Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/317

 as the quares of the ditances reciprocally; and then, by increaing the ditance of the great body till the differences of the right lines drawn from that to the others in repect of their length, and the inclinations of thoe lines to each other, be les than any given, the motions of the parts of the ytem will continue without errors that are not les than any given. And becaue by the mall ditance of thoe parts from each other, the whole ytem 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 decribe about the great body one of the conic ections (that is, a parabola or hyperbola when the attraction is but languid, and an ellipis when it is more vigorous) and by radii drawn thereto it will decribe area's proportional to the times, without any errors but thoe which arie from the ditances of the parts, which are by the uppoition exceeding mall, and may be diminihed at pleaure. Q. E. O.

By a like reaoning one may proceed to more compounded caes in infinitum.

In the econd cae, the nearer the very great body approaches to the ytem of two or more revolving bodies, the greater will the perturbation be of the motions of the parts of the ytem among themelves; becaue the inclinations of the lines drawn from that great body to thoe parts become greater; and the inequality of the proportion is alo greater.

But the perturbation will be greatet of all, if we uppose the accelerative attractions of the parts of the ytem towards the greatet body of all are not to each other reciprocally as the