Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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Mathematicas facultates habere demonſtrationes perfectiſſimas, quod
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ageometreti negare ſolent, ſed audacter aiunt exempla Ariſt. non eſſe vera:
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requiri veritatem exemplorum; in
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peccant, nam dictum
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illud vſurpari ſolet, & debet de exemplis moralibus. </
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<
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">at vero requiri confor
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mitatem exemplorum cum regulis traditis, nemo ſanæ mentis dubitabit.
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<
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">Verum iſti confundunt conformitatem cum veritate. </
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<
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">Veritas exemplo tunc
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ineſt, quando illud, quod in exemplo narratur, verè extitit, vt ſi quis in
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exemplum pudicitiæ afferret hiſtoriam Ioſephi,
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iſtud eſſet exemplum.
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<
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">quæ veritas in exemplis moralibus non ſemper eſt neceſſaria, talia exempla
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ſunt ſæpè parabolæ, & fabulæ, quæ nunquam extiterunt, v. g. narratur ab
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Ariſt. de quodam filio, qui patrem crudeliter traxerat, qui poſtea grandior
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factus, cum filium procreaſſet, ab eodem pariter raptatus eſt ipſe, vſque ad
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eundem locum, quo ipſe patrem ſuum impiè raptauerat. </
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">non eſt neceſſe, ta
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lem extitiſſe filium,
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neq;
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patrem. </
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<
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">Verumtamen ſemper conformitas exem
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pli cum regulis, & præceptis, quæ traduntur neceſſaria eſt, alioquin exem
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pla deſtruerent id, quod præceptio conſtruit,
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illiq́
">illique</
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contraria eſſet, quod om
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nino abſurdum foret. </
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<
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">non ſecus, ac ſi quis vellet alium docere characteres
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latinos,
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illiq́
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; barbaros, quos Gothicos vocant in exemplum proponeret. </
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">re
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quiritur igitur ſemper in omni exemplo conformitas cum eo, quod doce
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tur; in moralibus tamen non ſemper requiritur veritas, vti diximus; Alij
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verò dicunt non requiri in exemplis determinatam veritatem, ſed ſatis eſſe,
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ſi exemplum verum ſit ſecundum opinionem aliquorum:
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ſententiam
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non improbamus. </
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<
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">Exempla igitur ab Ariſt. paſſim ex mathematicis allata,
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congrua,
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conformiaq́
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; omninò ſunt ipſius doctrinæ, aliter ipſum perpetuò
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mentientem facimus. </
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<
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">Poſtremò illud etiam eſt aduertendum, fortè Ariſt. in
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præſenti textu ſpectaſſe
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nõ
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ad hanc Euclidianam demonſtrationem, ſed po
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tius ad Pithagoricam. </
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">Pithagorei enim eam aliter, quamuis per idem me
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dium, ſcilicet à cauſa materiali, demonſtrabant; conſtruebant enim aliter,
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vlla vtebantur diuiſione. </
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<
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">quod dictum velim propter nonnullos, qui ab
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huiuſmodi diuiſionibus abhorrent,
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timentq́
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; ne demonſtrationis perfectio
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ni per eas plurimum derogetur. </
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<
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id
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">Pithagoreorum demonſtrationem vide
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apud Clauium in ſcholio 32. primi Euclidis, quam ex Eudemo etiam Pro
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clus in comm. eiuſdem recitat.</
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37</
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<
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">Ibidem
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(Sed quemadmodŭm harmonica per Arithmeticam)
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vide ſupra tex. 20.</
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<
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">Ibidem
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(Demonſtratio autem non computatur in aliud genus; niſi, vt dictum
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eſt geometricæ demonſtrationes in Perſpectiuas, aut Mechanicas, & arithmeticæ in
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harmonicas)
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exempla ſubalternationis Perſpectiuæ, & Muſicæ in tex. 20. at
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tulimus; nunc Mechanicæ ſubalternationis, quam hic Ariſt. inſinuat, exem
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plum ſit illud, quod Archimedes prop. 14. primi Aequep. demonſtrat, ni
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mirum centrum grauitatis omnis trianguli eſſe punctum illud, in quo rectæ
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lineæ ab angulis trianguli ad dimidia latera oppoſita ductæ concurrunt. </
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triangulum A B C, à cuius angulis A, & B, ducantur duæ rectæ A D, B E, ita
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vt bifariam ſecent latera A C, B C, in punctis D, & E, & concurrant in F.
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<
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<
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Aequep. probauit centrum grauitatis eſſe in ea linea, quæ ducta ab angulo
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quouis ſecat oppoſitum latus bifariam, crit in linea A D,
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