Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/307

 the times, by radii drawn both to that centre and to other mutually.

The periodic time of two bodies S and P revolving round their common centre of gravity C, is to the periodic time of one of the bodies P revolving round the other S remaining unmoved and decribe a figure imilar and equal to thoe which the bodies decribe about each other mutually, in a ubduplicate ratio of the other body S to the um of the bodies S + P.

For by the demontration of the lat propoition, the times in which any imilar arcs PQ and pq are decribed, are in a ubduplicate ratio of the ditances CP and SP or sp, that is in it ubduplicate ratio of the body S to the um of the bodies S + P. And by compoition of ratio's the fums of the times in which all the imilar arcs PQ, and pq are decribed, that is, the whole times in which the whole imilar figures are decribed, are in the ame ubduplicate ratio. Q. E. D.