Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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tem axim, TX, igitur cyhndrus genitus in reuolutione ex, AX,
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dempto cylindro genito
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ex, CX, ad ſolidum ge-
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nitum in reuolutione ex
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ellipſi, BDMG, erit vt,
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AR, ad ellipſim, BDM
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G; </
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<
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">idem accidet, ſireuo-
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lutio ſiat circa axem pa-
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rallelam ipſi, AC, inclu-
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ſam duabus, FA, RC,
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verſus, A, C, puncta pro-
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ductis: </
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<
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">vocetur autem ſo-
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lidum genitum inreuolu-
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tione ex ellipſi, BDMG, anulus latus ellipticus altera parte ſtrictior.</
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">HInc inſimul patet, quod faſcia ſolida cylindrica (vt ita dicam)
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in reuolutione circa, TX, genita ex, AR, ad anulum geni-
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tum ex ellipſi, BDMG, in eadem reuolutione, eſt vt cylindrus ge-
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nitus ex, AR, dum reuolutio ſit circa, CR, ad anulum ſtrictum el-
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lipticum altera parte latiorem in eadem reuolutione circa, CR, at-
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ellipſi, BDMG, genitum; </
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<
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">nam ambo ſunt, vt, AR, ad ellipſim,
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BDMG, dem patet pro ſolidis ſimilaribus, &</
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">Quia verò dicta fa-
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ſcia ſolida genita ab, AR, ad cylindrum ab eodem, AR, genitum
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eſt, vt reſiduum quadrati, FX, dempto quadrato, RX, ad quadra-
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tum, FR, eſt. </
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<
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">cylindrus genitus ab, AX, ad cylindrum genitum
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ab, AR, vt quadratum, FX, ad quadratum, FR, cylindrus item
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genitusà, CX, ad eundem cy ndrum genitum ab, AR, eſt vt qua-
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dratum, RX, ad quadratum, RF, ergo hoc cylindro dempto à cy-
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lindro genito ab, AX, reliqua faſcia ſolida genita ex, AR, ad cy-
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lindrum genitum ex eodem, AR, erit vt reſiduum quadrati, FX, ab
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eo dempto quadi
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ato, RX, ad quadratum, FR, hanc ergo ratio-
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nem habebit etiam anulus latus ellipticus altera parte ſtrictior ad
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anulum ſtrictum ellipticum altera parte latiorem ex eadem ellipſi, B
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DMG, genitum; </
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">quia vero reſiduum quadrati, FX, dempto qua-
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drato, RX, eſtrectangulum ſub, XR, RF, bis cum quadrato, FR,
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ideſt rectangulum ſub, XF, FR, cum rectangulo ſub, XR, RF, .</
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</
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">iub, FR, ideò dictus
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anulus latus ad dictum anulum ſtrictum, erit vt rectangulum ſub
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compoſita ex, RX, XF, & </
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<
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vt compoſita ex, FX, XR, ad, RF, nempè vt, VR, ad, RF.</
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