Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

236[Figure 236] vt quadratum, ME,
ad quadratum, EF,
1130. huius. omnia verò quadra-
ta, BF, ſunt ſexcupla
omnium quadratorú
trilinei, BCF, . i. ſunt
ad illa, vt quadratum,
EF, ad eiuſdem {1/6}. er-
go, ex æquali, om-
nia quadrata, BM, ad
omnia quadrata trili-
nei, BCF, ſunt vt quadratum, EM, ad {1/6}. quadrati, EF, quod etiá
ſerua. Tandem omnia quadrata, BM, ad rectangula ſub, BF, FH,
ſunt vt quadratum, EM, ad rectangulum ſub, EF, FM, rectangu-
22Coroll. 1.
26. l. 2. la verò ſub, BF, FH, ad rectangula ſub trilineo, BFC, & ſub, C
M, ſunt vt, BF, ad trilineum, BCF, (nam, CM, eſt parallelogram-
mum) ideſt ſunt eorum tripla . i. ſunt vt, EF, ad {1/3}. EF, . i. vt rectan-
gulum, EF/M, ad rectangulum ſub {1/3}. EF, & ſub, FM, ergo, ex æ-
quali, omnia quadrata, BM, ad rectangula ſub trilineo, BCF, &
ſub, FH, erunt vt quadratum, EM, ad rectangulum ſub {1/3}. EF, &
ſub, FM, ad eadem verò bis ſumpta, vt quadratum, EM, ad re-
ctangulum bis ſub {1/3}. EF, & ſub, FM, ideſt ſemel ſub {2/3}. EF, ſub, F
M, ergo, colligendo, omnia quadrata, BM, ad omnia quadrata; C
M, ad omnia quadrata trilinei, BCF, & ad rectangula bis ſub tri-
lineo, BCF, & ſub, FH, . i. ad omnia quadrata figuræ, BFMH,
erunt vt quadratum, EM, ad quadratum, MF, rectangulum ſub
{2/3}. EF, & ſub, FM, vna cum {1/6}. quadrati, EF, quod oſtendere opus
erat.

COROLLARIVM.

_H_Inc colligimus omnia quadrata, BM, ad reſiduum, demptis ab
eiſdem omnibus quadratis figuræ, BFMH, eſſe vt quadratum,
EM, ad reſiduum, demptis à quadrato, EM, his omnibus . ſ. quadrato,
FM, rectangulo ſub, MF, & {2/3}. FE, cum {1/6}. quadrati, EF, hoc autem
reſiduum eſt rectangulum ſub, MF, & ſexquitertia, FE, cum {5/@}. qua-
drati, EF; nam ſi à quadrato, EM, dempſeris quadratum, FM, rema-
nebunt duo rectangula ſub, MF, FE, cum quadratum, FE, vlterius ſi à
rectangulo bis ſub, MF, FE, dempſeris rectangulum ſub, MF, & {2/3}.

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