Proposition LXII. Problem XXXVIII.
To determine the motions of two bodies which attract each other with forces reciprocally proportional to the ſquares of the diſtance between them, and are let fall from given places.
The bodies, by the laſt theorem, will be moved in the ſame manner as if they were attracted by a third placed in the common centre of their gravity; and by the hypotheſis that centre will quieſcent at the beginning of their motion, and therefore (by cor. 4. of the laws of motion) will be always quieſcent. The motions of the bodies are therefore to be determined (by Prob. 25.) in the ſame manner as if they were impelled by forces tending to that centre; and then we ſhall have the motions of the bodies attracting each other mutually. Q. E. I.
Proposition LXIII. Problem XXXIX.
To determine the motion: of two bodies attracting each other with forces reciprocally proportional to the ſquares of their diſtance, and going off from given places in given directions, with given velocities.
The motions of the bodies at the beginning being given, there is given alſo the uniform motion
