Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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& adæquatam, propter quam res eſt. </
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<
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s.005278
">Vbi notandum effectum re vera diſtin
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gui à ſua cauſa, eſſe enim quadratum (qui effectus eſt) non eſt habere, qua
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tuor angulos rectos ſolum:
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neq;
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habere quatuor latera æqualia ſolum, ſed
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vtrunq;
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ſimul in eodem; vnde reſultat totum, ſeu
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compoſitũ
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, quod eſt quid
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diuerſum à partibus ſeorſum ſumptis. </
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<
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id
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s.005279
">in demonſtratione autem hac, cauſa
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ſunt partes ſeorſim ſumptæ; effectus verò eſt compoſitum, ex earum vnione
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reſultans. </
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<
s
id
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s.005280
">Notandum præterea eandem demonſtrationem procedere à de
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finitione ſubiecti, nam illa duo quadrati eſſentialia, ex definitione eorum,
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quæ ſunt in conſtitutione petuntur, quæ conſtitutio eſt inſtar ſubiecti, vt ſu
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pra monui: ex hac autem definitione partium ſubiecti in demonſtratione
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contenta, eruitur definitio cauſalis ipſius paſsionis, quæ eſt, quadratum eſt
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figura habens quatuor angulos rectos, & quatuor latera æqualia, ex tali
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abbr
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cõ-ſtructione
">con
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ſtructione</
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producta. </
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<
s
id
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">Notandum tandem quouis modo ſiue à cauſa, ſiue ab
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effectu oſtendantur illa duo eſſentialia quadrati, ineſſe ipſi, nihil referre ad
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demonſtrationis perfectionem. </
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<
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">Satis. </
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<
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">n. </
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<
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">eſt, ſi habeamus rei cauſam
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abbr
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propriã
">propriam</
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>
,
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ita vt aliter ſe habere nequeat. </
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<
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id
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s.005285
">ſexcentæ huiuſmodi per formalem cauſam,
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apud Euclid. Archim Appoll. </
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">& alios Geometras reperies. </
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<
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">vide Appendi
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cem, ad finem operis, in qua omnes primi elem. </
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<
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">demonſtrationes reſolutas
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inuenies,
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plurimasq́
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; à cuſa formali.</
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</
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<
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id
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">Sed iam materialem cauſam indagemus,
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abbr
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idq́
">idque</
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; duce Ariſt. accipiamus igi
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tur celeberrimam illam 32. primi elem. </
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<
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id
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s.005290
">quam Mathematicis
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ſoiẽt
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aduerſa
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rij opponere. </
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">& quoniam ſupra tex. 23. 1. Poſter. nos eam per cauſam ma
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terialem procedere oſtendimus, ideò ne actum agamus,
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explicationẽ
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illam
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nunc opus eſt relegere. </
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<
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id
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">Hoc tamen loco partem ipſius primam, angulum,
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videlicet externum cuiuſuis trianguli, æqualem eſſe duobus internis, & op
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poſitis, examinabo; cuius medium, ſi ad rigorem demonſtrationis rediga
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tur, eſt hoc; externus angulus eſt diuiſibilis in duos angulos, quorum ſingu
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li ſingulis internis ſunt æ quales, ergo
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etiã
">etiam</
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totalis anguius erit æqualis am
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bobus internis ſimul ſumptis. </
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<
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id
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">Quod autem externus angulus ſit diuiſibilis
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in duas partes æquales internis angulis probat diuidendo illum per lineam
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illam oppoſito trianguli lateri parallelam, vnde ſtatim ex parallelarum na
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tura apparet partiales angulos anguli externi æquales eſſe internis triangu
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li; ex quo ſequitur totum externum angulum eſſe æqualem duobus internis
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ſimul ſumptis. </
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<
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id
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">Hic autem modus argumentandus, à partibus poſsibilibus ad
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totum, eſſe à cauſa materiali, apud omnes Philoſophos in
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cõfeſſo
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eſt, & Ari
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ſtot. ipſe tex. 3. 5. Metaph. id aſſerit. </
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<
s
id
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s.005295
">& tex. 11. 2. Poſter. vtitur ſimili
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exẽ-plo
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plo</
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ad
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materialẽ
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cauſam explicandam. </
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<
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id
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">quamuis autem Geometræ non di
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cant talem angulum, vel talem figuram eſſe
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abbr
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diuiſibilẽ
">diuiſibilem</
expan
>
in partes æquales alijs
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quibuſdam, ſed ſtatim diuidant, id faciunt breuitatis cauſa; vtuntur enim
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actu pro potentia, quia actus potentiam ſupponit, quòd optimè Ariſtot. 9.
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Metaphyſ. tex. 20. annotauit, ſic; Deſcriptiones quoque actu inueniuntur,
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diuidentes namque inueniunt, quòd ſi diuiſæ eſſent, manifeſtæ eſſent, nunc
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autem inſunt potentia, &c. </
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<
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id
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">Cuius loci noſtram ſuperius allatam explicatio
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nem habes. </
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<
s
id
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">per deſcriptiones autem intelligit Geometricas demonſtratio
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nes, vt ſæpius ſupra in opere oſtenſum eſt. </
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<
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">Innumeræ ſunt apud Geometras,
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quę per hanc poſsibilem diuiſionem procedunt,
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quęq;
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ideò ſunt à cauſa </
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