# Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER V. ptis omnibus quadratis, HQ, æquatur autem rectangulum, EM
N, cum rectangulo ſub, EM, & iub compoſita ex {1/3}. EM, & {1/2}. N
O, rectangulo ſub, EM, & ſub compoſita ex {1/3}. EM. integra, MN,
HGF, demptis omnibus quadratis, HQ, erunt vt rectangulum,
OEN, ad rectangulum ſub, EM, & ſub compoſita ex {1/3}. EM, in-
tegra, MN, & {1/2}. NO.

### 537.1.

In antec.
9. l. 2.
39. & Sch.
40. l. 1.
1. 2. Elem.

{1/3}. EM, integra, MN, & {1/2}. NO, . i. vt totum rectangulum ſub, O
EN, ad rectangulum ſub, EM, & ſub compoſita ex, EM, tripla,
MN, & , NX, . i. ſub, EM, & ſub compoſita ex, EX, & dupla, MN,
quæ oſtendenda erant.

## 538.THEOREMA V. PROPOS. V.

quadratis fruſti, HDFG, eſſe vt parallelepipedum ſub cõ-
pipedum ſub compoſita ex eadem, XE, & cum, EN, NM,

læ, DNF, ſunt vt, OE, ad compoſitam ex {1/2}. ON, & {1/3}. NE, ideò
per conuerſionem rationis, & conuertendo omnia quadrata, AF,
ta, AF, erunt vt compoſita ex {1/2}. ON, & {2/3}. NE, ad, OE, . i. ſum-
pta, NE, communialtitudine, vt rectangulum ſub compoſita ex
{1/2}. ON, & {2/3}. NE, & ſub, NE, ad rectangulum, OEN. Quoniam
fruſti, DHGF, habent rationem compoſitam ex ea, quam habent
NF, ad omnia quadrata, AF, . i. ex ea, quam habet rectangulum
ſub compoſita ex {1/2}. ON, & {2/3}. NE, & ſub, N E, ad rectangu-
lum, NEO; & ex ratione, quam habent omnia quadrata,