Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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Cap. 11. gra
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uia in fluido
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velocitati
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bus inæqua
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libus ferri
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debere.</
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PROP. CCXXXIX.
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Si à terminis duarum librarum æqualium, & æqualium
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radiorum duo pondera æqualia pendeant, ſed oppoſitis
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minora, pendulum prioris libræ ad pendulum poſterioris
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proportionem compoſitam habebit ex ratione differentiæ
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priorum ponderum ad eorum ſummam, & ex ratione
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ſummæ posteriorum ad differentiam eorumdem
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ponderũ
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.
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">SInt duæ libræ æquales AB, & NO bifariàm ſectæ
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in fulci mentis C, & K, atque ex A pendeat ma
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ius pondus D, ex N verò minus pondus G, atque iņ
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B, & O ſuſpendantur duo
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põ-dera
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dera</
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æqualia E, & M,
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quorũ
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ſingula minora ſint quàm D,
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vel G;
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reperiãturque
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duo ea
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rum centra grauitatum F, &
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H; dico pendulum CF ad K
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H proportionem
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compoſitã
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habere ex ratione ponderis D minus E ad D plus E,
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& ex ratione G plus M ad G minus M;
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quoniã
">quoniam</
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AC ad
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CF eſt vt D plus E ad D minus E (ex præcedenti) er
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go inuertendo FC ad CA, ſeu ad ei æqualem KN
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eã-dem
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dem</
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proportionem habet
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quã
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D minus E ad D plus
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E, & NK ad KH eamdem proportionem habet,
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quã
">quam</
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G plus M ad G minus M; habet verò FC ad HK pro
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portionem compoſitam ex ratione FC ad CA, ſeu ad
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NK, & ex ratione KN ad KH, ergo FC ad KH com
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poſitam proportionem habebit ex ijſdem proportio
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nibus D minus E ad D plus E, & ex G plus M ad G
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minus M. </
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