monstrated with me, and endeavoured by various examples to convince me of the truth of Euclid. He bade me, for instance, try to think of a line as the "edge" of a black surface imposed on a white surface; and as for a plane surface, length and breadth without thickness, he declared that the surface of still water was a perfect example of it. But, I replied to him in effect, you cannot think of water without depth; and so you cannot think of position in space which occupies no space; and that edge of the black surface is part of the black surface, not a thing in itself, to be considered apart from the black surface. In a word: these Euclid definitions, elementary as they are, necessary as they are, seem in a sense rooted in contradiction. They are the very foundation stones of the absolute science of mathematics;
