Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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55
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principijs huius)
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affert nunc exemplum alterius demonſtrationis, quæ non
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ex communibus, vt præcedens Bryſonis, ſed ex proprijs principijs oſtendit
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affectionem de ſubiecto proprio. </
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<
s
id
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s.001001
">Eſt autem illud exemplum toties decan
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tatum de triangulo habente tres angulos æquales duobus rectis angulis; id
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circo operæpretium eſſe puto explicare demonſtrationem, 32. primi Eucli
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dis, quæ iſtud ex proprijs principijs demonſtrat, & quam hoc loco Ariſto
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teles innuit, hoc enim modo ipſius Ariſt. mentem probè penetrare poteri
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mus. </
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<
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id
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s.001002
">ſit ergo
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abbr
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triãgulum
">triangulum</
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A B C. </
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<
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id
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s.001003
">Dico ag
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gregatum
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triũ
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ipſius angulorum A, B, C,
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eſſe æquale aggregato ex duobus angu
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lis rectis (vt autem melius intelligas, quæ
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ſequuntur, lege prius ea, quæ dicta ſunt
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in lib. 1. Priorum ſecto 3. cap. 1.) produ
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catur latus B C,
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vſq;
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in D, vt fiat angulus
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externus A C D; Iam ſic, quoniam
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abbr
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pro-batũ
">pro
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batum</
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eſt in 13. primi, duos angulos, quos
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facit linea A C, cum linea B D, ſcilicet angulos A C B, A C D, eſſe pares
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duobus rectis: & quia pariter in prima parte huius propoſ. </
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<
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id
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s.001004
">32. probatum
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eſt ab Euclide duos angulos A B, eſſe æquales externo angulo A C D: ſi ter
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tius angulus reliquus A C B, ſumatur bis, ſemel cum duobus angulis A, B,
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& ſemel cum externo A C D,
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abbr
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addẽtur
">addentur</
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æqualia æqualibus, & propterea tres
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anguli A, B, A C B, ſimul ſumpti, erunt æquales duobus A C D, A C B, ſimul
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ſumptis; ſed his duobus ſunt æquales duo recti, ergo cum quæ ſunt æqualia
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vni tertio, ſint etiam æqualia inuicem, erit aggregatum trium angulorum
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A, B, A C B, æquale aggregato duorum rectorum; quod erat demonſtran
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dum. </
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<
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">Medium
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abbr
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itaq;
">itaque</
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huius demonſtrationis, ſi res ad trutinam Logicam ex
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pendatur, eſt, quod partes aggregati
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triũ
">trium</
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>
<
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angulorũ
">angulorum</
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>
A, B, A C B, ſunt æqua
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les partibus aggregati
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abbr
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duorũ
">duorum</
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, & ideo
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aggregatũ
">aggregatum</
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, aggregato æqua
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le eſt. </
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<
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id
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">quod medium eſt in genere cauſæ materialis. </
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<
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id
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s.001007
">quod verò partes illius
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ſint æquales partibus huius, probatur, per dignitatem
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abbr
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illã
">illam</
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, quæ ſunt æqualia
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vni tertio, ſunt etiam inter ſe. </
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<
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id
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s.001008
">partes porrò aggregati trium angulorum
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erant hæ, anguli A, B, vna; altera verò angulus A C B; partes verò aggre
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gati duorum rectorum erant A C B, A C D, quibus partibus, illæ ſunt æqua
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les, & ideo totum toti æquale. </
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<
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id
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">quod medium eſt omnino intrinſecum, & ex
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proprijs ipſius trianguli, ſiue ex proprijs angulorum ipſius, cum ſint ipſius
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partes. </
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<
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id
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s.001010
">quod pariter medium ex parte paſſionis, quæ demonſtratur, eſt ex
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proprijs, cum ſint partes illius materiales. </
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>
<
s
id
="
s.001011
">per materiam autem oportet
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hoc loco intelligere materiam intelligibilem, ideſt quantitatem à qualita
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tibus abſtractam, & terminatam, de qua pluribus agemus infra in tractatu
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de natura mathematicarum. </
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<
s
id
="
s.001012
">Hinc videas eos magnopere decipi, qui pu
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tant, hanc demonſtrationem eſſe per extrinſeca, eò quod ad demonſtran
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dum producatur linea B C, in D, putantes lineam illam productam C D,
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eſſe demonſtrationis medium; lineæ
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expan
abbr
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namq;
">namque</
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huiuſmodi, quæ in demonſtra
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tionibus geometricis conſtruuntur, nunquam ſunt media propria demon
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ſtrationum, ſed tantummodo aſſumuntur ad probandum medium iam ex
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cogitatum eſſe veram cauſam concluſionis. </
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<
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id
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">Hinc etiam manifeſtè colligas </
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