Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ parallelogrammo, AG, altitudine, FI, ad cylindricum ſub baſi por-
tione, TCFEY, altitudine, IM, vna cum, {1/6}, cubi, TY. In elli-
pſi verò, vt parallelepipedum ſub baſi parallelogrammo, AG, alti-
tudine, FI, ad cylindricum ſub baſi portione, TCFEY, altitudi-
ne, MI, vna cum ea parte cubi, TY, ad quam eiuſdem cubi ſexta
pars ſit, vt quadratum, CE, primę diametri, ad quadratum ſecun-
dæ . ſ. ad quadratum, FH, vel, ſi diametri non ſint axes, vna cum
ea parte parallelepipedi ſub, TY, & rhombo, RZ, ad quam illius
pars ſexta ſit, vt quadratum, CE, primæ diametri ad quadratum
ſecundæ. Ducantur per, T, Y, ipſi, PQ, parallelæ, Τ Δ, Υ Φ, ſe-
cantes curuam, CFE, in punctis, R, V, quæ iungantur recta, R
V, producta in, B, K, quoniam ergo, EC, eſt diameter, ad quam
ordinatim applicantur, RT, VY, eas
quoq; bifariam ſecabit, eſt autem, ST,
æqualis, XY, ob parallelogrammum,
SY, ergo, VX, erit etiam æqualis ipſi,
RS, & tota, VY, toti, RT, cui etiam
eſt parallela, ergo, RV, TY, ſunt etiam
æquales, & parallelæ, eſtque, RV, in,
M, bifariam ſecta.

342.1.

0258-01

Diuidamus igitur omnia quadrata fi-
guræ, LCFEG, demptis omnibus
quadratis trilineorum, CLT, EGY, in
omnia quadrata figuræ, LCRT, dem-
ptis omnibus quadratis trilinei, LCT,
in omnia quadrata figuræ, GEVY,
demptis omnibus quadratis trilinei, E
GY, & in omnia quadrata figuræ, TR
FVY. Rurſus per rectam, RV, diui-
duntur omnia quadrata figuræ, TRF
VY, in omnia quadrata, YR, in om-
nia quadrata portionis, RFV, & in re-
ctangula bis ſub, YR, & portione, R
FV, his ſeparatis, ad eorum ſingula comparemus nunc omnia qua-
drata parallelogrammi, KG.

342.1.

Per D. 23.
lib. 2.

Igitur omnia quadrata, KG, ad omnia quadrata, RY, ſunt vt,
KB, ad, RV, vel vt parallelogrammum, KG, ad parallelogram-
mum, RY; omnia inſuper quadrata, KG, ad omnia quadrata, K
T, ſunt vt, BK, ad, KR, . i. vt, KG, ad, KT; item omnia qua-
drata, KT, ad omnia quadrata figuræ, LCRT, demptis omnibus
quadratis trilinei, LCT, . i. ad omnia quadrata portionis, RCT,
cum rectangulis bis ſub eadem, & ſub trilineo, CLT, ſunt vt, KT,

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