Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              Proclum, ita 1000. ad 500, & poſtea, vt Plato ad 1000. ita Proclus ad 500.
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              iuxta
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              merita, & quidem iſta eſt huiuſmodi moralis diſtributio, cum
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              modis argumentandi ab Euclide comprobatis, nitatur.</s>
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              311</s>
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              <s id="s.003676">Ibidem
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              (Hanc verò proportionalitatem Mathematici Geometricam vocant:
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              propterea quod in Geometrica euenit, vt eandem totum ad totum rationem habeat,
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              quam habet alterutrum, ad alterutrum)
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              ideſt, hanc duarum Geometricarum
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              rationum ſimilitudinem Mathematici proportionalitatem Geometricam
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              appellant, propterea quod in hac duarum rationum geometricarum ſimili­
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              tudine accidit, vt ſit totum ad totum, quemadmodum etiam partes toto­
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              rum, vt ſupra explicatum eſt; quod non accidit in duarum proportionum
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              arithmeticarum ſimilitudine; ſi enim ponamus has duas rationes arithme­
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              ticas ſimiles, vt 10. ad 8. ita 6. ad 4. quæ ſunt ſimiles, propter ſimiles exceſ­
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              ſus primorum, & ſecundorum terminorum, cum
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              exceſſus ſit binarij.
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              <s id="s.003677">non erit tamen totum 16. ad totum 12. in eadem ratione cum diuiſis ter­
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              minis, cum ibi ſit exceſſus binarij, hic verò quaternarij. </s>
              <s id="s.003678">hæc videtur eſſe
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              Ariſt. ratio; quam adhuc melius declaraſſe libet. </s>
              <s id="s.003679">Geometrica igitur pro­
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              portionalitas ita dicta eſt, quia quælibet proportio poteſt in materia Geo­
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              metrica, lineis, ſuperficiebus, & corporibus continuari in quatuor termi­
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              nis, ita vt proportionalitas, ſeu ſimilitudo rationum exurgat, quod in nu­
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              meris fieri ſemper nequit, cum plures ſint proportiones, quæ numeris ex­
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              primi nequeunt, vt ſunt eæ, quas irrationales appellant, cuiuſmodi eſt inter
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              diametrum, & coſtam eiuſdem quadrati, cuius nec proportio, nec propor­
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              tionalitas in numeris reperiri poteſt, quæ tamen in lineis, ſuperficiebus, ac
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              corporibus eſſe poſſunt: eſt enim vt diameter vnius quadrati ad latus eiuſ­
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              dem, ita idem latus ad aliam lineam inuentam per 11. 6. vel vt diameter ad
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              coſtam, ita quælibet alia linea ad aliam inuentam, per 12. 6. omnis igitur
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              proportionalitas rebus Geometricis ineſſe poteſt; non autem numeris, in
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              quibus ſolum poſſunt eſſe rationes rationales, ſeu
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              commenſurabilium;
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              latius igitur patet Geometrica hæc ſimilitudo, quàm Arithmetica, cùm
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              Geometrica complectatur tam rationales, quàm irrationales. </s>
              <s id="s.003680">meritò igi­
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              tur talis proportionalitas appellari debuit à rebus Geometricis, in quibus
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              ſemper reperitur, non autem ab Arithmeticis, cum quibus ſæpius reperiri
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              nequit. </s>
              <s id="s.003681">Vide Campanum in explicatione definitionis 3. 5. Elemen.</s>
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              312</s>
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              <s id="s.003684">Ibidem
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              (Non eſt autem continens hæc proportio: non enim vnus, & idem ter­
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              minus efficitur, & cui, & quod)
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              ideſt, hæc proportionalitas contracta ad res
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              practicas, non eſt continens, ideſt, quæ conſiſtat in tribus tantum terminis,
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              quorum medius eſt, ad quem refertur primus, & is qui refertur ad ter­
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              tium; ſed eſt diſiuncta, quia conſtat ſemper quatuor terminis, quorum duo
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              ſunt perſonæ aliquæ, reliqui verò duo ſunt res, quæ perſonis debentur, vt ſi
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              ſint Plato, & Proclus, quibus iuxta meritorum quantitatem debeant diuidi
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              1500. aurei, debent diuidi aurei in duas partes, quæ habeant eam propor­
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              tionem, quam habet Plato ad Proclum. </s>
              <s id="s.003685">quod ſi Plato duplum męruit quàm
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              Proclus, erit vt Plato ad Proclum, ita 1000. ad 500.</s>
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              <s id="s.003686">Ex quibus patet hanc analogiam in rebus agendis non niſi in quatuor
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              terminis conſiſtere poſſe, & ideo non eſſe continuam, ſed diſiunctam, vt vo­
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              lebat Ariſtot.</s>
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