Isaac Newton

“ For the attraction of every particle is reciprocally as the square of its distance from the centre of the attracting sphere (by prop. 74.) and is therefore the same as if that whole attracting force issued from 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. ”

“ Plate 22, Figure 5 Suposse a superficies as EFfe (Pl. 22 Fig. 5.) to have its breadth infinitely diminished, and to be just vanishing; and that the same superficies by its revolution round the axis PS describes a sphærical concavo-convex solid to the several equal particles of which there tend equal centripetal forces; I say that the force with which that solid attracts a corpuscle situate in P, is in a ratio compunded of the ratio of the solid and the ratio of the force with which the given particle in the place Ff would attract the same corpuscle. ”

“ 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. ”