Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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<
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<
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">figura, patet aceruum maio-
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rem parabolicum, HBEON, ad conoidem parabolicam geni-
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tam ex ſemiparabola, BHG, eſſe vt reliquum parallelepiped@ſub,
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GB, & </
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<
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<
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<
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FG, & </
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<
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">ſexquitertia, GH, ab eedẽ dẽpto {1/6}. </
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<
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quadrato, FG, ad dimidiũ parallepepidiſub, @BG, & </
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<
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</
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<
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xml:space
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">vt etiã erit quodlibet ſolidũ ſimilare genitũ ex figura, CBHF, dem-
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pto ſolido ſimilari genito ex trilineo, BCE, ad ſolidum ſibi ſimilare
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genitum ex ſemiparabola, BHG, iuxta communem regulam, HF.</
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xml:space
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">COROLLARIVM XXIV.</
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<
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<
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<
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<
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">fruſtum minus parabo-
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læ, quod eſt, DPG, cum Parallelogrammo, DG, & </
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<
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fig-0381-01
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260
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0381-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0381-01
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baſi parabolæ,
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ZAG, quæ eſt,
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ZG, &</
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<
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ſolitum exem-
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plum, reuolua-
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tur, DG, circa
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manentẽ axim,
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DP, & </
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<
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">iterum
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circa manentẽ
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axim, EG, fiet ergo ex reuolutione circa, DP, à parallelogrammo,
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DG, cylindrus, RG, & </
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<
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">à fruſto parabolæ minori, PDG, ſolidum,
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quod ſit, HDG, quodque vocetur, Aceruus minor parabolicus; </
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ex reuolutione circa; </
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<
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">EG, à parallelogrammo, DG, in alia figura
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cylindrus, DV, & </
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">à trilineo extra fruſtum minus parabolæ conſti-
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tuto ſolidum, DGX@, quod eſt fruſtum apicis parabolici refectum
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per circulum. </
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<
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">DX, quodque vocetur Fruſtum apicis parabolici. </
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tet ergo cylindrum, RG, ad aceruum minorem parabolicu, HDG,
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eſſe vt, ZP, ad compoſitam ex {1/3}. </
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<
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">ZP, & </
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<
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">{1/6}. </
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<
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xml:space
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">PG, ac cylindrum, DV,
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ad fruſtum apicis parabolici, DGX, eſſe vt, ZP, ad ſui reliquum,
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demptis ab ea {2/3}. </
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<
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<
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<
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">Sic autem etiam erit quodlibet
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ſolidum ſimilare genitum ex, DG, ad ſolidum ſibi ſimilare genitum
<
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ex fruſto minori, DGP, vt, inquam, in priori parte huius Theor.
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</
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<
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<
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">ſic etiam ſolidum quodlibet ſimilare genitum ex,
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DG, ad ſibi ſimilare genitum ex trilineo, DEG, iuxta </
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