Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/344

 abolute forces of the attractive bodies A and B will be to each other, as thoe very bodies A and B to which thee forces belong.

For the accelerative attractions of all the bodies B, C, D, towards A are by the uppoition equal to each other at equal ditances; and in like manner the accelerative attractions of all the bodies towards B are alo equal to each other at equal ditances. But the abolute attractive force of the body A is to the abolute attractive force of the body B, as the accelerative attraction of all the bodies towards A to the accelerative attraction of all the bodies towards B at equal ditances and o is alo the accelerative attraction of the body B towards A, to the accelerative attraction of the body A towards B. But the accelerative attraction of the body B towards A is to the accelerative attraction of the body A towards B as the mas of the body A to the mas of the body B; becaue the motive forces which (by the 2d, 7th, and 8th definition) are as the accelerative forces and the bodies attracted conjunctly, are here equal to one another by the third law. Therefore the abolute attractive force of the body A is to the abolute attractive force of the body B as the mas of the body A to the mas of the body B. Q. E. D.

Therefore if each of the bodies of the ytem A, B, C, D, &c. does ingly attract all the ret with accelerative forces that are reciprocally as the quares of the ditances from the attracting body; the abolute forces of all thoe bodies will be to each other as the bodies themelves.