76 Statics. 



val parts being decomposed into three other forces parallel rsspective- 

 ly to three rectangular co-ordinates, the sum of the forces, or quanti- 

 ties of motion, par all el to each of these three lines be equal to zero, the 

 forces which act in opposite directions being taken with con- 

 trary signs. 



1 27. When all the forces are in the same plane, it Is evident- 

 ly sufficient to decompose each force into two others parallel to 

 two assumed lines, these lines being perpendicular to each other, 

 and drawn in the same plane with the given forces ; for the forces 

 which are perpendicular to this plane being zero, the motion of 

 the centre of gravity in virtue of these forces is also zero. 



128. In all that we have said, we have supposed each of the 

 bodies which compose the system, to obey fully and freely the 

 force by which it is urged. But the same principles hold true 

 no less when the bodies are constrained in their motions, provi- 

 ded the obstacles do not proceed from a force foreign to the sys- 

 tem, that is, provided there are no impediments except those 

 which arise from the difficulty of yielding to these motions by 

 the manner in which they are disposed among themselves or 

 connected with each other. This we propose to demonstrate 

 after having first made known the general law of the equilibri- 

 um of bodies and the general law of their motion. 



General Principle of the Equilibrium of Bodies. 



129. Whatever be the forces (acting or resisting), applied to a 

 body, to a system of bodies, to a machine, &c., and vtfiatever be the 

 directions of these forces, if we conceive that each is decomposed 

 into three others parallel respectively to three rectangular co-ordinates, 

 it is necessary in order that all these forces should be in equilibri- 

 um, that the sum* of the forces which act parallel to each of these 

 co-ordinates, should be equal to zero. 



*By sum of the forces in what follows, is to be understood the sum 

 of those which act in one direction, minus the sum of those which 

 act in the opposite direction* 



