Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER III. tem axim, TX, igitur cyhndrus genitus in reuolutione ex, AX,
dempto cylindro genito
ex, CX, ad ſolidum ge-
nitum in reuolutione ex
ellipſi, BDMG, erit vt,
AR, ad ellipſim, BDM
G; idem accidet, ſireuo-
lutio ſiat circa axem pa-
rallelam ipſi, AC, inclu-
ſam duabus, FA, RC,
verſus, A, C, puncta pro-
ductis: vocetur autem ſo-
lidum genitum inreuolu-
tione ex ellipſi, BDMG, anulus latus ellipticus altera parte ſtrictior.

398.1.

0301-01

399. SECTIO II.

HInc inſimul patet, quod faſcia ſolida cylindrica (vt ita dicam)
in reuolutione circa, TX, genita ex, AR, ad anulum geni-
tum ex ellipſi, BDMG, in eadem reuolutione, eſt vt cylindrus ge-
nitus ex, AR, dum reuolutio ſit circa, CR, ad anulum ſtrictum el-
lipticum altera parte latiorem in eadem reuolutione circa, CR, at-
ellipſi, BDMG, genitum; nam ambo ſunt, vt, AR, ad ellipſim,
BDMG, dem patet pro ſolidis ſimilaribus, & c. Quia verò dicta fa-
ſcia ſolida genita ab, AR, ad cylindrum ab eodem, AR, genitum
eſt, vt reſiduum quadrati, FX, dempto quadrato, RX, ad quadra-
tum, FR, eſt. n. cylindrus genitus ab, AX, ad cylindrum genitum
ab, AR, vt quadratum, FX, ad quadratum, FR, cylindrus item
genitusà, CX, ad eundem cy ndrum genitum ab, AR, eſt vt qua-
dratum, RX, ad quadratum, RF, ergo hoc cylindro dempto à cy-
lindro genito ab, AX, reliqua faſcia ſolida genita ex, AR, ad cy-
lindrum genitum ex eodem, AR, erit vt reſiduum quadrati, FX, ab
eo dempto quadi [?] ato, RX, ad quadratum, FR, hanc ergo ratio-
nem habebit etiam anulus latus ellipticus altera parte ſtrictior ad
anulum ſtrictum ellipticum altera parte latiorem ex eadem ellipſi, B
DMG, genitum; quia vero reſiduum quadrati, FX, dempto qua-
drato, RX, eſtrectangulum ſub, XR, RF, bis cum quadrato, FR,
ideſt rectangulum ſub, XF, FR, cum rectangulo ſub, XR, RF, . i. rectangulum ſub compoſita ex, RX, XF, & iub, FR, ideò dictus
anulus latus ad dictum anulum ſtrictum, erit vt rectangulum ſub
compoſita ex, RX, XF, & ſub, FR, ad quadratum, FR, . i. erit
vt compoſita ex, FX, XR, ad, RF, nempè vt, VR, ad, RF.

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