Page:Ferrier Works vol 2 1888 LECTURES IN GREEK PHILOSOPHY.pdf/183

128, unless we are prepared to accept the Heraclitean doctrine of a thing being what it is not, and not being what it is. We say the circle is generated by the motion of a point which is continually changing its direction. Now let us examine this assertion carefully. We observe the fact that the point must have a direction, otherwise it could not continually change it. Now what is the direction which the point has and which it continually changes? The direction obviously is a straight direction, the direction is a straight line, and it is by getting out of this direction continually that it produces the curve or the circle. We must say, then, that when the point first starts it moves in a straight direction. Let it be moved just enough to enable you to conceive motion, and you will find that you must conceive it as moving straight, as moving in a straight line. Having then conceived this first motion in a straight line as something infinitesimally small, you may suppose the point to turn and make an angle, and then to move straight through another space infinitesimally small; you may suppose, I say, the circle to be generated in that way. But is the figure which you have thus generated a circle? It is not a circle: it is a polygon, with sides innumerable and infinitesimally small. If this were a circle, the circle would admit of being squared, and that, you are aware, is a problem which cannot be fully, but only approximately, resolved. This figure, then, I say, is not a circle: it is a polygon, although, from the extreme