Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/348

 to the ditances HP, LP; and any particles at HI and KL of the phærical uperficies, terminated by right lines paing through P, will be in the duplicate ratio of thoe ditances. Therefore the forces of thee particles exerted upon the body P are equal between themelves. For the forces are as the particles directly and the quares of the ditances inverely. And thee two ratio's compoe the ratio of equality. The attractions therefore being made equally towards contrary parts detroy each other. And by a like reaoning all the attractions through the whole phærical uperficies are detroyed by contrary attractions. Therefore the body P will not be any way impelled by thoe attractions. Q. E. D.

The ame things upposed as above, I ay that a corpucle placed without the phærical uperficies is attracted towards the centre of the phere with a force reciprocally proportional to the quare of its ditance from that centre.



Let AHKB, ahkb (Pl. 21. Fig. 5.) be two equal phærical uperficies decribed about the centres S, s; their diameters AB, ab; and let P and p be two corpucles ituate without the pheres in thoe diameters produced. Let there be drawn from the corpucles the lines PHK, PIL, phk, pil,