## Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ tionculam, ASB, . i. exratione, BH, ad, CE, quæ duæ rationes
componunt rationem parallelepipedi ſub altitudine, BH, baſi re-
altitudine, CE, baſi rectangulo, HCB, ergo triangulum, HNB,
ad portionculam, ASB, eſt vt parallelepipedum ſub altitudine,
E, baſi rectangulo, HCB, eſt autem, vt dicebatur, triangulum,
HNB, ad triangulum, HAB, vt rectangulum, HOB, vel qua-
dratum, HO, ad rectangulum, HCB, ideſt ſumpta, HB, com-
munialtitudine, vt parallelepipedum ſub altitudine, HB, baſi qua-
drato, HO, ad parallelepipedum ſub altitudine, HB baſi rectan-
gulo, HCB, ergo, colligendo, triangulum, HNB, ad portion-
culam, ASB, cum triangulo, ABH, ſilicet ad trilineum, HAS
B, erit vt parallelepipedum ſub altitudine, HB, baſi quadrato, H
O, ad parallelepipedum ſub altitudine compoſita ex, HB, CE,
baſi rectangulo, HCB; vel vt iſtorum quadrupla ſilicet vt paralle-
ctanguli, HCB. Quia verò parabola, HNB, eſt ſexquitertia trian-
guli, HNB, ideò erit ad ipſum, vt ſolidum ſexquitertium cubi, H
HASB, vt cubus, HB, ad parallelepipedum ſub altitudine com-
poſita ex, HB, CE, & ſub baſi quadruplo rectanguli, HCB, ergo
ex æquali parabola, HNB,
ſolidum ſexquitertium cubi, H
titudine compoſita ex, HB, C
HCB; vel vt iſtorum ſubſex-
quitertia ſilicet vt cubus, HB,
ab parallelepipedum ſub ea-
dem altitudine compoſita ex,
HB, CE, baſi triplo rectan-
guli, HCB, eſt enim quadruplum rectanguli, HCB, ſexquiter-
tium tripli eiuſdem rectanguli; hoc autem conſequens parallelepi-
pedum poteſt diuidi in parallelepipedum ſub altitudine, CE, baſi
triplo rectanguli, HCB, vel baſi rectangulo ſub, BC, & tripla,
CH, & in parallelepipedum ſub altitudine, HB, baſi etiam rectan-
gulo ſub, BCH, ter ſumpto, quoniam verò tripla, HC, & , CB,
CE, ſunt deinceps proportionales, ideò parallelepipedum, quod

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