Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

librij in D C. Nam eodem modo patebit, dari ra-
tionem ſolidi A B C, ad ſolidum D B C Z H ℟. Sed etiam datur ratio ex hypotheſi, D B C Z H ℟,
ad annulum ſtrictum ex D B C, circa C F. Ergo
ex æquali, dabitur ratio A B C, ſolidi ad prædi-
ctum annulum ſtrictum. Quare ex cit propoſit. 3. dabitur quoque in D C, centrum æquilibrij quæſi-
tum. Quod & c.

84. SCHOLIVM.

Ex his tribus propoſitionibus poſſumus necdum
ex ſola quadratura in finitarum parabolarum inuenire
rationem cylindrorum circumſcripto ũ ad infinitos
fuſos parabolicos; ſed etiam centrum grauitatis in-
finitarum parabolarum. Nam cum in propoſit. 4. lib. 4. & in ſcholijs eiuſdem, oſtenſum ſit in ſchema-
te illius propoſit. data qualibet ſemiparabola R B E,
cuius baſis R E, diameter B E, quæ reuoluatur
cum ſibi circumſcripto parallelogrammo R B, cir-
ca B S: cylindrum R K, eſſe ad ſolidum E R B Z k,
vt parallelogrammum R B, ad ſemiparabolam
E R B, cuius baſis E R, diameter E B, quæ ſit
gradus dupli, gradus ſemiparabolæ reuolutæ circa
S B; patet ex data quadratura infinitarum parabola-
rum, dari rationem cylindri R K, ad annuIum
E R B Z k. Data hac ratione, dabitur etiam ex pro-
poſit. anteced. ratio cylindri R k, velei æqualis or-
ti ex R B, circa R E, ad ſolidum ex E R B, circa

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