SEQUEL TO THE GENERALIZATION. 121 



these principles was published about the same time 

 by Euler, D. Bernoulli, and Darcy, under different 

 forms, in 1746 and 1747; the latter by Laplace. 



To these may be added a law, very celebrated in 

 its time, and the occasion of an angry controversy, 

 the Principle of least action. Maupertuis conceived 

 that he could establish a priori, by theological 

 arguments, that all mechanical changes must take 

 place in the world so as to occasion the least pos- 

 sible quantity of action. In asserting this, it was 

 proposed to measure the Action by the product 

 pf Velocity and Space ; and this measure being 

 adopted, the mathematicians, though they did not 

 generally assent to Maupertuis' reasonings, found 

 that his principle expressed a remarkable and use- 

 ful truth, which might be established on known 

 mechanical grounds. 



15. Analytical Generality. Connexion of Sta- 

 tics and Dynamics. Before I quit this subject, it 

 is important to remark the peculiar character which 

 the science of mechanics has now assumed, in con- 

 sequence of the extreme analytical generality which 

 has been given it. Symbols, and operations upon 

 symbols, include the whole of the reasoner's task ; 

 and though the relations of space are the leading 

 subjects in the science, the great analytical treatises 

 upon it do not contain a single diagram. The 

 Mecanique Analytique of Lagrange, of which the 

 first edition appeared in 1788, is by far the most 

 consummate example of this analytical generality. 



