Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

pe ex conſtructionē, vt D F, ad F O; & ratio D F,
ad F O (de foris ſumpta F L) componitur ex ratio-
ne D F, ad F L, & huius ad F O. Ergo etiam ra-
tio cylindri prædicti ex G C, ad ſolidum ex exceſſu
G C, ſupra hyperbolam componetur ex ijſdem ra-
tionibus. At ex ſchol. prim. propoſit. 3. lib. 3. ratio
prædicti cylindri ad antedictum ſolidum componi-
tur etiam ex ratione parallelogrammi G D, ad figu-
ram A G H C B, & ex ratione D F, ad interceptam
inter F, & centrum grauitatis figuræ A G H C B. Ergo etiam rationes D F, ad F L, & F L, ad FO,
erunt æquales rationibus G D, ad A G H C B, & D F, ad prædictam interceptam. Sed ex conſtru-
ctione, rationes G D, ad A G H C B, & D F, ad
F L, ſunt æquales. Ergo ſi hæ rationes auferantur à
prædictis, etiam reliquæ erunt æquales. Ergo ratio
L F, ad F O, erit æqualis rationi D F, ad interce-
ptam prædictam. Sed factum fuit ſupra vt L F, ad
F O, ſic D F, ad F k. Ergo k, erit centrum gra-
uitatis figuræ A G H C B. Quod erat oſtenden-


Inuento autem centro prædicto, facile erit etiam
centrum grauitatis hyperbolæ reperire. Si enim
ſupponamus F D, ſectam bifariam in O, & ſuppo-
namus k, eſſe centrum grauitatis figuræ A G H C B,
ſi fiat vt A B C, ad A G H C B, ſic reciprocè k O,


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