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

561541LIBER VII.

THEOREMA XXVI. PROPOS. XXVI.

IN figura prop. 46. oſtendemus, regula eadem retenta, re-
ctangulum ſolidum ſub, HP, PE, duplum eſſe rectangu-
liſolidi ſub, BZPD, DPG.

368[Figure 368] parallelogrammum, HG, cum fru-
ſto parabolæ, BZGD, & rectis, R
F, DP, fiat autem inſuper, AP,
æqualis, PD, & ducta, AM, paral-
lela, DP, iungatur, AD, ſecans, C
T, in, N. Cum ergo in dicta prop.
independenter ab indiuiſibilium methodo, cõcludatur rectangulũ’,
RTF, ad, STI, eſſe vt, PD, ad, DT, idpſum & hic tanquã demonſtra-
tũ reci piemus, ſed, PD, ad, DT, hoc eſt, CT, ad, TN, eſt vt quadra-
tum, CT, ad rectangulum, CTN, ergo rectangulum, RTF, ad, STI,
erit vt quadratum, CT, ad rectangulum, CTN, eſt autem, RF, vt-
cumq; ducta parallela, ZG, ergo modo conſueto oſtendemus ſoli-
dum rectangulum ſub, HP, PE, eſſe proportionaliter analogum
quadrato ſolido, MP, ſicut rectangulum ſolidum ſub, BZPD, DP
G, eſſe proportionalites analogum rectangulo ſolidoſub, MP, PA
D, & tandem concludemus hæc ſolida eſſe proportionalia, ideſt
rectangulum ſolidum ſub, HP, PE, ad rectang. ſolidum ſub, BZPD,
DPG, eſſe vt quadratum ſolidum MP, ad rectangulum ſolidum ſub,
MP, PDA, ideſt vt, MP, ad, PDA, ideſt concludemus rectangulum
ſolidum ſub, HP, PE, duplum eſſe rectanguli ſolidi ſub, BZPD, PD
11Cor. I. 13.
hu.u.s G, quod oſtendendum erat.