Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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archimedes
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s.005277
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16
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& adæquatam, propter quam res eſt. </
s
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<
s
id
="
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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abbr
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neq;
">neque</
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habere quatuor latera æqualia ſolum, ſed
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<
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abbr
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vtrunq;
">vtrunque</
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ſimul in eodem; vnde reſultat totum, ſeu
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abbr
="
compoſitũ
">compoſitum</
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>
, quod eſt quid
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diuerſum à partibus ſeorſum ſumptis. </
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>
<
s
id
="
s.005279
">in demonſtratione autem hac, cauſa
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ſunt partes ſeorſim ſumptæ; effectus verò eſt compoſitum, ex earum vnione
<
lb
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reſultans. </
s
>
<
s
id
="
s.005280
">Notandum præterea eandem demonſtrationem procedere à de
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lb
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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
<
expan
abbr
="
cõ-ſtructione
">con
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ſtructione</
expan
>
producta. </
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>
<
s
id
="
s.005281
">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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s.005282
">Satis. </
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<
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s.005283
">n. </
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<
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id
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s.005284
">eſt, ſi habeamus rei cauſam
<
expan
abbr
="
propriã
">propriam</
expan
>
,
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lb
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ita vt aliter ſe habere nequeat. </
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>
<
s
id
="
s.005285
">ſexcentæ huiuſmodi per formalem cauſam,
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apud Euclid. Archim Appoll. </
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>
<
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id
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s.005286
">& alios Geometras reperies. </
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<
s
id
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s.005287
">vide Appendi
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cem, ad finem operis, in qua omnes primi elem. </
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<
s
id
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s.005288
">demonſtrationes reſolutas
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inuenies,
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abbr
="
plurimasq́
">plurimasque</
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>
; à cuſa formali.</
s
>
</
p
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<
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type
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main
">
<
s
id
="
s.005289
">Sed iam materialem cauſam indagemus,
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abbr
="
idq́
">idque</
expan
>
; duce Ariſt. accipiamus igi
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tur celeberrimam illam 32. primi elem. </
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>
<
s
id
="
s.005290
">quam Mathematicis
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abbr
="
ſoiẽt
">ſolent</
expan
>
aduerſa
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lb
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rij opponere. </
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>
<
s
id
="
s.005291
">& quoniam ſupra tex. 23. 1. Poſter. nos eam per cauſam ma
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terialem procedere oſtendimus, ideò ne actum agamus,
<
expan
abbr
="
explicationẽ
">explicationem</
expan
>
illam
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nunc opus eſt relegere. </
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>
<
s
id
="
s.005292
">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
<
expan
abbr
="
etiã
">etiam</
expan
>
totalis anguius erit æqualis am
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bobus internis ſimul ſumptis. </
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>
<
s
id
="
s.005293
">Quod autem externus angulus ſit diuiſibilis
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in duas partes æquales internis angulis probat diuidendo illum per lineam
<
lb
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illam oppoſito trianguli lateri parallelam, vnde ſtatim ex parallelarum na
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lb
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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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>
<
s
id
="
s.005294
">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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abbr
="
cõfeſſo
">confeſſo</
expan
>
eſt, & Ari
<
lb
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ſtot. ipſe tex. 3. 5. Metaph. id aſſerit. </
s
>
<
s
id
="
s.005295
">& tex. 11. 2. Poſter. vtitur ſimili
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expan
abbr
="
exẽ-plo
">exem
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plo</
expan
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ad
<
expan
abbr
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materialẽ
">materialem</
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>
cauſam explicandam. </
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>
<
s
id
="
s.005296
">quamuis autem Geometræ non di
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cant talem angulum, vel talem figuram eſſe
<
expan
abbr
="
diuiſibilẽ
">diuiſibilem</
expan
>
in partes æquales alijs
<
lb
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quibuſdam, ſed ſtatim diuidant, id faciunt breuitatis cauſa; vtuntur enim
<
lb
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actu pro potentia, quia actus potentiam ſupponit, quòd optimè Ariſtot. 9.
<
lb
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Metaphyſ. tex. 20. annotauit, ſic; Deſcriptiones quoque actu inueniuntur,
<
lb
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diuidentes namque inueniunt, quòd ſi diuiſæ eſſent, manifeſtæ eſſent, nunc
<
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autem inſunt potentia, &c. </
s
>
<
s
id
="
s.005297
">Cuius loci noſtram ſuperius allatam explicatio
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nem habes. </
s
>
<
s
id
="
s.005298
">per deſcriptiones autem intelligit Geometricas demonſtratio
<
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nes, vt ſæpius ſupra in opere oſtenſum eſt. </
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>
<
s
id
="
s.005299
">Innumeræ ſunt apud Geometras,
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lb
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quę per hanc poſsibilem diuiſionem procedunt,
<
expan
abbr
="
quęq;
">quęque</
expan
>
ideò ſunt à cauſa </
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>
</
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</
chap
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</
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</
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</
archimedes
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