MECHANIC rOWERS. 81 



may sustain a weight at the point S of the lever A, 

 the power must here be to the weight in a ratio, 

 or proportion, compounded of the several ratios 

 which those powers that can sustain the weight by 

 the help of each lever, when used singly and apart 

 from the rest, have to the weight. For instance, 

 if the power which can sustain the weight P, by 

 the help of the lever A, be to the weight as 1 to 5 ; 

 and if the power which can sustain the same 

 weight, by the lever B alone, be to the weight as 

 1 to 4 ; and if the power which could sustain the 

 same weight by the lever C, be to the weight as 

 1 to 5 ; then the power which will sustain the 

 weight by help of the three levers joined together, 

 will be to the weight in a proportion consisting of 

 the several proportions multiplied together, of 1 to 

 4, and 1 to 5 ; that is, of 1 to 100. 



For since, in the lever A, a power equal to one- 

 fifth of the weight P pressing down the lever at L, 

 is sufficient to balance the weight, and since it is 

 the same thing whether that power be applied to 

 the lever A at L, or the lever B at S, the point S 

 bearing on the point L, a power equal to one-fifth 

 of the weight P, being applied to the point S of 

 the lever B, will support the weight ; but one- 

 fourth of the same power being applied to the 

 point L of the lever B, and pushing the same up- 

 ward, will as effectually depress the point S of the 

 same lever, as if the whole power were applied at 

 S ; consequently a power equal to one-fourth of 

 one-fifth, that is, one-twentieth of the weight P, 

 being applied to the point L of the lever B, and 

 and pushing up the same, will support the weight: 

 in like manner, it matters not whether that force 

 be applied to the point L of the lever B, or to the 

 point S of the lever C, since, if S be raised, L, 



