Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/324

 the motion; then in conequentia as far as B; and latly in antecedentia as it moves from B to C.

And from the ame reaoning it appears that the body P, cæteris paribus, moves more wiftly in the conjunction and oppoition than in the quadratures.

The orbit of the body P, cæteris paribus, is more curve at the quadratures than at the conjunction and oppoition. For the wifter bodies move, the les they deflect from a rectilienar path. And beides the force KL, or NM, at the conjunction and oppoition, is contrary the force with which the body T attracts the body P; and therefore diminihes that force; but the body P will deflect the les from a rectilinear path the les it is impelled towards the body T.

Hence the body P cæteris paribus goes farther from the body T at the quadratures than at the conjunction and oppoition. This is aid however, uppoing no regard had to the motion of eccentricity. For if the orbit of the body P be eccentrical, its eccentricity (as will be hewn preently by cor. 9.) will be greatet when the apides are in the yzygies; and thence it may ometimes comme to pas, that the body P in its near approach to the farther apis, may go farther from the body T at the yzygies, than at the quadratures.

Becaue the centripetal force of the central body T, by which the body P is retained in its orbits, is increaed at the quadratures by the addition caued by the force LM, and diminihed at the yzigies by the ubduction caued by the force KL; and by reason the force KL is greater