Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/312

 of the common centre of gravity, and the motion of the pace which moves along with this centre uniformly in a right line, and alo the very firt, or beginning motions of the bodies in repect of this pace. Then (by cor. 5. of the laws, and the lat theorem) the ubequent motions will be performed in the ame manner in that pace, as if that pace together with the common centre of gravity were at ret, and as if the bodies did not attract each other; but were attracted by a third body placed in that centre. The motion therefore in this moveable pace of each body going off from a given place, in a given direction, with a given velocity, and acted upon by a centripetal force tending to that centre, is to be determined by prob. 9. and 26. and at the ame time will be obtained the motion of the other round the ame centre. With this motion compound the uniform progreve motion of the entire ytem of the pace and the bodies revolving in it, and there will be obtained the abolute motion of the bodies in immovable pace. Q. E. I.

Suppoing forces with which bodies mutually attract each other to increae in a imple ratio of their ditances from the centres; it it required to find the motions of everal bodies among themelves.

Suppoe the two firt bodies T and L (Pl. 21. Fig. 1.) to have their common centre of gravity