Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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A, B, C, D, E, & F, H, I, K, L, quæ centra grauitatum̨
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partium aquæ eſſe intelligantur vt prius, & ductis ad
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horizontalem perpendicularibus AG, BV, CN, DO,
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FM, H3, &c. </
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<
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">pariterque coniunctis rectis DK, CI,
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BH. quia anguli ad L, E æquales ſunt in iſoſcele, &
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ſunt quoque anguli recti O & T, & hypothenuſæ DE,
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KL ſunt inter ſe æquales, ergo in ſimilibus triangulis
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DOE, & KTL latera DO, KT æqualia erunt & recta
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OE æqualis erit TL, & addita communi TE erit LE
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æqualis OT quæ
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minus quàm DK biſſecta erit in
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puncto Z, propter æquidiſtantiam & æqualitatem la
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terum DO, & TK. ſimiliter reliquæ rectæ lineæ NY
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& CI æquales erunt prioribus, & biſſectæ in puncto
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P, idemque de reliquis
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eſt. </
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">& quia canales,
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& moles aqueæ in eis contentæ AB, & FH, æquales
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ſunt, ergo BFH æqualis eſt AF; fiat iam HB ad BQ,
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vt BFH ad FH, vel potius vt FA ad AB: quare ſemiſ
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ſes antecedentium ad eaſdem conſequentes in
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eadẽ
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ratione erunt, nempè vt EA ad AB, ita erit XB ad B
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Q, & per conuerſionem rationis EA ad EB ſeu AG
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ad BV, vel GE ad EV, & tandem vt duplum GM ad
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duplum MN erit vt BX ad XQ, ſeu vt VX ad XN,
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vel vt BV ad QN. igitur erunt tres continuæ propor
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tionales AG, BV, & QN in eadem ratione quam ha
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bet MG ad MN, quare vt quadratum MG ad quadra
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tum MN, ita erit longitudine AG ad QN ideoquę
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duo puncta A & Q in parabola erunt. </
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Cap. 2. dę
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momentis
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grauium in
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fluido inna
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tantium</
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<
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laria fuerint ad horizontem, ſiuè ambo fuerint eiuſ-</
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