Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ regulam, ZG, vt in poſteriore dicti Theor. parte dictum eſt.

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529. COROLLARIVM XXV.

IN Propoſitione 48: ſumatur de figura Propoſit. 46. parabola. ZAG, cum baſi, ZG, & axi, AQ, & axi, AQ, & reſecto eius minori fruſto,
DPG, de eiuſdem figura adnuc ſumatur, AXG, trilineum, in quo
ducitur, DE, æquidiſtans ipſi, AX, & ſeorſim ponatur, vt autem fiat
ſolitum exemplum, reuoluatur parabola, ZAG, circa manentem
axim, AQ, & fruſtum minus eiuſdem, quod eſt, DPG, circa, DP,
ex quo fiat aceruus minor, RDG. Inſuper trilineum, AXG, reuo-
luatur circa, GX, vt fiat apex parabolicus, AGZ, & ex GDE, eius
fruſtum, GDY; patet igitur ex ipſa Prop. 48. aceruum minorem,
RDG, ad conoidem parabolicam, ZAG, habere rationem compo-
ſitam ex ea, quam habet compoſita ex {1/3}. ZP, & {1/6}. PG, ad, ZP, & ex ratione parallelepipedi ſub, DP, & quadrato, PG, ad dimidium
parallelepipedi ſub, AQ & quadrato, QG; & ſic etiã eſſe quodlibet
ſolidum ſimilare genitum ex fruſto parabolæ, DGP, ad ſibi ſimila-
re genitum ex ſemiparabola, AQG; iuxta communem regulam,
ZG. Item ex eadem Prop. patet apicem parabolicum, AGZ, ad
eius fruſtum, DGY, habere rationem compoſitam ex ea, quam
habet ſexta pars parallelepipedi ſub AQ, & quadrato, QG, ad pa-
rallelepipedum ſub, DP, & quadrato, PG, & ex ea, quam habet,
ZP, ad reſiduum, demptis ab eadem, ZP, {2/3}. ZP, cum {1/6}. PG: Sic
autem quoque erit quodcunque ſolidum ſimilare genitum ex trili-
neo, AXG, ad ſibi ſimilare genitum ex trilineo, GDE, iuxta com-
munem regulam, AX.

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