Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER IV. rallelepipedum ſub, AQ, & his ſpatijs . f. quadrato, PQ {1/2}. quadrati, QZ, & rectangulo ſub ſexquitertia, ZQ, & ſub, Q
P, ab eodem dempta {1/6}. para llelepipedi ſub, CD, & quadra-
to, QP,

Completo parallelogrammo, KP, omnia igitur quadrata trili-
nei, DPG, ad omnia qua-
drata figurę, CAZP, demp tis
omnibus quadratis trilinei, A
CD, habent rationem com-
poſitam ex ea, quam habent
omnia quadrata, DPG, ad
omnia quadrata, DG, . ſ. ex
ratione compoſitæ ex {1/3}. ZP,
& {1/6}. PG, ad, ZP, & ex ratio-
ne omnium quadratorum, D
G, ad omnia quadrata, KP, . i. ex ratione parallelepipedi ſub, D
P, & quadrato, PG, ad parallel epipedum ſub, AQ, & quadrato, Z
P, & tandem ex ratione omnium quadratorum, KP, ad omnia qua-
drata figuræ, CAZP, demptis omnibus quadratis trilinei, ACD,
. f. ex ratione parallelepipedi ſub, AQ, & quadrato, ZP, ad paralle-
pipedum ſub, AQ, & his ſpatijs . ſ. quadrato, PQ, {1/2}. quadrati,
QZ, & rectangulo ſub, PQ, & ſexquitertia, QZ, ab eodem dem-
pta {1/6}. parallelepipedi ſub, CD, & quadrato, PQ; duæ autem ra-
tiones parallelepipedi ſub, DP, & quadrato PG, ad parallelepipe-
dum ſub, AQ, & quadrato, ZP, & huius parallelepipedi ad paral-
lelepipedum ſub, AQ, & ſpatijs iam dictis, ab eodem dempta {1/6}. pa-
rallelepipedi ſub, CD, & quadrato, PQ, componunt rationem pa-
rallelepipedi ſub, DP, & quadrato, PG, ad parallelepipedum ſub,
AQ, & dictis ſpatijs ab eodem dempta {1/6}. parallelepipedi ſub, CD,
& quadrato, PQ, ergo omnia quadrata trilinei, DGP, ad omnia,
quadrata figuræ, CAZP, demptis omnibus quadratis trilinei, AC
D, erunt in ratione compoſita ex ea, quam habet {1/3}. ZP, cum {1/6}. P
G, ad, ZP, & ex ea, quam habet parallelepipedum ſub, DP, & qua-
drato, PG, ad parallelepipedum ſub, AQ, & his ſpatijs . f. quadra-
to, PQ, {1/2}. quadrati, QZ, cum rectangulo ſub, PQ, & ſexquitertia,
QZ, ab eodem parallelepipedo dempta {1/6}. parallelepipedi ſub, CD,
& quadrato, PQ, quod oſtendere opus erat.

487.1.

0363-01
47. huius.
34. huius.
Defin. 12.
l. 1.

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