MECHANICS 47 



simultaneously on the point P, the force PC tending to 

 draw the point P towards C, and the force PE tending 

 to draw the point P towards E, then if from the two 

 points C and E, equidistant from P, we draw two lines, 

 CD parallel to PE and ED parallel to PC, meeting 

 at D, the line PD will be the diagonal of the figure 

 PCDE, and will represent the resultant of the two 

 forces A and B. 



The points C and E have been here made equidistant 

 from P, because the two forces are supposed equal. 

 Were they, however, unequal, then the distance PC 

 FIG. 5. 



A ~ 



B 



would have to be made to bear the same proportion to 

 EP as the force A has to the force B a unit of length 

 representing a unit of force. In that case, instead of 

 forming a parallelogram (i.e., a straight-lined quadri- 

 lateral figure whose opposite sides are equal and parallel) 

 with adjacent sides equal, such sides would be unequal. 

 Now, it is a rule in mechanics, that if two forces acting 

 at a point be represented in magnitude and direction by 

 the sides of a parallelogram, the resultant force will be 

 represented in magnitude and direction by the diagonal 

 of the parallelogram passing through that point. 



Any number of forces acting on a single point can be 



