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

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355335LIBER IV. quadrata figuræ, CBNP, demptis omnibus quadratis quadrilinei, B
CPO;
& vtraque eſſe, vt cubum, DF. ad cubum, NO.
11_Ex 2. hu-_
_ius._
THEOREMA XXXIX. PROPOS. XLI
INeiſdem figuris oſtendemus, regulis adhuc ipſis, DM,
DF, omnia quadrata figuræ, CBDF, ad omnia quadra-
ta figuræ, CBNP, eſſe vt parallelepipedum ſub, BE, &

{1/2} {1/2}.
quadrati ipſius, DF, ad parallelepipedum ſub, BX, &
his ſpatijs ſimul compoſitis .
ſ. quadrato, XP: 1. quadrati,
NX, &
rectangulo ſub ſexquitertia, NX, & ſub, XP; Om-
nia verò quadrata figuræ, HBDM, ad omnia quadrata fi-
guræ, HBNV, eſſe vt parallelepipedum ſub, BE, &
his
ſpatijs .
ſ. quadrato, ME, 1. quadrati, ED, & rectangulo
ſub ſexquitertia, DE, &
ſub, EM, ad parallelepipedum ſub,
BX, &
his ſpatijs . ſ. quadrato, VX, 1. quadrati, XN, & re-
ctangulo, ſub ſexquitertia, NX, &
ſub, XV.
Ducatur per, N, ipſi, BE, parallela, NQ, in vtraq; figura, igi-
240[Figure 240] tur omnia quadrata
figuræ, CBDF, ad
omnia quadrata figu-
ræ, CBNP, habẽt ra-
tionem compoſitam
ex ea, quam habent
omnia quadrata figu-
ræ, CBDF, ad om-
nia quadrata, AF, .
i.
ex ea, quam habent
{3/2} {7/4}.
quadrati, DF, ad
quadratum, DF, &
ex ratione omnium quadratorum, AF, ad om-
2232. huius nia quadrata, AP, .
i. ex ratione, EB, ad, BX, & ex ratione om-
nium quadratorum, AP, ad omnia quadrata, QP, .
i. ex ratione
quadrati, GP, vel quadrati, DF, ad quadratum, PN, &
tandem
ex ratione omnium quadratorum, QP, ad omnia quadrata figurę, C
3334. huius. BNP, .
i. ex ratione quadrati, NP, ad quadratum, PX, cum {1/2}. quadra-
ti, XN, &
cum rectâgulo ſub ſexquitertia, NX, & ſub, XP, harum au-
tem rat onum iſtæ .
ſ. quam habent {1/2} {7/4}. quadrati, DF, ad quadratum,
DF, quadatum, DF, ad quadratum, NP, &
quadratum, NP, ad hęc
ſimul .
ſ. quadratum, PX, @. quadrati, NX, & rectangulum ſub ſex.

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