Page:Ferrier Works vol 2 1888 LECTURES IN GREEK PHILOSOPHY.pdf/184

minuteness of its sides, it may seem to be a circle. We have not formed our figure aright; we must try again. But first let us observe how we have blundered in our construction. We supposed the point to move in a straight line, the shortest that can be conceived, and then to change its direction, and move in another straight line, the shortest that can be conceived, and then to change its direction, and move in the direction of a third straight line, the shortest that can be conceived, and so on; and we thus constructed our apparent circle, which turns out to be a polygon. What, then, is our blunder? Our blunder, in one word, is this; that we supposed the point to be moving in a straight line, and then out of that straight line in the direction of another straight line; in short, we supposed the movement in the straight direction, and the movement out of the straight direction, to be successive, and not simultaneous. We must now, then, correct our blunder, and reconstruct our figure. The point at starting must move in a straight direction. There can be no doubt about that, we cannot conceive it otherwise; but it must in that very same movement move out of a straight direction. It must move both in it and out of it. It must travel continually in the direction of a straight line, and at the same time continually out of the direction of a straight line. It must move in a straight direction and out of a straight direction at once. Indeed this is what mathematicians themselves declare when they say that in forming the circle the motion