Chap. 2. PHILOSOPHY.

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portion to ED, as B bears to A ; CE is so much greater inproportion than ED, as A is less in proportion than B.

3 I. Now this being understood, the reason of the rulehere stated will easily appear. For if these two bodies wereput in motion, while the point E rested, the velocity, where-with A would move, would bear the same proportion to thevelocity, wherewith B would move, as E C bears to ED. Thevelocity therefore of each body, when the common centerof gravity rests, is reciprocally proportional to the body. Butwe have strewn above a , that if two bodies are so connected to-gether, that the putting them in motion will not move theircommon center of gravity ; the weight of those bodies willnot produce in them any motion. Therefore in any of thesemechanical engines, if, when the bodies are put into motion,their velocities are reciprocally proportional to their respectiveweights, whereby the common center of gravity would re-main at rest; 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 descrip-tion of each mechanical power.

32. T h e lever was first named above. This is a bar madeuse of to sustain and move great weights. The bar is ap-plied in one part to some strong support; as the bar AB (infig. 23, 24.) is applied at the point C to the support D. Insome other part of the bar, as E, is applied the weight to besustained or moved ; and in a third place, as F, is applied ano-ther weight or equivalent force, which is to sustain or move

a H 2 7, the