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

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tional to the diſtances HP, LP; and any particles at HI and KL of the ſphærical ſuperficies, terminated by right lines paſſing through P, will be in the duplicate ratio of thoſe diſtances. Therefore the forces of theſe particles exerted upon the body P are equal between themſelves. For the forces are as the particles directly and the ſquares of the diſtances inverſely. And theſe two ratio's compoſe the ratio of equality. The attractions therefore being made equally towards contrary parts deſtroy each other. And by a like reaſoning all the attractions through the whole ſphærical ſuperficies are deſtroyed by contrary attractions. Therefore the body P will not be any way impelled by thoſe attractions. Q. E. D.


Proposition LXXI. Theorem XXXI.

The ſame things ſupposed as above, I ſay that a corpuſcle placed without the ſphærical ſuperficies is attracted towards the centre of the ſphere with a force reciprocally proportional to the ſquare of its diſtance from that centre.

Plate 21, Figure 5
Plate 21, Figure 5


Let AHKB, ahkb (Pl. 21. Fig. 5.) be two equal ſphærical ſuperficies deſcribed about the centres S, s; their diameters AB, ab; and let P and p be two corpuſcles ſituate without the ſpheres in thoſe diameters produced. Let there be drawn from the corpuſcles the lines PHK, PIL, phk, pil,