Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/355

Rh mathematical, but orbs o extreamly thin, that their thicknes is as nothing; that is, the evanecent orbs; of which the phere will at lat conit, when the number of the orbs is increaed, and their thicknes diminihed without end. In like manner, by the points of which lines, urfaces and olids are aid to be compoed, are to be undertood equal particles whoe magnitude is perfectly incosiderable.

The ame things uppoed, I ay that a corpucle ituate without a force reciprocally proportional to the quare of its ditance form the centre.

For uppoe the phere to be divided into innumerable concentric phærical uperficies, and the attractions of the corpucle ariing from the everal uperficies will be reciprocally proportional to the quare of the ditance of the corpucle from the centre of the phere (by prop. 71.) And by compoition, the um of thoe attractions, that is, the attraction of the corpucle towards the entire phere, will be in the ame ratio. Q. E. D.

Hence the attractions of homogeneous pheres at equal ditances from the centres will be as the pheres themelves. For (by prop. 72.) if the ditances be proportional to the diameters of the pheres, the forces will be as the diameters. Let