94 Statics. 



we let fall the perpendiculars FL y FM, upon the directions p #, 

 q D) we shall have 



q : p : : FL : FM. 



In like manner, if from any point in the direction of the force 

 </, as D for example, we let fall the perpendiculars .DO, DQ, up- 

 on the directions of the force jo, and p, we shall have 



p : 9 :: Dp : DO. 



The force q may also be compared in the same way with the 

 force p exerted against the fulcrum. 



All these propositions hold true, whatever be the form of the 

 lever, and whatever be the directions of the two powers em- 

 ployed. 



1 60. When the directions of the two powers are parallel, in 

 which case the resultant, or force exerted against the fulcrum, is 



50 parallel to them, the perpendiculars, let fall from the same point 

 in the direction of one of these forces, upon the directions of the 

 Fig. 70. other two respectively, are all in the same straight line LFM. 

 We may say, therefore, in this case, having drawn the line LFM 

 perpendicular to the direction of the powers, that each force or 

 power is represented by the part of this straight line compre- 

 hended between the directions of the two others. 



161. If, moreover, the lever is straight, it will follow from the 

 circumstance of the triangles FLB, FMD, being similar, that the 

 parts FB) FD) BD) have the same ratio to each other as the 



Geom. P arts FL) FM) LM ; we may say, therefore, in this case that 

 2 02 ' each force is represented by the part of the lever comprehended 



between the directions of the two others. 



Thus, 



q : p :: FB : FD; 



that is, the powers are to each other in the inverse ratio of the 

 two arms of the lever FB, FD ; so that the power <?, in order to 

 be in equilibrium, must be as much smaller than />, as the arm 

 to which it is applied is longer than the arm to which p is appli- 

 ed. As to the force p exerted against the fulcrum, it is equal to 

 the sum of the two powers 7, p ; since these being represented 

 by FD) FB) the former, or p, is represented by BD. 



