S + P and S to S + P. And inverſely the principal axis of the ellipſis deſcribed about the moveable body, will be to the Principal axis of that deſcribed round the immoveable, as S + P to the firſt of two mean proportionals between S + P and S. Q. E. D.
Proposition LXI. Theorem XXIV.
If two bodies attracting each other with any kind of forces, and not otherwiſe agitated or obſtructed, are moved in any manner whatſoever; thoſe motion: will he the ſame, as if they did not at all attract each other mutually, but were both attracted with the ſame forces by a third body placed in their common centre of gravity; and the law of the attracting forces will be the ſame in reſpect of the diſtance of the bodies from the the common centre, as in reſpect of the diſtance between the two bodies.
For thoſe forces with which the bodies attract each other mutually, by tending to the bodies tend alſo to the common centre of gravity lying directly between them; and therefore are the ſame as if they proceeded from an intermediate body. Q. E. D.
