DEFINITIONS AND EDUCATION. 129 



from reality. The practitioner will always need it, 

 and for every pure geometrician there must be a 

 hundred practitioners. 



The engineer must receive a complete mathematical 

 training, but of what use is it to be to him, except to 

 enable him to see the different aspects of things and 

 to see them quickly? He has no time to split hairs. 

 In the complex physical objects that present them- 

 selves to him, he must promptly recognize the point 

 where he can apply the mathematical instruments we 

 have put in his hands. How could he do this if we left 

 between the former and the latter that deep gulf dug 

 by the logicians ? 



9. Beside the future engineers are other less numerous 

 pupils, destined in their turn to become teachers, and 

 so they must go to the very root of the matter ; a 

 profound and exact knowledge of first principles is 

 above all indispensable for them. Rut that is no 

 reason for not cultivating their intuition, for they 

 would form a wrong idea of the science if they never 

 looked at it on more than one side, and, besides, they 

 could not develop in their pupils a quality they did 

 not possess themselves. 



For the pure geometrician himself this faculty is 

 necessary : it is by logic that we prove, but by intui- 

 tion that we discover. To know how to criticize is 

 good, but to know how to create is better. You 

 know how to recognize whether a combination is 

 correct, but much use this will be if you do not 

 possess the art of .selecting among all the possible 

 combinations. Logic teaches us that on such and 

 such a road we are sure of not meeting an obstacle ; 



(1.777) J 



