from the body P, and will therefore attract that corpuſcle equally. And by a like reaſoning if the ſpaces DPF, EGCB be divided into particles by the ſuperficies of innumerable ſimilar ſpheroids concentric to the former and having one common axis, all theſe particles will equally attract on both ſides the body P towards contrary parts. Therefore the forces of the cone DPF, and of the conic ſegment EGCB are equal and by their contrariety deſtroy each other. And the caſe is the ſame of the forces of all the matter that lies without the interior ſpheroid PCBM. Therefore the body P is attracted by the interior ſpheroid PCBM alone, and therefore (by cor. 3. prop. 71.) its attraction is to the force with which the body A is attracted by the whole ſpheroid AGOD, as the diſtance PS to the diſtance AS. Q. E. D.
Proposition XCII. Theorem XLVI.
An attracting body being given, it is required to find the ratio of the decreaſe of the centripetal forces tending to its ſeveral points.
The body given muſt be formed into a ſphere, a cylinder, or ſome regular figure whoſe, law of attraction anſwering to any ratio of decreaſe may be found by prop. 80. 81 and 91. Then, by experiments, the force of the attractions muſt be found at ſeveral diſtances, and the law of attraction towards the whole, made known by that means, will give the ratio of the decreaſe of the forces of the ſeveral parts; which was to be found.
