as the ſquares of the diſtances reciprocally; and then, by increaſing the diſtance of the great body till the differences of the right lines drawn from that to the others in reſpect of their length, and the inclinations of thoſe lines to each other, be leſs than any given, the motions of the parts of the ſyſtem will continue without errors that are not leſs than any given. And becauſe by the ſmall diſtance of thoſe parts from each other, the whole ſyſtem is attracted as if it were but one body, it will therefore be moved by this attraction as if it were one body; that is, its centre of gravity will deſcribe about the great body one of the conic ſections (that is, a parabola or hyperbola when the attraction is but languid, and an ellipſis when it is more vigorous) and by radii drawn thereto it will deſcribe area's proportional to the times, without any errors but thoſe which ariſe from the diſtances of the parts, which are by the ſuppoſition exceeding ſmall, and may be diminiſhed at pleaſure. Q. E. O.
By a like reaſoning one may proceed to more compounded caſes in infinitum.
Cord 1. In the ſecond caſe, the nearer the very great body approaches to the ſyſtem of two or more revolving bodies, the greater will the perturbation be of the motions of the parts of the ſyſtem among themſelves; becauſe the inclinations of the lines drawn from that great body to thoſe parts become greater; and the inequality of the proportion is alſo greater.
Cor 2. But the perturbation will be greateſt of all, if we ſuppose the accelerative attractions of the parts of the ſyſtem towards the greateſt body of all are not to each other reciprocally as the
