Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/381

Rh as the quare of the ditance of the attracted body from the centre of the phere, will not be enibly increaed by the contact, and it will be till les increaed by it, if the attraction, in the reces of the body attracted, decreaes in a till les proportion. The propoition therefore is evident concerning attractive pheres. And the cae is the ame of concave phærical orbs attracting external bodies. And much more does it appear in orbs that attract bodies placed within them, becaue there the attractions diffued through the cavities of thoe orbs are (by prop. 70.) detroyed by contrary attractions, and therefore have no effects even in the place of contact. Now if from thee pheres and phærical orbs we take of way any parts remote from the place of contact, and add new parts any where at pleaure; we may change the figures of the attractive bodies at pleaure, but the parts added or taken away, being remote from the place of contact, will caue no remarkable exces of the attraction ariing from the contact: of the two bodies. Therefore the propoition holds good in bodies of all figures. Q. E. D.

If the forces of the particles of which an attractive body is compoed, decreae, in the reces of the attracted body, in a triplicate or more than triplicate ratio of the ditance from the particles; the attraction will be