Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ T CFEY, regula, TY, ſunt vt rectangulum ſub, FN, & tripla,
N H, . i. vt, {3/4}, quadrati, FH, ad rectangulum ſub, FI, & ſub, I
H N, . i. vt totum quadratum, FH, ad rectangulum ſub, FI, & ſub ſexquitertia ipſarum, IHN, . i. in circulo, vt quadratum, AP,
(quod æquatur quadrato, FH, ) ad
idem rectangulum ideſt ſumpta, FI,
communi altitudine, vt parallelepipe-
dum ſub, FI, & quadrato, AP, . i. vt parallelepipedum ſub, AP. vel, L
G, & parallelogrammo rectangulo
ſub, FI, ſiue, AL, & , LG, ad pa-
rallelepipedum ſub, FI, & ſub baſi
rectangulo ſub, FI, & ſub ſexquiter-
tia, IHN, ergo ex æquali omnia
quadrata figuræ, LCFE G, dem-
ptis omnibus quadratis trilineorum,
CLT, YGE, regula, FI, ad omnia
quadrata portionis, TCFE Y, regu-
la, TY, erunt vt cylindricus ſub, M
I, & ſub portione, TCFE Y, vna
cum, {1/6}, cubi, TY, ad parallelepipe-
dum ſub, FI, & ſub rectangulo ſub,
F I, & ſexquitertia, IHN; & hoc in
circulo.

347.1.

2. huius.
0268-01

In ellipſi autem eadem habebunt
rationem compoſitam exiam dicta ratione . ſ. ex ratione cylindrici
ſub, MI, & ſub portione, TGFE Y, vna cum ea parte cubi, vel
parallelepipedi ſub, RV, & rhombo, RZ, ad quam eiuſdem, {1/6}, ſit
vt quadratum, CE, ad quadratum, FH, ad parallelepipedum,
ſub, LG, & parallelogrammo, AG, & ex ratione quadrati, FH,
ad rectangulum ſub, FI, & ſub ſexquitertia ipſarum, IHN; quas
duas rationes in circulo in vna reſoluimus, quia in eo quadratum,
F H, æquatur quadrato, AP, quod cum in ellipſi non verificetur,
ideò has duas rationes componentes pro ipſa ellipſi retinuimus; quod oſtendere oportebat.

348. THEOREMA XXVII. PROPOS. XXVIII.

IN eadem ſuperioris figura oſtendemus, tum in circulo,
tum in ellipſi, omnia quadrata figuræ, LCFEG, dem-
ptis omnibus quadratis trilineorum, CLT, YGE, regula,

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