32. THE lever was first named above. This is a bar made use of to sustain and move great weights. The bar is applied in one part to some strong support; as the bar A B (in fig. 23, 24.) is applied at the point C to the support D. In some other part of the bar, as E, is applied the weight to be sustained or moved; and in a third place, as F, is applied another weight or equivalent force, which is to sustain or move the weight at E. Now here, if, when the level should be put in motion, and turned upon the point C, the velocity, wherewith the point F would move, bears the same proportion to the velocity, wherewith the point E would move, as the weight at E bears to the weight or force at F; then the lever thus charged will have no propensity to move either way. If the weight or other force at F be not so great as to bear this proportion, the weight at E will not be sustained; but if the force at F be greater than this, the weight at E will be surmounted. This is evident from what has been said above[60], when the forces at E and F are placed (as in fig. 23.) on different sides of the support D. It will appear also equally manifest in the other case, by continuing the bar B C in fig. 24. on the other side of the support D, till C G be equal to C F, and by hanging at G a weight equivalent to the power at F; for then, if the power at F were removed, the two weights at G and E would counterpoize each other, as in the former case: and it is evident, that the point F will be lifted up by the weight at G with the same degree of force, as by the other power applied to F; since, if the weight at E were removed, a weight hung at F equal to that at G would balance the lever, the distances C G and C F being equal. 33. IF the two weights, or other powers, applied to the lever do not counterbalance each other; a third power may be applied in any place proposed of the lever, which shall hold the whole in a just counterpoize. Suppose (in fig. 25.) the two powers at E and F did not equiponderate, and it were required to apply a third power to the point G, that might be sufficient to balance the lever. Find what power in F would just counterbalance the power in E; then if the difference between this power and that, which is actually applied at F, bear the same proportion to the third power to be applied at G, as the distance C G bears to C F; the lever will be counterpoized by the help of this third power, if it be so applied as to act the same way with the power in F, when that power is too small to counterbalance the power in E; but otherwise the power in G must be so applied, as to act against the power in F. In like manner, if a lever were charged with three, or any greater number of weights or other powers, which did not counterpoize each other, another power might be applied in any place proposed, which should bring the whole to a just balance. And what is here said concerning a plurality of powers, may be equally applied to all the following cases.