Sir I s a a c Newton’s Book I.

78

43. Suppose the line kI to be drawn through the mid-dle of the roller ; and from the place of the roller, wherethe cord, on which the weight G hangs, begins to leave theroller, as at -n, let the line mn be drawn perpendicularly tok I ; and from the point, where the cord holding the weightH begins to leave the wheel, as at 0, let the line op be drawnperpendicular to kl. This being done, the two lines opand m n represent two arms of a lever fixed on the axis kl- yconsequently the weight H will bear to the weight G the fameproportion, as mn bears to op. But m n bears the fame pro-portion to 0 y>, as the thickness of the roller bears to the dia-meter of the wheel; for mn is half the thickness of the roller,and op half the diameter of the wheel.

44. I f the wheel be put into motion, and turned onceround, that the cord, on which the weight G hangs, bewound once more round the axis; then at the fame time thecord, whereon the weight H hangs, will be wound off* fromthe wheel one circuit. Therefore the velocity of the weightG will bear the fame proportion to the velocity of die weightH, as the circumference of the roller to the circumference ofthe wheel. But the circumference of the roller bears the fameproportion to the circumference of the wheel, as the thick-ness of the roller bears to the diameter of the wheel, conse-quently the velocity of the weight G bears to the velocityof the weight H the fame proportion, as the thickness ofthe roller bears to the diameter of the wheel, which is theproportion that the weight H bears to the weight G. There-fore as before in the lever, so here also the general rule laid

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