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-
dum.

48. SCHOLIVMI.

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,

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer