30 Statics. 



represented by that part of the straight line which is comprehended 

 between the directions of the two others. 



53. It will hence be readily perceived how we ought to pro- 

 ceed in order to find the resultant of several parallel forces ; anfl 

 reciprocally, how we can substitute for a single force, any number 

 whatever of parallel forces. 



If, for example, it were proposed to reduce to a single force 



Fig. 15. the two parallel forces jo, <?, which act the same way ; any straight 



50> line ABC being drawn ; as the resultant p is equal to p -f 9, it 



is only necessary to find the point B through which this resultant 



50 must pass. Now we have 



p : g : : BC : AC, 

 that is, 



p : p + q : : BC : AC. 

 We have therefore only to take between the two points A, C, a 



237. point B such that jBC shall be equal to - . 



Fig. 16. If the two parallel forces are opposed to each other, the re- 

 50 sultant will be equal to their difference p <?, or q p. Sup- 

 pose p greater than q. Having drawn the line AC at pleasure, 

 it will be necessary to prolong AC beyond A^ with respect to C, 

 by a quantity AB, such that we shall have 



52 > p : ? : : BC : AC 



or 



p : p q :: BC : AC-, 



in other words, it is necessary to take BC equal to ? . 



p q 



If q is greater than jo, the point B will be in AC produced 

 beyond C with respect to A. 



Fig. 17. 54. if we had a third force r, we should first find the resultant 

 p' of the two forces p, q, and then seek the resultant p of the 

 two forces Q' and r, as if there were only these two ; that is, we 

 should proceed in precisely the same manner as we have done in 

 the preceding article. 



55. Hence, reciprocally, if we would decompose any force p 

 *$ 16 ' into two others parallel to it, we should take arbitrarily a line 



