Mechanics.

167

W E have here considered the Action orEffect of each of these Machines, as they

would

of Bodies and their common Centre of Gravity: Yetas Sir Isaac Newton has demonstrated the fame Thingin a different and most extensive Manner, which alsois the Consequence of a different Principle, viz. theComposition and Resolution of Forces and Ratios , it willbe proper to exhibit and explain that also, which is asfollows.

2. Suppose two Weights A, P, appended by theStrings M A, N P, at the Ends of unequal RadiiO M, O N, issuing from the Centre O of any Wheel,in a State of Equilibrium ; those Weights will be toeach other reciprocally as O L to O K, that is, A : P: : 0 L :0 K, or as the nearest Distances of their Linesof Direction from the Centre reciprocally.

3. For on the Centre O with the Radius O L de-scribe an Arch cutting the Thread M A in D, anddraw O D, which continue out to E, to which drawA E perpendicular, and compleat the ParallelogramA E D C. Now since K L passes through the CentreO, and is perpendicular to each String in the Points Kand L by Supposition ; it matters not whether the BodyA and P be suspended from the Points M and N, or Kand L, or D and L, since the Weight of the Bodies isthe same in either of those Points respectively.

4. Therefore let A D expound the whole Force ofthe Weight of the Body A, and let it be resolved intothe two Forces D E and A E, of which the formerdrawing directly from the Centre avails nothing inmoving round the Wheel ; but the other Part A E orC D, acting perpendicularly upon the End of the Ra-dius O D, has the same Force or produces the fameEffect as if it had acted perpendicularly at the End ofthe equal Radius O L.

5. Therefore the Weight of P will be express’d byD C (or AE) because of the Equilibrium ; and hencethe Weight of A is to that of P as A D to A E ; andbecause of the similar Triangles A ED and DOK,

M 4 we

PI. VIII.Fig. 2.