Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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compoſitam ex duabus rationibus ibidem appoſitis. </
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<
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fiat noſtrum exemplum, intelligatur in ipia (in qua dimittantur
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aſymptoti, & </
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<
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">rectæ, ad, DC, OV, VX, PO, PX,) BD, eſſe axem,
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circa quam reuoluatur figura, vt ex hypeibola, ADC, fiat conois
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hyperbolica, ADC; </
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<
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">vlterius per,
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OX, traducatur planum, OX, ere-
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ctum plano genitricis hyperbolæ,
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ADC, cuius pars in conoide con-
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cepta erit ellipſis, OX, cuius maior
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diameter, OX, minor autem in fi-
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gura propoſitionis linea, PO, ha-
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bemus igitur ex Prop. </
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<
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dem, ADC, ad conoidem, OVX,
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habere rationem compoſitam ex
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ratione rectanguli ſub, MB, HI,
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ad rectangulum ſub, RI, FB, & </
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">43. l. 1.
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Coro. 44.
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l. 1.</
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ratione parallelepipedi ſub altitu-
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dine hyperbolæ, ADC, baſi qua-
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drato, AC, ad parallelepipedum ſub altitudine hyperbolæ, OVX,
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baſi autem rectangulo ſub, XO, OP, veluti ſunt omnia quadrata
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hyperbolæ, ADC, regula, AC, ad omnia rectangula hyperbolæ,
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OVX, (regula, OX,) ſimilia rectangulo ſub, XO, OP, ſiue omnes
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circuli eiuſdem ad omnes ellipſes hyperbolæ, OVX, ſimiles ellipſi,
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33. l. 2.</
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cuius coniugati axes, vel diametri ſunt, XO, OP, XO, maior, OP,
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minor, nam omnes dicti circuli ſunt omnia plana conoidis, ADC,
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regula, AC, & </
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<
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">dictæ omnes ellipſes ſunt omnia plana conoidis, O
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VX, eandem autem rationem ſupradictæ comperiemus habere
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quæcunq; </
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">lolida non quidem ſimilaria inter ſe, ſed quorum om-
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nia plana ſint omnes figuræ ſimiles genitricium figurarum, ADC,
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OVX, a quibus genita dicuntur, quæ habeant inter ſeeandem ra-
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tionem ei, quam habet quadratum, AC, ad rectangulum, XOP.</
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BAD, HMQ, patet eorum rationem eſſe compoſitam ex ra-
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tionibus ibi explicatis, vbi videri poterunt. </
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">Quas quidem ratio-
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nes comperiemus etiam habere quæcunq; </
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">ſolida, licet etiam non
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ſimilaria ad inuicem, genita tamen ex eildem figuris, quarum om-
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nes figuræ ſimiles (inter ſe, quę ſunt vnius, vtriuſq; </
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genitricis diſſimiles) habeant eandem rationem, quam </
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