Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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Ex Libro ſecundo Priorum.
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">Ex cap. 21.
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(Quod faciunt, qui coalternas putant ſcribere, latent enim ipſe
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ſe ipſos talia accipientes, quæ non est poſſibile monstrare uon exiſtentibus
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coalternis)
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Vult Ariſt. exemplo mathematico explicare, quid ſit pe
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titio principij. </
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enim græca
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idem ſignificat, ac mutuus, & coalternus. </
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<
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exempli explicationem vtor figura textibus apponi ſolita, quæ eſt præſens.
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probat Euclides in 28. primi Elem. quod ſi
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linea recta quædam, vti E F, cadens ſuper
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duas rectas, vti ſunt A B, C D, fecerit angu
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los alternos ęquales, angulos
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A G H,
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G H D, ij enim dicuntur alterni; ſiue alios
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duos, nimirum B G H, G H C, hi enim ſunt
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alterni; probat inquam has duas li
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neas A B, C D, eſſe inuicem parallelas. </
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">Iam ſi quis vellet probare, ſe duas
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parallelas duxiſſe, hac ratione, quia ſcilicet faciunt prædictos angulos al
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ternos æquales; & probaret facere angulos alternos æquales, quia ſunt pa
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rallelæ, hic peteret principium, ideſt, illud, quod principio
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erat,
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afferret pro ratione, & cauſa, quod dicitur peti principium, quia tunc pe
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timus, vt concedatur nobis, id, quod principio, & primo omnium demon
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ſtrare propoſueramus. </
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">aduerte, quod characteres, qui ſunt in ſequentibus
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verbis huius loci, non appellant characteres figuræ appoſitæ; in quo quidam
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decepti, nullo pacto poterant locum hunc intelligere.</
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(Vt ſi volens monſtrare, quod diameter eſt incom
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menſ. argueret Zenonis rationem, quod non eſt moueri)
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ſuperius ſecto 3. lib. 1.
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fusè explicauimus hanc aſymmetriam, quam ſi quis vellet demonſtrare ea
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dem illa ratione, qua Zeno motum impugnabat, quia ſcilicet
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com
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munis, quæ debet vtramque, quantitatem menſurare, debet in menſurando
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infinitas partes pertranſire, nimirum medietates medietatum in infinitum,
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eſt autem impoſſibile pertranſire infinitas huiuſmodi partes, & propterea
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non poterit metiri,
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vnam,
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alteram ex
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, quæ putaban
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tur commenſurabiles, afferret hic, inquit Ariſt. non cauſam pro cauſa.</
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(Quoniam idem
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falſum per plures petitiones accidere
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nihil fortaſſe inconueniens, veluti coalternas coincidere; & ſi maior eſt extrinſecus
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angulus intrinſeco; & ſi triangulus habet plures rectos duobus)
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per plures poſi
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tiones ſubaudi falſas. </
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<
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">per coalternas intellige lineas æquidiſtantes, ſeu pa
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rallelas, vt in ſuperiori cap. monuimus. </
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mi Elem. oſtendit, quod ſi fuerint duæ parallelæ veluti in præcedenti figura,
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A B, C D, ſuper quas alia recta E F, incidat, neceſſario faciet angulum ex
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trinſecum E G B, v. g. æqualem interno, & oppoſito, & ad eaſdem partes,
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angulo videlicet G H D. ſi ergo inquit Ariſt ſupponamus iſtud falſum, an
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gulum ſcilicet E G B, externum eſſe maiorem angulo interno G H D, ſequi
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tur etiam falſum, videlicet lineas
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A B, C D, concurrere. </
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batur conſequentia hoc modo, quia ſi angulus E G B, maior eſt angulo </
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