a geometrical curve on which depends the doctrine of pendulums. It was demonstrated by Huygens, that from whatever point or height a heavy body oscillating on a fixed centre begins to descend, while it continues to move in a cycloid the time of its falls or oscillations will be equal to each other. It is likewise demonstrable, that it is the curve of quickest descent—that is, a body falling in it from any given point above, to another not exactly under it, will come to this point in a less time than in any other curve passing through those two points.

The genesis of a cycloid may be illustrated thus: If a wheel be made to roll along a right line till it has completed one revolution, a point fixed in that part of its circumference which at the commencement of the motion touches that right line, will have described a cycloid on a vertical plane—or, in other words, in its course through the air.

ENCYCLOPEDIA, or more properly EXCYCLOPEDIA (εκ κύκλου παιδεία, instruction in a circle), signifies the circle or compass of the arts and sciences; a term used to denote a dictionary of arts, sciences, and miscellaneous literature. See ENCYCLOPEDIA.