Borelli, Giovanni Alfonso - De motionibus naturalibus a gravitate pendentibus

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1
A, B, C, D, E, & F, H, I, K, L, quæ centra grauitatum̨
partium aquæ eſſe intelligantur vt prius, & ductis ad
horizontalem perpendicularibus AG, BV, CN, DO,
FM, H3, &c. pariterque coniunctis rectis DK, CI,
BH. quia anguli ad L, E æquales ſunt in iſoſcele, &
ſunt quoque anguli recti O & T, & hypothenuſæ DE,
KL ſunt inter ſe æquales, ergo in ſimilibus triangulis
DOE, & KTL latera DO, KT æqualia erunt & recta
OE æqualis erit TL, & addita communi TE erit LE
æqualis OT quæ non minus quàm DK biſſecta erit in
puncto Z, propter æquidiſtantiam & æqualitatem la
terum DO, & TK. ſimiliter reliquæ rectæ lineæ NY
& CI æquales erunt prioribus, & biſſectæ in puncto
P, idemque de reliquis dicendum eſt. & quia canales,
& moles aqueæ in eis contentæ AB, & FH, æquales
ſunt, ergo BFH æqualis eſt AF; fiat iam HB ad BQ,
vt BFH ad FH, vel potius vt FA ad AB: quare ſemiſ
ſes antecedentium ad eaſdem conſequentes in eadem
ratione erunt, nempè vt EA ad AB, ita erit XB ad B
Q, & per conuerſionem rationis EA ad EB ſeu AG
ad BV, vel GE ad EV, & tandem vt duplum GM ad
duplum MN erit vt BX ad XQ, ſeu vt VX ad XN,
vel vt BV ad QN. igitur erunt tres continuæ propor
tionales AG, BV, & QN in eadem ratione quam ha
bet MG ad MN, quare vt quadratum MG ad quadra
tum MN, ita erit longitudine AG ad QN ideoquę
duo puncta A & Q in parabola erunt.

Cap. 2. dę
momentis
grauium in
fluido inna
tantium

Conſtat ergo quòd ſi brachia ſiphonis perpendicu
laria fuerint ad horizontem, ſiuè ambo fuerint eiuſ-

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