Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/67

Rh ame effect as the weight P, if that weight is to the weight A as the force DC is to the force DA; that is (becaue of the imilar triangles ADC, DOK,) as OK to OD or OL. Therefore the weights A and P, which are reciprocally as the radii OK and OL that lie in the ame right line, will be equipollent, and o remain in equilibrio; which is the well known property of the Balance, the Lever, and the Wheel. If either weight is greater than in this ratio, its force to move the wheel will be o much greater.

If the weight p, equal to the weight P, is partly upended by the cord Np, partly utained by the oblique plane pG; draw pH, NH, the former perpendicular to the horizon, the latter to the plane pG; and if the force of the weight p tending downwards is repreented by the line pH, it may be reolved into the forces pN, HN. If there was any plane pQ, perpendicular to the cord pN, cutting the other plane pG in a line parallel to the horizon, and the weight p was upported only by thoe planes pQ, pG, it would pres thoe planes perpendicularly with the forces pN, HN; to wit, the plane pQ with the force pN, and the plane pG with the force HN. And therefore if the plane pQ was taken away, o that the weight might tretch the cord, becaue the cord, now utaining the weight, upplies the place of the plane that was removed, it will be trained by the ame force pN which preed upon the plane before. Therefore, the tenion of this oblique cord pN will be to that of the other perpendicular cord PN as pN to pH. And therefore if the weight p is to the weight A in a ratio compounded of the reciprocal ratio of the leat ditances of the cords PN, AM, from the centre of the wheel, Rh