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Sir Isaac Newton’s BookI.

when it fwings through the greater arch C D, fhall take up inits-Twing from C to D a longer time than in Twinging from Eto F, when it moves only in that leffer arch ; or the time inwhich the body let fall from C will defcend through the archC A is greater than the time, in which it will defcend throughthe arch EA, when let fall from E. But the ftrft: of-the/etimes will not hold the fame proportion to the latter, as thefirft arch C A bears to the other arch E A; which will appearthus. Let C G and E H be two horizontal lines. It has beenremarked above a , that the body in falling through the archC A will acquire as great a velocity at the point A, as it wouldhave gained by falling dire&ly down through GA ; and infalling through the arch E A it will acquire in the point A on-ly that velocity, which it would have got in falling throughH A. Therefore, when the body defcends through the great-er arch C A, it fhall gain a greater velocity, than when it paf-fes only through the leffer; fo that this greater velocity will inTome degree compenfate the greater length of the arch.

yq. The increafe of velocity, which the body acquiresin falling from, a greater height, has fuch an effect, that, ifftraight lines be drawn from A to C and E, the body wouldfall through the longer ftraight line C A juft in the fame time,as through the fhorter ftraight line E A. This is demonftrat-ed by the geometers, who prove, that if any circle, as ABCP(fig. 49.) be placed in a perpendicular fituation; a bodyfhall fall obliquely through every line, as A B drawn from theloweft point A in the circle to any other point in the circunv

Ȥ 20.

ference