Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/106



Every body, that moves in any curve line decribed in a plane, and by a radius, drawn to a point either immoveable, or moving forward with an uniform rectilinear motion, decribes about that point areas proportional to the times, is urged by a centripetal force directed to that point.

For every body that moves in a curve line, is (by law 1.) turned aide from its rectilinear coure by the action of ome force that impels it. And that force by which the body is turned off from its rectilinear coure, and is made to decribe, in equal times, the equal leat triangles SAB, SBG, SCD, &c. about the immovable point S, (by prop. 40. book 1. elem. and law 2.) acts in the place B, according to the direction of a line parallel to cC, that is, in the direction of the line BS; and in the place C, according to the direction of a line parallel to dD, that is, in the direction of the line CS, &c. And therefore acts always in the direction of lines tending to the immovable point S. Q. E. D.

And (by cor. 5. of the laws) it is indifferent whether the uperficies in which a body decribes a curvilinear figure be quiecent, or moves together with the body, the figure decrib'd, and its point S, uniformly forwards in right lines.