Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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BH, ad, CE.</
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ſtituto parallelogrammo ſuper, BH, circa axim, vel
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diametrum, RO, quod ſit, PH, iunctiſque, BR, RH, o-
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ſtendemus parallelogrammum, PH, ad fruſtum parabolæ,
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ASBHIM, eſſe vt, BH, ad, HC, cum, CE; </
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<
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gulum, RBH, ad idem fruſtum eſſe vt, BH, ad duplam,
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HC, CE.</
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">Parallelogrammum enim, PH, eſt ad triangulum, ABH, vt
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dupla, BH, ad ipſam, BH, triangulum verò, ABH, ad ſection-
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culam, ASB, eſt vt, BH, ad, CE, ergo, ex æquali, parallelo-
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grammum, PH, ad ſectionculam, ASB, eſt vt dupia, BH, ad,
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huius.</
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CE, & </
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B, MIH, erit vt dupla, BH, ad
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duplam, CE, ideſt vt, BH, ad, C
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E. </
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ad trapezium, ABHM, eſt vt, B
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H, ad, AM, cum dimidio exceſſus,
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BH, ſuper, AM, . </
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<
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CG, GH, ergo, colligendo, pa-
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rallelogrammum, PH, ad ſectionculas, ASB, MIH, cum trape-
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zio, ABHM, . </
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<
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">ad fruſtum parabolæ, ASBHIM, erit vt, BH,
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ad, HC, cum, CE. </
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<
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">Quia verò triangulum, RBH, eſt dimidium
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parallelogrammi, PH, ideò ad fruſtum, ASBH'IM, erit vt di-
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midia, BH, ad, HC, cum, CE, . </
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E, quod erat oſtendendum.</
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