Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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diſciplinis, idem tamen apud græcos
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ſunt, ac apud latinos diſci
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plinæ; verbum autem
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vſurpat hoc loco Ariſtoteles. </
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<
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">Porrò non
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eſt in mathematicis, ſicut in alijs paralogiſmus, quia in omni demonſtra
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tione maius extremum dicitur de omni medio, & rurſus medium dicitur de
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omni minori extremo, ac ſi diceret mathematicæ demonſtrationes ſunt in
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primo modo, qui barbarè à latinis recentioribus Barbara appellatur. </
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eſt autem pulcherrima mathematicarum commendatio, quippe præclarum
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eſt à laudato laudari. </
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<
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">In mathematicis, inquit, non accidit ſimiliter para
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logiſmus, ideſt, tam frequenter, quemadmodum in ſyllogiſmis dialecticis,
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quia modus argumentandi mathematicarum eſt perfectiſſimus, quippe in
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primo modo primæ figuræ.</
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<
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">Eodem tex.
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(Contingit autem quoſdam non ſyllogiſticè dicere, & quod ex vtriſ
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que conſequentia accipiunt, quemadmodum & Cæneus facit, quod ignis in multi
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plici proportione: etenim ignis celeriter gignitur, vt ait: & hæc est proportio. </
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autem non eſt ſyllogiſmus, niſi celerrimam proportio ſequatur multiplex: & ignem
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celerrima in motu proportio)
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verba illa (in multiplici proportione) græcè ſic
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ſe habent,
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quod melius redditur latinè in mul
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tiplici proportione, quemadmodum fecimus, quam in multiplicata, quem
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admodum in vulgata editione. </
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catam rationem interſit, optimè declarat noſter Clauius ad 4. definit. </
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<
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Elem. ex quo etiam loco pauca decerpam, quæ huic loco declarando con
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ducunt. </
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">Proportio igitur multiplex eſt habitudo inter duas quantitates in
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æquales, quarum maior continet minorem, bis, vel ter, vel quater, &c. </
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<
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de proportio multiplex habet ſub ſe genera infinita, quando enim maior
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continet minorem bis, dicitur Dupla: quando ter, Tripla: quando quater,
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Quadrupla: & ſic in infinitum: v. g. 2. ad 1. eſt proportio dupla; 3. ad 1. tri
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pla; 4. ad 1. quadrupla, &c. </
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<
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cis rationis. </
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per plures terminos, v. g. proportio quadrupla progrediatur hoc modo,
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1. 4. 16. 64. 256. &c. </
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<
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tur. </
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">hic vides primum ipſam quadruplam rationem in diſpoſitis terminis
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progredi, quia quilibet ſequens terminus ad præcedentem eſt quadruplus.
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<
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mentum, cum
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ad 256. excreuerint. </
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ſecundum multiplicem rationem, vnam ex prædictis intelligebat aliquam,
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quia quælibet illarum magnopere creſcit, ſi propagetur, vt ad 10. quinti
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definit. </
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<
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<
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tur igitur Cæneus in hunc modum; quod in multiplici ratione augetur, ce
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lerrimè augetur: ignis celerrimè augetur, ergo ignis in multiplici ratione
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augetur, quæ argumentatio vitioſa eſt, ex duabus quippe affirmatiuis in ſe
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cunda figura procedens, vt colligitur ex verbis illis tex.
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(Ex viriſque conſe
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quentia accipiunt
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) ex his mathematica huius locis patere ſatis poſſunt.</
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<
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Conuertuntur autem magis, quæſunt in mathematicis, quoniam nul
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lum accidens accipiunt (in quo quidem ijs præſtăt, quæ diſputationibus traduntur)
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ſed definitiones
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) Hæc eſt altera mathematicarum laus, vnde earum quoque
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præſtantia elucet, quia ſcilicet mathematicæ pro medijs vtuntur </
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