Source : Webster's Revised Unabridged Dictionary (1913)

Quadrate \Quad"rate\, v. i. [imp. & p. p. {Quadrated}; p. pr. &
   vb. n. {Quadrating}.] [See {Quadrate}, a.]
   To square; to agree; to suit; to correspond; -- followed by
   with. [Archaic]

         The objections of these speculatists of its forms do
         not quadrate with their theories.        --Burke.

Quadrate \Quad"rate\, a. [L. quadratus squared, p. p. of
   quadrare to make four-cornered, to make square, to square, to
   fit, suit, from quadrus square, quattuor four. See
   {Quadrant}, and cf. {Quadrat}, {Quarry} an arrow, {Square}.]
   1. Having four equal sides, the opposite sides parallel, and
      four right angles; square.

            Figures, some round, some triangle, some quadrate.
                                                  --Foxe.

   2. Produced by multiplying a number by itself; square. ``
      Quadrate and cubical numbers.'' --Sir T. Browne.

   3. Square; even; balanced; equal; exact. [Archaic] `` A
      quadrate, solid, wise man.'' --Howell.

   4. Squared; suited; correspondent. [Archaic] `` A generical
      description quadrate to both.'' --Harvey.

   {Quadrate bone} (Anat.), a bone between the base of the lower
      jaw and the skull in most vertebrates below the mammals.
      In reptiles and birds it articulates the lower jaw with
      the skull; in mammals it is represented by the malleus or
      incus.

Quadrate \Quad"rate\, n. [L. quadratum. See {Quadrate}, a.]
   1. (Geom.) A plane surface with four equal sides and four
      right angles; a square; hence, figuratively, anything
      having the outline of a square.

            At which command, the powers militant That stood for
            heaven, in mighty quadrate joined.    --Milton.

   2. (Astrol.) An aspect of the heavenly bodies in which they
      are distant from each other 90[deg], or the quarter of a
      circle; quartile. See the {Note} under {Aspect}, 6.

   3. (Anat.) The quadrate bone.

Quadrate \Quad"rate\, v. t.
   To adjust (a gun) on its carriage; also, to train (a gun) for
   horizontal firing.

Source : WordNet®

quadrate
     adj : having four sides and four angles
     n 1: a cubelike object
     2: a square-shaped object