideò re<lb/>ctè dicuntur componi ex pyramidibus, v. </s>

Line 4476

<s>primò quidem, quia accidit non repleri totum; nam in planis tres figuræ <lb/>videntur implere locum, Triangulus, Quadratum, & Sexangulus)<emph.end type="italics"/> per &longs;implicia <lb/>corpora intelligit quatuor elementa. </s>

<s>Vult enim probare quatuor elemen<lb/>ta non habere figuras illas mathematicas, quas illis Plato tribuebat, vt au<lb/>tem Ari&longs;t. </s>

<s>Vult enim probare quatuor elemen<lb/>ta non habere figuras illas mathematicas, quas illis Plato tribuebat, vt au<lb/>tem Ari&longs;t.

<s>rationem probè percipiamus, &longs;ciendum, quod implere totum, <lb/>&longs;iue locum, illæ figuræ dicuntur, quæ &longs;imul &longs;uis angulis in plano quopiam ad <lb/>vnum, <expan abbr="atq;">atque</expan> idem punctum vnitæ locum illum totum, qui cirea punctum il<lb/>lud con&longs;i&longs;tit, <expan abbr="cõtegunt">contegunt</expan>, ita vt nihil vacui inter ip&longs;as relinquatur. </s>

rationem probè percipiamus, &longs;ciendum, quod implere totum, <lb/>&longs;iue locum, illæ figuræ dicuntur, quæ &longs;imul &longs;uis angulis in plano quopiam ad <lb/>vnum, <expan abbr="atq;">atque</expan> idem punctum vnitæ locum illum totum, qui cirea punctum il<lb/>lud con&longs;i&longs;tit, <expan abbr="cõtegunt">contegunt</expan>, ita vt nihil vacui inter ip&longs;as relinquatur. </s>

<s>tales &longs;unt, <lb/>quibus fieri po&longs;&longs;unt pauimenta, oportet enim, vt &longs;imul vnitæ nihil vacui in <lb/>pauimento relinquant. </s>

Line 4538

<s>quia &longs;i liceret intelligere de irregularibus figuris, <lb/>infinitæ reperir entar figuræ tam planæ, quam &longs;olidæ, quæ vtrumque locum <lb/>complerent. </s>

<s>Aduertendum tandem Ari&longs;t. </s>

<s>Aduertendum tandem Ari&longs;t.

<s>videri loqui de repletione loci <lb/>&longs;olidi, quia tran&longs;it à planïs figuris ad &longs;olidas. </s>

videri loqui de repletione loci <lb/>&longs;olidi, quia tran&longs;it à planïs figuris ad &longs;olidas. </s>

<s>& quia &longs;i hæ duæ pyramis, & <lb/>cubus replent locum &longs;olummedo &longs;ecundum &longs;uas &longs;uperficies, quæ &longs;unt trian<lb/>gulum, & quadra<gap/>um, iam de his cum proximè ante dixi&longs;&longs;et, quid opus fui&longs;<lb/>&longs;et idem po&longs;t modum repetere. </s>

<s>ad hæc &longs;i in medium &longs;olida hæc duo profert, <lb/><expan abbr="ait&qacute;">aitque</expan>; ip&longs;a replere locum, intelligens, planum, profectò non loquitur forma<lb/>liter, ide&longs;t de ip&longs;is, vt &longs;oh da &longs;unt. </s>

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

<s>Quare Ari&longs;t.

<s>videretur &longs;ibi non con&longs;tare, <lb/>vel perperam exi&longs;tima&longs;&longs;e plura Tetraedra complere &longs;oliditatem. </s>

videretur &longs;ibi non con&longs;tare, <lb/>vel perperam exi&longs;tima&longs;&longs;e plura Tetraedra complere &longs;oliditatem. </s>

<s>deceptus <pb pagenum="86"/>fortè fuit Ari&longs;t. </s>

<s>deceptus <pb pagenum="86"/>fortè fuit Ari&longs;t.

<s>cò quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi<lb/>bus, verùm illæ non &longs;unt regulares, ide&longs;t <expan abbr="nõ">non</expan> &longs;unt Tetraedra, vt po&longs;tea o&longs;ten<lb/>dam. </s>

cò quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi<lb/>bus, verùm illæ non &longs;unt regulares, ide&longs;t <expan abbr="nõ">non</expan> &longs;unt Tetraedra, vt po&longs;tea o&longs;ten<lb/>dam. </s>

<s>Verum quidem e&longs;t octo cubos &longs;imul adactos &longs;oliditatem conficere, <lb/>quia ad id nece&longs;&longs;arij &longs;unt octo anguli &longs;olidi, quos octo cubi præbere po&longs;&longs;unt, <lb/>cum anguli ip&longs;orum &longs;int recti, & &longs;olidi. </s>

Line 4566

<s>ini<lb/>tio facto à 13. demon&longs;tratione, in quibus nulla reperitur proportio dupla <lb/>inter diametrum, & latus eiu&longs;dem alicuius ex illis &longs;olidis; ex quibus mani<lb/>fe&longs;tum e&longs;t, plures regulares pyramides quouis pacto &longs;imul vnitas nullo mo<lb/>do replere locum &longs;olidum. </s>

<s>cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t. </s>

<s>cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t.

<s>nullo <lb/>modo po&longs;&longs;e verificari de repletione &longs;olidi per plura Tetraedra, & omnes <lb/>tamen commentatores auctoritate Ari&longs;t. </s>

nullo <lb/>modo po&longs;&longs;e verificari de repletione &longs;olidi per plura Tetraedra, & omnes <lb/>tamen commentatores auctoritate Ari&longs;t.

<s>decepti pro ip&longs;o &longs;tarent, dubius, <lb/><expan abbr="anceps&qacute;">ancepsque</expan>; diu hæ&longs;i, neque quid quam mea Minerua a&longs;&longs;erere au&longs;us &longs;um, &longs;ed P. <lb/></s>

decepti pro ip&longs;o &longs;tarent, dubius, <lb/><expan abbr="anceps&qacute;">ancepsque</expan>; diu hæ&longs;i, neque quid quam mea Minerua a&longs;&longs;erere au&longs;us &longs;um, &longs;ed P. <lb/></s>

<s>Clauium præceptorem meum per literas con&longs;ului, qui in hunc modum hu<lb/>mani&longs;&longs;imè re&longs;pondit; cubus implet locum quater &longs;umptus, ad idem enim <lb/>punctum quatuor cubi coaptantur: &longs;ic etiam pyramis &longs;exies &longs;umpta, &longs;eu &longs;ex <lb/>pyramides ad idem punctum iunctæratione &longs;ub&longs;tantium <expan abbr="triangulor&utilde;">triangulorum</expan> æqui<lb/>laterorum. </s>

<s>Verum hac ratione non videntur implere locum lolidum, fa<lb/>teor; &longs;ed tamen Ari&longs;t. </s>

<s>Verum hac ratione non videntur implere locum lolidum, fa<lb/>teor; &longs;ed tamen Ari&longs;t.

in co tex. </s>

<s>non loquitur de repletione loci &longs;olidi. </s>

Line 4584

<s>&longs;i igitur libeat Ari&longs;totelem, quod fortè Clauius intendebat defendere, <lb/>dicendum e&longs;t cum eo Ari&longs;t non loqui de repletione loci &longs;olidi: <expan abbr="neq;">neque</expan> loqui <lb/>de cubo, & Tetraedro, quatenus &longs;unt corpora, &longs;ed quatenus habent &longs;uper<lb/>ficies, cubus quidem &longs;ex quadratas, Tetraedrum autem quatuor æquilate<lb/>ras &longs;uperficies, quæ duæ figuræ, vt &longs;upra in hoc textu vidimus, replent lo<lb/>cum: <expan abbr="atq;">atque</expan> hoc modo facimus Ari&longs;totelem non formaliter loquentem. </s>

<s>ex<lb/>aduersò ne videamur magis Ari&longs;t. </s>

<s>ex<lb/>aduersò ne videamur magis Ari&longs;t.

<s>quam veritatem &longs;equi, videtur dicen<lb/>dum, Ari&longs;totilem formaliter locutum e&longs;&longs;e, & vt patet ex rationibus &longs;upra <lb/>allatis de repletione &longs;olidi e&longs;&longs;e intelligendum, vt etiam intellexerunt omnes <lb/>huius loci expo&longs;itores; Verumtamen ip&longs;um erra&longs;&longs;e, dum plures pyramides <lb/>replere &longs;olidum exi&longs;timauit. </s>

quam veritatem &longs;equi, videtur dicen<lb/>dum, Ari&longs;totilem formaliter locutum e&longs;&longs;e, & vt patet ex rationibus &longs;upra <lb/>allatis de repletione &longs;olidi e&longs;&longs;e intelligendum, vt etiam intellexerunt omnes <lb/>huius loci expo&longs;itores; Verumtamen ip&longs;um erra&longs;&longs;e, dum plures pyramides <lb/>replere &longs;olidum exi&longs;timauit. </s>

<s>Vtrumuis dixerimus, non tamen Ari&longs;t. </s>

<s>Vtrumuis dixerimus, non tamen Ari&longs;t.

<s>ab om<lb/>ni crrore vindicabimus. </s>

ab om<lb/>ni crrore vindicabimus. </s>

<s>Hoc tamen certum e&longs;t, ex prædictis, Græcos om<lb/>nes pariter, ac Latinos, illos &longs;equentes, lapos e&longs;&longs;e, a&longs;&longs;erentes duodecim py<lb/>ramides complere &longs;olidum locum, <expan abbr="atq;">atque</expan> Dodecaedrum con&longs;tituere; nam py<lb/>ramides Dodecaedron con&longs;tituentes non &longs;unt regulares, ide&longs;t, non &longs;unt Te<pb pagenum="87"/>traedra (de quibus tamen Ari&longs;t. </s>

<s>loquitur) vt patet ex &longs;upradictis. </s>

loquitur) vt patet ex &longs;upradictis. </s>

<s>Indul<lb/>geas Lector, &longs;i hoc loco nece&longs;&longs;e fuit in Geometriæ penetralia ingredi: ope<lb/>ræpretium enim e&longs;t aliquando ip&longs;is Mathematicis &longs;atisfacere. </s>

Line 4608

<s>38. &longs;pecu<lb/>lationem 10. Benedicti de placitis Ari&longs;t. </s>

<s><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t. </s>

<s><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t.

<s>hoc loco <lb/>erroris notari, dum a&longs;&longs;eruit duodecim pyramides replere <expan abbr="loc&utilde;">locum</expan> corporeum, <lb/>ide&longs;t, vt exponit ip&longs;e, &longs;ex pyramides &longs;uper hexagonam aliquam figuram <lb/>&longs;uperficialem, & &longs;ex &longs;ub eadem, id præ&longs;tarent, cum potius maius vacuum <lb/>remaneat ad quamlibet partium &longs;upra, & infra, quam plenum. </s>

hoc loco <lb/>erroris notari, dum a&longs;&longs;eruit duodecim pyramides replere <expan abbr="loc&utilde;">locum</expan> corporeum, <lb/>ide&longs;t, vt exponit ip&longs;e, &longs;ex pyramides &longs;uper hexagonam aliquam figuram <lb/>&longs;uperficialem, & &longs;ex &longs;ub eadem, id præ&longs;tarent, cum potius maius vacuum <lb/>remaneat ad quamlibet partium &longs;upra, & infra, quam plenum. </s>

<s>hæc ip&longs;e. </s>

<s>&longs;ed <lb/>expo&longs;itio i&longs;ta puerili, ne dum Ari&longs;t. </s>

<s>&longs;ed <lb/>expo&longs;itio i&longs;ta puerili, ne dum Ari&longs;t.

<s>ingenio pror&longs;us indigna e&longs;t: vt propte<lb/>rea exi&longs;timem ca&longs;u potius eum Ari&longs;t. </s>

ingenio pror&longs;us indigna e&longs;t: vt propte<lb/>rea exi&longs;timem ca&longs;u potius eum Ari&longs;t.

<s>rectè reprehendi&longs;&longs;e, quam ex certa <lb/>&longs;cientia, cum illius erratum maiori errato conetur corrigere. </s>

rectè reprehendi&longs;&longs;e, quam ex certa <lb/>&longs;cientia, cum illius erratum maiori errato conetur corrigere. </s>

<s>Incidi po<lb/>&longs;tremò in Indicem librorum, quem Maurolyius &longs;uæ Co&longs;mographiæ præpo<lb/>nit, vbi &longs;ic ait: Demon&longs;tramus autem in libello de figuris planis, <expan abbr="&longs;olidis&qacute;">&longs;olidisque</expan>; <lb/>locum replentibus, cubos per &longs;e, pyramides verò cum octacdris compactas <lb/>dumtaxat implere locum, qua in re Auerroem erra&longs;&longs;e pueriliter manife&longs;tum <lb/>erit. </s>

Line 4740

<s>Eodem cap. <emph type="italics"/>(Con&longs;iderautes vtique, quæ nunc c&longs;tenduntur per Mathematica<emph.end type="italics"/><pb pagenum="90"/><emph type="italics"/>&longs;u<gap/>ficienter, for: è vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>e&longs;t pu<gap/>re <expan abbr="vnumquodq;">vnumquodque</expan> eorum quæ feruntur e&longs;&longs;e paruum magnitudinibus, quia vi<lb/>detur <gap/>&longs;picientibus, binc nobis &longs;ic)<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, quæ <lb/>pa&longs;&longs;im apud Ari&longs;t. </s>

<s>occurrunt, <expan abbr="pleriq;">plerique</expan> no&longs;træ ætatis con&longs;iderarent, qui nulla <lb/>ratione probari po&longs;&longs;e exi&longs;timant, Solem, v. </s>

occurrunt, <expan abbr="pleriq;">plerique</expan> no&longs;træ ætatis con&longs;iderarent, qui nulla <lb/>ratione probari po&longs;&longs;e exi&longs;timant, Solem, v. </s>

<s>terra e&longs;&longs;e centies &longs;exagies &longs;e<lb/>xies maiorem; &longs;ed c<gap/> iam, quod peius e&longs;t, negant e&longs;&longs;e maiorem; ad demon<lb/>&longs;trationes autem a&longs;tronomicas dicunt &longs;e exi&longs;timare eas e&longs;&longs;e fallaces; at que <lb/>impo&longs;libile e&longs;&longs;e nos res adeo à nobis di&longs;taptes &longs;ufficienter perue&longs;tigare: <lb/>quanto &longs;apientius, ac prudentius eorum Magi&longs;ter Ari&longs;t. </s>

<s>alibi &longs;æpius, &longs;ed hoc <lb/>præcipuè loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/>i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia præceptoris a&longs;&longs;equi poterunt.</s>

alibi &longs;æpius, &longs;ed hoc <lb/>præcipuè loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/>i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia præceptoris a&longs;&longs;equi poterunt.</s>

Line 4758

<s>4. <emph type="italics"/>(Quæ igitur astrorum e&longs;t, velox quidem; longè autem: quæ <lb/>verò Lunæ deor&longs;um quidem, tarda autem: quæautem Solis ambo hæc babet &longs;uffi<lb/>cienter)<emph.end type="italics"/> quæ igitur a&longs;trorum, ide&longs;t latio a&longs;trorum e&longs;t velox, &longs;ed procul à ter<lb/>ra; Lunæ verò latio terræ quidem proxima, tarda tamen: at verò Solis la<lb/>tio medio modo &longs;e habet inter vtrumque, ide&longs;t, quia <expan abbr="neq;">neque</expan> nimis vt a&longs;tra di<lb/>&longs;tat, <expan abbr="neq;">neque</expan> tardè &longs;icut Luna circunfertur. </s>

<s>exi&longs;timo Ari&longs;t. </s>

<s>exi&longs;timo Ari&longs;t.

<s>loqui de motu diur<lb/>no, quia &longs;ecundum hunc a&longs;tra inerrantia &longs;unt Sole citatiora, Sol verò ip&longs;a <lb/>Luna citior. </s>

loqui de motu diur<lb/>no, quia &longs;ecundum hunc a&longs;tra inerrantia &longs;unt Sole citatiora, Sol verò ip&longs;a <lb/>Luna citior. </s>

<s>Verumenimuerò illud non prætereundum, quod plurium inua<lb/>luerit opinio exi&longs;timantium Ari&longs;t. </s>

<s>Verumenimuerò illud non prætereundum, quod plurium inua<lb/>luerit opinio exi&longs;timantium Ari&longs;t.

<s>his verbis, Solem &longs;upra Lunam proximè <lb/>colloca&longs;&longs;e; quod tamen ex ip&longs;is nullo pacto deduci pote&longs;t; &longs;ed &longs;olummodo <lb/>ip&longs;um &longs;upra Lunam colloca&longs;&longs;e. </s>

his verbis, Solem &longs;upra Lunam proximè <lb/>colloca&longs;&longs;e; quod tamen ex ip&longs;is nullo pacto deduci pote&longs;t; &longs;ed &longs;olummodo <lb/>ip&longs;um &longs;upra Lunam colloca&longs;&longs;e. </s>

<s>quod &longs;i ita &longs;en&longs;i&longs;&longs;et venia dignus haberetur, <lb/>cum tunc temporis nondum fortè adinuentæ e&longs;&longs;ent demon&longs;trationes illæ <lb/>a&longs;tronomicæ, quibus ordo Planetarum certi&longs;&longs;imè con&longs;tat, <expan abbr="Sol&qacute;">Solque</expan>; medius in<lb/>ter Planetas collocatur. </s>

<s>At verò nulla ratione ferendi &longs;unt <expan abbr="quicunq;">quicunque</expan> no&longs;tra <lb/>hac tempe&longs;tate non &longs;olum Ari&longs;t. </s>

<s>At verò nulla ratione ferendi &longs;unt <expan abbr="quicunq;">quicunque</expan> no&longs;tra <lb/>hac tempe&longs;tate non &longs;olum Ari&longs;t.

<s>ita &longs;en&longs;i&longs;&longs;e, &longs;ed etiam contra firmi&longs;&longs;imas <lb/>aftronomorum demon&longs;trationes, quibus adeò Ari&longs;t. </s>

ita &longs;en&longs;i&longs;&longs;e, &longs;ed etiam contra firmi&longs;&longs;imas <lb/>aftronomorum demon&longs;trationes, quibus adeò Ari&longs;t.

<s>deferebat, vnica, vt pu<lb/>tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum à Luna locum occupare om<lb/>ni ope defendunt.</s>

deferebat, vnica, vt pu<lb/>tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum à Luna locum occupare om<lb/>ni ope defendunt.</s>

Line 4782

<s>3. <emph type="italics"/>(Quod accidit circa Mercurij stellam, quia enim modicum <lb/><expan abbr="&longs;upera&longs;c&etilde;dis">&longs;upera&longs;cendis</expan>, &longs;æpè non apparet, it a vt po&longs;t tempus multum appareat)<emph.end type="italics"/> quod Mer<lb/>curius non ni&longs;i rarò con&longs;pici po&longs;&longs;it, cau&longs;a e&longs;t, quia parum à Sole elongatur, <lb/>&longs;iue ip&longs;um antecedat, &longs;iue &longs;ub&longs;equatur. </s>

<s>ex quo fit, vt diu ferè &longs;imul cum So<lb/>le cit cumferatur, & propterea &longs;iue oriatur, &longs;iue occidat, parum &longs;upra ho<lb/>rizontem eleuatus apparere pote&longs;t, quod Ari&longs;t. </s>

<s>ait modicum <expan abbr="&longs;upera&longs;c&etilde;dit">&longs;upera&longs;cendit</expan>. <lb/></s>

ait modicum <expan abbr="&longs;upera&longs;c&etilde;dit">&longs;upera&longs;cendit</expan>. <lb/></s>

<s>vnde fit tum propter nimiam Solis vicinitatem, cuius lumine tegitur; tum <lb/>propter vapores, qui horizonti vt plurimum incumbunt, vt rarò, & po&longs;t ma<lb/>gna temporis interualla con&longs;piciatur. </s>

Line 4898

<s>quì igitur fieri potuerit, vt in hac corruptibili <expan abbr="m&utilde;di">mundi</expan> parte ex ma<lb/>teria adeò &longs;luxa, & vaga, quam illis Ari&longs;teteles &longs;upponit, tandiu perdura<lb/>re potui&longs;&longs;ent.</s>

<s><expan abbr="Atq;">Atque</expan> hæ &longs;unt rationes, quibus plurimi a&longs;tronomorum recentiorum, co<pb pagenum="94"/>metas ho&longs;ce motum æthereæ regioni conformem, contrà quam Ari&longs;t. </s>

<s>opi<lb/>natus e&longs;t, obtinui&longs;&longs;e, munifeftum e&longs;&longs;e volunt; ac proinde eorum locum, & <lb/>cur&longs;um in c&oelig;le&longs;ti mundi parte extiti&longs;&longs;e, &longs;e comproba&longs;&longs;e exi&longs;timant: qua de <lb/>re prudentis Lectoris e&longs;to iudicium: <expan abbr="neq;">neque</expan> enim, vt ille cecinit, no&longs;trum e&longs;t, <lb/>tantas componere lites.</s>

opi<lb/>natus e&longs;t, obtinui&longs;&longs;e, munifeftum e&longs;&longs;e volunt; ac proinde eorum locum, & <lb/>cur&longs;um in c&oelig;le&longs;ti mundi parte extiti&longs;&longs;e, &longs;e comproba&longs;&longs;e exi&longs;timant: qua de <lb/>re prudentis Lectoris e&longs;to iudicium: <expan abbr="neq;">neque</expan> enim, vt ille cecinit, no&longs;trum e&longs;t, <lb/>tantas componere lites.</s>

<s>Verumenimuerò Peripatetica omnis &longs;chola reclamat; C&oelig;lum e&longs;t inge<lb/>nerabile, & incorruptibile, mhil igitur noui c&oelig;lo pote&longs;t accidere. </s>

Line 4930

<s>5. <emph type="italics"/>(Ad hæc autem &longs;i quemadmodum o&longs;tenditur in ijs, quæ cir<lb/>ca Astrologiam &longs;peculationibus, Solis magnitudo maior e&longs;t quàm terræ; & diftax<lb/>tia multò maior a&longs;trorum ad terram quàm So is; &longs;icut Solis ad terram quàm Lu<lb/>næ; non <expan abbr="vtiq;">vtique</expan> longè alicubi à terra conus, qui à Sole, corijciet radios, <expan abbr="neq;">neque</expan> vtique <lb/>vmbraterræ, quæ vocatur nox, erit apud astra; &longs;ed ne<gap/>&longs;&longs;e Solem omnia a&longs;tra cir<lb/>cun&longs;picere, & nulli <gap/>p&longs;orum terram ob&longs;istere)<emph.end type="italics"/> ex dictis &longs;umma 1. cap. </s>

<s>3. huius, <lb/>& ex figura ibi de&longs;cripta, facilè e&longs;t intelligere præ&longs;entem locum; nam cum <lb/>Sol &longs;it multò maior terra, vt ibi probatur, ac minus di&longs;ter à terra quàm fixæ <lb/>&longs;tellæ, magis tamen quàm Luna, vt patet ex &longs;olari eclyp&longs;i, &longs;equitur nece&longs;&longs;a<lb/>riò vmbram terræ, quæ nox e&longs;t ip&longs;a, effici turbinatam, & valdè procul à ter<lb/>ra acumen coni vmbræ a&longs;cendet, &longs;ed paulò &longs;upra Lunam conus hic vmbræ <lb/>permittet radios Solis &longs;e ip&longs;um ambientes iterum &longs;imul committi, quod il<lb/>lis verbis <emph type="italics"/>(Conijciet radios)<emph.end type="italics"/> ide&longs;t committet radios expre&longs;&longs;it Ari&longs;t. </s>

<s>cum igi<lb/>tur vmbra apud Lunam &longs;it &longs;atis gracilis, breui &longs;upra Lunam de&longs;inet, neque <lb/>vllo pacto ad affixa &longs;ydera protendetur, <expan abbr="neq;">neque</expan> illis renebras offundet. </s>

cum igi<lb/>tur vmbra apud Lunam &longs;it &longs;atis gracilis, breui &longs;upra Lunam de&longs;inet, neque <lb/>vllo pacto ad affixa &longs;ydera protendetur, <expan abbr="neq;">neque</expan> illis renebras offundet. </s>

<s>quod <lb/>etiam experientia confirmat, cum nunquam a&longs;tra illa, quæ Soli opponuntur, <lb/><expan abbr="quæ&qacute;">quæque</expan>; vertex vmb æ co<gap/>limat, vllam <expan abbr="patiãtur">patiantur</expan> eclyp&longs;im. </s>

Line 4948

<s>Quæ autem in lactis circu<lb/>lo feruntur a&longs;tra, & Sol, ad quem fit reflexio, mouentur manentibus nobis, & &longs;i<lb/>militer, & æqualiter ad nos di&longs;tantia; à &longs;e ip&longs;is autem non æqualiter: aliquando <lb/>enim medijs noctibus Delphin oritur, aliquando verò diluculo. </s>

<s>partes autem lactis <lb/>eædem manent in vnoquoque; atqui non oportebat, &longs;i erat imago, &longs;ed non in ei&longs;dem <lb/>adhuc e&longs;&longs;et hæc pa&longs;&longs;io locis)<emph.end type="italics"/> in his Ari&longs;t. </s>

<s>confutat opinionem dicentium Gala<lb/>xiam apparere per quandam reflexionem vi&longs;us no&longs;tri ab illa parte c&ecedil;li, ceu, <lb/>ex quodam &longs;peculo ad Solem: probat autem hoc e&longs;&longs;e impo &longs;&longs;ibile ratione <lb/>de&longs;umpta ex parte Optices, quæ dicitur Catoptrica, &longs;iue &longs;pecularia, quia <lb/>tractat de vi&longs;ione reflexa, quæ fit mediante &longs;peculo, quam quidem rationem <lb/>&longs;i vellem mathematicè explicare, longa nimis, ac præter in&longs;titutum fieret <lb/>tractatio. </s>

confutat opinionem dicentium Gala<lb/>xiam apparere per quandam reflexionem vi&longs;us no&longs;tri ab illa parte c&ecedil;li, ceu, <lb/>ex quodam &longs;peculo ad Solem: probat autem hoc e&longs;&longs;e impo &longs;&longs;ibile ratione <lb/>de&longs;umpta ex parte Optices, quæ dicitur Catoptrica, &longs;iue &longs;pecularia, quia <lb/>tractat de vi&longs;ione reflexa, quæ fit mediante &longs;peculo, quam quidem rationem <lb/>&longs;i vellem mathematicè explicare, longa nimis, ac præter in&longs;titutum fieret <lb/>tractatio. </s>

<s>Pauca tamen addam, quæ Ari&longs;totelis <expan abbr="&longs;ent&etilde;tiam">&longs;ententiam</expan> &longs;atis per&longs;picuam <lb/>reddant. </s>

Line 4962

<s>ex qui<lb/>bus con&longs;tat fal&longs;am omninò e&longs;&longs;e eorum &longs;ententiam, qui Galaxiam per huiu&longs;<lb/>modi re&longs;lexionem fieri opinabantur. </s>

<s>Quæ dicta &longs;unt de &longs;peculo, & obiecto <lb/>&longs;atius e&longs;t a&longs;&longs;umpto aliquo &longs;peculo experiri, quàm ea pluribus ob&longs;curare: qua <lb/>etiam experientia Ari&longs;t. </s>

<s>ratio confirmabiaur.</s>

ratio confirmabiaur.</s>

Line 4974

<s>quæ differentia facit vt Sol <lb/>manife&longs;tè appareat nobis minor apogæus, quàm perigæus. </s>

<s>Sol præterea &longs;i<lb/>militer ip&longs;is inerrantibus &longs;tellis fit tantumdem modo remotior, modo pro<lb/>pinquior: &longs;ed fortè Ari&longs;t. </s>

<s>Sol præterea &longs;i<lb/>militer ip&longs;is inerrantibus &longs;tellis fit tantumdem modo remotior, modo pro<lb/>pinquior: &longs;ed fortè Ari&longs;t.

<s>i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/>per&longs;pecta erant.</s>

i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/>per&longs;pecta erant.</s>

<s>Ibidem <emph type="italics"/>(Aliquando enim medijs noctibus Delphin oritur)<emph.end type="italics"/> vt probet, Gala<lb/>xiam non &longs;emper &longs;eruare à Sole di&longs;tantiam eandem, accipit tanquam huius <lb/>rei &longs;ignum, manife&longs;tum, quod Delphini con&longs;tellatio aliquando medijs no<lb/>ctibus oriatur &longs;upra horizontem, aliquando verò diluculo; non ideò tamen <lb/>putes hanc rationem &longs;upponere Delphinum e&longs;&longs;e in ip&longs;o lacteo circulo, quod <lb/>tamen verum non e&longs;t, non enim e&longs;t in Galaxia, &longs;ed tamen illi proximus, vt <lb/>noctu videre e&longs;t in c&oelig;lo, vel etiam &longs;i mauis in globo a&longs;tronomico: non ta<lb/>men ob id Ari&longs;t. </s>

<s>ratio minus valida redditur, cum Delphinus &longs;emper Gala<lb/>xiæ eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s>

ratio minus valida redditur, cum Delphinus &longs;emper Gala<lb/>xiæ eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s>

Line 4998

<s>& quemadmodum halo, &longs;iue area omnibus <expan abbr="vndecunq;">vndecunque</expan> <lb/>a&longs;picientibus &longs;emper videntur in eodem c&oelig;li loco, hoc e&longs;t è regione Solis, <lb/>vel Lunæ; &longs;imiliter Galaxia in aere omnibus <expan abbr="vndecunq;">vndecunque</expan> intuentibus appa<lb/>reat in eadem c&oelig;li parte, ide&longs;t ex aduersò eorumdem &longs;yderum, quæ c&oelig;le<lb/>&longs;tem lacteam viam conficiunt. </s>

<s>Porrò qui &longs;ic mentem Ari&longs;t. </s>

<s>Porrò qui &longs;ic mentem Ari&longs;t.

<s>exponunt, nul<lb/>lo modo po&longs;&longs;unt à Mathematicis redargui per rationem de&longs;umptam à di<lb/>uer&longs;itate a&longs;pectus (quam po&longs;tea explicabo) quamuis phy&longs;icis rationibus re<lb/>fellantur. </s>

exponunt, nul<lb/>lo modo po&longs;&longs;unt à Mathematicis redargui per rationem de&longs;umptam à di<lb/>uer&longs;itate a&longs;pectus (quam po&longs;tea explicabo) quamuis phy&longs;icis rationibus re<lb/>fellantur. </s>

<s>Alij &longs;unt, quorum &longs;ententia magis videtur <expan abbr="improbãda">improbanda</expan>, cò quod <lb/>Ari&longs;t. </s>

Line 5048

<s>Summa 4. cap. </s>

<s>1. <emph type="italics"/>(In A&longs;ia igitur plurimi ex Parna&longs;&longs;o vocato monte videntur <lb/>&longs;tuentes)<emph.end type="italics"/> rectè dubitat Alexander, qua ratione mons Parna&longs;&longs;us ab Ari&longs;t. </s>

<s>po<lb/>natur in A&longs;ia, cum certò certius con&longs;tet, ip&longs;um in Græcia Europæ regione <lb/>&longs;itum e&longs;&longs;e. </s>

po<lb/>natur in A&longs;ia, cum certò certius con&longs;tet, ip&longs;um in Græcia Europæ regione <lb/>&longs;itum e&longs;&longs;e. </s>

<s>fortè legendum e&longs;t, vt vult Vicomercatus, ex Paropame&longs;&longs;o, non <lb/>autem ex Parna&longs;&longs;o, quamuis Græci codices aduer&longs;entur; Paropame&longs;&longs;um <lb/><expan abbr="namq;">namque</expan> Plinius, & Strabo in A&longs;ia collocant, <expan abbr="volunt&qacute;">voluntque</expan>; ip&longs;um e&longs;&longs;e iugum quod<lb/>dam montis Cauca&longs;i: Cauca&longs;um autem &longs;upra Pontum orifi, & <expan abbr="v&longs;q;">v&longs;que</expan> ad Hir<lb/>canum, & vltra mare per totam A&longs;iam &longs;e proferre, tradunt veteres Geo<lb/>graphi. </s>

Line 5100

<s>ac re&longs;pectu Græciæ, & maris Euxini vergit ad eam mundi pla<lb/>gam, vnde illis æ&longs;tiuo tempore Sol oritur. </s>

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

<s>ait Ari&longs;t.

<s>eum e&longs;&longs;e omnium mon<lb/>tium illius plagæ alti&longs;&longs;imum, quod probat primò, quia admodum à longè <lb/>cernitur, <expan abbr="nimir&utilde;">nimirum</expan> ab illo Euxini loco, qui Profunda vocatur, eò quòd à Nau<lb/>tis nu&longs;quam ibi fundus reperiatur. </s>

eum e&longs;&longs;e omnium mon<lb/>tium illius plagæ alti&longs;&longs;imum, quod probat primò, quia admodum à longè <lb/>cernitur, <expan abbr="nimir&utilde;">nimirum</expan> ab illo Euxini loco, qui Profunda vocatur, eò quòd à Nau<lb/>tis nu&longs;quam ibi fundus reperiatur. </s>

<s>& præterca à Nauigantibus in Stagnum, <lb/>&longs;iue in Meotidem paludem, quæ quidem loca minimùm di&longs;tant a Cauca&longs;o <lb/>560. milliaribus. </s>

<s>Secundò, probat il ius altitudinem ex eo, quòd &longs;ummi<lb/>tates ip&longs;ius <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam partem nocte, & ve&longs;peri à Sole illu&longs;trentur. </s>

<s>Lo<lb/>cum hunc fu<gap/>è pertractat eruditi&longs;&longs;imus Iacobus Mazonius &longs;ectione 3. & 4. <lb/>de Comparatione Platonis, & Ari&longs;t. </s>

<s>Lo<lb/>cum hunc fu<gap/>è pertractat eruditi&longs;&longs;imus Iacobus Mazonius &longs;ectione 3. & 4. <lb/>de Comparatione Platonis, & Ari&longs;t.

<s>quo in opere plurima habet ex Mathe<lb/>maticis de&longs;umpta, quibus naturalem Philo&longs;ophiam mirificè illu&longs;trat, <expan abbr="mani-fe&longs;tum&qacute;">mani<lb/>fe&longs;tumque</expan>; reddit, quàm nece&longs;&longs;ariæ &longs;int Mathematicæ ad philo&longs;ophicæ veri<pb pagenum="99"/>tatis in&longs;pectionem. </s>

quo in opere plurima habet ex Mathe<lb/>maticis de&longs;umpta, quibus naturalem Philo&longs;ophiam mirificè illu&longs;trat, <expan abbr="mani-fe&longs;tum&qacute;">mani<lb/>fe&longs;tumque</expan>; reddit, quàm nece&longs;&longs;ariæ &longs;int Mathematicæ ad philo&longs;ophicæ veri<pb pagenum="99"/>tatis in&longs;pectionem. </s>

<s>Is igitur &longs;ect. </s>

<s>5. de hoc Ari&longs;t. </s>

<s>5. de hoc Ari&longs;t.

<s>loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>multis an&longs;am dedit reprehendendi Ari&longs;t. </s>

loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>multis an&longs;am dedit reprehendendi Ari&longs;t.

<s>tanquam puerilia effutientem. </s>

tanquam puerilia effutientem. </s>

<s>tex<lb/>tus <expan abbr="itaq;">itaque</expan> Ari&longs;t. </s>

<s>tex<lb/>tus <expan abbr="itaq;">itaque</expan> Ari&longs;t.

<s>duplicem habet &longs;en&longs;um; alter à quo non abhorret <expan abbr="Alexãder">Alexander</expan>; <lb/>vt tertia illa pars ad montem referatur, qua&longs;i dicat, quod antequam Sol ima <lb/>montis illu&longs;tret, illuminat illius cacumen <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam montis partem: <lb/>&longs;ed hæc Mazonij expo&longs;itio nulla e&longs;t, cuiu&longs;libet enim montis etiam medio<lb/>cris altitudinis Sol illu&longs;trat non &longs;olum tertiam partem, &longs;ed & dimidium, & <lb/>duas tertias, & ferè totum, antequam ad planam illius ba&longs;im de&longs;cendat. <lb/></s>

duplicem habet &longs;en&longs;um; alter à quo non abhorret <expan abbr="Alexãder">Alexander</expan>; <lb/>vt tertia illa pars ad montem referatur, qua&longs;i dicat, quod antequam Sol ima <lb/>montis illu&longs;tret, illuminat illius cacumen <expan abbr="v&longs;q;">v&longs;que</expan> ad tertiam montis partem: <lb/>&longs;ed hæc Mazonij expo&longs;itio nulla e&longs;t, cuiu&longs;libet enim montis etiam medio<lb/>cris altitudinis Sol illu&longs;trat non &longs;olum tertiam partem, &longs;ed & dimidium, & <lb/>duas tertias, & ferè totum, antequam ad planam illius ba&longs;im de&longs;cendat. <lb/></s>

<s>Ego &longs;ic exponendum cen&longs;eo, vt Ari&longs;t. </s>

<s>Ego &longs;ic exponendum cen&longs;eo, vt Ari&longs;t.

<s>dicat, mane, ide&longs;t initio Crepu&longs;culi <lb/>matutini, & ve&longs;pere, ide&longs;t, in fine Crepu&longs;culi ve&longs;pertini ip&longs;ius tertiam par<lb/>tem illuminatam con&longs;pici ab ijs, quorum horizonti tunc incipit, vel de&longs;init <lb/>Crepu&longs;culum; ex quibus illi nece&longs;&longs;ariò re&longs;pectu Cauca&longs;i &longs;unt occidentales, <lb/>quì manè hoc vident, vti &longs;unt ij, qui in Euxino, &longs;eu Ponto, & Meotide naui<lb/>gant, vel loca proxima inhabitant: illi verò, qui in fine Crepu&longs;culi ve&longs;per<lb/>tini hoc cernunt, nece&longs;&longs;ariò re&longs;pectu Cauca&longs;i erunt orientales. </s>

dicat, mane, ide&longs;t initio Crepu&longs;culi <lb/>matutini, & ve&longs;pere, ide&longs;t, in fine Crepu&longs;culi ve&longs;pertini ip&longs;ius tertiam par<lb/>tem illuminatam con&longs;pici ab ijs, quorum horizonti tunc incipit, vel de&longs;init <lb/>Crepu&longs;culum; ex quibus illi nece&longs;&longs;ariò re&longs;pectu Cauca&longs;i &longs;unt occidentales, <lb/>quì manè hoc vident, vti &longs;unt ij, qui in Euxino, &longs;eu Ponto, & Meotide naui<lb/>gant, vel loca proxima inhabitant: illi verò, qui in fine Crepu&longs;culi ve&longs;per<lb/>tini hoc cernunt, nece&longs;&longs;ariò re&longs;pectu Cauca&longs;i erunt orientales. </s>

<s>Alter huius <lb/>loci &longs;en&longs;us e&longs;t, ait Mazonius, vt non de tertia montis parte, &longs;ed de tertia <lb/>noctis portione loquatur, ita vt manè. </s>

Line 5168

<s>&longs;ed papè in quos acu<pb pagenum="100"/>leos imprudens me conieci? </s>

<s>rident enim hoc Ari&longs;t. </s>

<s>rident enim hoc Ari&longs;t.

<s>dictum Mathematici, <lb/>putant enim eum pueriliter lap&longs;um e&longs;&longs;e. </s>

dictum Mathematici, <lb/>putant enim eum pueriliter lap&longs;um e&longs;&longs;e. </s>

<s>Cæterum ego pro præceptoris tu<lb/>rela, dico eum &longs;equutum e&longs;&longs;e famam. </s>

Line 5240

<s>lo<lb/>quatur non de tertia montis parte, &longs;ed noctis, ita vt dicat, circa initium <lb/>tertiæ partis noctis apicem montis illu&longs;trari, altitudo eius erit tantum<pb pagenum="102"/>modo 180. quot continet latus F V. vt vidimus, quæ quamuis illa minor &longs;it, <lb/>adhuc tamen ab&longs;urda e&longs;t.</s>

<s>Si v<gap/>rò dixerimus Ari&longs;t. </s>

<s>Si v<gap/>rò dixerimus Ari&longs;t.

<s>intelligere hæc omnia, non re&longs;pectu horizontis <lb/>Cauca&longs;i, &longs;ed alterius, cuius habitator in principio &longs;ui Crepu&longs;culi tertiam <lb/>Cauca&longs;i partem iam illu&longs;tratam videat, vti accideret &longs;i Cauca&longs;us &longs;tatuere<lb/>tur in L K, vbi incipit Crepu&longs;culum habitanti in F. tunc e&longs;&longs;et altitudo tanta, <lb/>quanta colligit Mazonius, &longs;i tamen Ari&longs;t. </s>

intelligere hæc omnia, non re&longs;pectu horizontis <lb/>Cauca&longs;i, &longs;ed alterius, cuius habitator in principio &longs;ui Crepu&longs;culi tertiam <lb/>Cauca&longs;i partem iam illu&longs;tratam videat, vti accideret &longs;i Cauca&longs;us &longs;tatuere<lb/>tur in L K, vbi incipit Crepu&longs;culum habitanti in F. tunc e&longs;&longs;et altitudo tanta, <lb/>quanta colligit Mazonius, &longs;i tamen Ari&longs;t.

<s>intelligatur de tertia montis par<lb/>te; e&longs;t enim L K, altitudo habituum 52. mill. </s>

intelligatur de tertia montis par<lb/>te; e&longs;t enim L K, altitudo habituum 52. mill. </s>

<s>& duæ tertiæ montis, quare <lb/>totus mons erit 78. &longs;i autem intelligatur circa tertiam noctis partem, mon<lb/>tis apicem illuminatum videri ab habitatore F, &longs;ic altitudo eins erit tan<lb/>tummodo 52. mill. </s>

Line 5292

<s>Eodem cap. <emph type="italics"/>(Ex Pyreneo autem, hic autem est mons ad occidentem æquino<lb/>ctiaiem in Gallia, flaunt l&longs;ter, & Tarte&longs;&longs;us, iste quidem extra columnas, I&longs;ter au<lb/>tem per totam Europam in Pontum Euxmum)<emph.end type="italics"/> Ari&longs;t. </s>

<s>fortè &longs;equutus e&longs;t Herodo<lb/>tum, qui falsò tradit I&longs;trum, &longs;ine Dannbium ex Pyreneis de&longs;luere, nam Iu<lb/>ce clarius con&longs;tat ip&longs;um ex ijs Alpibus, quæ Heluetiorum montes dicuntur, <lb/>propè Ba&longs;ileam ex Adula monte ortum ducere. </s>

fortè &longs;equutus e&longs;t Herodo<lb/>tum, qui falsò tradit I&longs;trum, &longs;ine Dannbium ex Pyreneis de&longs;luere, nam Iu<lb/>ce clarius con&longs;tat ip&longs;um ex ijs Alpibus, quæ Heluetiorum montes dicuntur, <lb/>propè Ba&longs;ileam ex Adula monte ortum ducere. </s>

<s><expan abbr="neq;">neque</expan> verum e&longs;t Tarte&longs;&longs;um, <lb/>quem & B&oelig;tim alij nominant ex Pyreneis de&longs;cendere. </s>

Line 5302

<s>extra tamen columnas Herculis qui&longs;quis &longs;it in Oceanum occidentale illa<lb/>bitur. </s>

<s>Igno&longs;cenda &longs;unt i&longs;ta Ari&longs;t. </s>

<s>Igno&longs;cenda &longs;unt i&longs;ta Ari&longs;t.

<s>tunc enim Geographia <expan abbr="nond&utilde;">nondum</expan> adoleuerat.</s>

tunc enim Geographia <expan abbr="nond&utilde;">nondum</expan> adoleuerat.</s>

<s>Ad fin<gap/>m eiu&longs;dem cap. <emph type="italics"/>(Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/>qui<gap/>am &longs;l<gap/>us, & iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> & hoc <pb pagenum="103"/>Ari&longs;t. </s>

<s>vt &longs;uperiora, ob Geographiæ illius &longs;eculi imperfectionem, nu&longs;quam <lb/>enim in tota Liguria quidpiam tale reperitur.</s>

vt &longs;uperiora, ob Geographiæ illius &longs;eculi imperfectionem, nu&longs;quam <lb/>enim in tota Liguria quidpiam tale reperitur.</s>

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

Line 5400

<s>Quod verò ad marium aggerationem &longs;pectat, dicimus ij&longs;dem aquis <lb/>magnam arenarum copiam perpetuò impertantibus, fieri aggerationem, <lb/>hoc e&longs;t littora quotidie magis cre&longs;cere, &longs;eu in mare ingredi, & con&longs;equen<lb/>ter mare recedere. </s>

<s>quod primò Ari&longs;t. </s>

<s>quod primò Ari&longs;t.

<s>te&longs;timonio in hoc cap. </s>

te&longs;timonio in hoc cap. </s>

<s>comprobatur, <lb/>cum quo pariter &longs;entiunt veteres Geographi, & Hi&longs;torici omnes. </s>

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

<s>Ari&longs;t.

<s>igi<lb/>tur in comprobationem huius adducit primò magnam Aegypti aggeratio<lb/>nem; pars enim illa Aegypti, quæ Delta, <expan abbr="Nili&qacute;">Nilique</expan>; donum appellatur ab He<lb/>rodoto, ex arenis, & limo, ex Aethyopiæ montibus &longs;imul cum Nilo in mare <lb/>delabentibus, e&longs;t conflata, <expan abbr="atq;">atque</expan> antiquo littori addita, cui locum paulatim <lb/>mare ce&longs;&longs;it; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; propterea donum Nili appellata, quod ab ip&longs;o illuc are<lb/>nas importante &longs;it facta. </s>

igi<lb/>tur in comprobationem huius adducit primò magnam Aegypti aggeratio<lb/>nem; pars enim illa Aegypti, quæ Delta, <expan abbr="Nili&qacute;">Nilique</expan>; donum appellatur ab He<lb/>rodoto, ex arenis, & limo, ex Aethyopiæ montibus &longs;imul cum Nilo in mare <lb/>delabentibus, e&longs;t conflata, <expan abbr="atq;">atque</expan> antiquo littori addita, cui locum paulatim <lb/>mare ce&longs;&longs;it; <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; propterea donum Nili appellata, quod ab ip&longs;o illuc are<lb/>nas importante &longs;it facta. </s>

<s>&longs;ecundum, Ari&longs;t. </s>

<s>&longs;ecundum, Ari&longs;t.

<s>exemplum e&longs;t Ammonia Regio, <lb/>cuius humiliora loca. </s>

exemplum e&longs;t Ammonia Regio, <lb/>cuius humiliora loca. </s>

Line 5462

<s>&longs;ed de his hactenus.</s><pb pagenum="107"/>

<s>Quoad magnum illud Diluuium, quod Ari&longs;t. </s>

<s>Quoad magnum illud Diluuium, quod Ari&longs;t.

<s>hoc capite exi&longs;timat po&longs;t <lb/>multa &longs;ecula reuolui, hoc veritati e&longs;&longs;e con&longs;entaneum argumento &longs;unt, ac <lb/>pariter admirationi varia <expan abbr="cõchiliorum">conchiliorum</expan> genera, quæ tùm in Apennino mon<lb/>te, tùm in Alpibus ob&longs;eruaui; <expan abbr="Ìdem&qacute;">Ìdemque</expan>; in alijs mundi partibus inueniri pu<lb/>to; præ&longs;ertim in tam immen&longs;a copia, <expan abbr="atq;">atque</expan> intra vi&longs;cera montium colloca<lb/>ta, quæ nulla vis humana illuc contuli&longs;&longs;er, ni&longs;i temporibus catacly&longs;mi ebul<lb/>lientibus aquis maris &longs;uper terram facta fui&longs;&longs;et hæc varia rerum maritima<lb/>rum cum terre&longs;tribus commixtio: quæ quidem optimè ex Pomponio Mela <lb/>comprobantur, qui libro 1. de Numidia &longs;ic narrat: interius, & longè &longs;atis <lb/>à litore, &longs;i fides res capit, mirum admodum, &longs;pinæ pi&longs;cium, <expan abbr="Muric&utilde;">Muricum</expan>, <expan abbr="O&longs;treo-rum&qacute;">O&longs;treo<lb/>rumque</expan>; fragmenta, &longs;axi atritu, vti &longs;olent fluctibus, & non differentia mari<lb/>nis, infixæ cautibus anchoræ, <expan abbr="alia&qacute;">aliaque</expan>; huiu&longs;modi &longs;igna, & ve&longs;tigia effu&longs;i olim <lb/><expan abbr="v&longs;q;">v&longs;que</expan> ad ea loca pelagi, in campis nihil alentibus e&longs;&longs;e inuenirique narrantur. <lb/></s>

hoc capite exi&longs;timat po&longs;t <lb/>multa &longs;ecula reuolui, hoc veritati e&longs;&longs;e con&longs;entaneum argumento &longs;unt, ac <lb/>pariter admirationi varia <expan abbr="cõchiliorum">conchiliorum</expan> genera, quæ tùm in Apennino mon<lb/>te, tùm in Alpibus ob&longs;eruaui; <expan abbr="Ìdem&qacute;">Ìdemque</expan>; in alijs mundi partibus inueniri pu<lb/>to; præ&longs;ertim in tam immen&longs;a copia, <expan abbr="atq;">atque</expan> intra vi&longs;cera montium colloca<lb/>ta, quæ nulla vis humana illuc contuli&longs;&longs;er, ni&longs;i temporibus catacly&longs;mi ebul<lb/>lientibus aquis maris &longs;uper terram facta fui&longs;&longs;et hæc varia rerum maritima<lb/>rum cum terre&longs;tribus commixtio: quæ quidem optimè ex Pomponio Mela <lb/>comprobantur, qui libro 1. de Numidia &longs;ic narrat: interius, & longè &longs;atis <lb/>à litore, &longs;i fides res capit, mirum admodum, &longs;pinæ pi&longs;cium, <expan abbr="Muric&utilde;">Muricum</expan>, <expan abbr="O&longs;treo-rum&qacute;">O&longs;treo<lb/>rumque</expan>; fragmenta, &longs;axi atritu, vti &longs;olent fluctibus, & non differentia mari<lb/>nis, infixæ cautibus anchoræ, <expan abbr="alia&qacute;">aliaque</expan>; huiu&longs;modi &longs;igna, & ve&longs;tigia effu&longs;i olim <lb/><expan abbr="v&longs;q;">v&longs;que</expan> ad ea loca pelagi, in campis nihil alentibus e&longs;&longs;e inuenirique narrantur. <lb/></s>

<s>neque locus ille Ouid. </s>

Line 5482

<s>1. ait multa e&longs;&longs;e maria, quæ ad inuicem non communicant. <lb/></s>

<s>Cap. 1. ait multa e&longs;&longs;e maria, quæ ad inuicem non communicant. <lb/></s>

<s>Eorum rubrum mare vnum e&longs;&longs;e; quod cum Oceano <expan abbr="Atlãtico">Atlantico</expan>, qui <lb/>e&longs;t extra Herculeum fretum ad occidentem parum videtur com<lb/>mi&longs;ceri &longs;iue Ari&longs;t. </s>

<s>pro Rubro mari intelligat Oceanum illum, qui <lb/>Arabiam, ac Per&longs;iam alluit, &longs;iue illius &longs;inum, qui Arabiam, <expan abbr="atq;">atque</expan> Aethiopiam <lb/>interluit, fal&longs;um e&longs;t ip&longs;um parum communicare cum occidentali Oceano, <lb/>vt quotidianis Lu&longs;itanorum nauigationibus ad Indos patet. </s>

pro Rubro mari intelligat Oceanum illum, qui <lb/>Arabiam, ac Per&longs;iam alluit, &longs;iue illius &longs;inum, qui Arabiam, <expan abbr="atq;">atque</expan> Aethiopiam <lb/>interluit, fal&longs;um e&longs;t ip&longs;um parum communicare cum occidentali Oceano, <lb/>vt quotidianis Lu&longs;itanorum nauigationibus ad Indos patet. </s>

<s>&longs;ed meritò hoc <lb/>Ari&longs;tot. </s>

Line 5524

<s><expan abbr="nõ">non</expan> autem <lb/>intelligunt de ortu Acronico, quia ante hunc ortum videbatur noctu, <expan abbr="itaq;">itaque</expan> <lb/>ortu Acronico non fit noua apparitio; ideo de hoc non intelligunt. </s>

<s>fit au<lb/>tem ortus hic Orionis, heliacus, & matutinus, de quo Ari&longs;t. </s>

<s>fit au<lb/>tem ortus hic Orionis, heliacus, & matutinus, de quo Ari&longs;t.

<s>hoc loco, & alij <lb/>auctores, no&longs;tra hac tempe&longs;tate paulò ante Solis ingre&longs;&longs;um in Cancrum, &longs;i<lb/>ue ante &longs;ol&longs;titium æ&longs;tiuum circa 22. Iunij.</s>

hoc loco, & alij <lb/>auctores, no&longs;tra hac tempe&longs;tate paulò ante Solis ingre&longs;&longs;um in Cancrum, &longs;i<lb/>ue ante &longs;ol&longs;titium æ&longs;tiuum circa 22. Iunij.</s>

<s>Eodem cap. <emph type="italics"/>(Incertus autem, & mole&longs;tus Orion e&longs;&longs;e videtur & occumbens, & <lb/>oriens, quia in tran&longs;mutatione temporis accidit occa&longs;us, & ortus, a&longs;tate, aut hye<lb/>me, & propter magnitudinem a&longs;tri dierum &longs;it aliqua pluralitas)<emph.end type="italics"/> hoc loco Vico<lb/>mercatus ex &longs;ententia a&longs;tronomorum occa&longs;um Orionis fieri autumni tem<lb/>pore, Sole Scorpionem ob&longs;idente docet, quod & verba Ari&longs;t. </s>

<s>clarè &longs;ignifi<lb/>cant, cum dicat ortum ip&longs;ius fieri æ&longs;tate; in tran&longs;mutatione verò temporis, <lb/>videlicet in autumno fieri occa&longs;um. </s>

clarè &longs;ignifi<lb/>cant, cum dicat ortum ip&longs;ius fieri æ&longs;tate; in tran&longs;mutatione verò temporis, <lb/>videlicet in autumno fieri occa&longs;um. </s>

<s>Porrò occa&longs;us hic fieri incipit primum <lb/>mane oriente Sole, <expan abbr="dicitur&qacute;">diciturque</expan>; occa&longs;us co&longs;micus, quia dum Sol e&longs;t in oriente, <lb/>Orion e&longs;t in occidente, & infra orizontem cadit: deinde paulò ante Solis or<lb/>tum, &longs;ed tamen nocturno tempore, ita vt occa&longs;us eius videri po&longs;&longs;it, donec <lb/>occidat parum po&longs;t Solis occa&longs;um, & tandem cum Sole ip&longs;o heliacè euane<lb/>&longs;cat. </s>

Line 5554

<s>Cum porrò in c&ecedil;lo &longs;it Canis maior, & Canis minor, qui & Procyon, ide&longs;t <lb/>Anticanis dicitur, exi&longs;timo Canem maiorem e&longs;&longs;e eum, qui vulgò Canicula <lb/>nominatur, <expan abbr="&longs;olet&qacute;">&longs;oletque</expan>; vehementes, ac noxios calores excitare. </s>

<s>de quo etiam <lb/>putò Ari&longs;t. </s>

<s>de quo etiam <lb/>putò Ari&longs;t.

<s>intelligere. </s>

intelligere. </s>

<s>eius porrò ortus in no&longs;tra poli eleuatione quadra<lb/>ginta quinque graduum, circa diem tertium Augu&longs;ti contingit, Sole autem <lb/>10. gradum Leonis occupante. </s>

Line 5576

<s>Terra &longs;it A B C H G F E D Z K. à cu<lb/>ius centro Z, educantur primo duæ lineæ rectæ Z R, Z S. ad circulum &longs;em<lb/>per apparentium maximum, quæ in terra tran&longs;eant per puncta B, K. & iun<lb/>gatur linea B K: iam vides conum S R Z, cuius ba&longs;is e&longs;t circulus &longs;emper ap<lb/>parens S R, vertex autem Z, in centro terræ, vt ait Ari&longs;tot. </s>

<s>educantur nunc <lb/>duæ aliæ rectæ ad tropicum Cancri Z T, Z Q, quæ in terra faciant puncta <lb/>I, C, <expan abbr="iungatur&qacute;">iungaturque</expan>; recta I C; hic pariter vides conum alterum T Q Z, cuius ba<lb/>&longs;is e&longs;t circulus Cancri, vertex verò centrum terræ Z. con&longs;idera iam figuram <lb/>B K I C, inter duas rectas B K, I C, & duos circuli terræ arcus contentam; <lb/>hanc Ari&longs;t. </s>

<s>appellat tympanum vnum terræ habitabile, quod e&longs;t ad Vr&longs;am, <lb/>ide&longs;t in &longs;eptentrionali plaga, in qua &longs;umus nos: quæ quidem portio &longs;i con&longs;i<lb/>deretur vt &longs;olida, & à reliqua terra præci&longs;a, erit corpus rotundum, <expan abbr="vtrinq;">vtrinque</expan> <lb/>tamen duobus planis circulis ad in&longs;tar tympani terminatum: Ductis dein<lb/>de &longs;imiliter alijs quattuor lineis à centro Z, ver&longs;us polum antarticum fit al<lb/>terum tympanum H D E G, au&longs;tralis terræ habitabilis, vt in figura manife<lb/>&longs;tum e&longs;t. </s>

appellat tympanum vnum terræ habitabile, quod e&longs;t ad Vr&longs;am, <lb/>ide&longs;t in &longs;eptentrionali plaga, in qua &longs;umus nos: quæ quidem portio &longs;i con&longs;i<lb/>deretur vt &longs;olida, & à reliqua terra præci&longs;a, erit corpus rotundum, <expan abbr="vtrinq;">vtrinque</expan> <lb/>tamen duobus planis circulis ad in&longs;tar tympani terminatum: Ductis dein<lb/>de &longs;imiliter alijs quattuor lineis à centro Z, ver&longs;us polum antarticum fit al<lb/>terum tympanum H D E G, au&longs;tralis terræ habitabilis, vt in figura manife<lb/>&longs;tum e&longs;t. </s>

<s>fui&longs;&longs;e autem huiu&longs;modi habitabilis terræ &longs;egmenta figuræ tympa<lb/>ni &longs;imilia, optimè declarant veteres figuræ geographicæ Ptol&ecedil;mei, & patet <lb/>etiam ex longitudine, & latitudine, vt benè ait Ari&longs;t. </s>

<s>quas Geographi por<lb/>tioni terræ habitabili attribuebant, longitudinem enim dixerunt eius di<lb/>men&longs;ionem ab occa&longs;u ad ortum: latitudinem autem à &longs;eptentrione in meri<lb/>diem, eò quòd illa multò hac longior e&longs;&longs;et. </s>

quas Geographi por<lb/>tioni terræ habitabili attribuebant, longitudinem enim dixerunt eius di<lb/>men&longs;ionem ab occa&longs;u ad ortum: latitudinem autem à &longs;eptentrione in meri<lb/>diem, eò quòd illa multò hac longior e&longs;&longs;et. </s>

<s>Ex quibus apparet habitatam <lb/>fui&longs;&longs;e veluti Zonam, terram ab occa&longs;u ad ortum præcingentem. </s>

<s>quæ Zona <lb/>&longs;i &longs;umatur cum &longs;oliditate, quam ambit, ab Ari&longs;t. </s>

<s>quæ Zona <lb/>&longs;i &longs;umatur cum &longs;oliditate, quam ambit, ab Ari&longs;t.

<s>tympano a&longs;&longs;imilatur.</s>

tympano a&longs;&longs;imilatur.</s>

Line 5648

<s>Summæ 2. cap. </s>

<s>3. de <expan abbr="v&etilde;tis">ventis</expan> <emph type="italics"/>(Oportet autem de &longs;itu &longs;imul rationes ex de&longs;criptio <lb/>ne con&longs;iderare)<emph.end type="italics"/> ide&longs;t rationes ventorum ex de&longs;criptione, ide&longs;t in figura ali<lb/>qua, vt in &longs;equenti con&longs;iderare; &longs;olet enim Ari&longs;t. </s>

<s>figuras, imò demon&longs;tratio<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;æpius in Logicis <lb/>monuimus.</s>

figuras, imò demon&longs;tratio<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;æpius in Logicis <lb/>monuimus.</s>

<s><emph type="italics"/>De&longs;criptus &longs;it igitur, vt clarior res euadat horizontis circulus quapropter, & <lb/>rotundus)<emph.end type="italics"/> vt in &longs;equenti figura circulus A G B H, de&longs;criptus horizontem <lb/>referret,</s><figure></figure><pb pagenum="112"/>

Line 5686

<s>Diameter autem K I, iuxta circulum &longs;emper con&longs;pi<lb/>cuum e&longs;&longs;e &longs;olet, non tamen exactè)<emph.end type="italics"/> ide&longs;t linea K I, &longs;olet in horizonte referre <lb/>diametrum circuli omnium &longs;emper apparentium maximi, eo quod &longs;it ferè <lb/>&longs;ub diametro illius, in qualibet enim &longs;phæra obliqua, ide&longs;t, in qua polus cle<pb pagenum="113"/>natur, intelligunt A&longs;tronomi circulum quendam &longs;emper apparentium ma<lb/>ximum, quem de&longs;cribunt ex ip&longs;o polo, tanquam centro, & interuailo v&longs;que <lb/>ad horizontem, circa ip&longs;um polum: hunc appellant &longs;emper apparentium, <lb/>maximum, quia intra hunc alios quamplurimos concipiunt circa eundem <lb/>polum, quorum minores &longs;emper &longs;unt polo propinquiores. </s>

<s>huius igitur dia<lb/>metrum vult Ari&longs;t. </s>

<s>huius igitur dia<lb/>metrum vult Ari&longs;t.

<s>per lineam, quæ à K, in I, duceretur (quamuis non exa<lb/>ctè) repre&longs;entari.</s>

per lineam, quæ à K, in I, duceretur (quamuis non exa<lb/>ctè) repre&longs;entari.</s>

<s><emph type="italics"/>Contrarij autem non &longs;unt his &longs;latibus, <expan abbr="neq;">neque</expan> ip&longs;i Me&longs;e, &longs;piraret enim <expan abbr="vtiq;">vtique</expan> aliquis <lb/>ab eo, in quo M. hoc enim illi e&longs;t &longs;ecundum diametrum; <expan abbr="neq;">neque</expan> Tra&longs;ciæ ab N, enim, <lb/>quod punctum per diametrum aduer&longs;um illi e&longs;t, &longs;piraret. </s>

<s>Ni&longs;i ab eo veniat, qui ta<lb/>men non longè progreditur ventus quidam, quem accolæ Phæniciam vocant. </s>

<s>maxi<lb/>mè igitur præcipui, & definiti venti hi &longs;unt: <expan abbr="hoc&qacute;">hocque</expan>, modo di&longs;po&longs;iti)<emph.end type="italics"/> &longs;upradicta por<lb/>rò omnia ex &longs;equenti figura optimè poterunt intelligi, quam diligenti ope<lb/>ra ad mentem Ari&longs;t. </s>

<s>ex græcis codicibus re&longs;tituere conatus &longs;um, cum ani<lb/>maduerterem figuras val dè deprauatas pa&longs;&longs;im apud <expan abbr="cõmentatores">commentatores</expan> reperiri. <lb/></s>

ex græcis codicibus re&longs;tituere conatus &longs;um, cum ani<lb/>maduerterem figuras val dè deprauatas pa&longs;&longs;im apud <expan abbr="cõmentatores">commentatores</expan> reperiri. <lb/></s>

<s>Porrò ad literam M, in figura &longs;crip&longs;i ventum Libonotum, quem Ari&longs;t. </s>

<s>Porrò ad literam M, in figura &longs;crip&longs;i ventum Libonotum, quem Ari&longs;t.

<s>qui<lb/>dem non ponit propter ip&longs;ius paruitatem; imò apertè dicit Hele&longs;pontum <lb/>non habere contrarium: &longs;ed feci, vt completum ventorum numerum, quem <lb/>alij tradunt, haberemus.</s>

qui<lb/>dem non ponit propter ip&longs;ius paruitatem; imò apertè dicit Hele&longs;pontum <lb/>non habere contrarium: &longs;ed feci, vt completum ventorum numerum, quem <lb/>alij tradunt, haberemus.</s>

<s><emph type="italics"/>Ex Tertio Meteororum.<emph.end type="italics"/></s>

Line 5752

<s>qui geometricam huius rci continet demon&longs;trationem, explicemus. </s>

<s>Suppo<lb/>nit igitur primò Ari&longs;t. </s>

<s>Suppo<lb/>nit igitur primò Ari&longs;t.

<s>lineas vi&longs;uales à &longs;ydere B, ad oculos no&longs;tros A, per <lb/>nubem roridam C D F, procedentes, in nube con&longs;imiliter refrangi, ide&longs;t <expan abbr="vn-diq;">vn<lb/>dique</expan> circa Solem, Lunamuè facere angulos refractionis æquales. </s>

lineas vi&longs;uales à &longs;ydere B, ad oculos no&longs;tros A, per <lb/>nubem roridam C D F, procedentes, in nube con&longs;imiliter refrangi, ide&longs;t <expan abbr="vn-diq;">vn<lb/>dique</expan> circa Solem, Lunamuè facere angulos refractionis æquales. </s>

<s>quod etiam <pb pagenum="115"/>patet ex 48. 10. Vitellionis; vt in figura, in qua &longs;ydus B, oculus A, nubes <lb/>C D F, radij vi&longs;uales tres refracti in nube &longs;int B C A, B D A, B E A, facien<lb/>tes con&longs;imilem refractionem, ide&longs;t angulos refractos B C A, B D A, B E A, <lb/>æquales in punctis C, D, F: <expan abbr="atq;">atque</expan> hoc e&longs;t con&longs;imilem facere refractionem. <lb/></s>

Line 5778

<s><emph type="italics"/>Qvod autem <expan abbr="neq;">neque</expan> circulum po&longs;&longs;ibile &longs;it fieri Iridis, <expan abbr="neq;">neque</expan> maiorem &longs;emicir<lb/>culo portionem, & de alijs accidentibus circa ip&longs;am, ex de&longs;criptione <lb/>erit con&longs;iderantibus manife&longs;tum)<emph.end type="italics"/> In Logicis &longs;æpius monui Ari&longs;t. </s>

<s>per <lb/>de&longs;criptiones intelligere geometricas demon&longs;trationes, quod <lb/>etiam hoc loco confirmatur, vbi Geometrica demon&longs;tratione quam de&longs;cri<lb/>ptionem appellat, Iridis figuræ accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/>circularis, nunquam tamen circulus integer, imò <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/>maior, &longs;ed tamen &longs;emicirculo minor.</s>

per <lb/>de&longs;criptiones intelligere geometricas demon&longs;trationes, quod <lb/>etiam hoc loco confirmatur, vbi Geometrica demon&longs;tratione quam de&longs;cri<lb/>ptionem appellat, Iridis figuræ accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/>circularis, nunquam tamen circulus integer, imò <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/>maior, &longs;ed tamen &longs;emicirculo minor.</s>

Line 5848

<s>atqui con<lb/>&longs;imiles anguli, &longs;iue æquales, non ni&longs;i in orbem po&longs;&longs;unt con&longs;titui; igitur an<lb/>gulorum æqualitas cau&longs;a erit rotundationis arcus. </s>

<s>h&ecedil;c e&longs;t &longs;umma totius di<lb/>&longs;cur&longs;us, quem pluribus, & nimis ob&longs;curè Ari&longs;t. </s>

<s>h&ecedil;c e&longs;t &longs;umma totius di<lb/>&longs;cur&longs;us, quem pluribus, & nimis ob&longs;curè Ari&longs;t.

<s>explicat.</s>

explicat.</s>

<s>Inquit igitur Ari&longs;t. </s>

Line 5886

<s>Verumenimuerò ad quid probatio hæc? </s>

<s>non po&longs;&longs;e duas <lb/>alias lineas in eodem plano, &c.? exi&longs;timo Ari&longs;t. </s>

<s>non po&longs;&longs;e duas <lb/>alias lineas in eodem plano, &c.? exi&longs;timo Ari&longs;t.

<s>idcircò hoc proba&longs;&longs;e, quia <lb/>&longs;i aliæ duæ lineæ habentes eandem rationem, po&longs;&longs;ent collocari in eodem <lb/>plano; e&longs;&longs;ent <expan abbr="permutãdo">permutando</expan> illæ duæ (in priori figura) G R, R K. <expan abbr="vtraq;">vtraque</expan> <expan abbr="vtriq;">vtrique</expan> <lb/>æquales prioribus G M, M K, per quas videtur Iris, cum enim K R, &longs;it æqua<lb/>lis ip&longs;i K M, erit, & G M, æqualis ip&longs;i G R, per 7. 5. & in eius &longs;cholio. </s>

idcircò hoc proba&longs;&longs;e, quia <lb/>&longs;i aliæ duæ lineæ habentes eandem rationem, po&longs;&longs;ent collocari in eodem <lb/>plano; e&longs;&longs;ent <expan abbr="permutãdo">permutando</expan> illæ duæ (in priori figura) G R, R K. <expan abbr="vtraq;">vtraque</expan> <expan abbr="vtriq;">vtrique</expan> <lb/>æquales prioribus G M, M K, per quas videtur Iris, cum enim K R, &longs;it æqua<lb/>lis ip&longs;i K M, erit, & G M, æqualis ip&longs;i G R, per 7. 5. & in eius &longs;cholio. </s>

<s>qua<lb/>re natura ageret tam per lineas breui&longs;&longs;imas <expan abbr="ag&etilde;do">agendo</expan> per has, quam per illas, <lb/><expan abbr="hoc&qacute;">hocque</expan>; pacto perhas etiam Iris videri po&longs;&longs;et. </s>

Line 5922

<s>polus e&longs;t punctum extra planum circuli, ex quo tamen <lb/>vt <expan abbr="c&etilde;tro">centro</expan> adhibito circino circuli periphæria de&longs;cribi pote&longs;t; &longs;ic polus æqua<lb/>toris e&longs;t idem, qui polus mundi: <expan abbr="centr&utilde;">centrum</expan> verò e&longs;t in plano &longs;ui cir culi, &longs;ic cen<lb/>trum æquatoris e&longs;t idem cum centro mundi, cum æquator per illud incedat.</s>

<s>Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t. </s>

<s>Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t.

<s>cum data &longs;it proportio linearum K M, & M G, in &longs;upe<lb/>riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex<lb/><figure id="fig56"></figure><lb/>ponatur alia linea recta B D. quæ diui<lb/>datur in partes B, & D. proportionales <lb/>cum lineis K M, G M, per 10. 6. cum <lb/>ergo K M, &longs;it minor quàm G M, per 19. <lb/>primi, quia in triangulo G M K, oppo<lb/>nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor quàm D, addatur iam ip&longs;i B. linea <lb/>nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, & D, per 11. 6. <lb/>hoc ordine, vt F B, ad D. ita D, ad B. </s>

cum data &longs;it proportio linearum K M, & M G, in &longs;upe<lb/>riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex<lb/><figure id="fig56"></figure><lb/>ponatur alia linea recta B D. quæ diui<lb/>datur in partes B, & D. proportionales <lb/>cum lineis K M, G M, per 10. 6. cum <lb/>ergo K M, &longs;it minor quàm G M, per 19. <lb/>primi, quia in triangulo G M K, oppo<lb/>nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor quàm D, addatur iam ip&longs;i B. linea <lb/>nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, & D, per 11. 6. <lb/>hoc ordine, vt F B, ad D. ita D, ad B. </s>

<s>Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>B, ad aliam, quæ &longs;it K P, in eadem figura per 12. 6. & à puncto P, ad M, iun<lb/>gatur recta P M. </s>

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<s>Porrò &longs;ciendum po&longs;&longs;e nos breuius polum prædictum inuenire, &longs;i nimirum <lb/><figure id="fig57"></figure><lb/>ad M, ducatur M P, faciens angulum K P M, æqua<lb/>lem angulo G M K, per 23. primi, erunt enim duo <lb/>triangula <expan abbr="æquiãgula">æquiangula</expan> G P M, K P M, angulus enim <lb/>P, e&longs;t communis, angulus verò M K P, e&longs;t æqualis <lb/>duobus G, & G M K, per 32. primi, ergo etiam <lb/>duobus ad M, &longs;iue toti G M P, & reliquus K M P, <lb/>reliquo, quare per 4.6. latera circa angulos æqua<lb/>les proportionalia erunt, & omologa G M, ad M K, ita G P, ad P M, quæ <lb/>æqualibus augulis &longs;ubtenduntur. </s>

<s><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habcbant etiam <lb/>triangula Ari&longs;t. </s>

<s><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habcbant etiam <lb/>triangula Ari&longs;t.

<s>in figura, de qua paulò ante dicebam. </s>

in figura, de qua paulò ante dicebam. </s>

<s>Verba illa <emph type="italics"/>(Quæ ali<lb/>b quam in &longs;emicirculo constituuntur)<emph.end type="italics"/> &longs;unt perperam in antiqua tran&longs;latione <lb/>tran&longs;lata, nam Græcè &longs;ic, <foreign lang="greek">ai alloqi tou_ hmixoxlnou/ sunisamenai,</foreign> transferenda <lb/>e&longs;&longs;ent, quæ in alio circuli loco concurrunt.</s>

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<s>&longs;ic enim &longs;ola portio S L T, appareret nobis, <expan abbr="e&longs;-&longs;et&qacute;">e&longs;<lb/>&longs;etque</expan>; rationabiliter con&longs;tituta. </s>

<s>Ex quibus 2. Ari&longs;t. </s>

<s>Ex quibus 2. Ari&longs;t.

<s>propo&longs;itio manife&longs;ta e&longs;t.</s>

propo&longs;itio manife&longs;ta e&longs;t.</s>

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<s>Ibidem <emph type="italics"/>(Minima autem cum in meridie, quanto enim &longs;uperius G, tanto in&longs;e<lb/>rius & polus, & centrum circuli erit)<emph.end type="italics"/> probat tertiam propo&longs;itionem, nimi<lb/>rum Sole exi&longs;tente in meridie minimam <expan abbr="omni&utilde;">omnium</expan> e&longs;&longs;e Iridis arcus portionem: <lb/>ratio autem e&longs;t, quia tunc G, &longs;iue Sol, e&longs;t alti&longs;&longs;imus &longs;upra horizontem, & <lb/>con&longs;equenter <foreign lang="greek">w;</foreign> centrum Iridis e&longs;t depre&longs;si&longs;&longs;imum, quare tunc maxima cir<lb/>culi Iridis portio ab&longs;condetur, & proinde minima apparebit, quod erat vl<lb/>timo <expan abbr="demõ&longs;trandum">demon&longs;trandum</expan>. </s>

<s>Non me latet has Ari&longs;t. </s>

<s>Non me latet has Ari&longs;t.

<s>figurationes e&longs;&longs;e apud Olym<lb/>piodorum nonnullis obiectionibus obnoxias, &longs;ed cum facilè dilui po&longs;&longs;int, & <lb/>etiam &longs;i non diluantur, &longs;aluetur tamen veritas Ari&longs;totelicæ demon&longs;tratio<lb/>nis, breuitati &longs;tudens, con&longs;ultò eas prætermitto.</s>

figurationes e&longs;&longs;e apud Olym<lb/>piodorum nonnullis obiectionibus obnoxias, &longs;ed cum facilè dilui po&longs;&longs;int, & <lb/>etiam &longs;i non diluantur, &longs;aluetur tamen veritas Ari&longs;totelicæ demon&longs;tratio<lb/>nis, breuitati &longs;tudens, con&longs;ultò eas prætermitto.</s>

<s>Aduertendum præterea Vicomercatum inordinatè citare librum Dato<lb/>rum Euclidis, & <expan abbr="quandoq;">quandoque</expan> etiam malè citare Euclidem ip&longs;um. </s>

Line 6028

<s>vel &longs;equentem no&longs;tram <lb/>de Iride additionem. </s>

<s>ego enim longiorem hanc, <expan abbr="atq;">atque</expan> impeditam Ari&longs;t. </s>

<s>ego enim longiorem hanc, <expan abbr="atq;">atque</expan> impeditam Ari&longs;t.

<s>tra<lb/>ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e<lb/>quutus &longs;um.</s>

tra<lb/>ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e<lb/>quutus &longs;um.</s>

Line 6080

<s>Quintò, &longs;equitur ex prædictis arcum videri &longs;emper &longs;ub &longs;tato, ac determi<lb/>nato reflexionis angulo, &longs;cilicet &longs;ub &longs;emirecto, <expan abbr="neq;">neque</expan> po&longs;&longs;e per alium videri. <lb/></s>

<s>quod etiam probari pote&longs;t ex Ari&longs;t. </s>

<s>quod etiam probari pote&longs;t ex Ari&longs;t.

<s>quia nimirum videmus arcum apparere <lb/>con&longs;imiliter in ambitu circulari, ergò nece&longs;&longs;ariò apparebit <expan abbr="vbiq;">vbique</expan> in toto il<lb/>lo ambitu per con&longs;imilem reflexionem, &longs;iue per æquales reflexionis angulos, <lb/>pro quibus omnibus vnus cernitur in figura angulus A B C.</s>

quia nimirum videmus arcum apparere <lb/>con&longs;imiliter in ambitu circulari, ergò nece&longs;&longs;ariò apparebit <expan abbr="vbiq;">vbique</expan> in toto il<lb/>lo ambitu per con&longs;imilem reflexionem, &longs;iue per æquales reflexionis angulos, <lb/>pro quibus omnibus vnus cernitur in figura angulus A B C.</s>

<s>Sextò, ad Iridis vi&longs;ionem, præter ea, requiri aeris rorantis multiplica<lb/>tionem; &longs;icuti enim nebulam videre nequimus, ni&longs;i aer exhalatione illa in<lb/>fectus multus &longs;it ante oculum no&longs;trum: &longs;ic etiam exi&longs;timo ad Iridis appari<lb/>tionem, opus e&longs;&longs;e plurima nube rore&longs;cente, vt ex multiplicatione guttula<lb/>rum, quarum aliæ po&longs;t alias &longs;int, totus tandem Iris appareat. </s>

Line 6258

<s>per quæ duo pun<lb/>cta intelligatur ducta recta linea A B, intelligatur <expan abbr="etiã">etiam</expan> <lb/>circulus A B C, qui &longs;ecet &longs;phæram per centrum C. & <lb/>per puncta A, B, ergo ex demon&longs;tratis ab Euclide li<lb/>nea A B, quæ coniungit puncta A B, cadet intra prædi<lb/>ctum circulum; &longs;ed linea hæc e&longs;t in plano tangente ex <lb/>&longs;uppo&longs;itione, circulus verò in &longs;phæra; ergò cum linea <lb/>cadat intra circulum, cadet etiam nece&longs;&longs;ariò planum <lb/>in quo e&longs;t linea, & cum linea cadat intra circulum, cadet etiam nece&longs;&longs;ariò <lb/>intra &longs;phæram; <expan abbr="idem&qacute;">idemque</expan>; faciet planum, quod eam nece&longs;&longs;ariò &longs;equatur, ergò <lb/>planum &longs;ecat &longs;phæram, non autem tangit, quod e&longs;t ab&longs;urdum, quia contra <lb/>hypothe&longs;im, &longs;upponunt autem Mathematici, entia hæc mathematica e&longs;&longs;e <lb/>perfecta, qualia in &longs;ublunaribus fortè non reperiuntur; ænea enim &longs;phæra <lb/>nulla erit perfectè rotunda, vel planum aliquod perfectè complanatum, vt <lb/>ip&longs;i &longs;upponunt, eò quod materiæ imperfectio, ac ruditas id nequaquam pa<lb/>tiatur. </s>

<s>quare cum huiu&longs;inodi entia non reperiantur ab&longs;tracta ab impura hac <lb/>materia, nullum erit inquit Ari&longs;t. </s>

<s>quare cum huiu&longs;inodi entia non reperiantur ab&longs;tracta ab impura hac <lb/>materia, nullum erit inquit Ari&longs;t.

<s>ab&longs;tractum planum, quod po&longs;&longs;it mathe<lb/>maticè, <expan abbr="atq;">atque</expan> adeò in vnico puncto mathematico &longs;phæram tangere. </s>

ab&longs;tractum planum, quod po&longs;&longs;it mathe<lb/>maticè, <expan abbr="atq;">atque</expan> adeò in vnico puncto mathematico &longs;phæram tangere. </s>

<s><expan abbr="hucu&longs;q;">hucu&longs;que</expan> <lb/>nece&longs;&longs;aria &longs;unt mathematica ad huius loci <expan abbr="intelligentiã">intelligentiam</expan>. </s>

Line 6280

<s>æquale altera parte longiori rectangulum æquilaterum <lb/>e&longs;&longs;e, talis autem definitio ratio conclu&longs;ionis. </s>

<s>dicens autem, quod tetragoni&longs;mus e&longs;t <lb/>medij inuentio rei cau&longs;am dicit)<emph.end type="italics"/> aggre&longs;&longs;urus Ari&longs;t. </s>

<s>dicens autem, quod tetragoni&longs;mus e&longs;t <lb/>medij inuentio rei cau&longs;am dicit)<emph.end type="italics"/> aggre&longs;&longs;urus Ari&longs;t.

<s>animæ definitionem præ<lb/>mittit duplicem e&longs;&longs;e definitionem, alteram &longs;cilicet, quæ explicat &longs;olum rei <lb/>e&longs;&longs;entiam, quam dicunt formalem definitionem; alteram verò, quæ præte<lb/>rea explicat etiam rei cau&longs;am, quam dicunt cau&longs;alem definitionem: vtram<lb/>que autem exemplo Geometrico explicat.</s>

animæ definitionem præ<lb/>mittit duplicem e&longs;&longs;e definitionem, alteram &longs;cilicet, quæ explicat &longs;olum rei <lb/>e&longs;&longs;entiam, quam dicunt formalem definitionem; alteram verò, quæ præte<lb/>rea explicat etiam rei cau&longs;am, quam dicunt cau&longs;alem definitionem: vtram<lb/>que autem exemplo Geometrico explicat.</s>

Line 6320

<s>13. dicta &longs;unt, illa enim omnia in hunc lo<lb/>cum quadrant. </s>

<s>Verum occurrit illa dubitatio; quod cum Ari&longs;t. </s>

<s>Verum occurrit illa dubitatio; quod cum Ari&longs;t.

<s>ibi dicat <lb/><emph type="italics"/>(Vox acuta quidem velox)<emph.end type="italics"/> hic autem <emph type="italics"/>(Non igitur velox e&longs;t acutum<emph.end type="italics"/>) repugnan<lb/>tia dicere videtur. </s>

ibi dicat <lb/><emph type="italics"/>(Vox acuta quidem velox)<emph.end type="italics"/> hic autem <emph type="italics"/>(Non igitur velox e&longs;t acutum<emph.end type="italics"/>) repugnan<lb/>tia dicere videtur. </s>

<s>cui dubitationi &longs;ic occurrendum; vt dicamus ibi Philo<lb/>&longs;ophum dicere vocem acutam e&longs;&longs;e velocem, quatenus acumen vocis oritur <pb pagenum="134"/>ex velocitate motus aerem impellentis. </s>

Line 6394

<s>8. <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> magis e&longs;t &longs;entire &longs;implex <gap/>xi&longs;tens, quàm mixtum, velut <lb/>vinum non temperatum, quàm temperatum; & mel, & colorem, & neten &longs;olam. <lb/></s>

<s>Cap. 8. <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> magis e&longs;t &longs;entire &longs;implex <gap/>xi&longs;tens, quàm mixtum, velut <lb/>vinum non temperatum, quàm temperatum; & mel, & colorem, & neten &longs;olam. <lb/></s>

<s>quàm in diapa&longs;on, quia ob&longs;curant &longs;e inu<gap/>cem)<emph.end type="italics"/> nete apud veteres mu&longs;icos erat <lb/>in mu&longs;icis in&longs;trumentis omnium chordarum acuti&longs;&longs;ima, cuiu&longs;modi apud <lb/>nos e&longs;t, quam vulgò canto appellant. </s>

Line 6404

<s>hæ duæ &longs;imul pul&longs;atæ <lb/>edebant conionantiam, quæ Diapa&longs;on dicitur, & vulgò octaua. </s>

<s>ex quibus <lb/>&longs;en&longs;us verberum Ari&longs;t. </s>

<s>ex quibus <lb/>&longs;en&longs;us verberum Ari&longs;t.

<s>manife&longs;tus e&longs;t.</s><pb pagenum="135"/>

manife&longs;tus e&longs;t.</s><pb pagenum="135"/>

Line 6432

<s>1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis æquales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos æqua<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s>

<s>Cap. 1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis æquales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos æqua<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s>

<s>lege annotata primo <lb/>Po&longs;ter. </s>

Line 6446

<s>3. <emph type="italics"/>(Sunt facilè remini&longs;cibilia, <expan abbr="quæcunq;">quæcunque</expan> habent ordinationem aliquam, <lb/>vt mathemata)<emph.end type="italics"/> h&ecedil;c Philo&longs;ophus dicensfp ectabat ad mirabilem illam, ac per<lb/>petuam de mon&longs;trationum connexionem, qua Geometræ omnes, & præci<lb/>puè Euclides opera &longs;ua ab initio ad finem v&longs;que, diuino planè ingenij acu<lb/>mine deduxerunt.</s>

<s>Cap. 3. <emph type="italics"/>(Sunt facilè remini&longs;cibilia, <expan abbr="quæcunq;">quæcunque</expan> habent ordinationem aliquam, <lb/>vt mathemata)<emph.end type="italics"/> h&ecedil;c Philo&longs;ophus dicensfp ectabat ad mirabilem illam, ac per<lb/>petuam de mon&longs;trationum connexionem, qua Geometræ omnes, & præci<lb/>puè Euclides opera &longs;ua ab initio ad finem v&longs;que, diuino planè ingenij acu<lb/>mine deduxerunt.</s>

<s><emph type="italics"/>Ex Libro de Somnijs.<emph.end type="italics"/></s>

Line 6456

<s>2. <emph type="italics"/>(Cur autem fallimur, cau&longs;a e&longs;t, quoniam non &longs;olum cum &longs;en&longs;ibile <lb/>mouetur apparent quælibet, &longs;ed etiam cum &longs;en&longs;us ip&longs;e mouetur, &longs;i eodem <lb/>modo moueatur, quemadmodum à &longs;en&longs;ibili. </s>

<s>Cap. 2. <emph type="italics"/>(Cur autem fallimur, cau&longs;a e&longs;t, quoniam non &longs;olum cum &longs;en&longs;ibile <lb/>mouetur apparent quælibet, &longs;ed etiam cum &longs;en&longs;us ip&longs;e mouetur, &longs;i eodem <lb/>modo moueatur, quemadmodum à &longs;en&longs;ibili. </s>

<s>dico autem velut terra vi<lb/>detur nauigantibus moueri, dummodo vi&longs;us ab alio)<emph.end type="italics"/> reddit rationem, <lb/>cur nauigantibus videatur terra ip&longs;a moueri, ac retrocedere, non autem <lb/>ip&longs;i nauigantes, quin potius ip&longs;i fibi &longs;tare videantur. </s>

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<s>3. <emph type="italics"/>(Quemadmodum igitur, &longs;i quem lateat &longs;uppo&longs;itus oculo digitus, non <lb/>&longs;olum app trebit, &longs;ed etiam putabitur duo, quod e&longs;t vnum. </s>

<s>Cap. 3. <emph type="italics"/>(Quemadmodum igitur, &longs;i quem lateat &longs;uppo&longs;itus oculo digitus, non <lb/>&longs;olum app trebit, &longs;ed etiam putabitur duo, quod e&longs;t vnum. </s>

<s>Si verò non lateat appa<lb/>rebit quidem, non putabitur tamen)<emph.end type="italics"/> e&longs;t hæc optica deceptio, quæ tunc accidit, <lb/>cum aliquod obiectum intuentes, interim digito alterum oculum &longs;ur&longs;um <lb/>pellimus, ita vt oculi propterea varient &longs;itum re&longs;pectu obiecti, &longs;iue non eo<pb pagenum="136"/>dem &longs;itu vterque obiectum intueatur, hoc e&longs;t, vt optici aiunt, axes vi&longs;uales <lb/>non amplius concurrunt &longs;imul in rem vi&longs;am. </s>

Line 6508

<s>2. <emph type="italics"/>(Sicut de præ&longs;tigio&longs;is, quæ per &longs;e mouentur, illi qui nondum &longs;peculati <lb/>&longs;unt cau&longs;am<emph.end type="italics"/>) verbis illis (<emph type="italics"/>Quæ per &longs;emouentur<emph.end type="italics"/>) vnica dictio <expan abbr="Græcare&longs;põdet">Græcare&longs;pondet</expan>, <lb/>Automata. </s>

<s>Cap. 2. <emph type="italics"/>(Sicut de præ&longs;tigio&longs;is, quæ per &longs;e mouentur, illi qui nondum &longs;peculati <lb/>&longs;unt cau&longs;am<emph.end type="italics"/>) verbis illis (<emph type="italics"/>Quæ per &longs;emouentur<emph.end type="italics"/>) vnica dictio <expan abbr="Græcare&longs;põdet">Græcare&longs;pondet</expan>, <lb/>Automata. </s>

<s>erant autem Automata apud veteres Gr&ecedil;cos machinæ qu&ecedil;dam, <lb/>quæ à Mathematicis Mechanicæ artis occultis quibu&longs;dam ingenijs, ea arte <lb/>con&longs;truebantur, vt à &longs;eip&longs;is de loco ad locum, ac &longs;i viuæ e&longs;&longs;ent &longs;pontè pro<lb/>grederentur; vnde, & automata, qua&longs;i &longs;pontanca dicebantur. </s>

Line 6522

<s>3. (<emph type="italics"/>Aut de &longs;ol&longs;titijs<emph.end type="italics"/>) quid &longs;ol&longs;titium, cur dicatur &longs;ol&longs;titium, & cur Sol <lb/>in <expan abbr="vtroq;">vtroque</expan> topico, quoad dierum incrementum, ac decrementum, & quoad <lb/>eleuationem eius, aut depre&longs;&longs;ionem meridianam, videatur moras trahere, <lb/>quamuis no&longs;trum &longs;it explicare, ob rei tamen facilitatem omittantur. </s>

<s>Cap. 3. (<emph type="italics"/>Aut de &longs;ol&longs;titijs<emph.end type="italics"/>) quid &longs;ol&longs;titium, cur dicatur &longs;ol&longs;titium, & cur Sol <lb/>in <expan abbr="vtroq;">vtroque</expan> topico, quoad dierum incrementum, ac decrementum, & quoad <lb/>eleuationem eius, aut depre&longs;&longs;ionem meridianam, videatur moras trahere, <lb/>quamuis no&longs;trum &longs;it explicare, ob rei tamen facilitatem omittantur. </s>

<s>Hoc <lb/>tantum &longs;cias velim &longs;ol&longs;titiorum cau&longs;am e&longs;&longs;e Zodiaci ad Tropicos longio<lb/>rem adhæ&longs;ionem, ide&longs;t, quòd Zodiacus propè contactum tropicorum ab ijs <lb/>parum recedat, cum ergo Sol motu proprio &longs;emper per Zodiacum inam<lb/>bulet, fit vt ip&longs;e <expan abbr="quoq;">quoque</expan> pariter modicum à tropicis remoueatur, imò pluri<lb/>mum &longs;ecus illos incedat, ita vt eo tempore, quo ad eos paulatim accedit, <lb/>aut ab eis paulatim recedit, qua&longs;i &longs;tare, &longs;iue quie&longs;cere apud eo&longs;dem videa<lb/>tur: <expan abbr="atq;">atque</expan> hinc etiam quantitas <expan abbr="dier&utilde;">dierum</expan>, ac noctium videatur ferè nihil variari; <lb/>& noua elcuatio, aut depre&longs;&longs;io Solis &longs;upra horizontem nuila ferè appareat.</s>

Line 6804

<s>1. (<emph type="italics"/>Mathematicorum quoque principia, elementa, & cau&longs;æ &longs;unt<emph.end type="italics"/>) <lb/>notanda &longs;unt hæc aduer&longs;us quo&longs;dam, qui negant in Mathemati<lb/>cis cau&longs;as reperiri, vt hinc <expan abbr="quoq;">quoque</expan> illis &longs;cientiam auferant. </s>

<s>enim<lb/>uerò apertè patet eos falli ex toto hoc Ari&longs;t. </s>

<s>enim<lb/>uerò apertè patet eos falli ex toto hoc Ari&longs;t.

<s>di&longs;cur&longs;u.</s>

di&longs;cur&longs;u.</s>

<s><emph type="italics"/>Ex Nono Metaphy&longs;icæ.<emph.end type="italics"/></s>

Line 6846

<s>tales &longs;unt quatuor anguli <lb/>ad &longs;uperiores partes lineæ B C, & ad punctum A, con&longs;tituti, qui, vt patet, <lb/><figure id="fig69"></figure><lb/>&longs;unt æquales duobus rectis B A D, D A C, <lb/>tales etiam &longs;unt in hac &longs;ecunda figura tres <lb/>anguli B C A, A C D, D C E, qui quidem <lb/>æquales &longs;unt duobus rectis angulis. </s>

<s>hoc <lb/>&longs;en&longs;i&longs;&longs;e Ari&longs;t. </s>

<s>hoc <lb/>&longs;en&longs;i&longs;&longs;e Ari&longs;t.

<s>patet ex demon&longs;tratione 32. <lb/>primi, quæ demon&longs;trat <expan abbr="memoratã">memoratam</expan> ab Ari<lb/>&longs;tot. </s>

patet ex demon&longs;tratione 32. <lb/>primi, quæ demon&longs;trat <expan abbr="memoratã">memoratam</expan> ab Ari<lb/>&longs;tot. </s>

<s>trianguli affectionem, & ad quam <lb/>propterea ip&longs;e &longs;pectabat, cuius figura e&longs;t <lb/>eadem cum hac &longs;ecunda, in qua Euclides o&longs;tendit prædictos tres angulos <lb/>æquari duobus rectis. </s>

Line 6870

<s>nunc &longs;olùm <pb pagenum="143"/><figure id="fig70"></figure><lb/>hæc addenda &longs;unt. </s>

<s>Re&longs;pondet Ari&longs;t. </s>

<s>Re&longs;pondet Ari&longs;t.

<s>quæ<lb/>&longs;ito pr&ecedil;cedenti, cur &longs;cilicet angulus in &longs;e<lb/>micirculo &longs;it rectus, qualis e&longs;t in figura <lb/>angulus A C B, <expan abbr="dicit&qacute;">dicitque</expan>; cau&longs;am e&longs;&longs;e, quia <lb/>in figura tres lineæ &longs;unt æquales, duæ ni<lb/>mirum, in quas ba&longs;is B A, diuiditur, quæ <lb/>&longs;unt B D, D A, & tertia, quæ ex medio <lb/>ba&longs;is erigitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; D C, cum omnes &longs;int <lb/>&longs;emidia metri ciu&longs;dem circuli. </s>

quæ<lb/>&longs;ito pr&ecedil;cedenti, cur &longs;cilicet angulus in &longs;e<lb/>micirculo &longs;it rectus, qualis e&longs;t in figura <lb/>angulus A C B, <expan abbr="dicit&qacute;">dicitque</expan>; cau&longs;am e&longs;&longs;e, quia <lb/>in figura tres lineæ &longs;unt æquales, duæ ni<lb/>mirum, in quas ba&longs;is B A, diuiditur, quæ <lb/>&longs;unt B D, D A, & tertia, quæ ex medio <lb/>ba&longs;is erigitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; D C, cum omnes &longs;int <lb/>&longs;emidia metri ciu&longs;dem circuli. </s>

<s>educta <expan abbr="itaq;">itaque</expan> linea D C, de potentia in actum, <lb/>&longs;i cuipiam trium harum linearum æqualitas innote&longs;cat, continuò ei etiam <lb/>manife&longs;tum erit angulum A C B, in &longs;emicirculo, e&longs;&longs;e rectum. </s>

Line 7126

<s>Cum igitur mo<lb/>uentes &longs;phæræ illæ quidem Saturni, ac Iouis &longs;int octo; reliquorum verò vi<lb/>gintiquinque, nam reliqui Planetæ <expan abbr="quinq;">quinque</expan> &longs;inguli &longs;phæras <expan abbr="quinq;">quinque</expan> mouentes <lb/>habent, quæ omnes &longs;imul numerum <expan abbr="vigintiquinq;">vigintiquinque</expan> explent: quarum omnium <lb/>&longs;olæ inferiores, quibus a&longs;trum affixum volebat, non indigebant reuoluente, <lb/>&longs;equitur duorum &longs;uperiorum Saturni, & Iouis, quorum octo erant mouen<lb/>tes, &longs;ex debere e&longs;&longs;e reuoluentes. </s>

<s>Inferiorum verò quatuor planetarum re<lb/>uoluentes erunt &longs;exdecim: &longs;ed hoc loco Ari&longs;t. </s>

<s>Inferiorum verò quatuor planetarum re<lb/>uoluentes erunt &longs;exdecim: &longs;ed hoc loco Ari&longs;t.

<s>memoria fallit, deberet enim <lb/>dicere, reliquorum <expan abbr="quinq;">quinque</expan> planetarum reuoluentes erunt vigintì, &longs;unt enim <lb/>planetæ &longs;eptem, quorum Saturno, ac Ioui &longs;upremis &longs;ex reuoluentes attri<lb/>buit habita ratione &longs;phæratum mouentium; reliquis igitur <expan abbr="quinq;">quinque</expan> planetis <lb/>habita ratione &longs;uorum orbium mouentium, 25. cum &longs;inguli habeant <expan abbr="quinq;">quinque</expan> <lb/>mouentes, habebunt ex prælcripto Calippi &longs;inguli 4. reuoluentes; ac pro<lb/>inde 20. in vniuer&longs;um erunt reuoluentes. </s>

memoria fallit, deberet enim <lb/>dicere, reliquorum <expan abbr="quinq;">quinque</expan> planetarum reuoluentes erunt vigintì, &longs;unt enim <lb/>planetæ &longs;eptem, quorum Saturno, ac Ioui &longs;upremis &longs;ex reuoluentes attri<lb/>buit habita ratione &longs;phæratum mouentium; reliquis igitur <expan abbr="quinq;">quinque</expan> planetis <lb/>habita ratione &longs;uorum orbium mouentium, 25. cum &longs;inguli habeant <expan abbr="quinq;">quinque</expan> <lb/>mouentes, habebunt ex prælcripto Calippi &longs;inguli 4. reuoluentes; ac pro<lb/>inde 20. in vniuer&longs;um erunt reuoluentes. </s>

<s>Omnium igitur &longs;phærarum tam <lb/>mouentium, quàm reuoluentium &longs;ummam ait, &longs;ed perperam, e&longs;&longs;e quinqua<lb/>gintaquinque; cum enim mouentes Saturni, & Iouis &longs;int 8. reliquorum au<lb/>tem 25. reuoluentes verò Saturni, & Iouis &longs;int 6. reliquorum autem, vt ip<lb/>&longs;e memoria fal&longs;us ponit, &longs;exdecim, conflant quidem &longs;ummam prædictam, <lb/>&longs;ed illi in memoria reuocandus e&longs;t, planeta ille, quem oblitus e&longs;t, cuius &longs;unt <lb/>quatuor reuoluentes, qui prioribus additi &longs;phærarum errantium numerum <lb/>quinquaginta nouem con&longs;tituent: quibus etiam addenda e&longs;t octaua &longs;phæra, <lb/>&longs;eu firmamentum, quod inerrantium &longs;edes e&longs;t, non enim &longs;olum errantium, <lb/>&longs;ed omnium c&oelig;le&longs;tium orbium numerum inue&longs;tigare volebat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; e&longs;&longs;ent <lb/>omnes &longs;ecundum Calippum &longs;ph&ecedil;ræ &longs;exaginta. </s>

Line 7196

<s>De dignitatibus, <expan abbr="admirandis&qacute;">admirandisque</expan>; Circuli proprietatibus.</s>

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

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

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

<s>Cvm vellet Ari&longs;t. </s>

<s>Cvm vellet Ari&longs;t.

<s>mirabilium effectuum, quos in Mechanicis admi<lb/>ramur, cau&longs;am referre in circulum: meritò ante omnia de admi<lb/>randa ip&longs;ius circuli natura di&longs;&longs;erit, quo minus mirum deinde vi<lb/>deatur prædictas mirabiles-operationes exip&longs;o procedere. </s>

mirabilium effectuum, quos in Mechanicis admi<lb/>ramur, cau&longs;am referre in circulum: meritò ante omnia de admi<lb/>randa ip&longs;ius circuli natura di&longs;&longs;erit, quo minus mirum deinde vi<lb/>deatur prædictas mirabiles-operationes exip&longs;o procedere. </s>

<s>quan<lb/>doquidem exadmiranda cau&longs;a admirabiles effectus prodire debeant. </s>

Line 7274

<s>vt e&longs;t pro<lb/>portio lateris B E, ad E C, latus, &longs;equeretur <lb/>ex demon&longs;tratis ip&longs;um B, ferri per <expan abbr="rectã">rectam</expan> B C, <lb/>quæ diameter e&longs;&longs;et quadrilateri B E C G. &longs;ed <pb pagenum="152"/>quia in nu&longs;la proportione fertur, propterea per circularem lineam B E C, <lb/>progreditur ad C, ita vt ip&longs;a diameter B D, in po&longs;itione A C, fiat perpendi<lb/>cularis priori diametro B D. ex quibus &longs;equitur eam moueri duobus moti<lb/>bus nullam rationem habentibus; quod erat intentum.</s>

<s>Hoc modo Ari&longs;t. </s>

<s>Hoc modo Ari&longs;t.

<s>probare conatur, lineam circulum de&longs;cribentem, dua<lb/>bus ferri lationibus, quæ nullam habeant analogiam: Yerùm, vt liberè fa<lb/>tear nullo modo mihi videtur intentum a&longs;&longs;equi, nam <expan abbr="neq;">neque</expan> ex dictis pater, <lb/>ip&longs;am duobus motibus ferri, quibus opus e&longs;&longs;et: neque patet eos (quamuis <lb/>concedantur) nullam inuicem habere analogiam: qui enim fieri pote&longs;t, vt <lb/>duo motus reperiantur, quì nulla &longs;e mutuò habitudine re&longs;piciant? </s>

probare conatur, lineam circulum de&longs;cribentem, dua<lb/>bus ferri lationibus, quæ nullam habeant analogiam: Yerùm, vt liberè fa<lb/>tear nullo modo mihi videtur intentum a&longs;&longs;equi, nam <expan abbr="neq;">neque</expan> ex dictis pater, <lb/>ip&longs;am duobus motibus ferri, quibus opus e&longs;&longs;et: neque patet eos (quamuis <lb/>concedantur) nullam inuicem habere analogiam: qui enim fieri pote&longs;t, vt <lb/>duo motus reperiantur, quì nulla &longs;e mutuò habitudine re&longs;piciant? </s>

<s>Præte<lb/>rea &longs;i B, ferretur illis motibus, non &longs;equitur debere moueri per lineam cir<lb/>cularem, cum præter lineam rectam &longs;int plures curuæ, quæ tamen non &longs;unt <lb/>circulares, vt &longs;unt &longs;ectiones parabolicæ, & lineæ &longs;pirales. </s>

Line 7318

<s>Ex quibus patere &longs;atis pote&longs;t, cur A B, longior à centro velocius mouea<lb/>tur quàm minor M A, &longs;eu cur puncta eiu&longs;dem B A, velocius vertuntur, quo <lb/>longius ab&longs;unt à centro A, ide&longs;t maiorem arcum B F, peractum e&longs;&longs;e à B, <lb/>quàm &longs;it arcus M L, peractus ab M, quod erat o&longs;tendendum.</s>

<s>Atque hic e&longs;t di&longs;cur&longs;us ille Ari&longs;t. </s>

<s>Atque hic e&longs;t di&longs;cur&longs;us ille Ari&longs;t.

<s>quo putat &longs;e cau&longs;am aperui&longs;&longs;e, cur lon<lb/>gior &longs;emidiameter velocius moueatur: quod num rectè attigerit, non puto <lb/>operæpretium e&longs;&longs;e hoc loco di&longs;cutere, præ&longs;ertim cum ad naturalem Philo<lb/>&longs;ophum &longs;pectet.</s>

quo putat &longs;e cau&longs;am aperui&longs;&longs;e, cur lon<lb/>gior &longs;emidiameter velocius moueatur: quod num rectè attigerit, non puto <lb/>operæpretium e&longs;&longs;e hoc loco di&longs;cutere, præ&longs;ertim cum ad naturalem Philo<lb/>&longs;ophum &longs;pectet.</s>

<s>Mihi tamen maximè con&longs;iderandum videtur hoc ip&longs;um quod a&longs;&longs;eruit, & <pb pagenum="154"/>ex &longs;e patet, remotiores &longs;cilicet partes diametrorum à centro velocius mo<lb/>ueri, quàm viciniores; ex hac enim maiori velocitate &longs;equitur maiore etiam <lb/>vi moueri, vnde & potentiæ mouenti in extremo eius vis augebitur, & plus <lb/>poterit quam &longs;ola &longs;ine vecte, e&longs;t enim vectis duæ &longs;emidiametri altera alte<lb/>ram longior; ex quibus fortè apparet vnde vectis vires oriantur.</s>

Line 7412

<s>& quia graue natura &longs;ua nequit a&longs;cendere, propterea <lb/>ablato pondere non reuertitur ad æquilibrium B C, cum centrum grauita<lb/>tis a&longs;cendere ne queat, quod tunc oporteret.</s>

<s>Sit libra N G, in &longs;ecunda figura, cuius perpendiculum, <expan abbr="&longs;imul&qacute;">&longs;imulque</expan>; directio<lb/>nis linea &longs;it K L M, quæ libram in prima po&longs;itione diuidit bifariam; impofi<lb/>to autem onere in N. N, trahetur ad O, & G, ad R, & K L, vbi K P. quare <lb/>maior e&longs;t O L, in quo <expan abbr="centr&utilde;">centrum</expan> grauitatis, & propterea grauior quàm &longs;it L R: <lb/>&longs;uperat enim O L, ip&longs;am L R, exce&longs;&longs;u duplæ P L, quod facilè apparet &longs;i po<lb/>natur tota O R, 10. & dimidia O P, & O R, 5. & P L, ponatur 2. erit enim <lb/>tunc O L, 7. & L R, 3. quæ hanc &longs;uperat 4. duplo &longs;cilicet ip&longs;ius P L, 2. qua<lb/>re ne&longs;cio cur Ari&longs;t. </s>

<s>dicat, ip&longs;am O L, &longs;uperare ip&longs;am L R, &longs;olùm quantitate <lb/>P L. </s>

dicat, ip&longs;am O L, &longs;uperare ip&longs;am L R, &longs;olùm quantitate <lb/>P L. </s>

<s>Quapropter etiam &longs;i onus auferatur, nece&longs;&longs;e e&longs;t ibi libram manere, <lb/>quia maior, & grauior ip&longs;ius pars deor&longs;um e&longs;t, nec pote&longs;t natura &longs;ua læui<lb/>tare, vel a&longs;cendere, vt oporteret, &longs;i ad pri&longs;tinum &longs;itum N G, re&longs;titui debe<lb/>ret. </s>

Line 7422

<s>Ex his, quæ&longs;tionis &longs;olutionem, textus explicationem, ac re&longs;titutio<lb/>nem habeto.</s>

<s>Aduertendum quoad &longs;ecundam libram, ne &longs;imul cum 10. Bapti&longs;ta Bene<lb/>dicto in libro &longs;peculationum immeritò Ari&longs;t. </s>

<s>Aduertendum quoad &longs;ecundam libram, ne &longs;imul cum 10. Bapti&longs;ta Bene<lb/>dicto in libro &longs;peculationum immeritò Ari&longs;t.

<s>erroris arguamus: ip&longs;e enim, <lb/>quia libram hanc non agnouit, au&longs;us e&longs;t affirmare, Ari&longs;tot. </s>

erroris arguamus: ip&longs;e enim, <lb/>quia libram hanc non agnouit, au&longs;us e&longs;t affirmare, Ari&longs;tot. </s>

<s>hoc loco fal&longs;um <lb/>pror&longs;us dixi&longs;&longs;e, cum dixit libram &longs;patto infimè collocato, non redire ad <lb/>pri&longs;tinam po&longs;itionem.</s>

Line 7490

<s>EI, qui &longs;uperiora intellexerit &longs;atis clara videtur. </s>

<s>Illud tamen non <lb/>omittendum, &longs;cilicet dicendum potius Remum e&longs;&longs;e vectem &longs;ecundi <lb/>generis, quàm primi, quod fortè Ari&longs;t. </s>

<s>Illud tamen non <lb/>omittendum, &longs;cilicet dicendum potius Remum e&longs;&longs;e vectem &longs;ecundi <lb/>generis, quàm primi, quod fortè Ari&longs;t.

<s>non animaduertit, nec Pic<lb/>colomineus, nam mare e&longs;t hypomoclion, re&longs;pectu enim nauis non <lb/>mouetur, &longs;ed manet, &longs;calmus autem &longs;imul cum tota naui e&longs;t pondus motum; <lb/>verè enim nauis ip&longs;a mouetur. </s>

non animaduertit, nec Pic<lb/>colomineus, nam mare e&longs;t hypomoclion, re&longs;pectu enim nauis non <lb/>mouetur, &longs;ed manet, &longs;calmus autem &longs;imul cum tota naui e&longs;t pondus motum; <lb/>verè enim nauis ip&longs;a mouetur. </s>

<s>mouens e&longs;t ip&longs;e remex. </s>

Line 7506

<s>Qvemadmodum in præcedenti quæ&longs;tione Ari&longs;t. </s>

<s>Qvemadmodum in præcedenti quæ&longs;tione Ari&longs;t.

<s>vectem &longs;ecundi ge<lb/>neris ad &longs;olutionem non adhibuit, vt par erat, & propterea ob&longs;cu<lb/>rior eua&longs;it, ita etiam in præ&longs;enti, qu&ecedil;&longs;tionem ad ve ctem primi ge<lb/>neris reducit, quæ ad alterum reducendà erat: <expan abbr="atq;">atque</expan> hinc ob&longs;curi<lb/>tas, atque prolixitas &longs;olutionis manauit. </s>

vectem &longs;ecundi ge<lb/>neris ad &longs;olutionem non adhibuit, vt par erat, & propterea ob&longs;cu<lb/>rior eua&longs;it, ita etiam in præ&longs;enti, qu&ecedil;&longs;tionem ad ve ctem primi ge<lb/>neris reducit, quæ ad alterum reducendà erat: <expan abbr="atq;">atque</expan> hinc ob&longs;curi<lb/>tas, atque prolixitas &longs;olutionis manauit. </s>

<s>E&longs;t enim propriè Temo, &longs;iue gu<lb/>bernaculum nauis, vectis &longs;ecundi generis, vt mox explicabo, e&longs;t enim temo <lb/><figure id="fig81"></figure><lb/>in&longs;trumentum in extrema nanis par<lb/>te, &longs;eu puppi affixum, vt in figura prç<lb/>&longs;enti vides tabellam, in qua B C D, <lb/>cuius manubrium A B, intra nauim <lb/>recipitur, quæ tabella, &longs;eu temo in <lb/>duobus cardinibus, vbi C, & D, cir<lb/>cumuertitur à Nauis gubernatore, <lb/>manubrium vbi A, tractante; ex qua <lb/>conuer&longs;ione nauigium, quò vult ip&longs;e <lb/>gubernator facilè dirigit, ip&longs;umque <lb/>nauigium huc illuc quamuis adeò magnum ip&longs;e &longs;olus impellit, & agitat. </s>

Line 7518

<s>quod <lb/>etiam hinc patere pote&longs;t, quia temo e&longs;t veluti remus, cuius &longs;calmus &longs;int car<lb/>dines C, D. &longs;icut ergo remus e&longs;t vectis &longs;ecundi generis, cuius pondus e&longs;t <lb/>&longs;ealmus, & mare hypomoclion; ita temo erit vectis eiu&longs;dem generis, cuius <lb/>pondus erit vbi cardines, fultura verò mare.</s>

<s>Quærit igitur Ari&longs;t. </s>

<s>Quærit igitur Ari&longs;t.

<s>vnde nam tantas vires paruus nauis temo guberna<lb/>tori &longs;uggerat, <expan abbr="re&longs;pondet&qacute;">re&longs;pondetque</expan>; propterea id contingere, quod temo vectis na<lb/>turam obtineat, cuius inquit onus e&longs;t mare, melius autem, vt dixi, dixi&longs;&longs;et <lb/>onus e&longs;&longs;e nauim, mare autem hypomoclion, mouens autem e&longs;t gubernator. <lb/></s>

vnde nam tantas vires paruus nauis temo guberna<lb/>tori &longs;uggerat, <expan abbr="re&longs;pondet&qacute;">re&longs;pondetque</expan>; propterea id contingere, quod temo vectis na<lb/>turam obtineat, cuius inquit onus e&longs;t mare, melius autem, vt dixi, dixi&longs;&longs;et <lb/>onus e&longs;&longs;e nauim, mare autem hypomoclion, mouens autem e&longs;t gubernator. <lb/></s>

<s>Differunt autem remus, & temo, quamuis <expan abbr="vterq;">vterque</expan> &longs;it vectis, quoniam remus <lb/>&longs;ecundum latitudinem nauis, &longs;eu ad latera nauis mari obnititur. </s>

Line 7534

<s>Po&longs;thæc &longs;equuntur huiu&longs;modi verba <emph type="italics"/>(In extremo autem, & non in medio <lb/>iacet, quoniam <expan abbr="mou&etilde;ti">mouenti</expan> facillimum est ab extremo motum mouere: prima enim pars <lb/>celerrimè fertur, quoniam quemadmodum in ijs, qu&oelig; feruntur in fine deficit latio, <lb/>&longs;ic ip&longs;ius continui in fine imbecili&longs;&longs;ima e&longs;t latio, imbecili&longs;&longs;ima autem ad <expan abbr="expell&etilde;dum">expellendum</expan> <lb/>est facilis, propter h&oelig;c igitur in puppi gubernaculum ponitur)<emph.end type="italics"/> quorum &longs;en&longs;us <lb/>videtur difficilis, <expan abbr="neq;">neque</expan> græcus textus excu&longs;andus e&longs;t, benè enim tran&longs;lata <lb/>&longs;unt. </s>

<s>Piccolominæus quidem plura quàm Ari&longs;t. </s>

<s>Piccolominæus quidem plura quàm Ari&longs;t.

<s>fatur, &longs;ed non clariora. </s>

fatur, &longs;ed non clariora. </s>

<s>dif<lb/>ficultas e&longs;t in verbis illis <emph type="italics"/>(Prima enim pars celerrimè fertur)<emph.end type="italics"/> & in illis <emph type="italics"/>(Sic ip<lb/>&longs;ius continui in fine imbecili&longs;&longs;ima eft latio)<emph.end type="italics"/> videtur velle dicere, quod quando <lb/>continuum aliquod proiectum fertur per aera, pars ip&longs;ius anterior ea e&longs;t, <lb/>quæ præ cæteris partibus principaliter mouetur, & ad cuius motum reliquæ <lb/>po&longs;teriores tanquam &longs;ub&longs;e quentes moueantur; qua&longs;i dicat tota vis lationis <lb/>e&longs;t in anteriori parte: &longs;iue ip&longs;i impetus maior ine&longs;t: videmus enim proiecta, <lb/>quorum vna pars e&longs;t cæteris grauior, quia ei parti melius imprimitur mo<lb/>tus, eam etiam fieri anteriorem in latione, quamuis initio fuerit po&longs;terior. <lb/></s>

Line 7596

<s>Sen&longs;us porrò horum verborum e&longs;t hic; &longs;i remus cirea &longs;calmum G, verte<lb/>retur, & tamen nauis ab eo non propelleretur, &longs;ed &longs;taret, tunc medium na<lb/>uis maneret vbi G, per motum enim remi impellitur in contrarias partes <lb/>ip&longs;i palmulæ B, quæ e&longs;t in mari, quia &longs;equitur motum alterius extremi A, <lb/>manubrij &longs;cilicet remi, qui e&longs;t in naui: quod autem nauigium à remo mo<lb/>neatur, &longs;ignum e&longs;t, quia manubrium A, non procederet vbi e&longs;t D, ni&longs;i pari<lb/>ter cum remo nauigium illor&longs;um con&longs;equeretur. </s>

<s>Hæc quidem Ari&longs;t. </s>

<s>Hæc quidem Ari&longs;t.

<s>circa <lb/>motum nauigij imperfectè admodum ni&longs;i textus corruptionem cau&longs;etur, di<lb/>xi&longs;&longs;e videatur. </s>

circa <lb/>motum nauigij imperfectè admodum ni&longs;i textus corruptionem cau&longs;etur, di<lb/>xi&longs;&longs;e videatur. </s>

<s>Quapropter operæpretium me facturum exi&longs;timo, &longs;i Petri <lb/>Nonij acuti&longs;&longs;imi Mathematici, &longs;ubtili&longs;&longs;imas, <expan abbr="&longs;citu&qacute;">&longs;cituque</expan>; digni&longs;&longs;imas in præ&longs;ens <lb/>problema anuotationes hoc loco de&longs;crip&longs;ero, ex quibus perfectè, ac ma<lb/>thematicè toti huic quæ&longs;tioni fit &longs;atis, quæ &longs;ic &longs;e habent.</s>

<s><emph type="italics"/>In Problema Mechanicum Arist. </s>

<s><emph type="italics"/>In Problema Mechanicum Arist.

<s>de motu Nauigij <lb/>ex remis, annotatio Petri Nonij.<emph.end type="italics"/></s>

de motu Nauigij <lb/>ex remis, annotatio Petri Nonij.<emph.end type="italics"/></s>

<s>Cvm olim di&longs;cipulis no&longs;tris mechanicas Ari&longs;t. </s>

<s>Cvm olim di&longs;cipulis no&longs;tris mechanicas Ari&longs;t.

<s>quæ&longs;tiones interpre<lb/>taremur, nonnulla circa problema illud annotauimus, cur magis <lb/>procedat nauigium, quam remi palmula in contrarium. </s>

quæ&longs;tiones interpre<lb/>taremur, nonnulla circa problema illud annotauimus, cur magis <lb/>procedat nauigium, quam remi palmula in contrarium. </s>

<s>Ari&longs;tot. <lb/></s>

Line 7646

<s>Nam quoniam duo latera <lb/>B D, & D K, trianguli B D K, duobus lateribus B D, & D E, <expan abbr="triãguli">trianguli</expan> B E D, <lb/>æqualia &longs;unt, &longs;ed minor e&longs;t angulus B D K, angulo B D E: minorigitur erit <lb/>ba&longs;is B K, ba&longs;e B E, per 24. primi, quod demon&longs;trandum erat</s>

<s>Præterea, quod Ari&longs;t. </s>

<s>Præterea, quod Ari&longs;t.

<s>ratiocinando &longs;umit tantum &longs;patium conficere na<lb/>uigium, quantum remi manubrium, ambiguum e&longs;t. </s>

ratiocinando &longs;umit tantum &longs;patium conficere na<lb/>uigium, quantum remi manubrium, ambiguum e&longs;t. </s>

<s>Nam remi manubrium <lb/>duabus fertur motionibus: vna propria, <expan abbr="circulari&qacute;">circularique</expan>; &longs;uper &longs;calmo: altera <lb/>verò, qua vnà fertur cum ip&longs;o nauigio. </s>

Line 7852

<s>Re<lb/>&longs;tat vt &longs;atisfaciam promi&longs;&longs;is.</s>

<s>Dictum e&longs;t ab Ari&longs;t. </s>

<s>Dictum e&longs;t ab Ari&longs;t.

<s>in textu <emph type="italics"/>(Sicut diameter ad diametrum, ita maior circu<lb/>lus ad maiorem)<emph.end type="italics"/> quæ verba intelligenda e&longs;&longs;e non de circulis, &longs;ed de periphæ<lb/>rijs, vti expo&longs;ui, manife&longs;tum e&longs;t ex 11. propo&longs;it. </s>

in textu <emph type="italics"/>(Sicut diameter ad diametrum, ita maior circu<lb/>lus ad maiorem)<emph.end type="italics"/> quæ verba intelligenda e&longs;&longs;e non de circulis, &longs;ed de periphæ<lb/>rijs, vti expo&longs;ui, manife&longs;tum e&longs;t ex 11. propo&longs;it. </s>

<s>5. Pappi Alexandrini, quæ <lb/>talis e&longs;t: Circulorum circunferentiæ inter &longs;e &longs;unt vt diametri. </s>

Line 7888

<s>æquales autem <lb/>di&longs;tantiæ <expan abbr="vtrinq;">vtrinque</expan> ab hypomoclio &longs;unt B A, A C, &longs;unt <lb/>enim ex centro eodem. </s>

<s>ex quibus manife&longs;tum e&longs;t hu<lb/>iu&longs;modi rotulam nullam vim mouenti addere, &longs;ed &longs;o<lb/>lum illud præ&longs;tat, vt omne tollat impedimentum, <lb/>quemadmodum ait Ari&longs;t. </s>

<s>manife&longs;tum etiam e&longs;t ma<lb/>iorem vim quamlibet, quam &longs;it ea, quæ &longs;u&longs;tinet, po&longs;&longs;e <lb/>idem pondus &longs;ur&longs;um mouere. </s>

manife&longs;tum etiam e&longs;t ma<lb/>iorem vim quamlibet, quam &longs;it ea, quæ &longs;u&longs;tinet, po&longs;&longs;e <lb/>idem pondus &longs;ur&longs;um mouere. </s>

<s>hæc & præ&longs;enti loco, & <lb/>&longs;equentibus lucem afferre po&longs;&longs;unt.</s><pb pagenum="172"/>

Line 7914

<s>Illud tamen, quod <lb/>magis nece&longs;&longs;arium e&longs;t, non omittam, vt &longs;cilicet difficultatibus quibu&longs;dam <lb/>occurram. </s>

<s>Et primo, quod Ari&longs;t. </s>

<s>Et primo, quod Ari&longs;t.

<s>ait, ea quæ per maiores circulos veluti <lb/>trochleas, &longs;eu rotulas trahuntur, facilius trahi, quàm ea, quæ per minores, <lb/>non videtur ex omni parte verom. </s>

ait, ea quæ per maiores circulos veluti <lb/>trochleas, &longs;eu rotulas trahuntur, facilius trahi, quàm ea, quæ per minores, <lb/>non videtur ex omni parte verom. </s>

<s>nam &longs;icuti in <expan abbr="præced&etilde;ti">præcedenti</expan> qnæ&longs;tione o&longs;ten<lb/>&longs;um e&longs;t ex Guido Vbaldo, trochlea &longs;implex, &longs;iue rotula illa &longs;triata, cui funis <lb/>&longs;upernè inditur, vt in &longs;uperiori figura; nullas addit vires potentiæ, quia re<lb/>ducitur ad vectem, cuius fultura &longs;it in medio ip&longs;ius. </s>

Line 7942

<s>cuius hanc accipe fi<lb/>guram. </s>

<s>Quærit igitur Ari&longs;t. </s>

<s>Quærit igitur Ari&longs;t.

<s>cur huiu&longs;<lb/>modi &longs;cytalæ facilius moueantur, quo <lb/>maiores ip&longs;arum &longs;unt rotæ. </s>

cur huiu&longs;<lb/>modi &longs;cytalæ facilius moueantur, quo <lb/>maiores ip&longs;arum &longs;unt rotæ. </s>

<s>Cui quæ<lb/>&longs;tioni &longs;imul, ij&longs;demque verbis, quibus <lb/>quæ&longs;tioni de maioribus rotulis re&longs;pondet, &longs;ed non &longs;atisfacit ob eandem ra<lb/>tionem, quam ibi attuli. </s>

Line 7970

<s>&longs;imiliter quæ maiora &longs;unt, <lb/>etiam &longs;i ex eadem materia con&longs;tent difficilius mouentur quàm minora, vt <lb/>rota maior ferrea, quàm minor etiam ferrea. </s>

<s>Habet hæc quæ&longs;tio tres par<lb/>tes, quibus Ari&longs;t. </s>

<s>Habet hæc quæ&longs;tio tres par<lb/>tes, quibus Ari&longs;t.

<s>re&longs;pondet dicens, quod graue e&longs;t ægrè moneri non &longs;olum <lb/>contra nutum &longs;uum, idc&longs;t &longs;ur&longs;um, &longs;ed etiam in obliquum, &longs;eu ad latera, quia <lb/>grauia deor&longs;um <expan abbr="nutãt">nutant</expan>, non &longs;ur&longs;um, nec in tran&longs;uer&longs;um: ideo libræ cum one<lb/>re, quia &longs;unt grauiores, & rota ferrea quàm lignea, & ferrea ctiam maior, <lb/>quàm minor grauior e&longs;t, ideò difficilius agitatur.</s>

re&longs;pondet dicens, quod graue e&longs;t ægrè moneri non &longs;olum <lb/>contra nutum &longs;uum, idc&longs;t &longs;ur&longs;um, &longs;ed etiam in obliquum, &longs;eu ad latera, quia <lb/>grauia deor&longs;um <expan abbr="nutãt">nutant</expan>, non &longs;ur&longs;um, nec in tran&longs;uer&longs;um: ideo libræ cum one<lb/>re, quia &longs;unt grauiores, & rota ferrea quàm lignea, & ferrea ctiam maior, <lb/>quàm minor grauior e&longs;t, ideò difficilius agitatur.</s>

<s>Contra quam re&longs;pon&longs;ionem &longs;ic fortè obijcies; in præcedenti enim quæ<pb pagenum="174"/>&longs;tione dictum e&longs;t ab Ari&longs;t. </s>

<s>Contra quam re&longs;pon&longs;ionem &longs;ic fortè obijcies; in præcedenti enim quæ<pb pagenum="174"/>&longs;tione dictum e&longs;t ab Ari&longs;t.

<s>maiores trochleas, & &longs;cytalas, minoribus facilius <lb/>commoueri, hic autem dicit maiorem rotam difficilius quàm minorem mo<lb/>ueri. </s>

maiores trochleas, & &longs;cytalas, minoribus facilius <lb/>commoueri, hic autem dicit maiorem rotam difficilius quàm minorem mo<lb/>ueri. </s>

<s>Hanc obiectionem Piccolomineus di&longs;&longs;imula&longs;&longs;e videtur, cui ego, inge<lb/>nuè fateor, me &longs;atisfacere ne&longs;cire, vt enim in præcedenti annotaui, nulla <lb/>mihi ratio Ari&longs;t. </s>

<s>excu&longs;andi occurrit, alijs fortè occurret. </s>

excu&longs;andi occurrit, alijs fortè occurret. </s>

<s>In præ&longs;enti au<lb/>tem benè quidem re&longs;pondet, &longs;ed tamen intimam rei cau&longs;am non attingit.</s>

Line 8078

<s>2. de Oratore, vbi <lb/>&longs;ic, non audeo dicere de talibus viris, &longs;ed tamen ita narrare &longs;ole<lb/>bat Sceuola, conchas, eos, & vmbilicos ad Caietam, & ad Lucri<lb/>num legere con&longs;ueui&longs;&longs;e. </s>

<s>hos autem vmbilicos exponunt Grammatici e&longs;&longs;e <lb/>lapillos paruos, acrotundos, polito&longs;que, de quibus etiam Ari&longs;t. </s>

<s>hos autem vmbilicos exponunt Grammatici e&longs;&longs;e <lb/>lapillos paruos, acrotundos, polito&longs;que, de quibus etiam Ari&longs;t.

<s>loquitur. <lb/></s>

loquitur. <lb/></s>

<s>Quare decipitur Piccolomineus dum negat, nos harum crocarum latinum <lb/>nomen habere. </s>

Line 8102

<s>in A, verò onus ip&longs;ius ligni, deor&longs;um tendens <lb/>premit, quod nunc e&longs;t in&longs;tar potentiæ motricis, quare A, & C, &longs;unt &longs;ibi in<lb/>uicem, & potentiæ, & pondera. </s>

<s>In minori autem ligno, onus ligni in D, <pb pagenum="177"/><figure id="fig94"></figure><lb/>fultura manus in E, potentia alterius ma<lb/>nus in F. iam inquir Ari&longs;t. </s>

<s>In minori autem ligno, onus ligni in D, <pb pagenum="177"/><figure id="fig94"></figure><lb/>fultura manus in E, potentia alterius ma<lb/>nus in F. iam inquir Ari&longs;t.

<s>maius lignum <lb/>A B C, magis flectitur, quamuis cra&longs;&longs;ius <lb/>&longs;it, quàm lignum D E F, quod e&longs;t tenuuius, <lb/>&longs;ed multò breuius; quia in maiori onus <lb/>ip&longs;ius ligni, quod circa A, deor&longs;um pre<lb/>mit <expan abbr="lõgius">longius</expan> di&longs;tat ab hypomoclio B, quàm <lb/>in minori ligno. </s>

maius lignum <lb/>A B C, magis flectitur, quamuis cra&longs;&longs;ius <lb/>&longs;it, quàm lignum D E F, quod e&longs;t tenuuius, <lb/>&longs;ed multò breuius; quia in maiori onus <lb/>ip&longs;ius ligni, quod circa A, deor&longs;um pre<lb/>mit <expan abbr="lõgius">longius</expan> di&longs;tat ab hypomoclio B, quàm <lb/>in minori ligno. </s>

<s>Ex quo &longs;equitur iuxta <lb/>ip&longs;ius principia, vt onus A, facilius lignum mouere, aut inflectere <lb/>po&longs;&longs;it.</s>

Line 8148

<s>Hvius quæ&longs;tionis &longs;en&longs;us, ac verba optimè intelligentur ex &longs;equen<lb/>tibus. </s>

<s>Trochlea, vt patet ex &longs;uperioribus Ari&longs;t. </s>

<s>Trochlea, vt patet ex &longs;uperioribus Ari&longs;t.

<s>e&longs;t orbiculus in <lb/>periphæria &longs;triatus, vna cum toto loculumento, cui in&longs;eritur: <lb/>cuius imaginem ad 8. quæ&longs;t. </s>

e&longs;t orbiculus in <lb/>periphæria &longs;triatus, vna cum toto loculumento, cui in&longs;eritur: <lb/>cuius imaginem ad 8. quæ&longs;t. </s>

<s>exhibui. </s>

Line 8182

<s>aduerte præterea vectem hunc e&longs;&longs;e mobilem, &longs;imul cum <expan abbr="fulcim&etilde;to">fulcimento</expan>, quia dum <lb/>ex parte M, &longs;ur&longs;um tollitur &longs;imul cum toto orbiculo, ac loculamento, &longs;ub<lb/>&longs;equitur etiam alterum extremum L, quod fune fulcitur, & in ip&longs;o fune &longs;ur<lb/>&longs;um ver&longs;us D, a&longs;cendit; & hoc modo inferius tignum cum onere tandem ad<lb/>&longs;uperius tignum &longs;ublatum erit. </s>

<s>hinc verum dixi&longs;&longs;e Ari&longs;t. </s>

<s>hinc verum dixi&longs;&longs;e Ari&longs;t.

<s>con&longs;tat, trochleam <lb/>&longs;cilicet idem e&longs;&longs;e, ac vectem. </s>

con&longs;tat, trochleam <lb/>&longs;cilicet idem e&longs;&longs;e, ac vectem. </s>

<s>quod tamen de &longs;olo inferiori orbiculo intelli<lb/>gi debet, &longs;uperior enim rotula quamuis vectis fiat, non tamen vires vllas <lb/>potentiæ tribuit, cum eius hypomoclion &longs;it in medio, quemadmodum &longs;upra <lb/>ad 8. quæ&longs;t. </s>

Line 8216

<s>Bapti&longs;ta Benedictus pariter erra&longs;&longs;e videtur in &longs;uis &longs;peculationibus, cum <lb/>inferiores tantummodo vice vectium fungantur, vt probatum e&longs;t.</s>

<s><expan abbr="Atq;">Atque</expan> ex his &longs;atis mihi videtur textus, ac &longs;en&longs;us Ari&longs;t. </s>

<s><expan abbr="Atq;">Atque</expan> ex his &longs;atis mihi videtur textus, ac &longs;en&longs;us Ari&longs;t.

<s>illu&longs;trari.</s>

illu&longs;trari.</s>

<s><emph type="italics"/>QVÆSTIO XVIIII.<emph.end type="italics"/></s>

Line 8294

<s>Et ip&longs;e doli fabricator Epeus. </s>

<s>qui cum &longs;oluendi voti cau&longs;a <lb/>vellet &longs;ecurim, &longs;iue bipennem, qua in equi Durij molitione v&longs;us fuerat, Mi<lb/>neruæ Deæ, quod &longs;ibi in eo opere faciendo auxilio fui&longs;&longs;et, dedicare, <expan abbr="eam&qacute;">eamque</expan>; <lb/>vt Ari&longs;t. </s>

<s>in libello de admirandis audit. </s>

in libello de admirandis audit. </s>

Line 8324

<s>Antequam ad textus explicationem accedamus, con&longs;ultius e&longs;&longs;e iu<lb/>dico veteris &longs;tateræ figuram, atque de&longs;criptionem præmittere, <lb/>quàm ex hoc Ari&longs;t. </s>

<s>Antequam ad textus explicationem accedamus, con&longs;ultius e&longs;&longs;e iu<lb/>dico veteris &longs;tateræ figuram, atque de&longs;criptionem præmittere, <lb/>quàm ex hoc Ari&longs;t.

<s>loco, magna mihi licuit cum delectatione col<lb/>ligere: quod etiam antiquitatis &longs;tudio&longs;is pergratum fore non du<lb/>bito: <expan abbr="atq;">atque</expan> hinc etiam ineptas, <expan abbr="atq;">atque</expan> ad&longs;cititias textus huius figuras tanquam <lb/>adulterinas reijcere; <expan abbr="in&qacute;">inque</expan>; earum locum veras re&longs;tituere licebit. </s>

loco, magna mihi licuit cum delectatione col<lb/>ligere: quod etiam antiquitatis &longs;tudio&longs;is pergratum fore non du<lb/>bito: <expan abbr="atq;">atque</expan> hinc etiam ineptas, <expan abbr="atq;">atque</expan> ad&longs;cititias textus huius figuras tanquam <lb/>adulterinas reijcere; <expan abbr="in&qacute;">inque</expan>; earum locum veras re&longs;tituere licebit. </s>

<s>erat igitur <lb/><figure id="fig100"></figure><lb/>&longs;tatera, quantum ex Ari&longs;t. </s>

<s>erat igitur <lb/><figure id="fig100"></figure><lb/>&longs;tatera, quantum ex Ari&longs;t.

<s>conijcio <lb/>primum ha&longs;ta oblonga, qualis e&longs;t in <lb/>præ&longs;enti figura A B, ex cuius altero <lb/>extremo B, pendebat appendicu<lb/>lum, quod propriè æquipondium <lb/>dicitur: ex altera verò extremitate <lb/>A, lanx vna pendebat; in qua carnes, aliæuè merces ponderabantur: in me<lb/>dia <expan abbr="deniq;">denique</expan> ha&longs;ta paribus interuallis plures trutinæ, ex quibus &longs;ingulis modo <lb/>hac, modo illa, prout pondus emptoris po&longs;tulabat &longs;u&longs;pendebatur, <expan abbr="atq;">atque</expan> in<lb/>terim tantum mercis lanci imponebatur, donec æquipondio præpondera<lb/>ret in æquilibrio. </s>

conijcio <lb/>primum ha&longs;ta oblonga, qualis e&longs;t in <lb/>præ&longs;enti figura A B, ex cuius altero <lb/>extremo B, pendebat appendicu<lb/>lum, quod propriè æquipondium <lb/>dicitur: ex altera verò extremitate <lb/>A, lanx vna pendebat; in qua carnes, aliæuè merces ponderabantur: in me<lb/>dia <expan abbr="deniq;">denique</expan> ha&longs;ta paribus interuallis plures trutinæ, ex quibus &longs;ingulis modo <lb/>hac, modo illa, prout pondus emptoris po&longs;tulabat &longs;u&longs;pendebatur, <expan abbr="atq;">atque</expan> in<lb/>terim tantum mercis lanci imponebatur, donec æquipondio præpondera<lb/>ret in æquilibrio. </s>

<s>&longs;ingulæ autem trutinæ ad aliquod determinatum pondus <lb/>trutinandum, erant con&longs;titutæ, v. </s>

Line 8414

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

<s>Tempore Ari&longs;t.

<s>vt colligitur ex hac quæ&longs;tione, ad frangendas nu<lb/>ces peculiare in&longs;trumentum ligneum adhibeant, quod erat in&longs;tar <lb/>forcipis, ita tamen concinnatum, vt non ad &longs;cindendum, nec ad <lb/>extrahendum, &longs;ed ad frangendum per <expan abbr="cõpre&longs;&longs;ionem">compre&longs;&longs;ionem</expan> e&longs;&longs;et aptum. <lb/></s>

vt colligitur ex hac quæ&longs;tione, ad frangendas nu<lb/>ces peculiare in&longs;trumentum ligneum adhibeant, quod erat in&longs;tar <lb/>forcipis, ita tamen concinnatum, vt non ad &longs;cindendum, nec ad <lb/>extrahendum, &longs;ed ad frangendum per <expan abbr="cõpre&longs;&longs;ionem">compre&longs;&longs;ionem</expan> e&longs;&longs;et aptum. <lb/></s>

<s>cuius hanc qualemcum que figuram in&longs;pice. </s>

Line 8598

<s>harû quan<lb/>titas &longs;i per 47. primi, & per ra<lb/>dicis quadratæ extractionem <lb/>inueniatur, erit &longs;umma earum <lb/>pedum quadraginta cum dimi<lb/>dio; quæ quantitas præcedenti <lb/>maior e&longs;t &longs;ex pedibus cum di<lb/>midio.</s>

<s><expan abbr="Atq;">Atque</expan> hic e&longs;t &longs;en&longs;us Ari&longs;t. </s>

<s><expan abbr="Atq;">Atque</expan> hic e&longs;t &longs;en&longs;us Ari&longs;t.

<s>quamuis tex. </s>

quamuis tex. </s>

<s>ip&longs;ius propter nimiam tam in græ<lb/>cis, quàm in latinis codicibus corruptionem, totus re&longs;titui nequiuerit.</s><figure></figure><pb pagenum="192"/>

Line 8722

<s>In 35. & vltima de vortice quamuis vide atur mathematicam &longs;apere, e&longs;t <lb/>tamen phy&longs;ica. </s>

<s>Eius autem re&longs;olutiones tres ab Ari&longs;t. </s>

<s>Eius autem re&longs;olutiones tres ab Ari&longs;t.

<s>allatas, fal&longs;as e&longs;&longs;e <lb/>&longs;u&longs;picor; experientia enim docet, quod &longs;i quippiam ponatur &longs;upra rotam <lb/>figuli, id non ad centrum, &longs;ed extra rotam proijcitur. </s>

allatas, fal&longs;as e&longs;&longs;e <lb/>&longs;u&longs;picor; experientia enim docet, quod &longs;i quippiam ponatur &longs;upra rotam <lb/>figuli, id non ad centrum, &longs;ed extra rotam proijcitur. </s>

<s>&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip &longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer<lb/>gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, quæ in ip&longs;a &longs;unt, &longs;imul cum <lb/>illa ad centrum per plures conuolutiones deducantur. </s>

Line 8736

<s><emph type="italics"/>AD ALEXANDRVM.<emph.end type="italics"/></s>

<s>Cvm plures libellum hunc Ari&longs;t. </s>

<s>Cvm plures libellum hunc Ari&longs;t.

<s>attribuant, cogor loca ip&longs;ius ma<lb/>thematica ex in&longs;tituto exponere.</s>

attribuant, cogor loca ip&longs;ius ma<lb/>thematica ex in&longs;tituto exponere.</s>

Line 8770

<s>Cum au<lb/>tem in toto die &longs;int 24. horæ & &longs;emper &longs;int &longs;imul in mundo duo æ&longs;tus, & tu<lb/>mores, fit vt &longs;int pariter &longs;emper in mundo duo fluxus, qui tumores illos co<lb/>mitantur; necnon duo refluxus, qui eo&longs;dem &longs;ub&longs;equantur; hinc fit vt <expan abbr="vni-cuiq;">vni<lb/>cuique</expan> illorum &longs;ex heræ <expan abbr="conueniãt">conueniant</expan>, &longs;ex fluxui, &longs;ex refluxui, qui &longs;ub Luna fiunt; <lb/>&longs;ex verò fluxui, & &longs;ex tandem refluxui Lunæ auer&longs;is, quæ totam Lunæ circa <lb/>mundum periodum 25. horarum expleant. </s>

<s>Cau&longs;am autem cur mare hoc <lb/>modo &longs;tatis horis, paulò tamen &longs;erius ob Lunæ tardiorem ortum &longs;emper <lb/>cre&longs;cat, & decre&longs;cat antiqui omnes in Lunam retulerunt, vt primus omnium <lb/>Ari&longs;t. </s>

<s>hoc loco, deinde Strabo, Pomponius Mela, Plinius, Solinus, & alij <lb/>plures idem &longs;en&longs;erunt. </s>

hoc loco, deinde Strabo, Pomponius Mela, Plinius, Solinus, & alij <lb/>plures idem &longs;en&longs;erunt. </s>

<s>Lunam &longs;cilicet eam habere vim in mare, vt pars il<lb/>la, quæ Lunæ &longs;irbiacet, &longs;iue quam Luna radijs ferit, æftuet, & turgeat; non <lb/>aliter pars maris huic antipoda, & auer&longs;a, quamuis tota terræ moles inter <lb/><figure id="fig111"></figure><lb/>ip&longs;am, & Lunam interpona<lb/>tur, æ&longs;tuat, fluxumque, ac re<lb/>fluxum quamuis priori mi<lb/>norem, efficit. </s>

Line 8926

<s>7. <emph type="italics"/>(Quod Imagunculas animatas e&longs;&longs;e, &c.)<emph.end type="italics"/> huiu&longs;modi imagines, & <lb/>&longs;tatuas, quæ &longs;pontè mouebantur Græci appellarunt Automata, ide&longs;t &longs;pon<lb/>tanea, cuiu&longs;modi &longs;unt automata Heronis, Alexandrini, quæ adhuc extant.</s>

<s>Cap. 7. <emph type="italics"/>(Quod Imagunculas animatas e&longs;&longs;e, &c.)<emph.end type="italics"/> huiu&longs;modi imagines, & <lb/>&longs;tatuas, quæ &longs;pontè mouebantur Græci appellarunt Automata, ide&longs;t &longs;pon<lb/>tanea, cuiu&longs;modi &longs;unt automata Heronis, Alexandrini, quæ adhuc extant.</s>

<s><emph type="italics"/>IN LIBELLVM<emph.end type="italics"/></s>

Line 8944

<s>Numero 100. Quæ de I&longs;tro, &longs;iue Dannubio tradit, eum &longs;cilicet <lb/>e&longs;&longs;e bifidum, <expan abbr="altero&qacute;">alteroque</expan>; ramo in Pontum, altero verò in Mediterraneum ex<lb/>onerari: &longs;unt contra omnes recentiores Geographos; apparet tamen eam <lb/>fui&longs;&longs;e veterum nonnullorum opinionem, quos <expan abbr="&longs;e&qacute;uutus">&longs;equutus</expan> Ari&longs;t. </s>

<s>deceptus e&longs;t, <lb/>à quibus etiam multò po&longs;t fal&longs;i &longs;unt Diodorus, Pomponius, & Solinus, qui <lb/>I&longs;trum I&longs;triæ Prouincìæ fluuium faciunt, quem ex I&longs;tro Germaniæ veluti ra<lb/>mum contra omnem veritatem deriuant. </s>

deceptus e&longs;t, <lb/>à quibus etiam multò po&longs;t fal&longs;i &longs;unt Diodorus, Pomponius, & Solinus, qui <lb/>I&longs;trum I&longs;triæ Prouincìæ fluuium faciunt, quem ex I&longs;tro Germaniæ veluti ra<lb/>mum contra omnem veritatem deriuant. </s>

<s>Verùm hoc illis-condonandum <lb/>præ&longs;ertim antiquioribus, cum tunc temporis Geographia parum e&longs;&longs;et <lb/>exculta.</s>

Line 9080

<s>Apotome <lb/>enim, vt &longs;upra dictum e&longs;t, ne dum ex duobus nominibus con&longs;tat, verum ip<lb/>&longs;a e&longs;t re&longs;iduum lineæ maioris, &longs;i minor ab ip&longs;a detrahatur. </s>

<s>Verumenimuero <lb/>vox illa <emph type="italics"/>(Compo&longs;itam)<emph.end type="italics"/> in nullo codice reperitur, quare pro arbitrio, atque <lb/>ex Geometriæ in&longs;citia addita, tolli debet, ne tantæ in&longs;citiæ Ari&longs;t. </s>

<s>ip&longs;e re<lb/>darguatur. </s>

ip&longs;e re<lb/>darguatur. </s>

<s>hæc in hunc locum &longs;ufficiant.</s>

Line 9148

<s>te&longs;timonio, <expan abbr="veterum&qacute;">veterumque</expan>; Philo&longs;ophorum omnium <lb/>comprobatas, negare non verentur Demon&longs;trationes.</s>

<s>Cæterùm Ari&longs;t. </s>

<s>Cæterùm Ari&longs;t.

<s>iterum opinionem <expan abbr="a&longs;&longs;er&etilde;tium">a&longs;&longs;erentium</expan> lineas in&longs;ecabiles hoc mo<lb/>do confutat: nam &longs;i inquit, lineam illam, quam vocant in&longs;ecabilem, e&longs;t non <lb/>&longs;olum linea, &longs;ed etiam linea recta, illi conueniret rectæ lineæ definitio, &longs;ed <lb/>nullo modo pote&longs;t ci conuenire, ergò tollendæ &longs;unt de rerum natura huiu&longs;<lb/>modi lineæ. </s>

iterum opinionem <expan abbr="a&longs;&longs;er&etilde;tium">a&longs;&longs;erentium</expan> lineas in&longs;ecabiles hoc mo<lb/>do confutat: nam &longs;i inquit, lineam illam, quam vocant in&longs;ecabilem, e&longs;t non <lb/>&longs;olum linea, &longs;ed etiam linea recta, illi conueniret rectæ lineæ definitio, &longs;ed <lb/>nullo modo pote&longs;t ci conuenire, ergò tollendæ &longs;unt de rerum natura huiu&longs;<lb/>modi lineæ. </s>

<s>Porrò definitio lineæ e&longs;t, vt &longs;it longitudo latitudinis expers, & <lb/>&longs;i recta &longs;it ex æquo &longs;ua interiacet puncta extrema, ergò ip&longs;a linea media erit <lb/>inter duo indiuidua extrema puncta; at verò linea, quam ip&longs;i volunt e&longs;&longs;e <lb/>indiuiduum quoddam, qua ratione medium erit inter alia duo indiuidua? <lb/></s>

Line 9320

<s>39. <emph type="italics"/>(Aranei &longs;tatim cum editi &longs;unt, fila mittunt, non ab intrin&longs;eco <lb/>tanquam excrementum, vt Democritus ait, &longs;ed ab extrin&longs;eco de &longs;uo cor<lb/>pore, veluti cortice; aut more eorum animalium, quæ &longs;uos villos iacu<lb/>lantur, vt hystricis)<emph.end type="italics"/> Cum olim in hunc locum incidi&longs;&longs;em, ince&longs;&longs;ic <lb/>animum meum illa cupido, vt &longs;cilicet certò &longs;cirem, numiure, an iniuria <lb/>Ari&longs;t. </s>

<s>Cap. 39. <emph type="italics"/>(Aranei &longs;tatim cum editi &longs;unt, fila mittunt, non ab intrin&longs;eco <lb/>tanquam excrementum, vt Democritus ait, &longs;ed ab extrin&longs;eco de &longs;uo cor<lb/>pore, veluti cortice; aut more eorum animalium, quæ &longs;uos villos iacu<lb/>lantur, vt hystricis)<emph.end type="italics"/> Cum olim in hunc locum incidi&longs;&longs;em, ince&longs;&longs;ic <lb/>animum meum illa cupido, vt &longs;cilicet certò &longs;cirem, numiure, an iniuria <lb/>Ari&longs;t. </s>

<s>Democritum hoc loco reijceret, Araneum fila ab intrin&longs;eco emitte<lb/>re a&longs;&longs;erentem: quapropter ad magi&longs;tram rerum experientiam confugi, ac<lb/>cepto manu bacillo Araneum quendam ex ijs, qui circulares telas, quas <lb/><expan abbr="nõnulli">nonnulli</expan>, & quidem aptè labyrinthos appellant, ingenio <expan abbr="vtiq;">vtique</expan> mathematico <lb/>contexunt, lic adij, vt Araneus pro arbittio &longs;uper bacillum liberè inambu<lb/>laret, dum ip&longs;e interim curio&longs;ius illum ob&longs;eruarem, quanam videlicet ex <lb/>parte filum foras ederet; cum ecce tibi Araneus experienti mihi vltrò fa<lb/>uens &longs;e &longs;e ex baculo demi&longs;it, ita tamen, vt ex filo &longs;uo in aere &longs;u&longs;pen&longs;us re<lb/>maneret. </s>

Line 9332

<s><expan abbr="Araneum&qacute;">Araneumque</expan>; vno pede filum illud retinere, ne amplius exi<lb/>ret, <expan abbr="longius&qacute;">longiusque</expan>; fieret, quàm &longs;uo con&longs;ilio par e&longs;&longs;et. </s>

<s>coegi deinde ip&longs;um a&longs;cen<lb/>dere, & de&longs;cendere &longs;æpius, donec certò certius, mihi con&longs;titi&longs;&longs;et filum illud <lb/>non ab extrin&longs;eco, vt hoc loco Ari&longs;t. </s>

<s>affirmat, &longs;ed ab intrin&longs;eco quippe ex <lb/>&longs;ece&longs;&longs;u prodire, ac proinde veri&longs;&longs;imam e&longs;&longs;e quamuis ab Ari&longs;t. </s>

affirmat, &longs;ed ab intrin&longs;eco quippe ex <lb/>&longs;ece&longs;&longs;u prodire, ac proinde veri&longs;&longs;imam e&longs;&longs;e quamuis ab Ari&longs;t.

<s>reiectam De<lb/>mocriti &longs;ententiam. </s>

reiectam De<lb/>mocriti &longs;ententiam. </s>

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

<s>cum Ari&longs;t.

<s>pariter errauit Vly&longs;&longs;es Aldobrandus in &longs;uo <lb/>de in&longs;ectis pulcherrimo, <expan abbr="atq;">atque</expan> docti&longs;&longs;imo Opere.</s>

pariter errauit Vly&longs;&longs;es Aldobrandus in &longs;uo <lb/>de in&longs;ectis pulcherrimo, <expan abbr="atq;">atque</expan> docti&longs;&longs;imo Opere.</s>

<s>Verumenimuerò opportunè accidit, vt huius dubitationis &longs;olutio, aliam <lb/>mihi alterius quæ&longs;tionis, iam olim &longs;ummis votis expetitam afferret expli<lb/>cationem. </s>

Line 9394

<s>7. <emph type="italics"/>(Etenim habentia pedes, quoniam &longs;uper <expan abbr="vtrumq;">vtrumque</expan> oppo&longs;itorum cru<lb/>rum vici&longs;&longs;im &longs;tant, pondus&queacute; &longs;ustinent, nece&longs;&longs;e habent altero progredien<lb/>te, inflectere alterum; æqualia namque longitudine nata &longs;unt habere op<lb/>po&longs;ita membra. </s>

<s>Cap. 7. <emph type="italics"/>(Etenim habentia pedes, quoniam &longs;uper <expan abbr="vtrumq;">vtrumque</expan> oppo&longs;itorum cru<lb/>rum vici&longs;&longs;im &longs;tant, pondus&queacute; &longs;ustinent, nece&longs;&longs;e habent altero progredien<lb/>te, inflectere alterum; æqualia namque longitudine nata &longs;unt habere op<lb/>po&longs;ita membra. </s>

<s>& quod ponderi &longs;ub&longs;tat rectum e&longs;&longs;e oportet, vt perpen<lb/>diculum ad terram. </s>

Line 9408

<s>10. te&longs;tatur, eam appellant geometræ, quæ in triangulo rectangulo recto <lb/>angulo &longs;ubtenditur, vnde & denominata e&longs;t hypotenu&longs;a, ide&longs;t &longs;ubten&longs;a, vt <lb/><figure id="fig126"></figure><lb/>in triangulo A B C, cuius angulus B, rectus &longs;it, recta <lb/>A C, angulo recto B, &longs;ubten&longs;a, hypotenu&longs;a dicitur. <lb/></s>

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

<s>Ari&longs;t.

<s>igitur ait, quod antequam animal ambulare in<lb/>cipiat, dum &longs;cilicet manet, habet crura, quæ manent <lb/>recta, &longs;iue perpendicularia horizonti, cum autem in<lb/>cipit progredi nece&longs;&longs;e e&longs;t <expan abbr="vtr&utilde;q;">vtrunque</expan> crus inclinari ad ho<lb/>rizontem. </s>

igitur ait, quod antequam animal ambulare in<lb/>cipiat, dum &longs;cilicet manet, habet crura, quæ manent <lb/>recta, &longs;iue perpendicularia horizonti, cum autem in<lb/>cipit progredi nece&longs;&longs;e e&longs;t <expan abbr="vtr&utilde;q;">vtrunque</expan> crus inclinari ad ho<lb/>rizontem. </s>

<s>nam primum crus in ingre&longs;lu prolatum fit <lb/>hypotenu&longs;a, quia &longs;cilicet &longs;ubtendit angulum rectum, <lb/>quem facit alterum crus adhuc quie&longs;cens, cum hori<pb pagenum="214"/>zonte; vt in &longs;uperiori triangulo, &longs;i concipiamus crura fui&longs;&longs;e duo latera A B, <lb/>A D, quæ manente animali, fui&longs;&longs;ent ambo &longs;imul in &longs;itu A B, perpendicula<lb/>ria horizonti; incipiens autem animal ambulare, proferat primo crus A D, <lb/>A D, fiet hypotenu&longs;a trianguli A B C, & quia crus hoc A D, factum hypo<lb/>tenu&longs;a æquale e&longs;t alteri manenti A B, nequit totius veræ hypotenufæ A C, <lb/>officio fungi, quæ æquiualet toti A D, & præterea interiacenti D C, vrea au<lb/><figure id="fig127"></figure><lb/>tem hypotenu&longs;a debet e&longs;&longs;e maior, quia opponitun <lb/>maiori angulo nimirum recto B, quam latus A B, <lb/>quod angulo acuto C, opponitur per 19. primi, & <lb/>propterea ni&longs;i alterum &longs;ub&longs;equens crus A B, incli<lb/>netur, vt in &longs;ecunda figura, non pote&longs;t hypotenu&longs;a <lb/>A D, terram attingere, <expan abbr="atq;">atque</expan> hac de cau&longs;a nece&longs;&longs;e <lb/>e&longs;t, vt initio gre&longs;&longs;us <expan abbr="vtrumq;">vtrumque</expan> crus, quod prius per<lb/>pendiculare erat, inclinetur; inclinato igitur crure <lb/>A B, antror&longs;um tunc prolatum crus A C, terram <lb/>contingit, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; factus e&longs;t primus gre&longs;&longs;us B C.</s>

Line 9458

<s>1. <emph type="italics"/>(Primum quidem in animalibus: oportet enim &longs;i moueatur aliqua <lb/>particularum quie&longs;cere ahquam, & propter hoc, & flexus animalibus <lb/>in&longs;unt: tanquam enim centro vtuntur flex: bus & fit tota pars, in qua <lb/>e&longs;t flexus & vna, & duæ; & recta, & flexa, quæ permutatur potentia, <lb/>& actu, propter flexum. </s>

<s>Cap. 1. <emph type="italics"/>(Primum quidem in animalibus: oportet enim &longs;i moueatur aliqua <lb/>particularum quie&longs;cere ahquam, & propter hoc, & flexus animalibus <lb/>in&longs;unt: tanquam enim centro vtuntur flex: bus & fit tota pars, in qua <lb/>e&longs;t flexus & vna, & duæ; & recta, & flexa, quæ permutatur potentia, <lb/>& actu, propter flexum. </s>

<s>cum autem flectitur, & mouetur, hoc quidem &longs;ignum mo-<emph.end type="italics"/><lb/><figure id="fig129"></figure><lb/><emph type="italics"/>etur, illud autem manet in flexibus, quemadmodum <expan abbr="vtiq;">vtique</expan> &longs;i dia<lb/>metri, quæ quidem A D, maneat, quæ cutem B, moueatur, & <lb/>fiat A C, &longs;ed hic quidem videtur, &longs;ecundum omnem modum in<lb/>diui&longs;ibile e&longs;&longs;e centrum. </s>

Line 9496

<s>5. <emph type="italics"/>(Quemadmodum autem &longs;pontanea mouentur paruo motu facto)<emph.end type="italics"/> Spon<lb/>tanea i&longs;ta erant machinæ, quæ à &longs;eip&longs;is mouebantur, quas Græci automata <lb/>dixerunt, cuin&longs;modi &longs;unt Automata Heronis Alexandrini, quæ adhuc <expan abbr="extãt">extant</expan>.</s>

<s>Cap. 5. <emph type="italics"/>(Quemadmodum autem &longs;pontanea mouentur paruo motu facto)<emph.end type="italics"/> Spon<lb/>tanea i&longs;ta erant machinæ, quæ à &longs;eip&longs;is mouebantur, quas Græci automata <lb/>dixerunt, cuin&longs;modi &longs;unt Automata Heronis Alexandrini, quæ adhuc <expan abbr="extãt">extant</expan>.</s>

<s>8. E&longs;t ibi quoddam triangulum cum elementis more geometrarum <lb/>depictum, vnde locus ille videri po&longs;&longs;it mathematicus, verumtamen nullo <lb/>modo geometriæ auxilio indiget.</s>

<s>Cap. 8. E&longs;t ibi quoddam triangulum cum elementis more geometrarum <lb/>depictum, vnde locus ille videri po&longs;&longs;it mathematicus, verumtamen nullo <lb/>modo geometriæ auxilio indiget.</s>

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

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<s>Eodem cap. <emph type="italics"/>(Qui enim con&longs;ultat quærere videtur, & re&longs;oluere prædicto modo, <lb/>quemadmodum de&longs;ignationes)<emph.end type="italics"/> Per de&longs;ignationes Ari&longs;t. </s>

<s>intelligere geometri<lb/>cas demon&longs;trationes &longs;æpius dictum e&longs;t in logicis textibus, quod pariter ex <lb/>hoc loco confirmatur. </s>

intelligere geometri<lb/>cas demon&longs;trationes &longs;æpius dictum e&longs;t in logicis textibus, quod pariter ex <lb/>hoc loco confirmatur. </s>

<s>quando autem ait <emph type="italics"/>(Re&longs;olutre prædicto modo, quemad<lb/>modum de&longs;ignationes)<emph.end type="italics"/> innuit re&longs;olutionem geometricam, de qua abundè di<lb/>ctum e&longs;t in explicatione tituli librorum Re&longs;olutoriorum; quam expo&longs;ui, ni<lb/>hil aliud e&longs;&longs;e, quam medij inqui&longs;itionem ad id, quod propo&longs;itum fuerit de</s>

<s><arrow.to.target n="marg297"></arrow.to.target><lb/>mon&longs;trandum. </s>

<s>veram autem, <expan abbr="atq;">atque</expan> germanam fui&longs;&longs;e huiu&longs;modi explicatio<lb/>nem, hoc loco Ari&longs;t. </s>

<s>veram autem, <expan abbr="atq;">atque</expan> germanam fui&longs;&longs;e huiu&longs;modi explicatio<lb/>nem, hoc loco Ari&longs;t.

<s>ip &longs;e confirmat, cum hanc re&longs;olutionem dicat e&longs;&longs;e &longs;imi<lb/>lem con&longs;ultationi, &longs;iue inqui&longs;itioni mediorum ad finem in rebus practicis <lb/>con&longs;equendum; ip &longs;a verò e&longs;t inqui&longs;itio mediorum ad id, quod in rebus &longs;pe<lb/>culatiuis propo&longs;itum e&longs;t, demon&longs;trandum. </s>

ip &longs;e confirmat, cum hanc re&longs;olutionem dicat e&longs;&longs;e &longs;imi<lb/>lem con&longs;ultationi, &longs;iue inqui&longs;itioni mediorum ad finem in rebus practicis <lb/>con&longs;equendum; ip &longs;a verò e&longs;t inqui&longs;itio mediorum ad id, quod in rebus &longs;pe<lb/>culatiuis propo&longs;itum e&longs;t, demon&longs;trandum. </s>

<s>con&longs;ultatio igitur e&longs;t in rebus <lb/>practicis, quod in &longs;peculatiuis e&longs;t re&longs;olutio.<lb/><arrow.to.target n="marg298"></arrow.to.target></s>

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<s>Ad con&longs;tituendam proportionalitatem ne<lb/>ce&longs;&longs;arij &longs;unt omninò quatuor termini, quod quidem primum per&longs;picuum <lb/>e&longs;t in ea proportionalitate, quam Difiunctam vocant, quæ e&longs;t huiu&longs;modi, <lb/>vt 9. ad 6. ita 3. ad 2. deinde <expan abbr="ver&utilde;">verum</expan> e&longs;t etiam in ea, quam continuam dicunt, <lb/>quæ talis e&longs;t, vt 9. ad 6. ita 6. ad 4. quæ in tribus quidem terminis 9. 6. 4. <lb/>con&longs;i&longs;tit, &longs;ed tamen, qnia medius 6. <expan abbr="vtrumq;">vtrumque</expan> re&longs;picit extremum, ideò vices <lb/>duorum gerit, ac proinde e&longs;t, ac &longs;i hoc modo termini di&longs;ponantur 9. 6. 6. 4. <lb/>vbi 6. bis ponitur, <expan abbr="&longs;unt&qacute;">&longs;untque</expan>; quatuor huius etiam proportionalitatis termini. <lb/></s>

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

<s>hinc Ari&longs;t.

<s>textum &longs;atis intelligere poteris.</s>

textum &longs;atis intelligere poteris.</s>

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<s>quare etiam totum ad totum, quod di&longs;tributio binatim copulat. </s>

<s>quæ &longs;i <lb/>etiam ita compo&longs;ita fuerint, iustè copulat)<emph.end type="italics"/> Accipit Ari&longs;t. </s>

<s>quæ &longs;i <lb/>etiam ita compo&longs;ita fuerint, iustè copulat)<emph.end type="italics"/> Accipit Ari&longs;t.

<s>illum argumentandi <lb/>modum, quem Geometræ alternam rationem vocant, <expan abbr="quàm&qacute;">quàmque</expan>; definit. </s>

illum argumentandi <lb/>modum, quem Geometræ alternam rationem vocant, <expan abbr="quàm&qacute;">quàmque</expan>; definit. </s>

<s>12. <lb/>5. exponunt, vt eam rebus ip&longs;is accommodet, <expan abbr="atq;">atque</expan> in praxim deducat; e&longs;t <lb/>autem huiu&longs;modi, &longs;int primum quatuor termini proportionales, ide&longs;t, vt <lb/>primus ad &longs;ecundum, ita tertius ad quartum. </s>

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<s>non erit tamen totum 16. ad totum 12. in eadem ratione cum diui&longs;is ter<lb/>minis, cum ibi &longs;it exce&longs;&longs;us binarij, hic verò quaternarij. </s>

<s>hæc videtur e&longs;&longs;e <lb/>Ari&longs;t. </s>

<s>hæc videtur e&longs;&longs;e <lb/>Ari&longs;t.

<s>ratio; quam adhuc melius declara&longs;&longs;e libet. </s>

ratio; quam adhuc melius declara&longs;&longs;e libet. </s>

<s>Geometrica igitur pro<lb/>portionalitas ita dicta e&longs;t, quia quælibet proportio pote&longs;t in materia Geo<lb/>metrica, lineis, &longs;uperficiebus, & corporibus continuari in quatuor termi<lb/>nis, ita vt proportionalitas, &longs;eu &longs;imilitudo rationum exurgat, quod in nu<lb/>meris fieri &longs;emper nequit, cum plures fint proportiones, quæ numeris ex<lb/>primi nequeunt, vt &longs;unt eæ, quas irrationales appellant, cuiu&longs;modi e&longs;t inter <lb/>diametrum, & co&longs;tam eiu&longs;dem quadrati, cuius nec proportio, nec propor<lb/>tionalitas in numeris reperiri pote&longs;t, quæ tamen in lineis, &longs;uperficiebus, ac <lb/>corporibus e&longs;&longs;e po&longs;&longs;unt: e&longs;t enim vt diameter vnius quadrati ad latus eiu&longs;<lb/>dem, ita idem latus ad aliam lineam inuentam per 11. 6. vel vt diameter ad <lb/>co&longs;tam, ita quælibet alia linea ad aliam inuentam, per 12. 6. omnis igitur <lb/>proportionalitas rebus Geometricis ine&longs;&longs;e pote&longs;t; non autem numeris, in <lb/>quibus &longs;olum po&longs;&longs;unt e&longs;&longs;e rationes rationales, &longs;eu <expan abbr="rer&utilde;">rerum</expan> commen&longs;urabilium; <lb/>latius igitur patet Geometrica hæc &longs;imilitudo, quàm Arithmetica, cùm <lb/>Geometrica complectatur tam rationales, quàm irrationales. </s>

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<s>hic contradi&longs;tincta e&longs;t à proportionalitate Geometrica: quia Arithmetica <lb/>hæc analogia attenditur &longs;olum, iuxta eundem exce&longs;&longs;um numerorum, non, <lb/>autem iuxta proportionem, &longs;eu habitudinem terminorum ad inuicem, quod <lb/>maximè in Geometrica &longs;pectatur. </s>

<s>propterea Mathematici <expan abbr="c&etilde;&longs;ent">cen&longs;ent</expan> eam vo<lb/>candam e&longs;&longs;e potius medietatem Arithmeticam, quam proportionalita<lb/>tem, cum quibus nunc Ari&longs;t. </s>

<s>con&longs;entit.</s>

con&longs;entit.</s>

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<s>quid &longs;it, quod <lb/>puer fieri Mathematicus pote&longs;t, &longs;apiens autem naturalis non pote&longs;t. </s>

<s>An quia illa <lb/>per ab&longs;tractionem &longs;unt, horum autem principia ab experientia &longs;umuntur)<emph.end type="italics"/> Ex hoc <lb/>loco manife&longs;tè apparet Ari&longs;t. </s>

<s>An quia illa <lb/>per ab&longs;tractionem &longs;unt, horum autem principia ab experientia &longs;umuntur)<emph.end type="italics"/> Ex hoc <lb/>loco manife&longs;tè apparet Ari&longs;t.

<s>exi&longs;timare principia Mathematica nullo mo<lb/>do nobis per experientiam innote&longs;cere, quod nonnulli negant.</s>

exi&longs;timare principia Mathematica nullo mo<lb/>do nobis per experientiam innote&longs;cere, quod nonnulli negant.</s>

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<s>1. (<emph type="italics"/>Nec enim lufcitia e&longs;t numerus pariter par<emph.end type="italics"/>) vt &longs;cilicet dicebat <lb/>Pythagoras. </s>

<s>Cap. 1. (<emph type="italics"/>Nec enim lufcitia e&longs;t numerus pariter par<emph.end type="italics"/>) vt &longs;cilicet dicebat <lb/>Pythagoras. </s>

<s>Porrò definit. </s>

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<s>2. (<emph type="italics"/>Ab&longs;urdum enim &longs;it, volenti o&longs;tendere triangulum duobus rectis æqua<lb/>les habere angulos, &longs;umere principinm huiu&longs;modi, anima immortalis est<emph.end type="italics"/>) Repete, <lb/>quæ de hac trianguli proprietate fusè &longs;crip&longs;i lib. </s>

<s>Cap. 2. (<emph type="italics"/>Ab&longs;urdum enim &longs;it, volenti o&longs;tendere triangulum duobus rectis æqua<lb/>les habere angulos, &longs;umere principinm huiu&longs;modi, anima immortalis est<emph.end type="italics"/>) Repete, <lb/>quæ de hac trianguli proprietate fusè &longs;crip&longs;i lib. </s>

<s>1. Priorum, &longs;ect. </s>

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<s>10. <emph type="italics"/>(Vt enim habuerint principia, ita, quæ de principijs ortum ducunt, <lb/>Per&longs;picuè autem licet hoc in Geometria magis intueri, vbi cum aliqua &longs;ump&longs;eris <lb/>principia, vt ea habuerint, ita etiam, quæ ip&longs;a con&longs;equuntur <gap/> velut &longs;i triangulum <lb/>duobus rectis æquales habet angulos, quadratum <expan abbr="quoq;">quoque</expan> quatuor angulis rectis ha-<emph.end type="italics"/><pb pagenum="221"/><emph type="italics"/>beat nece&longs;&longs;e e&longs;t. </s>

<s>Cap. 10. <emph type="italics"/>(Vt enim habuerint principia, ita, quæ de principijs ortum ducunt, <lb/>Per&longs;picuè autem licet hoc in Geometria magis intueri, vbi cum aliqua &longs;ump&longs;eris <lb/>principia, vt ea habuerint, ita etiam, quæ ip&longs;a con&longs;equuntur <gap/> velut &longs;i triangulum <lb/>duobus rectis æquales habet angulos, quadratum <expan abbr="quoq;">quoque</expan> quatuor angulis rectis ha-<emph.end type="italics"/><pb pagenum="221"/><emph type="italics"/>beat nece&longs;&longs;e e&longs;t. </s>

<s>& &longs;i tria gulum &longs;ecus, ita etiam, & quadratum commutabitur, <lb/>ex altera parte enim ei re&longs;pondet. </s>

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<s>16. <emph type="italics"/>(In Geometria &longs;i quidem cum quis dixerit quadrangul&ubreve; quatuor rectis <lb/>æquales habere, & percunctatur propter quid, occurrit, quia etiam triangul&ubreve; duo<lb/>bus rectis æquales habet. </s>

<s>Cap. 16. <emph type="italics"/>(In Geometria &longs;i quidem cum quis dixerit quadrangul&ubreve; quatuor rectis <lb/>æquales habere, & percunctatur propter quid, occurrit, quia etiam triangul&ubreve; duo<lb/>bus rectis æquales habet. </s>

<s>in his igitur ex determinato &longs;ibi principio propter quid <lb/>a&longs;&longs;ump&longs;erunt)<emph.end type="italics"/> Lege, quæ proximè in præcedenti loco expo&longs;ui, ea enim om<lb/>nia huc etiam pertinent. </s>

<s>hoc &longs;olum addendum ad illorum verborum (<emph type="italics"/>Ex de<lb/>terminato &longs;ibi principio propter quid a&longs;&longs;ump&longs;erunt<emph.end type="italics"/>) intelligentiam, ide&longs;t ex vna <lb/>conclu&longs;ione demon&longs;trata, tanquam principio alia demon&longs;trant; quod rectè <lb/>fieri Ari&longs;t. </s>

<s>in primo Po&longs;ter. </s>

in primo Po&longs;ter. </s>

<s>docet.</s>

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<s>31. (<emph type="italics"/>A qui proportionale in quatuor nihilominus perficitur: nam quem<lb/>admodum A, ad B, ita C, ad D.<emph.end type="italics"/>) ide&longs;t proportionalitas in quatuor terminis <lb/>con&longs;i&longs;tit, quemadmodum pluribus &longs;upra lib. </s>

<s>Cap. 31. (<emph type="italics"/>A qui proportionale in quatuor nihilominus perficitur: nam quem<lb/>admodum A, ad B, ita C, ad D.<emph.end type="italics"/>) ide&longs;t proportionalitas in quatuor terminis <lb/>con&longs;i&longs;tit, quemadmodum pluribus &longs;upra lib. </s>

Line 9872

<s>5 (<emph type="italics"/>Vt &longs;i duplum multiplicium primum est, non licet multiplex com<lb/>muniter prædicatum &longs;eparari, quippe, quod duplo prius e&longs;t<emph.end type="italics"/>) Inter pro<lb/>portionum genera vnum e&longs;t, quod dicitur multiplex, quod &longs;ub &longs;e <lb/>infinitas &longs;pecies continet, vt Duplum, Triplum, Quadruplum, & c. <lb/></s>

<s>Cap. 5 (<emph type="italics"/>Vt &longs;i duplum multiplicium primum est, non licet multiplex com<lb/>muniter prædicatum &longs;eparari, quippe, quod duplo prius e&longs;t<emph.end type="italics"/>) Inter pro<lb/>portionum genera vnum e&longs;t, quod dicitur multiplex, quod &longs;ub &longs;e <lb/>infinitas &longs;pecies continet, vt Duplum, Triplum, Quadruplum, & c. <lb/></s>

<s>in infinitum. </s>

<s>vbi vides, cur Ari&longs;t. </s>

<s>vbi vides, cur Ari&longs;t.

<s>dixerit duplum e&longs;&longs;e primum inter multi<lb/>plicia, cum verè naturali ordine numerorum ip&longs;i primus debeatur locus. <lb/></s>

dixerit duplum e&longs;&longs;e primum inter multi<lb/>plicia, cum verè naturali ordine numerorum ip&longs;i primus debeatur locus. <lb/></s>

<s>Vides etiam cur non liceat, Multiplex ip&longs;um genus commune prædicatum <lb/>omnibus &longs;peciebus veluti Idæam &longs;eparari; tunc enim ait, ip&longs;um mul<lb/>tiplex ab&longs;tractum e&longs;&longs;et prius ordine ip&longs;o primo multiplici, &longs;ci<lb/>licet duplo; & Duplum non e&longs;&longs;et primum inter mul<lb/>tiplicia, quæ <expan abbr="vtraq;">vtraque</expan> &longs;unt ab&longs;urda; non igitur <lb/>illud tanquam Idæam licet &longs;epa<lb/>ratum ponere.</s><pb pagenum="222"/>

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<s>7. <emph type="italics"/>(Nam&longs;i habenti trigono duos rectos, nece&longs;&longs;e e&longs;t tetragonum qua<lb/>tuor rectis con&longs;tare, manife&longs;tum e&longs;t, quod trigonus duos rectos habens <lb/>cau&longs;a eius exi&longs;tat. </s>

<s>Cap. 7. <emph type="italics"/>(Nam&longs;i habenti trigono duos rectos, nece&longs;&longs;e e&longs;t tetragonum qua<lb/>tuor rectis con&longs;tare, manife&longs;tum e&longs;t, quod trigonus duos rectos habens <lb/>cau&longs;a eius exi&longs;tat. </s>

<s>Verùm &longs;i quid in trigono mutaris, nece&longs;&longs;arium e&longs;t, & <lb/>in tetragono mutes, vt &longs;i tres habuerunt, &longs;ex; & &longs;i quatuor, octo; &longs;in <lb/>verò non mutes, vt illud, ita hoc <expan abbr="quoq;">quoque</expan> habeat nece&longs;&longs;e e&longs;t)<emph.end type="italics"/> Lege prius, quæ &longs;upra <lb/>lib. </s>

Line 9910

<s>10. <emph type="italics"/>(Multa verò opinione concipiunt, quæ penes nos non &longs;unt, vt diame<lb/>trum commen&longs;urabilem e&longs;&longs;e)<emph.end type="italics"/> Quæ lib. </s>

<s>Cap. 10. <emph type="italics"/>(Multa verò opinione concipiunt, quæ penes nos non &longs;unt, vt diame<lb/>trum commen&longs;urabilem e&longs;&longs;e)<emph.end type="italics"/> Quæ lib. </s>

<s>1. Priorum, &longs;ecto 3. cap. </s>

Line 9928

<s>Problematicè verò, <lb/>ide&longs;t, vt opere ip&longs;o efficiamus <expan abbr="triãgulum">triangulum</expan> illud, nondum à quoquam ritè per<lb/>actum e&longs;t: & propterea problema hoc difficile admodum cen&longs;endum e&longs;t, <lb/>præ&longs;ertim cum tota Geometrarum antiquitas, <expan abbr="atq;">atque</expan> po&longs;teritas in ip&longs;um fru<lb/>&longs;tra <expan abbr="hucu&longs;q;">hucu&longs;que</expan> in&longs;udauerit, <expan abbr="atq;">atque</expan> adeò etiam moraliter impo&longs;&longs;ibile exi&longs;timan<lb/>dum e&longs;t. </s>

<s>quo &longs;en&longs;u locutum e&longs;&longs;e Ari&longs;t. </s>

<s>quo &longs;en&longs;u locutum e&longs;&longs;e Ari&longs;t.

<s>hoc loco crediderim, dum ait, illud <lb/>fieri non po&longs;&longs;e. </s>

hoc loco crediderim, dum ait, illud <lb/>fieri non po&longs;&longs;e. </s>

<s>ab&longs;olutè tamen a&longs;&longs;erere non debemus e&longs;&longs;e impo&longs;&longs;ibilem, cum <lb/>nulla id demon&longs;tratione certum &longs;it, imò ego &longs;impliciter, vt aiunt, credo e&longs;<lb/>&longs;e po&longs;&longs;ibilem, cum alia theoremata, <expan abbr="atq;">atque</expan> problemata (quale e&longs;t pytagoreum <lb/>illud celebre, quod 47. locum in primo Elemen. </s>

Line 9940

<s>12. (<emph type="italics"/>Si triangulo duo recti, nece&longs;&longs;um e&longs;t hoc con&longs;equi<emph.end type="italics"/>) ide&longs;t, &longs;i triangu<lb/>lum habet tres angulos æquales duobus rectis, nece&longs;&longs;e e&longs;t con&longs;equi, vt &longs;upe<lb/>rius &longs;epius dixit, quod quadrilaterum habeat quatuor angulos æquales qua<lb/>tuor rectis, lib. </s>

<s>Cap. 12. (<emph type="italics"/>Si triangulo duo recti, nece&longs;&longs;um e&longs;t hoc con&longs;equi<emph.end type="italics"/>) ide&longs;t, &longs;i triangu<lb/>lum habet tres angulos æquales duobus rectis, nece&longs;&longs;e e&longs;t con&longs;equi, vt &longs;upe<lb/>rius &longs;epius dixit, quod quadrilaterum habeat quatuor angulos æquales qua<lb/>tuor rectis, lib. </s>

Line 9958

<s>12. (<emph type="italics"/>luxta&queacute; diametrum iungit<emph.end type="italics"/>) ide&longs;t diametraliter opponit, quæ <lb/>e&longs;t omnium maxima oppo&longs;itio, ita vt quæ diametraliter oppo&longs;ita <lb/>&longs;unt, amplius di&longs;tare nequeant, quia diameter e&longs;t maxima om<lb/>nium di&longs;tantia, &longs;iue fit diameter quadrilateræ figuræ, &longs;iue circuli.</s>

<s>Cap. 12. (<emph type="italics"/>luxta&queacute; diametrum iungit<emph.end type="italics"/>) ide&longs;t diametraliter opponit, quæ <lb/>e&longs;t omnium maxima oppo&longs;itio, ita vt quæ diametraliter oppo&longs;ita <lb/>&longs;unt, amplius di&longs;tare nequeant, quia diameter e&longs;t maxima om<lb/>nium di&longs;tantia, &longs;iue fit diameter quadrilateræ figuræ, &longs;iue circuli.</s>

<s><emph type="italics"/>Ex Libro 3. Politicorum.<emph.end type="italics"/></s>

Line 9968

<s>2. (<emph type="italics"/>Ceu harmoniam earumdem rocum aliam e&longs;&longs;e dicimus, & modò <lb/>Doricam, modò Phrygiam vocitamus<emph.end type="italics"/>) Harmonias Doricam, & Phry<lb/>giam veteres Mu&longs;ici, vt Ari&longs;toxenes, Euclides, Ptolæmeus vocant <lb/>Tonos, & Modos, Dorium &longs;cilicet, & Phrygium. </s>

<s>Cap. 2. (<emph type="italics"/>Ceu harmoniam earumdem rocum aliam e&longs;&longs;e dicimus, & modò <lb/>Doricam, modò Phrygiam vocitamus<emph.end type="italics"/>) Harmonias Doricam, & Phry<lb/>giam veteres Mu&longs;ici, vt Ari&longs;toxenes, Euclides, Ptolæmeus vocant <lb/>Tonos, & Modos, Dorium &longs;cilicet, & Phrygium. </s>

<s>per mu&longs;icum au<lb/>tem modum intelligebant quandam vocum con&longs;titutionem, &longs;eu rithmum, <lb/>quem nos hodie vulgò ariam vocamus, vt doctè explicat Io&longs;ephus Zarlinus <lb/>in 4. parte In&longs;titut. </s>

Line 9992

<s>vnde prouerbium illud vetus ortum habuit, à Dorio ad <lb/>Phrygium, ide&longs;t à rebus alti&longs;&longs;imis, & &longs;erijs ad humiles, & iucundas. </s>

<s>Hos <lb/>ambos &longs;olos Plato, & Ari&longs;t. </s>

<s>Hos <lb/>ambos &longs;olos Plato, & Ari&longs;t.

<s>in Rempublicam admi&longs;erunt. </s>

in Rempublicam admi&longs;erunt. </s>

<s>Lydius demum <lb/>modus erat horribilis, m&oelig;&longs;tus, ac tri&longs;tis, <expan abbr="ideo&qacute;">ideoque</expan>; lamentationibus, ac la<lb/>crymis aptus. </s>

Line 10016

<s>3. (<emph type="italics"/>Eodem&queacute; modo in harmonijs, vt quidam tradunt: nam & in illis <lb/>po&longs;uerunt duas &longs;pecies, vnam Doricam, alteram Phrygiam: cæteras <lb/>verò omnes vel ad Doricam, vel ad Phrygiam referri.<emph.end type="italics"/></s>

<s>Cap. 3. (<emph type="italics"/>Eodem&queacute; modo in harmonijs, vt quidam tradunt: nam & in illis <lb/>po&longs;uerunt duas &longs;pecies, vnam Doricam, alteram Phrygiam: cæteras <lb/>verò omnes vel ad Doricam, vel ad Phrygiam referri.<emph.end type="italics"/></s>

<s>Vide proximè in præcedenti loco dicta, quæ omnia ita etiam <lb/>huic loco quadrant, vt præterea nihil de&longs;ideretur.</s>

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<s>1. (<emph type="italics"/>Quare opus e&longs;t partim arithmetica æquitate vti, partim ea, quæ <lb/>e&longs;t &longs;ecundum dignitatem.<emph.end type="italics"/></s>

<s>Cap. 1. (<emph type="italics"/>Quare opus e&longs;t partim arithmetica æquitate vti, partim ea, quæ <lb/>e&longs;t &longs;ecundum dignitatem.<emph.end type="italics"/></s>

<s>Arithmeticam medietatem &longs;upra explicaui lib. </s>

Line 10052

<s>12. & vlt. (<emph type="italics"/>In Republica verò Platonis Socrates de mutation bus loqui<lb/>tur, nec tamen rectè. </s>

<s>Cap. 12. & vlt. (<emph type="italics"/>In Republica verò Platonis Socrates de mutation bus loqui<lb/>tur, nec tamen rectè. </s>

<s>illius enim Reip. </s>

Line 10070

<s>præterea &longs;en&longs;ui radix, non autem cubus quadrare pote&longs;t. </s>

<s>Porrò &longs;ciendum <lb/>Ari&longs;t. </s>

<s>Porrò &longs;ciendum <lb/>Ari&longs;t.

<s>locum hunc ex Platonis lib. </s>

locum hunc ex Platonis lib. </s>

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<s>quam ob cau&longs;am Theon Smyrnæus, qui Mathematica Plato<lb/>nis loca commentarijs illu&longs;trauit, hi&longs;ce tenebris lucem nullam afferre au&longs;us <lb/>e&longs;t, verùm eas di&longs;&longs;imulans cautè declinauit. </s>

<s>cùm igitur præ&longs;ens Ari&longs;t. </s>

<s>cùm igitur præ&longs;ens Ari&longs;t.

<s>locus <lb/>&longs;it illius Platonici particula quædam, quid mirum, &longs;i non mmori ob&longs;curita<lb/>te, ac difficultate impeditus &longs;it? </s>

locus <lb/>&longs;it illius Platonici particula quædam, quid mirum, &longs;i non mmori ob&longs;curita<lb/>te, ac difficultate impeditus &longs;it? </s>

<s>vnde etiam &longs;i quitor huius explicationem, <lb/>ab illius explicatione p<gap/>tendam e&longs;&longs;e. </s>

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<s>12. <pb pagenum="225"/>illius commentarij propè finem præ&longs;ens Ari&longs;t. </s>

<s>12. <pb pagenum="225"/>illius commentarij propè finem præ&longs;ens Ari&longs;t.

<s>locus ex præmi&longs;&longs;is ab eo bre<lb/>uiter, ac dilucidè declaratur. </s>

locus ex præmi&longs;&longs;is ab eo bre<lb/>uiter, ac dilucidè declaratur. </s>

<s>quæ explanatio, quoniam mihi præ cæteris ar<lb/>ridet, eam hoc loco, explicatiorem tamen, referam. </s>

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<s>5. (<emph type="italics"/>Mu&longs;icam verò omnes fatemur e&longs;&longs;e ex iucundi&longs;&longs;imis, &longs;iue nuda &longs;it, <lb/>&longs;iue cum melodia<emph.end type="italics"/>) Quamuis latina interpretatio pro melodia, di<lb/>cat, modulatione, Gr&ecedil;cus tamen textus habet <foreign lang="greek">meta melwdias,</foreign> ide&longs;t <lb/><expan abbr="c&utilde;">cum</expan> melodia. </s>

<s>Cap. 5. (<emph type="italics"/>Mu&longs;icam verò omnes fatemur e&longs;&longs;e ex iucundi&longs;&longs;imis, &longs;iue nuda &longs;it, <lb/>&longs;iue cum melodia<emph.end type="italics"/>) Quamuis latina interpretatio pro melodia, di<lb/>cat, modulatione, Gr&ecedil;cus tamen textus habet <foreign lang="greek">meta melwdias,</foreign> ide&longs;t <lb/><expan abbr="c&utilde;">cum</expan> melodia. </s>

<s>per Mu&longs;icam nudam, forte Ari&longs;toteles intelligit eam, <lb/>quæ &longs;olis &longs;onis <expan abbr="ab&longs;q;">ab&longs;que</expan> oratione con&longs;tat; per melodiam verò intelligit eam, <lb/>quam Io&longs;ephus Zarlinus in 2. parte &longs;uarum In&longs;titutionum Mu&longs;icalium defi<lb/>nit, quæ e&longs;t concentus plurium vocum harmonicus cum rithmo, & oratio<lb/>ne, ide&longs;t, qua canitur oratio aliqua &longs;ub aliquo rithmo, aut modo, &longs;iue vt <lb/>nunc loquimur, con qualche aria.</s>

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<s>2. tractaui, <expan abbr="earum&qacute;">earumque</expan>; proprieta<lb/>tes, quas hic Ari&longs;t. </s>

<s>2. tractaui, <expan abbr="earum&qacute;">earumque</expan>; proprieta<lb/>tes, quas hic Ari&longs;t.

<s>recen&longs;et ibi connumeraui.</s>

recen&longs;et ibi connumeraui.</s>

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<s>7 (<emph type="italics"/>Con&longs;iderandum vtrum omnibus vtendum &longs;it harmonijs, & rithmis<emph.end type="italics"/>) <lb/>Vide quæ &longs;upra lib. </s>

<s>Cap. 7 (<emph type="italics"/>Con&longs;iderandum vtrum omnibus vtendum &longs;it harmonijs, & rithmis<emph.end type="italics"/>) <lb/>Vide quæ &longs;upra lib. </s>

<s>3. Politic. </s>

Line 10312

<s>quemadmodum faciunt; qui <gap/>a&longs;a militaria <lb/>partiuntur. </s>

<s>At cæteræ lineæ, quæ per lineas compo&longs;itam figuram &longs;ecant, eam cor<lb/>rumpunt: committitur enim rectilmea figura in argulis, vel &longs;ecundum angulos)<emph.end type="italics"/><lb/>Vt rectè problema hoc percipiamus, proponenda e&longs;t figura rectilinea, & <lb/>vna ex ijs, quæ paralle logramma dicuntur, vt &longs;unt Quadratum, Quadrila<lb/><figure id="fig131"></figure><lb/>terum, Rhombus, Rhomboides, cuiu&longs;mo<lb/>di e&longs;t præ&longs;ens, aliter verba Ari&longs;t. </s>

<s>illi non <lb/>&longs;emper quadrarent, quia illarum diameter <lb/>illas &longs;emper bifariam non &longs;e caret. </s>

illi non <lb/>&longs;emper quadrarent, quia illarum diameter <lb/>illas &longs;emper bifariam non &longs;e caret. </s>

<s>quemad<lb/>modum videre e&longs;t in trapezio. </s>

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<s>e&longs;t autem hæc; Denarius componitur ex quaternario, ide&longs;t ex qua<lb/>tuor primis numeris cubis, &longs;cilicet 1. 9. 27. 64. qui &longs;unt cubi, & &longs;imul additi <lb/>con&longs;tituunt decem denas, ide&longs;t <expan abbr="c&etilde;tum">centum</expan>. </s>

<s>quæ cum nulli Mathematicæ demon<lb/>&longs;trationi innitatur, nec vniuer&longs;alis &longs;it, ex &longs;e apparct, quàm &longs;it <expan abbr="comm&etilde;titia">commentitia</expan>, <lb/>& ab Ari&longs;t. </s>

<s>mente aliena. </s>

mente aliena. </s>

<s>Enimuerò me antea ip&longs;ius commentarijs carui&longs;<lb/>&longs;e gaui&longs;us &longs;um, quibus ni&longs;i carui&longs;&longs;em, veritate ip&longs;a carui&longs;&longs;em, acquieui&longs;&longs;em <lb/>enim illius fictioni, quæ <expan abbr="vtcunq;">vtcunque</expan> videtur quadrare, <expan abbr="hoc&qacute;">hocque</expan>; pacto veritatis in<lb/>quirendæ occafio &longs;ublata fui&longs;&longs;et.</s>

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<s>Ibidem <emph type="italics"/>(An quod vmnes homines digitis decem lege naturali creantur? </s>

<s>it aque <lb/>&longs;ui numeri qua&longs;i calculos adipt&longs;centes hac eadem multitudine, cætera <expan abbr="quoq;">quoque</expan> nume<lb/>rant)<emph.end type="italics"/> hæc Ari&longs;t. </s>

<s>it aque <lb/>&longs;ui numeri qua&longs;i calculos adipt&longs;centes hac eadem multitudine, cætera <expan abbr="quoq;">quoque</expan> nume<lb/>rant)<emph.end type="italics"/> hæc Ari&longs;t.

<s>ratio confirmatur ex recentiorum relationibus de populis <lb/>Bra&longs;iliæ, qui cum per &longs;ummam barbariem, in omni rerum ignoratione ver<lb/>&longs;arentur, ex digitis tamen, <expan abbr="vtcunq;">vtcunque</expan> numerabant. </s>

ratio confirmatur ex recentiorum relationibus de populis <lb/>Bra&longs;iliæ, qui cum per &longs;ummam barbariem, in omni rerum ignoratione ver<lb/>&longs;arentur, ex digitis tamen, <expan abbr="vtcunq;">vtcunque</expan> numerabant. </s>

<s><expan abbr="cum&qacute;">cumque</expan>; vellent &longs;ignificare <lb/>quinque dicebant, manum vnam: cum verò decem dicebant, manus duas: <lb/>cum viginti dicebant, manus, & pedes. </s>

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<s>Quæ&longs;tio autem e&longs;t <lb/>de inæquali incremento, ac decremento vmbrarum Solis, quæ propriè de <lb/>vmbris in plano horizontali proiectis, quas rectas vmbras appellant intel<lb/>ligenda e&longs;t: hæ enim inæqualiter cre&longs;cunt, & decre&longs;cunt, &longs;i guidem mane <lb/>plurimum, po&longs;tea parum, tandem nihil ferè circa meridiem minuuntur, po<lb/>&longs;itis tamen æqualibus temporibus. </s>

<s>Quærit igitur Ari&longs;t. </s>

<s>Quærit igitur Ari&longs;t.

<s>cur cum Sol eodem <lb/>vigore feratur, non idem tamen incrementum, decrementumuè vmbrarum <lb/>exultet? </s>

cur cum Sol eodem <lb/>vigore feratur, non idem tamen incrementum, decrementumuè vmbrarum <lb/>exultet? </s>

<s>pro cuius intelligentia, ac &longs;olutione in&longs;picienda e&longs;t figura &longs;equens: <lb/>in qua &longs;emicirculus, &longs;iue arcus A B C, &longs;it is, per quem Sol incedit, dum ele<lb/>uatur &longs;upra horizontem H I; & quia Sol vniformiter &longs;candit hunc arcum, <pb pagenum="231"/><figure id="fig132"></figure><lb/>&longs;int duo arcus æquales A B, B C. <lb/>in plano autem horizontis ere<lb/>ctum &longs;it corpus G D, quod à So<lb/>le con&longs;piciatur, &longs;iue illuminetur. <lb/></s>

Line 10482

<s>So<lb/>le tandem in C. <expan abbr="radio&qacute;">radioque</expan>; C D F. <lb/>vmbra erit G F. </s>

<s>Dicit ergò Ari&longs;t. </s>

<s>Dicit ergò Ari&longs;t.

<s>quod cum anguli A D B, B D C, &longs;int ex <lb/>æqualibus arcubus A B, B C. ad centrum D, con&longs;tituti, erunt æquales, qua<lb/>re erunt etiam æquales alij duo anguli illis ad verticem oppo&longs;iti, per 15. <lb/>primi, qui &longs;unt contenti in triangulo G D I. quod <expan abbr="triã">triam</expan> gulum fit à radio pri<lb/>mo D I, re con&longs;pecta à Sole G D, & vmbra G I. anguli inquam F D E, E D I, <lb/>qui &longs;unt ad verticem prædictis angulis, erunt, & ip&longs;i æquales inuicem.</s>

quod cum anguli A D B, B D C, &longs;int ex <lb/>æqualibus arcubus A B, B C. ad centrum D, con&longs;tituti, erunt æquales, qua<lb/>re erunt etiam æquales alij duo anguli illis ad verticem oppo&longs;iti, per 15. <lb/>primi, qui &longs;unt contenti in triangulo G D I. quod <expan abbr="triã">triam</expan> gulum fit à radio pri<lb/>mo D I, re con&longs;pecta à Sole G D, & vmbra G I. anguli inquam F D E, E D I, <lb/>qui &longs;unt ad verticem prædictis angulis, erunt, & ip&longs;i æquales inuicem.</s>

<s>Supponit præterea pro certo radium D I, qui cæteris longius prolabitur, <lb/>e&longs;&longs;e maiorem propinquiore D E. <expan abbr="ip&longs;um&qacute;">ip&longs;umque</expan>; D E, maiorem e&longs;&longs;e reliquo radio <lb/>D F. oportet autem <expan abbr="radi&utilde;">radium</expan> B E, terminari in puncto E, quod &longs;it citra radium <lb/>D I. & radium D F, de&longs;inere in F, citra radium D E, aliter &longs;equitur lineam <lb/>rectam B E, vel C F, &longs;ecare lineam recta A I, in pluribus punctis, quàm vno <lb/>D. quod e&longs;t impo&longs;&longs;ibile. </s>

Line 10500

<s><emph type="italics"/>Maiores&queacute; cadunt altis de montibus vmbræ.<emph.end type="italics"/></s>

<s>Aduerte verba illa (<emph type="italics"/>Angulus D E, maior, quam E F, angulo D G, est<emph.end type="italics"/>) e&longs;&longs;c <lb/>mendo&longs;a, etiam in græco textu; vnde, & malè in latinum tran&longs;lata: <expan abbr="neq;">neque</expan> in <lb/>græco e&longs;t vox, angulus: aliter Ari&longs;t. </s>

<s>quæ&longs;tioni non &longs;atisfaceret. </s>

quæ&longs;tioni non &longs;atisfaceret. </s>

<s>quare di<lb/>cendum, & interpretandum videtur, quemadmodum à me factum e&longs;t.</s>

Line 10516

<s>2. hoc idem proponat, ac &longs;oluere contendat: Verùm nec Ari&longs;t. </s>

<s>2. hoc idem proponat, ac &longs;oluere contendat: Verùm nec Ari&longs;t.

<s>nec Vi<lb/>tellio intellectui &longs;atisfaciunt mathematico: probabilia tamen afferunt. </s>

nec Vi<lb/>tellio intellectui &longs;atisfaciunt mathematico: probabilia tamen afferunt. </s>

<s>op<lb/>timè hae de re Maurolicus, in &longs;uis Po&longs;thumis, naper editis Photi&longs;mis, & Ke<lb/>plerus, in paralip. </s>

<s>ad Vitell. </s>

<s>Sen&longs;um Ari&longs;t. </s>

<s>Sen&longs;um Ari&longs;t.

<s>ac textum pariter per paraphra<lb/>&longs;im exponam, ita tamen, vt eius textus ex hac paraphra&longs;i omninò cl<gap/>rus <lb/>euadat. </s>

ac textum pariter per paraphra<lb/>&longs;im exponam, ita tamen, vt eius textus ex hac paraphra&longs;i omninò cl<gap/>rus <lb/>euadat. </s>

<s>Quærit igitur; cur lumen Solis ingrediens per quadrangul<gap/>ia, &longs;eu <lb/>triangularia foramina, vel etiam per rimalas, cùm po&longs;tea recipiatur in pia<pb pagenum="232"/>no &longs;atis ab illo foramine remoto, vt in pariete, vel pauimento, non recipi<lb/>tur in eadem figura, per quam ingre&longs;&longs;um e&longs;t; quamuis. </s>

Line 10568

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

<s><expan abbr="Atq;">Atque</expan> hæc e&longs;t &longs;olutio admirandi huius effectus ab Ari&longs;t. </s>

<s><expan abbr="Atq;">Atque</expan> hæc e&longs;t &longs;olutio admirandi huius effectus ab Ari&longs;t.

<s>allata, quæ <lb/>quoniam non paucas habet difficultates, aliam ex Maurolyco de<lb/>&longs;umptam, quæ &longs;atis demon&longs;tratiua e&longs;t, afferam.</s>

allata, quæ <lb/>quoniam non paucas habet difficultates, aliam ex Maurolyco de<lb/>&longs;umptam, quæ &longs;atis demon&longs;tratiua e&longs;t, afferam.</s>

<s>Primò igitur illud Per&longs;pectiuus principium &longs;tatuendum e&longs;t, ex <lb/>quolibet corporis lucidi puncto, ad quodlibet medij punctum, lumen rectis <lb/>lineis quoquouer&longs;us emicare, ita vt lumen à quouis puncto lucidi, tanquam <lb/>à centro <expan abbr="circumquaq;">circumquaque</expan> effu&longs;um in modum &longs;phæræ diffundatur.</s>

Line 10702

<s>& ante omnia experire in pila aliqua lumini lucernæ, aut candelæ obiecta, <lb/>& circumlata, omnes illius &longs;pheræ illuminationes, vt ibi docui. </s>

<s>videbis enim <lb/>qua ratione linea illa, quæ confinium e&longs;t partis illuminatæ, & partis ob&longs;cu<lb/>ræ, aliquando videatur lunularis, aliquando oualis, aliquando recta linea, <lb/>quorum rationem Ari&longs;t. </s>

<s>in præ&longs;enti problemate inquirit. </s>

in præ&longs;enti problemate inquirit. </s>

<s>lege præterea, &longs;i <lb/>plenam huius rei cognitionem de&longs;ideras, propo&longs;it. </s>

Line 10794

<s>de Ordine <lb/>c&oelig;lorum, vnde huius textus expo<lb/>&longs;itionem in hunc modum licebit af<lb/>ferre. </s>

<s>Quando igitur Ari&longs;t. </s>

<s>Quando igitur Ari&longs;t.

<s>quærit, <lb/>cur Luna maiores proijciat vm<lb/>bras, qua Sol, debet &longs;upponere So<lb/>lem, & Lunam e&longs;&longs;e in eadem altitu<lb/>dine &longs;upra horizontem, v. </s>

quærit, <lb/>cur Luna maiores proijciat vm<lb/>bras, qua Sol, debet &longs;upponere So<lb/>lem, & Lunam e&longs;&longs;e in eadem altitu<lb/>dine &longs;upra horizontem, v. </s>

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<s>quæ quidem <lb/>non &longs;oluunt quæ&longs;tionem, &longs;ed eam difficiliorem reddunt. </s>

<s>Quapropter non <lb/>videtur Ari&longs;t. </s>

<s>Quapropter non <lb/>videtur Ari&longs;t.

<s>volui&longs;&longs;e hoc di&longs;cutere, &longs;ed &longs;olum tanquam mirum quodam <lb/>proponere. </s>

volui&longs;&longs;e hoc di&longs;cutere, &longs;ed &longs;olum tanquam mirum quodam <lb/>proponere. </s>

<s>quod &longs;i quid mutire liceat, vbi tantus philo&longs;ophus admirabun<lb/>dus obmutc&longs;cit, dixerim propterea ba&longs;im bullæ non adumbrari ab vmbra <lb/>ip&longs;ius bullæ, quia cum bulla &longs;it &longs;phærica, & tran&longs;parens, Solis lumen eam <lb/>peruadit, <expan abbr="atq;">atque</expan> ex &longs;uperficie concaua ad illius ba&longs;im partim re&longs;lectitur, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; <lb/>eam illuminat. </s>

Line 10974

<s>Notandum quoad ver&longs;ionem latinam Theodori Gazæ, quod vbi &longs;unt ver<lb/>ba illa <emph type="italics"/>(Aut colei violuntur)<emph.end type="italics"/> in græco e&longs;t, <foreign lang="greek">xolntrou<gap/> n'farpazousi.</foreign> quorum ver<lb/>borum paraphra&longs;im omi&longs;i, quia the &longs;auri, aut lexica græca nullam huius ver<lb/>bi notionem afferunt, quæ huic loco quadret, dicunt enim ex Athenæo <foreign lang="greek">tou<gap/><lb/>x<gap/>lnqrcus</foreign>, &longs;ignificare ficus maturas: Suidas verò ait e&longs;&longs;e quoddam plantæ ge<lb/>nus: quorum neutrum ad rem facit. </s>

<s>propterea vel textus corruptus e&longs;t, vel <lb/>metaphoricè v&longs;us e&longs;t Ari&longs;t. </s>

<s>propterea vel textus corruptus e&longs;t, vel <lb/>metaphoricè v&longs;us e&longs;t Ari&longs;t.

<s>hoc verbo, cuius metaphoræ modò intelligen<lb/>tiam non habemus.</s>

hoc verbo, cuius metaphoræ modò intelligen<lb/>tiam non habemus.</s>

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<s>21. <lb/>eiu&longs;dem 11. &longs;ic po&longs;&longs;umus explicare: e&longs;&longs;e corpus rotundum <expan abbr="oblong&utilde;">oblongum</expan>, æqua<lb/>lis vtrinque cra&longs;&longs;itiei, cuius duæ ba&longs;es &longs;unt circuii: <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti fru&longs;tum co<lb/>lumnæ. </s>

<s>his cognitis poteris nullo negotio totius problematis &longs;olutionem <lb/>ex textu Ari&longs;t. </s>

<s>his cognitis poteris nullo negotio totius problematis &longs;olutionem <lb/>ex textu Ari&longs;t.

<s>percipere.</s>

percipere.</s>

Line 11034

<s>explicatio, vt huic in&longs;eruiat. </s>

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

<s>Ari&longs;t.

<s>autem pulchrè, & aptè a&longs;&longs;imilat refle<lb/>xionem corporum reflexioni radiorum vi&longs;ualium ex &longs;peculis; vbi, vt docent <lb/>Per&longs;pectiui, radius vi&longs;ualis &longs;peculo incidens, facit &longs;emper angulum æqua<lb/>lem ei, quem facit radius reflexus; e&longs;t enim apud eos axioma, angulus in<lb/>cidentiæ æqualis e&longs;t angulo reflexionis.</s>

autem pulchrè, & aptè a&longs;&longs;imilat refle<lb/>xionem corporum reflexioni radiorum vi&longs;ualium ex &longs;peculis; vbi, vt docent <lb/>Per&longs;pectiui, radius vi&longs;ualis &longs;peculo incidens, facit &longs;emper angulum æqua<lb/>lem ei, quem facit radius reflexus; e&longs;t enim apud eos axioma, angulus in<lb/>cidentiæ æqualis e&longs;t angulo reflexionis.</s>

<s><emph type="italics"/>SECTIO XIX.<emph.end type="italics"/></s>

Line 11182

<s>An quod eius <lb/>cantus & perdifficilis est, & cantandi primordium obtinet? </s>

<s>difficilis autem pro<lb/>pter inten&longs;ionem, & compre&longs;&longs;ionem vocis e&longs;t, quibus in rebus e&longs;t labor, & difficul<lb/>tas: corrumpi autem quæ&queacute; maximè &longs;olent, quoties labore acrius opprimuntur)<emph.end type="italics"/><lb/>Quærit Ari&longs;t. </s>

<s>cur qui eam vocem cantant, quæ Parhypate dicitur, non mi<lb/>nus defatigetur, <expan abbr="vocem&qacute;">vocemque</expan>; perdat, quam qui Neten, aut aliam ex acutiori<lb/>bus vocibus, ip&longs;i Nete proximam, vt Paranetem. </s>

cur qui eam vocem cantant, quæ Parhypate dicitur, non mi<lb/>nus defatigetur, <expan abbr="vocem&qacute;">vocemque</expan>; perdat, quam qui Neten, aut aliam ex acutiori<lb/>bus vocibus, ip&longs;i Nete proximam, vt Paranetem. </s>

<s>ratio dubitandi e&longs;t, quia <lb/>Parhypate e&longs;t vox grauis, & quæ paruo interuallo di&longs;tat à graui&longs;&longs;ima om<lb/>nium Hypate: at verò Nete, <expan abbr="aliæ&qacute;">aliæque</expan>; illi viciniores &longs;unt acuti&longs;&longs;imæ, <expan abbr="magnis&qacute;">magnisque</expan>; <lb/>ab Hypate di&longs;tant interuallis. </s>

Line 11202

<s>vide illius loci explanationem. </s>

<s>Iam ve<lb/>rò difficile admodum e&longs;&longs;e cantare per &longs;emitonia, <lb/>per&longs;picuum e&longs;t cantoribus, quod oporteat, vt ait <lb/>Ari&longs;t. </s>

<s>Iam ve<lb/>rò difficile admodum e&longs;&longs;e cantare per &longs;emitonia, <lb/>per&longs;picuum e&longs;t cantoribus, quod oporteat, vt ait <lb/>Ari&longs;t.

<s>vocem, quantum opus e&longs;t, intendere, &longs;imul <lb/>ac comprimere, ne &longs;cilicet in maius iu&longs;to inter<lb/>uallum erumpat.</s>

vocem, quantum opus e&longs;t, intendere, &longs;imul <lb/>ac comprimere, ne &longs;cilicet in maius iu&longs;to inter<lb/>uallum erumpat.</s>

<s>Verum dubitabis, cur Ari&longs;t. </s>

<s>Verum dubitabis, cur Ari&longs;t.

<s>ponat &longs;emitonium <lb/>ab Hypate ad Parhypatem, cùm &longs;uperius <expan abbr="dict&utilde;">dictum</expan> &longs;it, <lb/>&longs;umitonium e&longs;&longs;e tantummodo inter Mi, & Fa, ide&longs;t <lb/>inter Lychanon, & Me&longs;en. </s>

ponat &longs;emitonium <lb/>ab Hypate ad Parhypatem, cùm &longs;uperius <expan abbr="dict&utilde;">dictum</expan> &longs;it, <lb/>&longs;umitonium e&longs;&longs;e tantummodo inter Mi, & Fa, ide&longs;t <lb/>inter Lychanon, & Me&longs;en. </s>

<s>Sciasigitur alios aliter <lb/><expan abbr="interuallor&utilde;">interuallorum</expan> ordinem feci&longs;&longs;e: inter quos Lychaon <pb pagenum="251"/>antiqui&longs;&longs;imus Mu&longs;icus &longs;ie ea di&longs;po&longs;uit; vt in præ&longs;enti ordine, vbi, vt vides <lb/>inter hypatem, & perhypatem, e&longs;t &longs;emitonij interuallum. </s>

<s>ad hunc Lichaonis <lb/>igitur ordmem videtur Ari&longs;t. </s>

<s>ad hunc Lichaonis <lb/>igitur ordmem videtur Ari&longs;t.

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

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

<s>ego verò &longs;uperius communiorem <lb/>viam, nec adeò antiquam &longs;equutus &longs;um. </s>

Line 11290

<s>Re&longs;pondet enim id non omninò verum <lb/>cen&longs;eri debere, nam vtramque quidem hypa<lb/>tem, &longs;cilicet & neten a&longs;&longs;umebant; triten verò <lb/><expan abbr="omittebãt">omittebant</expan>. </s>

<s>quibus verbis ordinem, quem Ter<lb/>pander inuexit, in&longs;inuare videtur, nam vt ait <lb/>Pau&longs;anias in Lachonicis, Timothæus quatuor <lb/>chordas, antiquis &longs;eptem chordis à Terpan<lb/>dro ordinatis addidit, quarum &longs;eptem chor<lb/>darum hic erat ordo, & nomenclatura, & in<lb/>terualla; è quibus triten ademptam videre e&longs;t, <lb/>vt Ari&longs;t. </s>

<s>innuit.</s>

innuit.</s>

<s>Subdit po&longs;tea aliam rationem dicens; fortè &longs;atius e&longs;&longs;e dicere neten qui<lb/>dem antiquitus fui&longs;&longs;e prætermi&longs;&longs;am, relicta hypate, co quod hypate, cum <lb/>di&longs;tet per octauam, &longs;eu per Diapa&longs;on à Nete, erat illius Antiphonum, ide&longs;t, <lb/>erat vox eiu&longs;dem naturæ, & ferè eadem cum ea. </s>

Line 11502

<s>16. <emph type="italics"/>(Qua de cau&longs;a Antiphonum &longs;uauius est &longs;ymphono? </s>

<s>An quia in an<lb/>tiphono manife&longs;tior est ip&longs;a con&longs;onantia, quàm eùm ad &longs;ympboniam cantatur: ne<lb/>oe&longs;&longs;e exim e&longs;t in &longs;ymphonia alteram vocem alteri vni&longs;onam e&longs;&longs;e; ita vt duæ in ean<lb/>dem coale&longs;centes altera alteram offu&longs;care po&longs;&longs;it)<emph.end type="italics"/> Per antiphonum intelligit nunc <lb/>Ari&longs;t. </s>

<s>con&longs;onantiam ex vocibus <expan abbr="differ&etilde;tibus">differentibus</expan> conflatam, cuiu&longs;modi e&longs;t Dia<lb/>pa&longs;on, Diapente, & Diate&longs;&longs;aron: per &longs;ymphonum intelligit con&longs;onantiam <lb/>ex vocibus eiu&longs;dem inten&longs;ionis, &longs;iue ex vni&longs;onis. </s>

con&longs;onantiam ex vocibus <expan abbr="differ&etilde;tibus">differentibus</expan> conflatam, cuiu&longs;modi e&longs;t Dia<lb/>pa&longs;on, Diapente, & Diate&longs;&longs;aron: per &longs;ymphonum intelligit con&longs;onantiam <lb/>ex vocibus eiu&longs;dem inten&longs;ionis, &longs;iue ex vni&longs;onis. </s>

<s>non me latet aliter Mu&longs;i<lb/>cos antiphonas, &longs;ymphonas, ac homophonas accipere. </s>

Line 11516

<s>&longs;ed hoc loco ita accipiendas e&longs;&longs;e, vti dixi, manife&longs;tum e&longs;t ex <lb/>Ari&longs;t. </s>

<s>&longs;ed hoc loco ita accipiendas e&longs;&longs;e, vti dixi, manife&longs;tum e&longs;t ex <lb/>Ari&longs;t.

<s>contextu. </s>

contextu. </s>

<s>Aitigitur &longs;uauiorem e&longs;&longs;e antiphonarum con&longs;onantiam, <lb/>quam vni&longs;onarum; quia ibi con&longs;onantia melius percipitur; nam in vocibus <lb/>vni&longs;onis, vox alteri voci con&longs;onans, cundem cum illa edit &longs;onum, ita vt duæ <lb/>in vnam, <expan abbr="eandem&qacute;">eandemque</expan>; pror&longs;us coale&longs;cant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; altera alteram offu&longs;cet, vnde <lb/>con&longs;onantia, quæ ex pluribus con&longs;tare debet, non percipitur.</s>

Line 11718

<s>alij <expan abbr="cãtus">cantus</expan> ex oppo&longs;ito bonos mo<lb/>res referunt, vt grauitatem, temperantiam, ea&longs;titatem; qui quidem ex pro<lb/>borum hominum natura prodire &longs;olent, <expan abbr="eos&qacute;">eosque</expan>; decent. </s>

<s>Illud in prophanis <lb/>canticis, i&longs;tud verò in Eccle&longs;ia&longs;ticis quotidie experimur; cur autem Audi<lb/>bilia præ cætéris mores referant, cau&longs;am Ari&longs;t. </s>

<s>Illud in prophanis <lb/>canticis, i&longs;tud verò in Eccle&longs;ia&longs;ticis quotidie experimur; cur autem Audi<lb/>bilia præ cætéris mores referant, cau&longs;am Ari&longs;t.

<s>refert in motum illum, qui <lb/>in &longs;onis, & vocibus percipitur. </s>

refert in motum illum, qui <lb/>in &longs;onis, & vocibus percipitur. </s>

<s><expan abbr="neq;">neque</expan> hic motus e&longs;t is, quo &longs;onus aures immu<lb/>tat, hoc enim commune e&longs;t omnibus &longs;en&longs;orijs, vt à &longs;uis obiectis immuten<lb/>tur, & afficiantur: &longs;ed is e&longs;t, qui prædictam aurium immutationem &longs;ubfe<lb/>quitur, <expan abbr="intellectu&qacute;">intellectuque</expan>; percipitur, v.g. </s>

Line 11742

<s>alia qui<lb/>dem animalia non habent &longs;en&longs;ationem ordinationis, & inordinationis mo<lb/>tuum, quibus rithmus, & harmonia nomen e&longs;t. </s>

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

<s>Ari&longs;t.

<s>infra probl. </s>

infra probl. </s>

<s>38. &longs;ic. <lb/></s>

Line 11836

<s>De qualitatibus horum modorum plura veteres, ac Zarlinus ip&longs;e citato <lb/>loco: <expan abbr="nos&qacute;">nosque</expan>; nonnulla &longs;upra in Politicis diximus. </s>

<s>Quod ad hunc locum &longs;pe<lb/>ctat, videndum quales e&longs;&longs;ent Hypodorius, & Hypophrygius: quod Ari&longs;t. </s>

<s>Quod ad hunc locum &longs;pe<lb/>ctat, videndum quales e&longs;&longs;ent Hypodorius, & Hypophrygius: quod Ari&longs;t.

<s>ip<lb/>&longs;e infra Problem. </s>

ip<lb/>&longs;e infra Problem. </s>

<s>49. docet, ait enim, modum hypophrygium animos Lym<lb/>phatis, &longs;imiles reddere, <expan abbr="cogere&qacute;">cogereque</expan>; debacchari: Hypodorium verò e&longs;&longs;e mo<lb/>dum magnificum, con&longs;tantem, grauemque. </s>

Line 11848

<s>ex quibus <lb/>intelligere po&longs;&longs;umus Problema præ&longs;ens; modus &longs;cilicet Hypodorius, & Hy<lb/>pophrygius à choro Trag&oelig;diarum arcebantur, quia carebant anti&longs;trophis, <lb/>quibus chorus gaudebat; chorus enim non imitabatur varios mores, <expan abbr="va-rios&qacute;">va<lb/>riosque</expan>; hominum affectus, &longs;ed eodem &longs;eruato affectu per ea&longs;dem &longs;trophas ad <lb/>finem <expan abbr="v&longs;q;">v&longs;que</expan> perueniebat. </s>

<s>erant autem prædicti duo modi &longs;cenis idonei, quia <lb/>in &longs;cena varios mores, affectus, & animi pa&longs;&longs;iones imitabantur, <expan abbr="atq;">atque</expan> ad eo&longs;<lb/>dem variè auditorum animos impellebant; ad quod peragendum ip&longs;i erant <lb/>idonei te&longs;te Ari&longs;t. </s>

<s>citato loco. </s>

citato loco. </s>

<s>cùm præ&longs;ertim anti&longs;trophis carerent, quæ ob<lb/>&longs;i&longs;tere variæ, ac multiplici imitationi poterant. </s>

Line 11898

<s>is igitur erat Melopæus, qui res &longs;ubiectas harmonicæ &longs;cientiæ, vt <lb/>&longs;unt &longs;onus, interualla, genera, modi, con&longs;onantiæ, di&longs;&longs;onantiæ ritè in v&longs;um <lb/>vocabat: vnde cantilenas humana oratione con&longs;tructas ad decorum, ide&longs;t <lb/>pro rei argumento conuenientibus rythmis modulabatur. </s>

<s>Antiquitus igi<lb/>tur Melopæiæ magis &longs;tudebant, quàm Ari&longs;t. </s>

<s>Antiquitus igi<lb/>tur Melopæiæ magis &longs;tudebant, quàm Ari&longs;t.

<s>tempe&longs;tate, quia tunc tempo<lb/>ris magis erant in tragædijs cantilenæ in v&longs;u, quam po&longs;tea.</s>

tempe&longs;tate, quia tunc tempo<lb/>ris magis erant in tragædijs cantilenæ in v&longs;u, quam po&longs;tea.</s>

Line 11984

<s>34. <emph type="italics"/>(Cur bis Diapente, aut bis Diate&longs;&longs;aron <expan abbr="cõ&longs;onantia">con&longs;onantia</expan> <expan abbr="cõponi">componi</expan> non pote&longs;t, <lb/>bis a&ubreve;<gap/> Diapa&longs;on pote&longs;t? </s>

<s>An, quòd bis Diapente, non bis Diate&longs;&longs;aron e&longs;t: &longs;ed Dia<lb/>te&longs;&longs;aron, & Diapente in vn&abreve; Diapa&longs;on concurrunt)<emph.end type="italics"/> Quamuis textus <expan abbr="aliquantul&utilde;">aliquantulum</expan> <lb/><expan abbr="&etilde;t">ent</expan> græcus corruptus &longs;it, verumtamen &longs;en&longs;um Ari&longs;t. </s>

<s>ex &longs;equentibus percipie<lb/>mus. </s>

ex &longs;equentibus percipie<lb/>mus. </s>

<s>Pro intelligentia igitur huius problematis placet hic de&longs;cribere <expan abbr="demõ-&longs;trationem">demon<lb/>&longs;trationem</expan> 16. lib. </s>

Line 12136

<s><expan abbr="Neq;">Neque</expan> difficile e&longs;t canere graue, quia a natura e&longs;t habere ar<lb/>teriam magnam, & ideo multum aeris ciere, & proinde canere, quæ enim <lb/>naturaliter fiunt, facilè fiunt.</s>

<s>Obijces, Ari&longs;t. </s>

<s>Obijces, Ari&longs;t.

<s>in Probl. </s>

in Probl. </s>

<s>26. & 47. dixi&longs;&longs;e contrarium, fcilicet facilius <lb/>e&longs;&longs;e canere acutum, quam graue, ibi enim re&longs;pondet: vtrum, quod facilius <lb/>acutum, quam graue cantatur? </s>

<s>Re&longs;pondeo primùm, Ari&longs;t. </s>

<s>Re&longs;pondeo primùm, Ari&longs;t.

<s>ibi non a&longs;&longs;ere<lb/>re, &longs;ed dubitanter loqui. </s>

ibi non a&longs;&longs;ere<lb/>re, &longs;ed dubitanter loqui. </s>

<s>&longs;ecundò, hæc ab eo dicta e&longs;&longs;e problematicè, ide&longs;t <lb/>non con&longs;equenter, &longs;ed quæ po&longs;&longs;int in <expan abbr="vtramq;">vtramque</expan> partem di&longs;putari.</s>

Line 12460

<s>Per &longs;uperius Tetrachordum intelligere debemus Acutius, &longs;ic enim finis <lb/>illius erit principium inferioris, ide&longs;t grauioris Tetrachordi; vult enim <lb/>Ari&longs;t. </s>

<s>Per &longs;uperius Tetrachordum intelligere debemus Acutius, &longs;ic enim finis <lb/>illius erit principium inferioris, ide&longs;t grauioris Tetrachordi; vult enim <lb/>Ari&longs;t.

<s>vt &longs;upra non &longs;emel vi&longs;um e&longs;t, acutiorem &longs;onum Tetrachordi e&longs;&longs;e illius <lb/>principium. </s>

vt &longs;upra non &longs;emel vi&longs;um e&longs;t, acutiorem &longs;onum Tetrachordi e&longs;&longs;e illius <lb/>principium. </s>

<s>vide præ&longs;ertim num. </s>

Line 12650

<s>talis ap<lb/>paret limo <foreign lang="greek">eterofqalmw,</foreign> &longs;eu &longs;traboni, vt duplicata illi videatur. </s>

<s>propter po&longs;itio<lb/>nem verò id fit, quia &longs;ctlicet oculus &longs;uo medio non &longs;it constitutus)<emph.end type="italics"/> Quæcunque ab <lb/>Ari&longs;t. </s>

<s>propter po&longs;itio<lb/>nem verò id fit, quia &longs;ctlicet oculus &longs;uo medio non &longs;it constitutus)<emph.end type="italics"/> Quæcunque ab <lb/>Ari&longs;t.

<s>hoc loco læuiter attinguntur, exactè ab opticis Alhazeno, & Vitell. <lb/></s>

hoc loco læuiter attinguntur, exactè ab opticis Alhazeno, & Vitell. <lb/></s>

<s>pertractantur. </s>

Line 12668

<s>Quando ait <emph type="italics"/>(Et alterum ad dextram, & ad &longs;ini&longs;tram)<emph.end type="italics"/> &longs;ignificat nos po&longs;&longs;e <lb/>mouere alterum oculum, altero manente, quoquouer&longs;us: quod non video <lb/>quomodo verum &longs;it, alij fortè videbunt.</s>

<s>Quando ait <emph type="italics"/>(<expan abbr="Atq;">Atque</expan> &longs;int in medio mouendi &longs;e &longs;e)<emph.end type="italics"/> per medium mouendi intel<lb/>ligit Ari&longs;t. </s>

<s>Quando ait <emph type="italics"/>(<expan abbr="Atq;">Atque</expan> &longs;int in medio mouendi &longs;e &longs;e)<emph.end type="italics"/> per medium mouendi intel<lb/>ligit Ari&longs;t.

<s>punctum, quod concipitur e&longs;&longs;e in medio inter &longs;ur&longs;um, & deor<lb/>&longs;um; necnon inter dextrum, & &longs;ini&longs;trum oculorum in naturali po&longs;itione <lb/>manentium.</s>

punctum, quod concipitur e&longs;&longs;e in medio inter &longs;ur&longs;um, & deor<lb/>&longs;um; necnon inter dextrum, & &longs;ini&longs;trum oculorum in naturali po&longs;itione <lb/>manentium.</s>

<s>Quando ait <emph type="italics"/>(Eodemque in puncto vi&longs;um habent)<emph.end type="italics"/> & <emph type="italics"/>(Quiverò in eodem pun<lb/>cto pupillas habent)<emph.end type="italics"/> per idem <expan abbr="p&utilde;ctum">punctum</expan> intelligo illud, quod in vno oculorum <lb/>habet eandem po&longs;itionem cum altero puncto alterius oculi, &longs;ic duo oculi <lb/>habebunt pupillas in codem puncto, quando eas habebunt con&longs;imiliter lo<lb/>catas, & habebunt eandem in <expan abbr="vtroq;">vtroque</expan> oculo po&longs;itionem.</s>

<s>Quando ait <emph type="italics"/>(Dimotum contuendi principi&ubreve; habet<emph.end type="italics"/>) ide&longs;t, locum pupillæ non <lb/>habet in eodem &longs;itu, in quo oporteret, ide&longs;t non habet con&longs;imilem &longs;itum re<lb/>&longs;pectu &longs;ur&longs;um, & deor&longs;um, dextror&longs;um, & &longs;ini&longs;tror&longs;um, alteri pupillæ.</s>

<s>Quando ait <emph type="italics"/>(Perinde vt ille, cut res vna geminari oculo &longs;uppre&longs;&longs;o videtur)<emph.end type="italics"/> vt <lb/>rectius ea, quæ hoc loco ab Ari&longs;t. </s>

<s>Quando ait <emph type="italics"/>(Perinde vt ille, cut res vna geminari oculo &longs;uppre&longs;&longs;o videtur)<emph.end type="italics"/> vt <lb/>rectius ea, quæ hoc loco ab Ari&longs;t.

<s>dicuntur, percipi po&longs;&longs;int, explicandum <pb pagenum="276"/>prius exi&longs;timo, cur quamuis geminatos oculos habeamus, res tamen vnicæ <lb/>non &longs;olent geminatæ videri, dummodo oculi à naturali &longs;uo &longs;itu non luxen<lb/>tur, quod etiam à Vitell. </s>

dicuntur, percipi po&longs;&longs;int, explicandum <pb pagenum="276"/>prius exi&longs;timo, cur quamuis geminatos oculos habeamus, res tamen vnicæ <lb/>non &longs;olent geminatæ videri, dummodo oculi à naturali &longs;uo &longs;itu non luxen<lb/>tur, quod etiam à Vitell. </s>

<s>propo&longs;it. </s>

Line 12884

<s>4. Cùm iam <expan abbr="cõ&longs;tet">con&longs;tet</expan> foramini vuæ G H I, à pupilla in ip&longs;o ver&longs;ante nomen <lb/>inditum e&longs;&longs;e; nec non vnde &longs;it ea pupilla, & cur tam parua; quæritur iam, <lb/>quid &longs;it pupilla, &longs;eu Iris minor, an &longs;cilicet &longs;it foramen illud vueæ, an potius <lb/>chri&longs;tallinus humor, qui in illud intruditur, <expan abbr="vacuum&qacute;">vacuumque</expan>; illius replet? </s>

<s>Re<lb/>&longs;pondeo, Ari&longs;t. </s>

<s>Re<lb/>&longs;pondeo, Ari&longs;t.

<s>humorem ip&longs;um <expan abbr="chri&longs;tallin&utilde;">chri&longs;tallinum</expan> appella&longs;&longs;e pupillam: Galenum <lb/>tum chri&longs;tallinum, tum foramen ip&longs;um: aptè tamen <expan abbr="vtrumq;">vtrumque</expan> dici exi&longs;timo. <lb/></s>

humorem ip&longs;um <expan abbr="chri&longs;tallin&utilde;">chri&longs;tallinum</expan> appella&longs;&longs;e pupillam: Galenum <lb/>tum chri&longs;tallinum, tum foramen ip&longs;um: aptè tamen <expan abbr="vtrumq;">vtrumque</expan> dici exi&longs;timo. <lb/></s>

<s>Chri&longs;tallinum quidem & quia replet vacuum illud, <expan abbr="atq;">atque</expan> è regione illius pu<lb/>pillæ imaguncula &longs;pectatur. </s>

Line 13080

<s><emph type="italics"/>De&longs;ubiecto Geometræ, & Arithmeticæ, quod &longs;olet dici <lb/>Materia intelligibilis. </s>

<s>Primò, agemus de puris Mathematicis Geometria, & Arithmetica, <lb/>quarum e&longs;t diuer&longs;a ratio à medijs, A&longs;tronomia, &longs;cilicet Per&longs;pecti<lb/>ua, Mechanica, & Mu&longs;ica. </s>

Line 13168

<s>Similiter aliquando plures anguli partiales componunt tanquam mate<lb/>riam totalem angulum. </s>

<s>Idem dicendum de alijs &longs;imilibus, pariter e&longs;&longs;e ali<lb/>cuius dimidium, aut tertiam partem, aut duplum, aut reliquum cuiu&longs;piam <lb/>totius, referuntur ad veram cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; te&longs;te Ari&longs;t. </s>

tex. </s>

Line 13250

<s>Sed ne longior &longs;im, innumeras pene alias apud omnes Geometras reperies <lb/>omnino e&longs;&longs;entiales, quas prætero: cadem pror&longs;us de Arithmetic&ecedil; defini<lb/>tionibus &longs;unt intel igenda, vt cas con&longs;ideranti &longs;tatim patebit. </s>

<s>Quod &longs;i quis <lb/>iam fateatur ha&longs;ce definitiones e&longs;&longs;entiales e&longs;&longs;e, &longs;ed tamen adhuc Ma h ma<lb/>ticis ill<gap/>s definitiones cau&longs;ales, quas demon&longs;tratio requirit, deneget; is &longs;i<lb/>bi refragrantem audiat Ari&longs;t. </s>

qui tex. </s>

<s>12. 2. de Anima; ait Tetragoni&longs;mi <lb/>extare duas definit: ones, vnam formalem, &longs;eu e&longs;&longs;entialem, qu&ecedil; e&longs;t, Tetrago<lb/>ni&longs;mus e&longs;t eff<gap/>ctio quadrati æqualis dato æquilatero; altera verò cau&longs;alis, <lb/>&longs;cilicet Terragoni&longs;mus e&longs;t inuentio medi&ecedil; proportionalis, quia linea illa me <lb/>dia proportionali, e&longs;t cau&longs;a quadrati æqualis datæ flguræ: vide no&longs;tram hu<lb/>ius loci explicationem. </s>

Line 13292

<s><emph type="italics"/>De medio Demonstrationum Geometriæ, & Arith<lb/>meticæ, &longs;eu, An &longs;int potißimæ Demon&longs;trationes. <lb/></s>

<s>Coguntur huius tempe&longs;tatis Mathematici ea, quæ antiqui&longs;simo po&longs;<lb/>&longs;e&longs;sionis iure tutò hactenus po&longs;siderunt, à nonnullis recentioribus <lb/>ea diripere volentibus, omni conatu tutari. </s>

Line 13302

<s>profectò nullus fatetur ip&longs;e &longs;e primum inter recentiores hanc veritatem <lb/>olfeci&longs;&longs;e, &longs;ed verè omnium etiam antiquorum primus ip&longs;e fuit, nam duos, <lb/>vel tres, quos ex antiquis in &longs;uam &longs;ententiam pertrahere conatur, re vera, <lb/>vt infra patebit, minimè pertrahit.</s>

<s>Primo igitur antiquorum auctoritates, præcipuè verò Ari&longs;t. </s>

<s>Primo igitur antiquorum auctoritates, præcipuè verò Ari&longs;t.

<s>pro parte af<lb/>firmatiua afferemus. </s>

pro parte af<lb/>firmatiua afferemus. </s>

<s>& verò indignum, <expan abbr="atq;">atque</expan> &longs;uperuacaneum exi&longs;timo, cùm <lb/>co, qui Ari&longs;t. </s>

<s>Analyticos po&longs;teriores legerit, de ip&longs;ius &longs;ententia di&longs;putare, <lb/><expan abbr="cius&qacute;">ciusque</expan>; mentem, qua&longs;i in fru&longs;ta locis aliquot citandis &longs;ecare, cùm totis duo<lb/>bus libris nihil aliud agere videatur, quàm <expan abbr="perfectã">perfectam</expan> Demon&longs;trationis id&ecedil;am <pb pagenum="11"/>ex Geometricis delineare; quippe qui omnes conditiones, <expan abbr="omnia&qacute;">omniaque</expan>; ad per<lb/>fectam demon&longs;trationem nece&longs;&longs;aria, <expan abbr="vbiq;">vbique</expan> Geometricis demon&longs;trationibus <lb/>attribuat, <expan abbr="id&qacute;">idque</expan>; non &longs;olùm præceptis, &longs;ed etiam exemplis perpetuò confir<lb/>met: ego quidem nihil vnquam Ari&longs;t. </s>

<s>clarius expre&longs;si&longs;&longs;e, nihil fu&longs;ius com<lb/>proba&longs;&longs;e exi&longs;timo, quàm Geometriæ demon&longs;trationes omnibus numeris ab<lb/>&longs;olutas e&longs;&longs;e, ita vt Philo&longs;opho indignum omninò videatur &longs;ententiam ip&longs;ius <lb/>adeò manife&longs;tam aliò detorquere; &longs;atius e&longs;&longs;et, meo iudicio, palàm peri<lb/>patetici nomen ex hac parte deponere, quàm hoc modo Peripateticorum <lb/>doctrinam, vt nonnulli faciunt, vel di&longs;simulare, vel tam perperam interpre<lb/>tari. </s>

clarius expre&longs;si&longs;&longs;e, nihil fu&longs;ius com<lb/>proba&longs;&longs;e exi&longs;timo, quàm Geometriæ demon&longs;trationes omnibus numeris ab<lb/>&longs;olutas e&longs;&longs;e, ita vt Philo&longs;opho indignum omninò videatur &longs;ententiam ip&longs;ius <lb/>adeò manife&longs;tam aliò detorquere; &longs;atius e&longs;&longs;et, meo iudicio, palàm peri<lb/>patetici nomen ex hac parte deponere, quàm hoc modo Peripateticorum <lb/>doctrinam, vt nonnulli faciunt, vel di&longs;simulare, vel tam perperam interpre<lb/>tari. </s>

<s>quamuis igitur &longs;atis e&longs;&longs;et lectorem ad libros analyticos, <expan abbr="corum&qacute;">corumque</expan>; in<lb/>terpretes amandare, non grauabor tamen loca aliquot &longs;electa, atque adeò <lb/>manife&longs;ta in medium afferre, vt magnopere mirandum &longs;it <expan abbr="cõtrariæ">contrariæ</expan> opinio<lb/>nis authores ea pro libiro interpretari. </s>

<s>quorum primus &longs;it tex. </s>

<s>23. primi Po<lb/>&longs;ter. <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> antem &longs;cimus non &longs;e<gap/>nndum accidens, quando &longs;ecundum illud <lb/>cogno&longs;ctmus, &longs;ecundum quod ine&longs;t, ex principijs ill us, &longs;ecundum quod illud, vt <lb/>duobus rectis æquales habere, cui inest per &longs;e ex principijs huius)<emph.end type="italics"/> vbi manife&longs;tè <lb/>vides Ari&longs;t. </s>

<s>a&longs;&longs;erere demon&longs;trationem illam, qua Geometra o&longs;tendit, omne <lb/><expan abbr="triãgulum">triangulum</expan> habere tres angulos æquales duobus rectis procedere ex primis, <lb/>immediatis, ex ijs, quæ &longs;unt per &longs;e, & &longs;ecundum quod ip&longs;um; nullo autem <lb/>modo ex ijs, quæ &longs;unt per accidens. </s>

a&longs;&longs;erere demon&longs;trationem illam, qua Geometra o&longs;tendit, omne <lb/><expan abbr="triãgulum">triangulum</expan> habere tres angulos æquales duobus rectis procedere ex primis, <lb/>immediatis, ex ijs, quæ &longs;unt per &longs;e, & &longs;ecundum quod ip&longs;um; nullo autem <lb/>modo ex ijs, quæ &longs;unt per accidens. </s>