Page:Ferrier Works vol 2 1888 LECTURES IN GREEK PHILOSOPHY.pdf/185

130 of the point is continually changing its direction. The word continually here implies that the point is ever moving out of the direction in which it is moving. It implies that the changes in the point's direction are not successive but simultaneous, that it is moving in a direction in which it is not moving, and not moving in a direction in which it is moving; that the motion in the straight direction both is and is not, and that the motion out of the straight direction both is and is not. The tangent proves that the point's motion is everywhere straight; the circle itself proves that the point's motion is everywhere not straight. The point cannot move entirely in a straight direction, making turns and angles at intervals, otherwise we should obtain, as we have seen, and as is, indeed, quite obvious, a polygon, and not a circle: neither can the point move entirely out of the straight, otherwise the direction which is continually changing would be altogether lost. The conclusion, then, is, that the point at every limit or infinitely in all portions of its transit is moving both in and out of a straight direction, and that these two opposite determinations, or contrary predicates, are conciliated and made one in the movement which generates the curve.

23. This and the other examples which I have adduced have been brought forward as aids by which you may habituate your minds to conception of continuous change, that is, of a series of changes so