the greater diſtance be diminiſhed in that ratio; and the diſtances now being equal, the attraction will be increaſed in the duplicate of that ratio; and therefore will be to the other attraction in the triplicate of that ratio; that is, in the ratio of the ſpheres.
Cor. 2. At any diſtances whatever; the attractions are as the ſpheres applied to the ſquares of the diſtances.
Cor. 3. If a corpuſcle placed without an homogeneous ſphere is attracted by a force reciprocally proportional to the ſquare of its diſtance from the centre, and the ſphere conſiſts of attractive particles; the force of every particle will decreaſe in a duplicate ratio of the diſtance from each particle.
Proposition LXXV. Theorem XXXV.
If to the ſeveral points of a given ſphere there tend equal centripetal force; decreſing in a duplicate ratio of the diſtances from the points; I ſay that another ſimilar ſphere will be attracted by it with a force reciprocal proportional to the ſquare of the diſŧance of the centres.
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
