Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

analogum cum figura A B C, conſtante ex duabus
ſemiparabolis. Ergo & quatuor ſolida ſecundæ fi-
guræ ſimul erunt proportionaliter analoga cum fi-
gura A B C. Sed ex ſchol. 2. propoſit. 2. lib. 3. cen-
trum grauitatis figuræ A B C, ſic diuidit B D, vt
pars terminata ad B, ſit ad partem terminatam ad
D, vt numerus parabolæ ternario auctus ad nume-
rum parabolæ vnitate auctum. Ergo & centrum gra-
uitatis quatuor ſolidorum ſecundæ figuræ ſimul ſic
ſecabit V X, vt pars terminata ad V, ſit ad partem
terminatam ad X, vt numerus parabolæ ternario
auctus ad numerum parabolæ vnitate auctum. Sup-
ponatur à perito geometra, ſic diuiſa in ℟. Item ex
propoſit. 18. lib. 4. de infin. parab. conſtat centrum
grauitatis ſolidi ex ſemiparabola D B C, in prima
figura circa C F, ſic diuidere F C, vt pars termi-
nata ad F, ſit ad partem terminatam ad C, vt
duplus numerus parabolæ ternario auctus, ad du-
plum numerum vnitate auctum. Ergo & centrum
grauitatis ſolidorum extremorum in ſecunda figura,
ſic ſecabunt lineas circa quas ſemiparabolæ intelli-
guntur reuolutæ. Cum ergo talia ſolida ſint ex inſti-
tuto ſic diſpoſita, vt commune amborum centrum
grauitatis cadat in V X: ſi ergo V X, ſic diuida-
tur in +, vt V +, ſit ad + X, vt duplus nume-
rus parabolæ ternario auctus, ad duplum numerum
parabolæ vnitate auctum; + erit centrum grauita-
tis illorum ſolidorum ſimul. Cum ergo in VX, ſit
centrum grauitatis tam quatuor ſolidorum ſimul,

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