How did this great master attain to such perfection? The form of his demonstrations does not suggest an intimacy with the logic of his immediate predecessor Aristotle; but from him he might easily have obtained the whole notion of a strictly deductive science, which, starting from the smallest possible number of primary data, proceeds to derive from these by strict demonstration proposition after proposition. Philosophers of our own time have often expressed wonder at the clearness with which these data are laid down. They are three in kind: first the _common notions_, which apply to all science and all practical life, such as “the whole is greater than its part”; secondly, the _axioms_ peculiar to our intuition of space, such as “two right lines cannot enclose a space”; and thirdly the very simple _postulates_, which amount to the use of a ruler and compass with a pencil. There are besides very careful definitions, so careful that they are at first obscure, because they apply to the ideal construction of the mind in its intuition of pure space and do not concern themselves about the flaws of actual figures. Thus his “point which has no parts” is not nothing at all, but the minimum of definite place; his right line, “which lies in the same way (όμαλῶς) between any two points taken upon its length,” is simply unity of direction. Every other line varies in direction in some of its successive parts. This is a direct appeal to intuition, without which we can make no beginning in the science of space. Such also is the axiom about parallel lines. Such is also the proof by superposition, to show that two triangles, if some of their measurements be the same, must wholly coincide.