Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/382

270 vatly tronger in the point of contact than when the attracting and attracted bodies are eparated from each other though by never o mall on interval.

For that the attraction is infinitely increaed when the attracted corpucle comes to touch an attracting phere of this kind appears by the olution of problem 41. exhibited in the econd and third examples. The ame will alo appear (by comparing thoe examples and therorem 41. together) of attractions of bodies concavo-convex orbs, whether the attracted bodies be placed without the orbs, or in the cavities whithin them. And by adding to or taking from thoe pheres and orbs, any attractive matter any where without the place of contact, o that the attractive bodies may receive any aigned figure, the propoition will hold good of all bodies univerally. Q. E. D.

if two bodies imilar to each other, and coniting of matter equally attractive, attract eparately two corpucles proportional to thoe bodies, and in a like ituation to them; the accelerative attractions of the corpucle towards the entire bodies will be as