322302GEOMETRIÆ
tionculam, ASB, .
i.
exratione, BH, ad, CE, quæ duæ rationes
11Ex Co-
tol.antec. componunt rationem parallelepipedi ſub altitudine, BH, baſi re-
ctangulo, HOB, vel quadrato, OH, ad parallelepipedum ſub
altitudine, CE, baſi rectangulo, HCB, ergo triangulum, HNB,
ad portionculam, ASB, eſt vt parallelepipedum ſub altitudine,
BH, baſi quadrato, HO, ad parallelepipedum ſub altitudine, C
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-
lepipedum ſub eadem altitudine, HB, baſi quadruplo quadrati, H
O, ideſt quadrato, HB, ſilicet vt cubus, HB, ad parallelepipedum
ſub eadem altitudine compoſita ex, HB, CE, baſi quadruplo re-
221.huius. ctanguli, HCB. Quia verò parabola, HNB, eſt ſexquitertia trian-
guli, HNB, ideò erit ad ipſum, vt ſolidum ſexquitertium cubi, H
B, ad cubum, HB, eſt autem triangulum, HNB, ad trilineum,
HASB, vt cubus, HB, ad parallelepipedum ſub altitudine com-
poſita ex, HB, CE, & ſub baſi quadruplo rectanguli, HCB, ergo
216[Figure 216]
ex æquali parabola, HNB,
ad trilineum, HASB, erit vt
ſolidum ſexquitertium cubi, H
B, ad parallelepipedum ſub al-
titudine compoſita ex, HB, C
E, baſi quadruplo rectanguli,
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-
3338.1.2. 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,
11Ex Co-
tol.antec. componunt rationem parallelepipedi ſub altitudine, BH, baſi re-
ctangulo, HOB, vel quadrato, OH, ad parallelepipedum ſub
altitudine, CE, baſi rectangulo, HCB, ergo triangulum, HNB,
ad portionculam, ASB, eſt vt parallelepipedum ſub altitudine,
BH, baſi quadrato, HO, ad parallelepipedum ſub altitudine, C
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-
lepipedum ſub eadem altitudine, HB, baſi quadruplo quadrati, H
O, ideſt quadrato, HB, ſilicet vt cubus, HB, ad parallelepipedum
ſub eadem altitudine compoſita ex, HB, CE, baſi quadruplo re-
221.huius. ctanguli, HCB. Quia verò parabola, HNB, eſt ſexquitertia trian-
guli, HNB, ideò erit ad ipſum, vt ſolidum ſexquitertium cubi, H
B, ad cubum, HB, eſt autem triangulum, HNB, ad trilineum,
HASB, vt cubus, HB, ad parallelepipedum ſub altitudine com-
poſita ex, HB, CE, & ſub baſi quadruplo rectanguli, HCB, ergo
ad trilineum, HASB, erit vt
ſolidum ſexquitertium cubi, H
B, ad parallelepipedum ſub al-
titudine compoſita ex, HB, C
E, baſi quadruplo rectanguli,
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-
3338.1.2. 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,