m.j THE GEOMETRICAL ORDER 211 



But, as geometry is necessarily prior to them (since these 

 operations have not as their end to construct space and 

 cannot do otherwise than take it as given) it is evident 

 that it is a latent geometry, immanent in our idea of space, 

 which is the main spring of our intellect and the cause of its 

 working. We shall be convinced of this if we consider 

 the two essential functions of intellect, the faculty of de- 

 duction and that of induction. 



Let us begin with deduction. The same movement 

 by which I trace a figure in space engenders its properties: 

 they are visible and tangible in the movement itself; I 

 feel, I see in space the relation of the definition to its 

 consequences, of the premisses to the conclusion. All 

 the other concepts of which experience suggests the idea 

 to me are only in part constructive a priori; the definition 

 of them is therefore imperfect, and the deductions into 

 which these concepts enter, however closely the conclusion 

 is linked to the premisses, participate in this imperfection. 

 But when I trace roughly in the sand the base of a tri- 

 angle, as I begin to form the two angles at the base, I 

 know positively, and understand absolutely, that if these 

 two angles are equal the sides will be equal also, the figure 

 being then able to be turned over on itself without there 

 being any change whatever. I know it before I have 

 learnt geometry. Thus, prior to the science of geometry, 

 there is a natural geometry whose clearness and evidence 

 surpass the clearness and evidence of other deductions. 

 Now, these other deductions bear on qualities, and not on 

 magnitudes purely. They are, then, likely to have been 

 formed on the model of the first, and to borrow their force 

 from the fact that, behind quality, we see magnitude 

 vaguely showing through. We may notice, as a fact, 

 that questions of situation and of magnitude are the first 

 that present themselves to our activity, those which in- 



