Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/356

270 the greater ditance be diminihed in that ratio; and the ditances now being equal, the attraction will be increaed 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 pheres.

At any ditances whatever; the attractions are as the pheres applied to the quares of the ditances.

If a corpucle placed without an homogeneous phere is attracted by a force reciprocally proportional to the quare of its ditance from the centre, and the phere conits of attractive particles; the force of every particle will decreae in a duplicate ratio of the ditance from each particle.

If to the everal points of a given phere there tend equal centripetal force; decreing in a duplicate ratio of the ditances from the points; I ay that another imilar phere will be attracted by it with a force reciprocal proportional to the quare of the diŧance of the centres.

For the attraction of every particle is reciprocally as the quare of its ditance from the centre of the attracting phere (by prop. 74.) and is therefore the ame as if that whole attracting force iued from