Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

755. 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.

Sumatur . n. de illius ſchemate
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
G, quod oſtendendum erat.

755.1.

0561-01
Cor. I. 13.
hu.u.s

756. ANNOTATIO.

PRop. 46. igitur reſtaurata, ſtylo noſtro ſequentium propoſitio-
num demonſtrationes proſequemur ab hac vſque a d 51. inclu-
fiuè, quæ quidem veritatem habere comperitur ex prop. 22. hu us. Scholium autem ſequens retineatur vt ib, ſubſtituendo tamen no-
mini omnium ſimilium figurarum hocaliud, nempe quotcunque
ſimiles figuras & c. vt in examine lib. 3. animaduerſum eſt. His ve-
rò prædemonſtratis ſubſequentia Corollaria vſq; ad finem lib. 4. ſo-
lita nominum mutatione facta, cuncta facillimè deducentur per
iam oſtenſa circa quadrata, ſeu rectangula ſolida ſub talibus, & ta-

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