Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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339319LIBER IV. autem vt, OC, ad, CQ, ita, ſumpta, QC, communi altitudine,
rectangulum ſub OC, CQ, ad quadratum, QC, ergo ratio com-
poſita ex ea, quam habet, OC, ad, CQ, & quadratum, QC, ad
quadratum, CO, eſt eadem compoſitæ ex ea, quam habet rectan-
gulum ſub, OC, CQ, ad quadratum, CQ, & quadratum, CQ,
ad quadratum, CO, . i. eademei, quam habet rectangulum ſub,
QC, CO, ad quadratum, CO, . i. eadem ei, quam habet, QC, ad,
CO; ergo omnia quadrata trianguli, DAF, ad omnia quadrata
trianguli, MHC, vel omnia quadrata parabolæ, DAF, ad om-
nia quadrata parabolæ, MHC, regulis iam dictis, erunt vt, QC,
ad, CO, quod ſerua.
Vlterius omnia quadrata parabolæ, MHC, ad rectangula ſub
11Exantec. parabola, MHC, & trilineo, HRC, regula, MC, ſunt vt, M
C, ad, CR, vel ad, CX, . i. vt, OC, ad, CQ, ergo omnia qua-
drata parabolæ, DAF, regula, DF, ad rectangula ſub parabola,
MHC, & trilineo, HRC, regula, MC, habebunt rationem
compoſitam ex ea, quam habet, QC, ad, CO, & ex ea quam
habet, CO, ad, QC, ideſt habebunt eandem rationem, quam
habet, QC, ad, QC, ideſt eruntillis æqualia, quod oſtende-
re opus erat.
_H_Inc patet omnia quadrata parabolæ, DAF, regula, DF, ad om-
nta quadrata parabolæ, MHC, regula, MC, eſſe vt QC, ad,
CO, vel, XC, ad CM, vel, DF, (quæ eſt æqualis ipſi, XC,) ad, MC,
dumdiametri, AZ, HO, ſunt æquales, vt in Theoremate oſtenſum eſt.

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