how the same suppression of positive reality, the same inversion of a certain original movement, can create at once extension in space and the admirable order which mathematics finds there. There is, of course, this difference between the two cases, that words and letters have been invented by a positive effort of humanity, while space arises automatically, as the remainder of a subtraction arises once the two numbers are posited.[80] But, in the one case as in the other, the infinite complexity of the parts and their perfect coördination among themselves are created at one and the same time by an inversion which is, at bottom, an interruption, that is to say, a diminution of positive reality. * * * * * All the operations of our intellect tend to geometry, as to the goal where they find their perfect fulfilment. 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 deduction 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 constructible _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 triangle, 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 intelligence externalized in action resolves even before reflective intelligence has appeared. The savage understands better than the civilized man how to judge distances, to determine a direction, to retrace by memory the