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,
& {1/2}. NO, ergo omnia quadrata, SF, ad omnia quadrata fruſti, D
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.
0390-01
9. l. 2.
39. & Sch.
40. l. 1.
1. 2. Elem.

Omnia verò quadrata trianguli, DMF, ad eadem erunt, vt {1/3}. rectanguli, OEN, ad rectangulum ſub, EM, & ſub compoſita ex
{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.

IN eadem figura, regula eadem retenta, oſtendemus om-
mnia quadrata, AF, demptis omnibus quadratis hyper-
bolæ, DNF, ad omnia quadrata, SF, demptis omnibus
quadratis fruſti, HDFG, eſſe vt parallelepipedum ſub cõ-
poſita ex ipſa, XE, EN, & ſub quadrato, NE, ad parallele-
pipedum ſub compoſita ex eadem, XE, & cum, EN, NM,
& ſub quadrato, ME.

Quia enim omnia quadrata, AF, ad omnia quadrata hyperbo-
læ, DNF, ſunt vt, OE, ad compoſitam ex {1/2}. ON, & {1/3}. NE, ideò
per conuerſionem rationis, & conuertendo omnia quadrata, AF,
demptis omnibus quadratis hyperbolæ, DNF, ad omnia quadra-
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
verò omnia quadrata, AF, demptis omnibus quadratis hyperbo-
læ, DNF, ad omnia quadrata, SF, demptis omnibus quadratis
fruſti, DHGF, habent rationem compoſitam ex ea, quam habent
omnia quadrata, AF, demptis omnibus quadratis hyperbolæ, D
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,
AF, ad omnia quadrata, SF, ideſt ex ea, quam habet, NE,
ad, EM, & tandem ex ea, quam habent omnia quadrata, SF,
ad omnia quadrata, SF, demptis omnibus quadratis fruſti, HDF

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