Chap. 2. PHILOSOPHY. 73

hold the whole in a just counterpoize. Suppose (in sig.27.)the two powers at E and F did not equiponderate, and it wererequired to apply a third power to the point G, that might besufficient to balance the lever. Find what power in F wouldjust counterbalance the power in E ; then is the differencebetween this power and that, which is actually applied at F,bear the fame proportion to the third power to be applied atG, as the distance C G bears to C F ; the lever will be coun-terpoized by the help of this third power, if it be so appliedas to act the same way with the power in F, when that poweris too small to counterbalance the power in E ; but other-wise the power in G must be so applied, as to act against thepower in F. In like manner, if a lever were charged with three,or any greater number of weights or other powers, which didnot counterpoize each other, another power might be appliedin any place proposed, which should bring the whole to ajust balance. And what is here said concerning a plurality ospowers, may be equally applied to all the following cafes.

34. If the lever ffiould constst of two arms making anangle at the point C (as in fig. 26.) yet if the forces are ap-plied perpendicularly to each arm, the same proportion willhold between the forces applied, and the distances of the cen-ter, whereon the lever rests, from the points to which theyare applied. That is, the weight at E will be to the force inF in the same proportion, as C F bears to C E.

37. But whenever the forces applied to the lever act ob-liquely to the arm, to which they are applied . (as in stg. 27.)

L then