Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/66

Corollary II.

Pl. I. Fig. 2

And hence is explained the compoſition of any one direct force AD, out of any two oblique forces AB and BD; and, on the contrary, the reſolution of any one direct force AD into two oblique forces AB and BD: which compoſition and reſolution are abundantly confirmed from mechanics. (Fig. 2.)

As if the unequal Radii OM and ON drawn from the centre O of any wheel, ſhould ſuſtain the weights A and P by the cords MA and NP; and the forces of thoſe weights to move the wheel were required. Through the centre O draw the right line KOL, meeting the cords perpendicularly in K and L; and from the centre O, with OL the greater of the diſtances OK and OL, deſcribe a circle, meeting the cord MA in D: and drawing OD, make AC parallel and DC perpendicular thereto. Now, it being indifferent whether the points K, L, D, of the cords be fixed to the plane of the wheel or not, the weights will have the ſame effect whether they are ſuſpended from the points K and L, or from D and L. Let the whole force of the weight A be repreſented by the line AD, and let it be reſolved into the forces AC and CD; of which the force AC, drawing the radius OD directly from the centre, will have no effect to move the wheel: but the other force DC, drawing the radius DO perpendicularly, will have the ſame effect as if it drew perpendicularly the radius OL equal to OD; that is, it will have the