Chap. 2. PHILOSOPHY. 71

portion to ED, as B bears to A ; CE is fo much greater inproportion than E D, as A is lefs in proportion than B.

31. Now this being underdood, the reafon of the rulehere dated will ealily appear. For if thele two bodies wereput in motion, while the point E reded, the velocity, where-with A would move, would bear the fame proportion to thevelocity, wherewith B would move, as E C bears to E D. Thevelocity therefore of each body, when the common center°f gravity reds, is reciprocally proportional to the body. Butwe have Ihewn above a , that if two bodies are lb connected to-gether, that the putting them in motion will not move theircommon center of gravity ; the weight of thofe bodies willriot produce in them any motion. Therefore in any of thelernechanical engines, if, when the bodies are put into motion,their velocities are reciprocally proportional to their refpedtiveWeights, whereby the common center of gravity would re-tuam at red; the bodies will not receive any motion from theirWeight, that is, they will equiponderate. But this perhapsWill be yet more clearly conceived by the particular defcrip-ti°n of each mechanical power.

3The lever was fird named above. This is a bar madeufe of to fudain and move great weights. The bar is ap-plied in one part to fome drong liipport; as the bar A B (in%• 2 - 3 , 2.4.) is applied at the point C to the fupport D. Infome other part of the bar, as E, is applied the weight to befudained or moved ; and ill a third place, as F, is applied ano-* er weight or equivalent force, which is to fudain or move

a § 27. the