Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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Cap. 2. de
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momentis
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grauium in
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fluido inna
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Cap. 2. dę
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momentis
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grauium in
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PROP. IV.
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In canali seu ſiphone habente duo brachia directa, &
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perpendiculariter eleuata ad horizontem, fluidi
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in eo deſcendentis centrum grauitatis cur
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uo itinere per lineam parabolicam
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deſcendit.
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">IN ſiphone TFGV ſint duo canales TF & GV pa
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ralleli inter ſe, & erecti perpendiculariter ad ba
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ſim FG, & ad horizontem, & quilibet eorum æquè
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craſſus ſit; capacitas verò portionis cylindri TF ſu
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pra horizontalem per V eductam vt eſt TA in primo
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caſu, & TC in ſecundo, ſit æqualis
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capacitati GV, quæ ſecetur iņ
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quotcumque partes æquales à qua
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ternario menſuratas in X, Y, Z, I,
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L, 2, & puncta A, B, C, D, E, ſint
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centra grauitatum cylindrorum T
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F, XF, YF, ZF, & AF, vel CF, pa
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riterque H, I, K, L ſint centra gra
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uitatum cylindrorum GI, GL, G2,
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GV, & quia centra grauitatum A,
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& B, bifariam ſecant cylindros T
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F, XF, ergo TF ad XF ſe habet vt
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AF, ad BF, & per conuerſionem̨
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rationis, & permutando TF ad AF
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eamdem rationem habet, quàm TX ad AB, quarę
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AB ſemiſſis eſt ipſius TX, non ſecus ac HG mediatas </
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