120 HISTORY OF MECHANICS. 



bably not yet have discovered the laws of motion ; 

 if we had lived in a world in which there were no 

 fluids, we should have no idea how insufficient a 

 complete possession of the general laws of motion 

 may be, to give us a true knowledge of particular 

 results. 



14. Various General Mechanical Principles. 

 The generalized laws of motion, the points to which 

 I have endeavoured to conduct my history, include 

 in them all other laws by which the motions of 

 bodies can be regulated; and among such, several 

 laws which had been discovered before the highest 

 point of generalization was reached, and which thus 

 served as stepping-stones to the ultimate principles. 

 Such were, as we have seen, the Principles of the 

 Conservation of vis viva, the Principle of the Con- 

 servation of the motion of the center of gravity, 

 and the like. These principles may, of course, be 

 deduced from our elementary laws, and were finally 

 established by mathematicians on that footing. 

 There are other principles which may be similarly 

 demonstrated ; among the rest, I may mention the 

 Principle of the Conservation of areas, which ex- 

 tends to any number of bodies a law analogous to 

 that which Kepler had observed, and Newton de- 

 monstrated, respecting the areas described by each 

 planet round the sun. I may mention also, the Prin- 

 ciple of the Immobility of the plane of maximum 

 areas, a plane which is not disturbed by any mutual 

 action of the parts of any system. The former of 



