Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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lineæ erunt interſe, vtrectangula ſub partibus baſis ab ei-
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ſdem æquidiſtantibus conſtitutis.</
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<
s
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">Sit ergo parabola, FCH, circa axim, vel diametrum, CG, ad
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quam ordinatim applicetur recta linea vtcunq; </
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">FH, ducantur dein-
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de intra parabolam axi, vel diametro, CG, parallelæ vtcunque, A
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N, MO, baſim, FH, in punctis, N, O, diuidentes. </
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<
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ctam, AN, ad rectam, MO, eſſe vt rectangulum, FNH, ad re-
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ctangulum, FOH; </
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<
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">ducatur per, M, ipſi, FH, parallela, MI; </
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ergo, GC, ad, CI, vt quadratum, GH, ad quadratum, IM, vel
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40. lib. 1.</
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ad quadratum, GO, ergo, perconuerſionem rationis, GC, ad, G
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0308-01
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I, vel ad, MO, erit vt quadratum, H
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G, ad ſuireliquum, dempto quadrato,
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GO, hoc autem reſiduum eſt rectan-
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gulum ſub, GOH, bis, vna cum qua-
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drato, OH, quod eſt æqualerectan-
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gulo, FOH, nam rectangulum, GO
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H, cum quadrato, OH, æquatur re-
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ctangulo, GHO, .</
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<
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FG, OH, cui ſi iunxeris rectangulum
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ſub, GO, & </
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<
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">eadem, OH, conſurget
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integrum rectangulum, FOH, æqualerectangulis ſub, GOH, bis,
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vna cum quadrato, OH, ergo, CG, ad, MO, erit vt quadratum,
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GH, .</
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uertendo, MO, ad, CG, erit vtrectang. </
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GF; </
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<
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">codem modo oſtendemus, CG, ad, AN, eſſe vt idem rectan-
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gulum, HGF, ad rectangulum, FNH, ergo ex æquali, & </
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<
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tendo, AN, ad, MO, erit vt rectangulum, FNH, ad rectangulum,
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FOH, quod oſtendere oportebat. </
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<
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MO, ordinatim applicatæ ad baſim parabolæ, FCH, ſcilicet ad
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ipſam, FH.</
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cta linea, ſiat autem parallelogrammum, & </
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habentia circa communem angulum dictam applicatam, & </
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abſciſſam à baſiab vtrauis extremitatum eiuſdem, vel ſint
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duæ ad baſim vtcunque ordinatim applicatæ, ſub alterutra
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quarum, & </
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logrammum, & </
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