But by “reasoning” about the “properties” of these lines and triangles in plane two-dimensional space, we should arrive at the conclusion that the angles of a triangle were equal to 180°, and neither more nor less. We should then think of a straight line as still a _path_ along which we move in imagination, and a path which still has some width. But we imagine the width of the path to become less and less, so that, even if we imagine ourselves to become thinner and thinner, we should be unable to deviate either to the right or left in moving along the path, because the thinner we make ourselves the thinner becomes also the path. We imagine our intuition of a deviation to the right or left becoming keener and keener, so that, no matter how small the deviation we should still be able to appreciate it by the extra exertion which it would involve. We think of a point as a little spot, and we think of ourselves as being very small indeed, so that we can move about on this spot. But we can reduce the area of the spot more and more, until it becomes “infinitesimally” small; and at the same time we think of ourselves as becoming smaller and smaller, so that we can still move about on the spot. But we think of the area of the spot as becoming so small that no matter how small we make ourselves we are unable to move on it. This means that we substitute conceptual lines and points and triangles for the perceptual ones of our experience, and then we operate in imagination with these concepts. That is to say, we carry our modes of exertional activity to their _limits_,[3] in the way which we have tried to indicate above--a process of thought which is the foundation of the reasoning of the infinitesimal calculus. [3] See appendix, p. 346. What we call space, therefore, depends on our intuition of bodily exertion. This intuition includes the knowledge that a certain change has occurred as the consequence of the expenditure of a certain amount of bodily energy, and that, as the result of this change, the relation of the rest of the universe to our body has become different. We think of our body as the origin, or centre, of a system of co-ordinates:-- [Illustration: FIG. 4.]