The Collaborative International Dictionary of English v.0.48:

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]
   [1913 Webster]

         The objections of these speculatists of its forms do
         not quadrate with their theories.        --Burke.
   [1913 Webster]