Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER III. ergo omnia quadrata, AR, ad omnia quadrata ellipſis, BDMG,
cum rectangulis bis ſub eadem, & ſub trilineis, BCG, GRM, erunt
vt, AR, ad ellipſim, BDMG. Eodem modo, ſumpta pro regula,
CR, oſtendemus omnia quadrata, AR, ad omnia quadrata ellipſis,
BDMG, vna cum rectangulis bis ſub eadem, & ſub trilineis, DAB,
CG, eſſe vt, AR, ad ellipſim, BDMG, quod oſtendere oportebat.

353.1.

Coroll. 1.
26. lib. 2.
A. 23. 1. 2.
0274-01
Exantec.

354. COROLLARIVM.

_H_Inc babetur omnia quadrata, AR, regula, FR, ad omnia quadra@
ta ellipſis, BDGM, vna cum rectangulis bis ſub eadem, & ſub
trilineis, BCG, GRM, eſſe vt omnia quadrata, AR, regula, CR, ad
omnia quadrata ellipſis, BDMG, vna cum rectangulis bis ſub eadem,
& ſub trilineis, DAB, BCG; vtraq; enim oſtenſa ſunt eſſe, vt, AR,
ad ellipſim, BDMG.

355. THEOREMA XXXII. PROPOS. XXXIII.

ASſumpta antecedentis figura, dimiſſis lineis, EG, DV,
producantur ad eandem partem, AC, FR, in, TX,
ita vt, AT, ſit æqualis, FX, & iungatur, TX, ergo ipſa, A
X, CX, erunt parallelogramma. Dico igitur, omnia qua-
drata, AR, cum [?] rectanguli [?] s bis ſub, AR, RT, ad omnia
quadrata ellipſis, BDMG, cum rectangulis bis ſub eadem,
& quadrilineo, BGMXT, eſſe vt, AR, ad ellipſim, BDM
G, regula, FX.

Omnia. n. quadrata, AR, ad rectangula bis ſub ellipſi, BDMG,
& ſub trilineis, BCG, GRM, vna cum
omnibus quadrati [?] s eiuldem ellipſis, BD
MG, ſunt vt, AR, ad ellipſim, BDM
G, item rectangula ſub, AR, RT, ad re-
ctangula ſub ellipſi, BDMG, & ſub, R
T, ſunt vt, AR, ad ellipſim, BDMG,
& eadem bis ſumpta ſunt pariter, vt, AR,
ad ellipſim, BDMG, ergo omnia qua-
drata, AR, cum rectangulis bis ſub, A
R, RT, ad omnia quadrata ellipſis, B
DMG, cum rectangulis bis ſub eadem, & ſub trilineis, BCG,
GRM, & cum rectangulis bis ſub eadem, & ſub, RT, ideſt cum

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