Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/302



If two bodies attract each other mutually with forces of any kind, and in the mean time revolve about the common centre of gravity; I ay that by the ame forces there may be decribed round either body unmoved, a figure imilar and equal to the figure are which the bodies o moving decribe round each other mutually.

Let the bodies S and P (Pl. 20. Fig. 7.) revolve about their common centre of gravity C. proceeding from S to T and from P to Q From the given point s, let there be continually drawn sp, sq, equal and parallel to SP, TQ and the curve pqv, which the point p decribes in its revolution round the immovable point s, will be imilar and equal to the curves, which the bodies S and P decribe about each other mutually; and therefore by theor. 20. imilar to the curves ST and PQV which the ame bodies decribe about their common centre of gravity C; and that becaue the proportions of the lines SC, CP, and SP or sp, to each other, are given.

. The common centre of gravity C (by cor. 4 of the laws of motion) is either at ret, or moves uniformly in a right line. Let us firt uppoe it at ret, and in s and p let there be placed two bodies, one immovable in s, the other