Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/386

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298
Mathematical Principles
Book I.

particles of any body whatever RSTV, is the ſame as if the body, without removing its centre of gravity, were to put on the form of a globe. Q. E. D.

Cor. Hence the motion of the attracted body Z will be the ſame, as if the attracting body RSTV were ſphærical; and therefore if that attracting body be either at reſt, or proceed uniformly in a right line; the body attracted will move in an ellipſis having its centre in the centre of gravity of the attracting body.


Proposition LXXXIX. Theorem XLVI.

If there be ſeveral bodies conſiſting of equal particles whoſe forces are as the diſtance of the places from each; the force compounded of all the forces by which any corpuſcle is attracted, will tend to the common centre of gravity of the attracting bodies; and will be the ſame as if thoſe attracting bodies, preſerving their common centre of gravity, ſhould unite there, and be formed into a globe.

This is demonſtrated after the ſame manner as the foregoing propoſition.

Cor. Therefore the motion of the attracted body will be the ſame as if the attracting bodies, preferring their common centre of gravity, ſhould