Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/357

Rh one ingle corpucle placed in the centre of this phere. But this attraction is as great, as on the other hand the attraction of the ame corpucle would be, if that were it elf attracted by the everal particles of the attracted phere with the ame force with which they are attracted by it. But that attraction of the corpucle would be (by prop. 74.) reciprocally proportional to the quare of its ditance from the centre of the phere; therefore the attraction of the phere, equal thereto, is alo in the ame ratio. Q. E. D.

The attractions of pheres towards other homogeneous pheres, are as the attracting pheres applied to the quares of the ditances of their centres from the centres of thoe which they attract.

. The cae is the ame when the attracted phere does alo attract. For the everal points of the one attract the everal points of the other with the ame force with which they themelves are attracted by the others again; and therefore ince in all attractions (by law 3.) the attracted and attracting point are both equally acted on, the force will be doubled by their mutual attractions, the proportions remaining.

Thoe everal truths demontrated above concerning the motion of bodies about the focus of the conic ections, will take place when an attracting phere is placed in the focus, and the bodies move without the phere.

Thoe things which were demontrated before of the motion of bodies about the centre of the conic ections take place when the motions are performed within the phere.