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

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268
Mathematical Principles
Book I.

ſituation to thoſe two ſolids, will be attracted by them will be to each other as the diameters of the ſolids.

Proposition LXXIII. Theorem XXXIII.

If to the ſevaral points of a given ſphere there tend equal centripetal forces decreaſing in a duplicate ratio of the diſŧances from the points; I ſay that a corpuſcle placed within ſphere is attracted by a force proportional to its diſŧance from the centre.

Plate 21, Figure 6
Plate 21, Figure 6

In the ſphere ABCD (Pl. 21. Fig. 6.) deſcribed about the centre S, let there be placed the corpuſcle P; and about the ſame centre S, with the interval SP, conceive deſcribed an interior ſphere PEQF. It is plain (by prop. 70.) that the concentric ſphærical ſupericies of which the difference AEBF of the ſpheres is compoſed, have no effect at all upon the body P; their attractions being deſtroyed by contrary attractions. There remains therefore only the attraction of the interior ſphere PEQF And (by prop. 72.) this is as the diſtance PS. Q. E. D.

Scholium

By the ſuperficies of which I here imagine the ſolidg compoſed, I do not mean ſuperficies purely