Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

25. PROPOSITIO XII.

Si fiat vt ſemihyperbola ad dimidium parallelogrammi ſibi
circumſcripti, ſic compoſita ex ſemilatere tranſuerſo hy-
perbolæ, & ex tertia parte axis eiuſdem, ad aliam: dein-
de fiat vt compoſita ex latere tranſuerſo & ex axi, ad
inuentam, ſic baſis ſemihyperbolæ ad ſui partem abſcin-
dendam incipiendo ab axi. Centrum grauitatis ſemihy-
perbolæ erit in line a per punctum ducta axi parallela.

ESto hyperbola A B C, cuius axis B E; centrum
G; latus tranſuerſum F B; parallelogrammum
ei circumſcriptum ſit D C; ſitque B H, tertia pars
B E; & fiat vt A B E, ad dimidium D E, ſic G H,
ad E k; & pariter fiat vt F E, ad E k, ſic A E, ad
E L; ac per L, ducatur L M, parallela B E. Dico
in M L, eſſe centrum grauitatis ſemihyperbolæ
A B E. Intelligamus D E, cum ſemihyperbola. A B E, rotari circa B E. Quoniam ex propoſit. 5. 7. & 11. cylindrus D C, eſt ad conoides A B C, vt
F E, ad G H; & ratio F E, ad GH (de foris ſumpta
E k) componitur ex rationibus F E, ad E k, & hu-
ius ad G H. Ergo etiam ratio cylindri ad conoides
componetur ex ijſdem rationibus. Sed ex ſchol. 1. propoſit. 3. lib. 3. ratio cylindri ad conoides compo-
nitur etiam ex ratione dimidij D E, ad A B E, & ex
ratione A E, ad interceptam inter E B, & centrum
æquilibrij A B E, ſeù grauitatis duplicatæ A B E,

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