equidiſtant, one on one ſide, the other on the other, from the centre of the ſphere; G and g the interſections of the planes and the axis; and H any point in the plane EF. The centripetal force of the point H upon the corpuſcle P, exerted in the direction of the line PH is as the diſtance PH; and (by cor. 2. of the laws) the ſame exerted in the direction of the line PG, or towards the centre S, is at the length PG. Therefore the force of all the points in the plane EF (that is of that whole plane) by which the corpuſcle P is attracted towards the centre S is as the diſtance PG multiplied by the number of thoſe points, that is as the ſolid contained under that plane EF and the diſtance PG. And in like manner the force of the plane ef by which the corpuſcle P is attracted towards the centre S, is as at plane drawn into its diſtance Pg, or as the equal plane EF drawn into that diſtance P; and the ſum of the forces of both planes as are plane EF drawn into the ſum of the diſtances PG + Pg, that is as that plane drawn into twice the diſtance PS of the centre and the corpuſcle; that is, as twice the plane EF drawn into the diſtance PS, or as the ſum of the equal planes EF + ef drawn into the ſame diſtance. And by a like reaſoning the forces of all the planes in the whole ſphere, equidiſtant on each ſide from the centre of the ſphere, are as the ſum of thoſe planes drawn into the diſtance PS, that is, as the whole ſphere and the diſŧance PS conjunctly. Q. E. D.
Case 2. Let now the corpuſcle P attract the ſphere AEBF. And by the ſame reaſoning it will appear that the force with which the ſphere is attracted is as the diſtance PS. Q. E. D.
