Borelli, Giovanni Alfonso - De motionibus naturalibus a gravitate pendentibus

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Cap. 2. de
momentis
grauium in
fluido inna
tantium

Cap. 2. dę
momentis
grauium in
fluido inna
tantium

PROP. IV.

In canali seu ſiphone habente duo brachia directa, &
perpendiculariter eleuata ad horizontem, fluidi
in eo deſcendentis centrum grauitatis cur
uo itinere per lineam parabolicam
deſcendit.

IN ſiphone TFGV ſint duo canales TF & GV pa
ralleli inter ſe, & erecti perpendiculariter ad ba
ſim FG, & ad horizontem, & quilibet eorum æquè
craſſus ſit; capacitas verò portionis cylindri TF ſu
pra horizontalem per V eductam vt eſt TA in primo
caſu, & TC in ſecundo, ſit æqualis

7[Figure 7]
capacitati GV, quæ ſecetur iņ
quotcumque partes æquales à qua
ternario menſuratas in X, Y, Z, I,
L, 2, & puncta A, B, C, D, E, ſint
centra grauitatum cylindrorum T
F, XF, YF, ZF, & AF, vel CF, pa
riterque H, I, K, L ſint centra gra
uitatum cylindrorum GI, GL, G2,
GV, & quia centra grauitatum A,
& B, bifariam ſecant cylindros T
F, XF, ergo TF ad XF ſe habet vt
AF, ad BF, & per conuerſionem̨
rationis, & permutando TF ad AF
eamdem rationem habet, quàm TX ad AB, quarę
AB ſemiſſis eſt ipſius TX, non ſecus ac HG mediatas

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