Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/358

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If pheres be however diimilar (as to denity of matter and attractive force) in the progres right onward from the centre to the circumference; but every where imilar, at every given diŧance from the centre, on all ides round about; and the attractive force of every point decreaes in the duplicate ratio of the ditance of the body attracted; I ay that the whole force with which one of thee pheres attracts the other, will be reciprocally proportional to the force of the ditance of the centres.

Imagine everal concentric imilar pheres, AB, CD, EF, &c. (Pl. 22. Fig. 1.) the innermot of which added to the outermot may compoe a matter more dene towards the centre, or ubducted from them may leave the ame more lax and rare. Then by prop. 75. thee pheres will attract other imilar concentric phere GH, IK, LM, &c, each the other, with forces reciprocally proportional to the quare of the ditance SP. And by compoition or diviion, the um of all thoe forces, or the exces of any of them above the others; that is, the entire force with which the whole phere AB (compoed of an concentric pheres or of their