24 Statics. 



For, according to what has been shown, ./ID, AB, are to be taken 

 in the ratio of the velocities which they are capable of giving to 

 the body m. Now the first being capable of producing the 

 quantity of motion n u, is capable of giving to the body m the 



28 velocity -- . For the same reason the second, or the force q, is 



capable of giving to the body m, the velocity . The lines AD, 



AB, are consequently to be taken according to the following pro- 

 portion ; 



but nv oi) 



: :: nu : ov. 

 m m 



We see therefore that AD, AB, must be in the ratio of the quan- 

 tities of motion nu, ov, which are the measures respectively of 

 the forces p, q. 



What has now been remarked, will be found useful in com- 



paring the effects of different forces applied to different bodies. 



38. The general proposition above demonstrated is of the great- 



est importance, as almost every thing we have to offer, consists in 



an application of it. 



40. From what has been said, it will be seen that it is imma- 

 terial whether we regard a body as urged by the combined action 



Fig.5,6.of the two forces AB, AD, whioh make with each other 

 any assumed angle, or whether we regard it as urged by the 

 single action of a force represented by the diagonal AE. 



And reciprocally, it amounts to the same thing, whether we 

 consider a body as urged by a single force AE, or by two forces 

 represented by the two sides of a parallelogram of which the 

 single force AE is the diagonal. Let a body, for example, be 

 supposed to pass from A to E by a uniform motion in one second. 

 or let it be supposed to move through AB at such a rate as to 

 describe it in one second, while in the same time this line is car- 

 ried parallel to itself along AE ; in this case, as in the former, 

 the body will merely describe the line AE. 



41. The two forces AB, AD, meeting at the point A, are 

 Geom. necessarily in the same plane. Since, therefore, they have 

 321 ' for their resultant the diagonal AE, which is in the plane of 



