Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

ſecetur in P, vt Q P, ſit ad P L, vt dimidia G B, ad
tertiam partem B D. Dico P, eſſe centrum graui-
tatis conoidis hyperbolici A B C. Inſcribantur co-
noides parabolicum E B F, & coni, vt factum eſt ſu-
pra. Quoniam ex ſchol. 2. propoſit 4. Q, eſt cen-
trum grauitatis tam differentiæ conorum, quam dif-
ferentiæ conoideorum, & vt oſtenditur à multis, & etiam à nobis lib. 4. propoſit. 14, L, eſt centrum
grauitatis conoidis parabolici E B F; ergo ſi L Q, ſic
diuidatur in P, vt ſit reciprocè Q P, ad P L, vt co-
noides E B F, ad differentiam conoideorum, erit P,
centrũ grauitatistotius conoidis hyperbolici A B C. Sed vt conoides E B F, ad differentiam conoi-
deorum, ſic dimidia G B, ad tertiam partem D B,
vt ſtatim patebit. Ergo patet propoſitum.

Aſſumptum vero patet ex dictis. Quia facile pa-
tebit conoides E B F, eſſe ad differentiam conoi-
deorum, ſeù ad differentiam conorum, vt dimidium
quadrati D E, ad tertiam partem rectanguli A E C. Sed cum ex data hypotheſi, ſit diuidendo, & con-
uertendo, quadratum D E, ad rectangulum A E C,
vt G B, ad B D. Erit & vt dimidium quadrati D E,
ad tertiam partem rectanguli A E C, ſic dimidia
G B, ad tertiam partem B D.

28. SCHOLIV M.

Siquis verò ſcire cupiat, in qua proportione ſece-
tur tota B D, à centro grauitatis P, hoc tali diſcur-

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