Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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374354GEOMETRIÆ

22D

TAndem, quod eadem ſolida ſint in tripla ratione tangen-
tium, vel ſecantium parabolas; ſi tangentes ad ſecantes ſe-
miparabolas, ex quibus in reuolutione generantur, habeant ean-
dem rationem.

COROLLARIVM IX.

IN Propoſ. 31. expoſiea figura, & vt fiat noſtrum exemplum re-
uoluto, AC, circa manentem axim, AB, patet ſolidum, quod

255[Figure 255] in reuolutione fit ex trilineo, AD
C, ad ſolidum, quod fit ex trilineo,
MFC, eſſe vt quadratum, AB, ad
quadratum, BE, & vniuerſaliter, ſo-
lidum ſimilare genitum ex, AC,
dempto ſolido ſimilari genito ex ſe-
miparabola, ACB, ad ſibi ſimilare
genitum ex, EC, dempto ſolido ſi-
milari genito ex fruſto, EMCB,
eſſe vt quadratum, AB, ad quadratum, BE, genita, in quam in-
tellige iuxta communem regulam, BC.

COROLL X. SECTIO PRIOR.

IN Prop. 32. expoſita figura, & vt fiat noſtrum exemplum re-
uoluto, AF, circa manentem axim, CF, patebit cylindrum
in reuolutione genitum ex AF, ad ſolidum genitum ex parabola,
DBF, eſſe vt, AF, ad parabolam, DBF, & ita eſſe quodlibet ſo-
lidum ſimilare genitum ex, AF, ad ſibi ſimilare genitum ex figu-
ra, CBDF, dempto ſolido ſimilari genito ex trilineo, BCF; cy-
lindrum verò genitum ex, AF, . ſ. AM, ad ſolidum in reuolutione
genitum ex figura, CBDF, eſſe vt, AF, ad parabolam,

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