one ſingle corpuſcle placed in the centre of this ſphere. But this attraction is as great, as on the other hand the attraction of the ſame corpuſcle would be, if that were it ſelf attracted by the ſeveral particles of the attracted ſphere with the ſame force with which they are attracted by it. But that attraction of the corpuſcle would be (by prop. 74.) reciprocally proportional to the ſquare of its diſtance from the centre of the ſphere; therefore the attraction of the ſphere, equal thereto, is alſo in the ſame ratio. Q. E. D.
Cor. 1. The attractions of ſpheres towards other homogeneous ſpheres, are as the attracting ſpheres applied to the ſquares of the diſtances of their centres from the centres of thoſe which they attract.
Cor. 2.. The caſe is the ſame when the attracted ſphere does alſo attract. For the ſeveral points of the one attract the ſeveral points of the other with the ſame force with which they themſelves are attracted by the others again; and therefore ſince 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.
Cor. 3. Thoſe ſeveral truths demonſtrated above concerning the motion of bodies about the focus of the conic ſections, will take place when an attracting ſphere is placed in the focus, and the bodies move without the ſphere.
Cor. 4. Thoſe things which were demonſtrated before of the motion of bodies about the centre of the conic ſections take place when the motions are performed within the ſphere.
