mathematical, but orbs ſo extreamly thin, that their thickneſs is as nothing; that is, the evaneſcent orbs; of which the ſphere will at laſt conſiſt, when the number of the orbs is increaſed, and their thickneſs diminiſhed without end. In like manner, by the points of which lines, ſurfaces and ſolids are ſaid to be compoſed, are to be underſtood equal particles whoſe magnitude is perfectly incoſsiderable.
Proposition LXXIV. Theorem XXXIV.
The ſame things ſuppoſed, I ſay that a corpuſcle ſituate without a force reciprocally proportional to the ſquare of its diſtance form the centre.
For ſuppoſe the ſphere to be divided into innumerable concentric ſphærical ſuperficies, and the attractions of the corpuſcle ariſing from the ſeveral ſuperficies will be reciprocally proportional to the ſquare of the diſtance of the corpuſcle from the centre of the ſphere (by prop. 71.) And by compoſition, the ſum of thoſe attractions, that is, the attraction of the corpuſcle towards the entire ſphere, will be in the ſame ratio. Q. E. D.
Cor. 1. Hence the attractions of homogeneous ſpheres at equal diſtances from the centres will be as the ſpheres themſelves. For (by prop. 72.) if the diſtances be proportional to the diameters of the ſpheres, the forces will be as the diameters. Let
