DEFINITIONS AND EDUCATION. 137 



and it is much more philosophical than it would 

 appear at first sight. What is geometry for the 

 philosopher? It is the study of a group. And what 

 group? That of the movements of solid bodies. How 

 are we to define this group, then, without making some 

 solid bodies move? 



Are we to preserve the classical definition of par- 

 allels, and say that we give this name to two straight 

 lines, situated in the same plane, which, being pro- 

 duced ever so far, never meet? No, because this 

 definition is negative, because it cannot be verified 

 by experience, and cannot consequently be regarded 

 as an immediate datum of intuition, but chiefly because 

 it is totally foreign to the notion of group and to the 

 consideration of the motion of solid bodies, which is, 

 as I have said, the true source of geometry. Would 

 it not be better to define first the rectilineal trans- 

 position of an invariable figure as a motion in which 

 all the points of this figure have rectilineal trajectories, 

 and to show that such a transposition is possible, 

 making a square slide on a ruler? From this experi- 

 mental verification, raised to the form of an axiom, 

 it would be easy to educe the notion of parallel and 

 Euclid's postulate itself. 



Mechanics. 



I need not go back to the definition of velocity or 

 of acceleration or of the other kinematic notions : 

 they will be more properly connected with ideas of 

 space and time, which alone they involve. 



On the contrary, I will dwell on the dynamic 

 notions of force and mass. 



There is one thing that strikes me, and that is, how 



