Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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91</
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<
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">Tex. 68. (
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Aut enim ad ipſum quid eſt, reducitur ipſum propter quid in immo
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bilibus, vt in Mathematicis, ad definitionem enim recti, aut commenſurabilis, aut
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alius cuiuſpiam reducitur vltimum
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) ex his manifeſtè videas Mathematicas
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de-mõſtrare
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monſtrare</
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per cauſam formalem, cum cauſam ipſam ad ipſum quid eſt, ideſt,
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ad definitionem reducant. </
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<
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tuli: ſed etiam ſequentis loci exemplum de triangulo idem apertè manife
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ſtat; in quo probat duos angulos A C B, A C D, eſſe rectos, ex definitione
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ipſorum, ſiue ex definitione lineæ perpendicularis A C, quod idem eſt.</
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92</
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<
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">Tex 89. (
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Eſt autem neceſſarium in Mathematicis, & in his, quæ ſecundum
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naturam fiunt quaſi eodem modo; quoniam enim hoc rectum eſt, neceſſe eſt, trian
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gulum tres angulos habere æquales duobus rectis; ſed non, ſi hoc, illud; ſed ſi hoc
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non eſt,
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neq;
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rectum eſt.
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) cum animaduerterim non parum eſſe diſſenſionis, &
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difficultatis in exemplo hoc mathematico explicando, ita vt recentiores
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quidam textum
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hũc
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pro arbitratu ſuo perperam latinè verterint: ideò pri
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mum ex græcis codicibus interpretationem hanc veram attuli. </
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<
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">deinde, quia
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etiam græci in exemplo mathematico enodando, vel malè, vt Simplicius;
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vel obſcurè nimis, vt reliqui; Latini verò vel nihil, vel peius multò loquun
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tur, ideò ſic ego exponendum cenſui. </
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<
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">cum velit Ariſt. oſtendere neceſſita
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tem, quæ in ſcientijs inter præmiſſas, ſeu medium, & concluſionem reperi
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tur, affert exemplum illud mathematicum ſibi familiare, demonſtrationem
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ſcilicet illam, qua oſtenditur, omne triangulum habere tres angulos æqua
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les duobus rectis angulis, cuius fuſiſſimam explicationem inuenies ſupra in
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primo Priorum, ſecto 3. cap. 1. quam neceſſe eſt, conſulas. </
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<
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huius paſſionis accipit lineam perpendicularem, quam innuit verbis illis
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(quoniam enim hoc rectum eſt
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) vt in figura ſit triangulum A B C,
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ſitq́
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; vt latus
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A C, ſit perpendiculare
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cũ
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latere B C, & pro
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ducatur B C, in D; tunc triangulum A B C,
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habere tres angulos, A, B, & A C B, æquales
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duobus rectis planum erit: nam
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latus A C,
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ſit perpendiculare (quod Ariſt. dicit, cum
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re-ctũ
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ctum</
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hoc ſit) erunt duo anguli deinceps A C B,
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A C D, recti, ex definitione lineæ perpendicu
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laris, cum ergo duo anguli A, & B, externo,
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rectoq́
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; A C D, ſint æquales per
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32. primi, & reliquus angulus A C B, communis, ideſt, ſit angulus triangu
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li, & angulus vnus lineæ perpendicularis, & ideò rectus; manifeſtè apparet,
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tres angulos A, B, A C B, eſſe æquales neceſſariò duobus rectis, ex poſitio
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ne illius recti, ſiue lateris perpendicularis, quia ex verò, verum neceſſariò
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ſequitur; non tamen poſita hac paſſione, ſiue concluſione, habere ſcilicet
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tres angulos æquales duobus rectis, neceſſariò ſequitur illud eſſe rectum,
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ideſt latus illud A C, eſſe perpendiculare ad latus B C, quia verum
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ſequi poteſt ex verò, & falsò. </
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<
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tia, ſi triangulum non habet hanc proprietatem, ne
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que illud rectum eſt, ideſt,
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neq;
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latus prædi
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ctum erit
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, quia falſum
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non, niſi ex falſo ſequitur.</
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