22 Statics. 



are at right angles to each other, we may always substitute a 

 single one, provided that this single one is such as to cause the 

 body to describe the diagonal of a right-angled parallelogram, 

 the sides of which would be described in the same time, each 

 separately, by the action of the force of which it represents the 

 direction. 



The single force AE, which results from the action of the 

 two forces AB, AD, is called the resultant of these two forces. 

 As the lines AB, AD, represent the effects which the forces q and 

 p are singly capable of producing, and AE the effect which they 

 are able to produce conjointly, we may regard AB, AD, AE, as 

 representing these forces themselves. 



We may thus consider any single force AE, as being the result 

 of two other forces AB, AD, the directions of which are at right 

 angles to each other, provided that, the first being represented by 

 the diagonal AE, the others are represented by the sides AB, 



AD, of this same right-angled parallelogram. For the single force 



AE, therefore we may substitute the two forces AB, AD, since 

 these two will in fact only produce AE. 



38. In general, whatever be the angle formed by the directions of 

 Fig.5, 6. the two forces p and q which act at the same time upon a body m, this 

 body will still describe the diagonal AE, of the parallelogram DA 

 BE, the sides of which represent, in the directions of the forces, the 

 effects which they are separately capable of producing; and the body 

 mill describe this diagonal in the same time in which by the action of 

 either of the two forces, it would have described the side which repre- 

 sents this force. 



Through the point A let the line FAH be drawn perpendicular 

 to the diagonal AE, and through the points D and B, let DF, BH, 

 be drawn parallel, and DG, BI, perpendicular to the diagonal AE. 

 Instead of the force p, represented by AD, the diagonal of the 

 rectangular parallelogram FAGD, we may take the two for- 

 37. ces AF, AG. For the same reason, instead of the force q, 

 represented by the diagonal AB, of the rectangular parallelogram 

 AHBI, we may take the two forces AH, AL We may therefore, 

 instead of the two forces p and q, substitute the four forces AF, 

 AG,AH, AI ; and these cannot but have the same resultant as 

 the two forces p and q. Now of these four forces, the two AH. 



