A single quantity of excess is that which suffices in nature to be added to one of the two equal weights of a balance, and it will make that one weight always victor over the other; and this weight is among bodies as the point is on a surface. That weight descends less which is sustained by a stronger support. And that part of the support resists less which is situated more distant from its fixing-point. (Whence that thing will be of easier movement which is sustained by a weaker resistance.) And that thing which resists less is more easily removed from its place. And that thing which resists less is removed by a lesser power, and is carried on in a longer motion. That proportion will hold between the one motion and the other as holds between the powers from which they arise.

af-bgrm-71 - a - n. See that a and b are always right angles. The proportion that g b has with g n, such has weight 1 with 7. According to some; but here experience does not confirm it, because the weights that make resistance one against the other ... Those weights which in equal time are victor one over the other, such proportion holds from the one to the other as holds that of their opposite motions, once the excess has been taken away from the victor. That proportion which the descent of the angle m from the position f has with the space m r, such has been the motion made by weight 1 with weight 7, and such is the quantity of weight 1 compared with weight 7. Yet experiment, before you set down such a rule as general.

That proportion which motion b has with motion a, such will weight a have with weight b.

1 1 a b - 1 1 2 a b - 3 1 1 2 4 a b. That part of the support resists less which is more remote from its fixing-point.

g h - a b. See that, g feeling half less weight than h, the motion of g will be half again as long as the motion made by h.

16 16 - 32. This weight is divided among 8 cords, and the ninth alone sustains only what is given to it by the eighth cord.