Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/311



To determine the motions of two bodies which attract each other with forces reciprocally proportional to the quares of the ditance between them, and are let fall from given places.

The bodies, by the lat theorem, will be moved in the ame manner as if they were attracted by a third placed in the common centre of their gravity; and by the hypotheis that centre will quiecent at the beginning of their motion, and therefore (by cor. 4. of the laws of motion) will be always quiecent. The motions of the bodies are therefore to be determined (by Prob. 25.) in the ame manner as if they were impelled by forces tending to that centre; and then we hall have the motions of the bodies attracting each other mutually. Q. E. I.

To determine the motion: of two bodies attracting each other with forces reciprocally proportional to the quares of their ditance, 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 alo the uniform motion