Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/363

Rh

And if there be compoed a new phere out of innumerable corpucles uch as p, ituate within the firt phere AEBF; it may be proved as before that the attraction whether, ingle of one phere towards the other, or mutual of both towards each other, will be as the ditance pS of the centres. Q. E. D.

If pheres in the progreion from the centre to the circumference be however diimimar and unequable, but imilar on every ide round about at all given diŧances from the centre; and the attractive force of every point be as the diŧance of the attracted body; I ay that the entire force with which two pheres of this kind attract each other mutually is proportional to the centres of the pheres.

This is demontrated from the foregoing propoition in the ame manner as the 76th propoition was demontrated from the 75th

Thoe things that were above demontrated in prop. 10. and 64. of the motion of bodies round the centres of conic ections, take place when all the attractions are made by the force of phærical bodies of the condition above