Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/111

 imple, or, according to cor. 2. of the laws, compounded out of everal forces) we ubduct (by the ame cor.) that whole accelerative force, by which the other body is urged; the whole remaining force by which the firt body is urged, will tend to the other body T, as its centre.

And, if thee areas are proportional to the times nearly, the remaining force will tend to the other body T nearly.

And vice vera, if the remaining force tends nearly to the other body T, thoe areas will be nearly proportional to the times.

If the body L, by a radius drawn to the other body T, decribes areas, which compared with the times, are very unequal; and that other body T be either at ret or moves uniformly forward in a right line: the action of the centripetal force tending to that other body T, is either none at all, or it is mix'd and compounded with very powerful actions of other forces: and the whole force compounded of them all, if they are many, is directed to another (immovable or moveable) centre. The ame thing obtains, when the other body is moved by any motion whatoever; provided that centripetal force is taken, which remains after ubducting that whole force acting upon that other body T.

Becaue the equable decription of areas indicates that a centre repected by that force with which the body is mot affected, and by which it is drawn back from its rectilinear motion, and retained in its orbit;