Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/309

 S + P and S to S + P. And inverely the principal axis of the ellipis decribed about the moveable body, will be to the Principal axis of that decribed round the immoveable, as S + P to the firt of two mean proportionals between S + P and S. Q. E. D.

If two bodies attracting each other with any kind of forces, and not otherwie agitated or obtructed, are moved in any manner whatoever; thoe motion: will he the ame, as if they did not at all attract each other mutually, but were both attracted with the ame forces by a third body placed in their common centre of gravity; and the law of the attracting forces will be the ame in repect of the ditance of the bodies from the the common centre, as in repect of the ditance between the two bodies.

For thoe forces with which the bodies attract each other mutually, by tending to the bodies tend alo to the common centre of gravity lying directly between them; and therefore are the ame as if they proceeded from an intermediate body. Q. E. D.