Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/352

268 ituation to thoe two olids, will be attracted by them will be to each other as the diameters of the olids.

If to the evaral points of a given phere there tend equal centripetal forces decreaing in a duplicate ratio of the diŧances from the points; I ay that a corpucle placed within phere is attracted by a force proportional to its diŧance from the centre.

In the phere ABCD (Pl. 21. Fig. 6.) decribed about the centre S, let there be placed the corpucle P; and about the ame centre S, with the interval SP, conceive decribed an interior phere PEQF. It is plain (by prop. 70.) that the concentric phærical upericies of which the difference AEBF of the pheres is compoed, have no effect at all upon the body P; their attractions being detroyed by contrary attractions. There remains therefore only the attraction of the interior phere PEQF And (by prop. 72.) this is as the ditance PS. Q. E. D.

By the uperficies of which I here imagine the olidg compoed, I do not mean uperficies purely