16 NEWTON S PRINCJPIA. 



perseveres in the straight line it moves in, unless in so 

 far as some other force alters its direction ; and as by the 

 second law any new force impressed tends to move it in its 

 own direction, it follows that, if two forces, not in the 

 same nor in directly opposite directions, act at one time, 

 and by an instantaneous impulse, on any body at rest, it 

 must move in such a direction as that it shall be found both 

 in a line parallel to the direction of the one force, and in 

 a line parallel to the direction of the other ; that is to say, 

 in the diagonal of a parallelogram whose two contiguous 

 sides are in the directions of the two forces, and are respec 

 tively equal to the space each force would carry it through 

 in its own direction. Moreover, as each force separately 

 would have carried it to the end of the line of its direc 

 tion in the given time, it must move through the diagonal 

 in the same time which it would have taken to move 

 through either side if either force had acted alone. 

 Thus the direction of every motion occasioned by any two 

 forces acting at an angle to each other, may always be 

 found by completing the parallelogram of which the direc 

 tions of those forces are the contiguous sides ; and so of 

 any motion occasioned by any number of forces whatever 

 acting angularly. And, conversely, every motion of a 

 moving body may be resolved into two, of which the one 

 is in any given direction whatever, and the other is found 

 by completing the parallelogram, whereof that given direc 

 tion is one of the sides, and the direction the body moves 

 in is the diagonal. 



From this resolution of forces it is easily shown, that 

 if any weights or other powers acting in parallel lines 

 are applied to the opposite ends of a lever moving on a 

 centre or fulcrum, the effect of each will be directly as its 

 distance from that centre, in other words, as the length of 

 the contiguous arm of the lever ; consequently, that if the 



