Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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per, C, ipſi, DF, parallela, CB, & </
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<
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<
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">ad, BC, in, P, Q, iunganturque, AC, HC, & </
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<
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">à puncto, M,
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ducatur, MX, parallela axi, vel diametro, AP; </
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Q, eſt parallela ipſi, MX, & </
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cabit etiam, XC, bifariam in Q; </
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">& </
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">quia parabola, ABC, ad pa-
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rabolam, MHFC, eſt vt cubus, BC, ad cubum, CX, vel vt cu-
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bus, PC, ad cubum, CQ, ideò ſemiparabola, APC, ad ſemipa-
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rabolam, HOC, erit vt cubus, PC, ad cubum, CQ, & </
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<
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dem ſubſexquitertia .</
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<
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erit vt cubus, PC, ad cubum, CQ: </
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angula habent interſerationem compoſitam exratione baſium, &</
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altitudinum, vel linearum à verticibus earundem ductarum æqua-
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19. 1. 2.</
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liter baſibus inclinatarum; </
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<
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">ideò triangulum, APC, ad triangu-
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lum, HOC, habebit rationem compoſitam ex ratione baſis, PA,
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ad baſim, OH, vel, AR, illi æqualem, & </
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Q, quæ vel ſunt altitudines, vellineæ ductæ à communi vertice, C,
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cum æquali inclinatione ad baſes, AP, &</
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AP, HQ, ſunt parallelæ, eſt autem vt,
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PA, ad AR, ita quadratum, PC, ad
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quadratum, RF, ergo triangulum, A
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PC, ad triangulum, HOC, habebit
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rationem compoſitam ex ea, quam ha-
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bet quadratum, PC, ad quadratum, R
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F, & </
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">ex ea, quam habet, PC, ad CQ,
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quia verò triangulum, APC, ad trian-
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gulum, HOC, eſt vt cubus, PC, ad
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cubum, CQ, ideò ad illud habet etiam rationem compoſitam ex
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ea, quam habet, PC, ad CQ, & </
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<
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">ex ratione quadrati, PC, ad qua-
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dratum, CQ, ergo iſtæ duæ rationes, ſcilicet quam habet, PC,
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ad, CQ, & </
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">quadratum, PC, ad quadratum, RF, componunt
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eandem rationem, quam iſtæ duæ, ſcilicet ratio, PC, ad, CQ, & </
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quadrati, PC, ad quadratum, CQ, eſt autem in his communis
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ratio, quam habet, PC, ad, CQ, ergo reliqua ratio, quam habet
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quadratum, PC, ad quadratum, CQ, erit eadem ei, quam habet
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quadratum idem, PC, ad quadratum, RF, ergo quadratum, C
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Q, erit æquale quadrato, RF, &</
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">Quoniam autem parabola, BAC, ad parabolam, DAF, eſt vt
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cubus, BC, ad cubum, DF, .</
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item oſtenſum eſt parabolam eandem, BAC, ad parabolam, MH
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FC, eſſe vt cubum, PC, ad cubum, CQ, ideò parabola, DAF,
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ad parabolam, MHFC, erit vt cubus, RF, ad cubum, QC, ſunt
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autem, QC, RF, inter ſe æquales, vtoſtenſum eſt, & </
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