Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/395

Rh from the body P, and will therefore attract that corpucle equally. And by a like reaoning if the paces DPF, EGCB be divided into particles by the uperficies of innumerable imilar pheroids concentric to the former and having one common axis, all thee particles will equally attract on both ides the body P towards contrary parts. Therefore the forces of the cone DPF, and of the conic egment EGCB are equal and by their contrariety detroy each other. And the cae is the ame of the forces of all the matter that lies without the interior pheroid PCBM. Therefore the body P is attracted by the interior pheroid 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 pheroid AGOD, as the ditance PS to the ditance AS. Q. E. D.

An attracting body being given, it is required to find the ratio of the decreae of the centripetal forces tending to its everal points.

The body given mut be formed into a phere, a cylinder, or ome regular figure whoe, law of attraction anwering to any ratio of decreae may be found by prop. 80. 81 and 91. Then, by experiments, the force of the attractions mut be found at everal ditances, and the law of attraction towards the whole, made known by that means, will give the ratio of the decreae of the forces of the everal parts; which was to be found.