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From 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]