The Collaborative International Dictionary of English v.0.48:

Brachystochrone \Bra*chys"to*chrone\, n. [Incorrect for
   brachistochrone, fr. Gr. bra`chistos shortest (superl. of
   brachy`s short) + ? time : cf. F. brachistochrone. ] (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.
   [1913 Webster]