Cavalieri, Buonaventura
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Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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<
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">THEOREMA II. PROPOS. II.</
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">SI intra parabolam ducantur vtcunque duæ ad axim, vel
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diametrum eiuſdem ordinatim applicatę lineę, abſciſſæ
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abijſdem parabolæ, erunt inter ſe, vt cubi dictarum linea-
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rum ordinatim applicatarum.</
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<
s
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">Sint ergo intra parabolam circa axim, veldiametrum, CG, con-
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ſtitutam, duæ adipſum ordinatim applicatæ rectæ lineæ, FH, OM,
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parabolas, OCM, FCH, abſc ndentes. </
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<
s
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xml:space
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">Dico ergo parabolam, F
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CH, ad parabolam, OCM, eſſe vt cubum, FH, ad cubum, OM;
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</
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<
s
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xml:space
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">conſtituantur circa axes, vel diametros, CI, CG, & </
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<
s
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echoid-s6991
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xml:space
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preserve
">in eiſdem ba-
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ſibus, OM, FH, cum dictis parabolis parallelogramma, AH, RM. </
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201
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0307-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0307-01
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Quoniam ergo ęquiangula paral
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lelogramma habent rationem ex
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lateribus compoſitam, ſunt au-
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tem parallelogramma, AH, R
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M, æquiangula, nam, OM, eſt
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parallela ipſi, FH, ideò paralle-
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logrammum, AH, ad parallelo-
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grammum, RM, habebit ratio-
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nem compoſitam ex ea, quam ha
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bet, FA, ad, RO, .</
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<
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">i. </
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CI, .</
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<
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xml:space
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">quadratum, FH, ad qua-
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">38. Ec
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Schol. 40.
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lib. 1.</
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dratum, OM, & </
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">ex ea, quam habet, FH, ad, OM, ſed etiam cu-
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bus, FH, ad cubum, OM, habet rationem compoſitam ex ea, quam
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habet quadratum, FH, ad quadratum, OM, & </
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">D. Corol.
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4. Gener.
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34, lib. 2.</
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bet, FH, ad, OM, ergo parallelogrammum, AH, ad parallelo-
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grammum, RM, & </
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<
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">conſequenter parabola, FCH, ad parabolam,
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OCM, (quia ſunt dictorum parallelogrammorum ſubſexquialterę)
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erit vt cubus, FH, ad cubum, OM, quodoſtendere opus erat.</
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<
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">THEOREMA III. PROPOS. III.</
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<
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">SI in parabola ducatur quædam recta linea ad eiuſdem
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axim, vel diametrum ordinatim applicata; </
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inde ipſx
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axi, vel diametro æquidiſtantes rectæ lineævſque
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ad curuam parabolicam, & </
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<
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quæ baſis erit eiuſdem parabolæ; </
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