Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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extrinſeca rei, de qua demonſtratur; quinimò ſubiectum ipſius ſunt. </
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<
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id
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s.005257
">Quia
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verò facta conſtructione, ſtatim perſpicuè apparet ortum eſſe triangulum,
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æquilaterum, non eſt illi curę probare illud eſſe triangulum, ſed quia an ſit
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æquilaterum ignoratur, idcircò totus demonſtrationis diſcurſus verſatur in
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demonſtranda trium illarum linearum æqualitate.</
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<
s
id
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s.005258
">Quem
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abbr
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quidẽ
">quidem</
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diſcurſum continere cauſam, quamuis per ſe pateat, vt mox
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apparebit, non deeſt
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abbr
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tamẽ
">tamen</
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Procli authoritas adeò clara, vt magnopere mi
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rer Piccolomineum Procli ſtudioſum, eam non vidiſſe: Proclus enim in
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abbr
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cõ-men
">conm
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men</
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. huius demonſtrationis hæc habet; quando autem per deſcriptionem
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circulorum, quod conſtructum eſt triangulum æquilaterum eſſe oſtenditur,
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à cauſa apprehenſio fit; ſimilitudinem. </
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<
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">n. </
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<
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id
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s.005260
">& æqualitatem circulorum cauſam
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dicimus eſſe æqualitatis laterum illius trianguli. </
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<
s
id
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s.005261
">Quibus verbis non ſolum
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authoritas, ſed ratio etiam optima, cur hæc ſit demonſtratio à cauſa, con
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tinetur, quia nimirum oſtendit cauſam æqualitatis laterum eſſe, quia ſint
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ſemidiametri æqualium circulorum. </
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<
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id
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s.005262
">Quæ argumentatio procedit à defini
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tione ſubiecti, quod eſt circulus: quamuis non tota, ſed tantum quatenus
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neceſſaria eſt, afferatur, ideſt definitio ſemidiametrorum, quod ad demon
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ſtrandum ſufficit, vt benè notat Zabarella, loquens de hac ipſa demonſtra
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tione; cùm igitur medium ſit definitio ſubiecti, patet eam eſſe perfectam
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demonſtrationem, in qua paſſionis oſtenſæ allata eſt propria, & adæquata
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cauſa, quæ eſt natura circuli. </
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<
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id
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s.005263
">
<
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abbr
="
ſicq́
">ſicque</
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>
; Euclides optimè demonſtraujt ex con
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ſtructione, quàm præceperat, gigni triangulum æquilaterum. </
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<
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id
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s.005264
">Subiectum
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igitur eſt il a circulorum, ac linearum configuratio, medium definitio cir
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culi, paſſio triangulum
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abbr
="
æquilaterũ
">æquilaterum</
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>
. </
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<
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id
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s.005265
">ex qua
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abbr
="
demõſtratione
">demonſtratione</
expan
>
erui poteſt etiam
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definitio paſſionis cauſalis, ideſt, eſſe triangulum æquilaterum ex tali
<
expan
abbr
="
cõſtru-ctione
">conſtru
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ctione</
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>
ortum. </
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<
s
id
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s.005266
">Quare huic nihil deeſt ad perfectam
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abbr
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demonſtrationẽ
">demonſtrationem</
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>
. </
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<
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id
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s.005267
">ex qui
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bus videas, quàm immeritò nonnulli eam impugnent, putantes eam eſſe per
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extranea; cauſa erroris fuit, quia exiſtimarunt abſolutè demonſtrari
<
expan
abbr
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triã-gulum
">trian
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gulum</
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illud eſſe æquilaterum. </
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<
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id
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">verùm decepti ſunt, quia in hoc, & in omni
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bus alijs problematis, demonſtratur talem conſtructionem parere triangu
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lum, vel
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abbr
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quadratũ
">quadratum</
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>
, vel quid aliud, vt patet Euclidem, vel obiter
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abbr
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inſpiciẽti
">inſpicienti</
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>
.</
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</
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<
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<
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id
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">Placet adhuc alteram à formali cauſa procedentem expendere. </
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<
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id
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s.005270
">ea eſt 46.
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primi elem. </
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<
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id
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s.005271
">quæ ſimiliter problema eſt, quo docet Euclides, qua ratione ſu
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pra data recta linea quadratum deſcribatur. </
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<
s
id
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s.005272
">tradit igitur quandam linea
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rum conſtructionem, ex qua poſtea demonſtrat ortum eſſe quadratum, ita
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vt conſtructio illa ſit loco ſubiecti, de qua demonſtratvr eſſe quadratum. </
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<
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id
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s.005273
">non
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igitur intendit, vt nonnulli falsò putant,
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demõſtrare
">demonſtrare</
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abſolutè illud eſſe qua
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dratum, ſed ex tali conſtructione ortum eſſe quadratum duo autem ſunt de
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eſſentia quadrati, primum habere quatuor latera æqualia, ſecundum habe
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re quatuor angulos rectos, vt ex definitione conſtat. </
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<
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id
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s.005274
">Neutrum autem ſine
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altero ſufficit,
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nã
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& Rhombus quatuor latera æqualia habet, & Altera par
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te longius habet quatuor angulos rectos, neutrum tamen quadratum eſt. </
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<
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id
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">ſi
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verò
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vtrunq;
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ſimul cuipiam figuræ competat, illam neceſſariò quadratum
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eſſe efficient. </
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<
s
id
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">Probat igitur Euclid. vtraq, euidenter ineſſe illi figuræ ex vi
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illius conſtructionis, & ideò illi quadrati definitionem competere. </
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<
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id
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">Quare
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hęc erit potiſſima demonſtratio, cùm cauſam afferat
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abbr
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intrinſecã
">intrinſecam</
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>
, </
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</
archimedes
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