[See next.]
1. Math. The curve traced in space by a point in the circumference (or on a radius) of a circle as the circle rolls along a straight line.
The common cycloid is that traced by a point in the circumference of the circle, and has cusps where this point meets the straight line; that traced by a point within the circle is a prolate cycloid (with inflexions); by a point without the circle, a curtate cycloid (with loops).
1661. Boyle, Spring of Air (1682), 101. Each point will by this compound motion describe on the plain … a perfect cycloid.
1727. Swift, Gulliver, Voy. Laputa, ii. A pudding [cut] into a cycloid.
1812–6. Playfair, Nat. Phil. (1819), I. 135. The line in which a heavy body descends in the least time from one given point to another … is an arch of a cycloid…. Hence the cycloid is called the line of swiftest descent.
b. Companion to the cycloid: the curve formed by successive positions of the point of intersection of a horizontal line drawn through a fixed point in the circumference of the rolling circle with a vertical line through its point of contact with the (horizontal) line on which it rolls.
1857. Whewell, Hist. Induct. Sc., II. 244. The curve must be of the nature of that which is called the companion to the cycloid.
2. Zool. A cycloid fish: see next.
1847. Ansted, Anc. World, x. 246. Two orders of Fishes … the Ctenoids and Cycloids.
