Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

82. PROPOSITIO XXXIX.

Datis ijſdem, quœ in antecedenti propoſitione in primo
ſehemate, datur centrum æquilibrij figuræ in
linea, quæ eſt radius rotationis.

SEd dentur eadem, quæ ſupra in primo ſchema-
te. Dico dari in D C, quæ eſt radius rotatio-
nis, centrum æquilibrij ſemifiguræ D B C. Cum
enim exanteced. propoſit datis ijs, detur etiam ra-
tio cylindri ad alterum ſolidorum. Ergo dabitur e-
tiam ratio ſolidorum ad inuicem; nempe dabitur ra-
tio ſolidi A B C, ad ſolidum D B C H V. Sed ex
propoſit. 4. lib. 3. ſolidum ad ſolidum eſt vt pars D C,
terminata à D, & àcentro æquilibrij figuræ D B C,
ad reliquam partem D C. Quare patet propo-
ſitum.

83. PROPOSITIO XL.

Fi ſecundo ſchemate datis ijſdem, & dataratione annu-
li lati ex ſernifigura ad annulum ſtrictum eiuſdem,
dabitur prœdictum centrum.

SEd in ſecundo ſchemate, vltra data in ante-
cedenti, detur etiam ratio annuli lati
D B C Z H ℟, ad annulum ſtrictum exeadem D B C,
reuoluta circa F C. Dico dari eius centrum æqui-

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