ciprocally as the ſquare of the diſtance of the attracted body from the centre of the ſphere, will not be ſenſibly increaſed by the contact, and it will be ſtill leſs increaſed by it, if the attraction, in the receſs of the body attracted, decreaſes in a ſtill leſs proportion. The propoſition therefore is evident concerning attractive ſpheres. And the caſe is the ſame of concave ſphærical orbs attracting external bodies. And much more does it appear in orbs that attract bodies placed within them, becauſe there the attractions diffuſed through the cavities of thoſe orbs are (by prop. 70.) deſtroyed by contrary attractions, and therefore have no effects even in the place of contact. Now if from theſe ſpheres and ſphærical orbs we take of way any parts remote from the place of contact, and add new parts any where at pleaſure; we may change the figures of the attractive bodies at pleaſure, but the parts added or taken away, being remote from the place of contact, will cauſe no remarkable exceſs of the attraction ariſing from the contact: of the two bodies. Therefore the propoſition holds good in bodies of all figures. Q. E. D.
Proposition LXXXVI. Theorem XLUUU.
If the forces of the particles of which an attractive body is compoſed, decreaſe, in the receſs of the attracted body, in a triplicate or more than triplicate ratio of the diſtance from the particles; the attraction will be
