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From: Webster's Revised Unabridged Dictionary (1913)

 Bra·chys·to·chrone n.  Math. A curve, in which a body, starting from a given point, and descending solely by the force of gravity, will reach another given point in a shorter time than it could by any other path. This curve of quickest descent, as it is sometimes called, is, in a vacuum, the same as the cycloid.