Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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genitricium figurarum, quales ſunt parabolæ, BDF, CEG, dicta ex
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ijſdem genita iolida iuxta regulas baſes abſciſſarum parabolarum,
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ſi dictæ figuræ ſimiles fuerint inter ſe, vt prædicti circuli, vel ſimi-
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les e lipſes, vel vt omnia quadrata, & </
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rabolis, & </
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">figuris diſtantiarum earundem, regulis ſemper pro vna-
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quaque earundem parabolarum baſibus ſumptis, erunt inter ſe, vt
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quadrata diametrorum abſciſſarum per ducta plana parabolarum,
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intellige tamen reſecantia plana ſemper in ſupradictis eſſe erecta
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plano genitricium figurarum, vt planum per, CG, erectum para-
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bolæ, ADH, plano, ſimiſiter & </
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<
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">quod per, BF, ſiue in conoide, ſiue
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in alijsiam dictis ſolidis, vt ſupradictum eſt genitis.</
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">EXponatur parabola, ACE, circa axim, CM, in baſi, AE, cui
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paraliela ducatur vtcunque, BD, intra ipſam, & </
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">iungatur, BE,
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fig-0371-01
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0371-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0371-01
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ducaturque, RS, diameter parabolæ,
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BRE, & </
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reuo uatur parabola, ACE, circa axim
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manentem, CM, vt fiant conoides
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parabolicæ, ACE, BCD, & </
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">per BE,
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ducatur planum erectum plano para-
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bolæ, ACE, ſcindens fruſtum conoi-
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dis, BAED, in duas portiones, ſcilicer,
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BAE, BDE. </
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">Dico ergo portionem, BAE, ad portionem, BDE,
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(reſecta, CO, æquali ipſi, RS,) eſſe vt quadratũ, MO, cũ rectangulo
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bis ſub, MOC, ad quadratum, ON, cum rectangulo bis ſub, ONC.</
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">Nam conois, ACE, ad conoidem, BRE, eſt vt quadratum, MC,
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ad quadratum, SR, vel ad quadratum, OC, ergo, per conuerſionem
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rationis, & </
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bolicam, ACE, erit vt reſiduum quadrati, MC, dempto quadrato,
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OC, ad quadratum, MC, .</
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bis ſub, MOC, ad quadratum, MC, quod ſerua. </
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dem, ACE, ad conoidem, BRE, diximus eſſe vt quadratum, MC,
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ad quadratum, CO, eadem autem conois, ACE, ad conoidem, BCD,
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eſt vt quadratum, MC, ad quadratum. </
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">CN, ergo conois, ACE, ad
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reliquum dempta conoide, BCD, à conoide, BRE, erit vt idem qua-
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dratum, MC, ad reliquum, dempto quadrato, CN, à quadrato, CO,
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.</
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nois, ACE, ad portionem ſolidam, BDE, vt quadratum, MC, ad
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quadratum, ON, cum rectangulo bis ſub, ONC, erat autem </
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