28 OUTLINES OF NATURAL PHILOSOPHY. 



is, by the motion which it produces in a given 

 time. 



a. Two forces are said to be represented by two lines y 

 when the motions which they singly produce are in 

 the directions of those lines, and proportional to 

 them. 



62. Let a body at A (fig. 2.) be acted on by two 

 forces at the same instant, one of which acting 

 alone, would cause it to move uniformly over AB, 

 in a given time ; and the other acting alone, would 

 cause it to move over AC, at right angles to AB, 

 in the same time. The velocity of the body in the 

 one of these directions, will not be changed by the 

 force impelling it in the other. 



For if the motion of A in the direction AB, is acce- 

 lerated by the force AC, it will be retarded by the 

 action of the opposite force AC'; but it must also 

 be accelerated by AC', for AC and AC' are alike 

 situated in respect of AB. Now, this is absurd ; 

 therefore, &c. 



The velocity of a body in the direction of a line diffe- 

 rent from its own path, is measured as in 53. 



63. If the lines which each of two forces, acting, 

 singly, would have caused a body to describe in 

 the same time, be at right angles to one another, 

 the line which it will describe in that time, when 

 both the forces act on it at once, is the diagonal 

 of the rectangle under the two first-mentioned 

 lines. 



2 64. If 



