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The Collaborative International Dictionary of English v.0.48:

Excogitate \Ex*cog"i*tate\v. t. [imp. & p. p. Excogitated; p. pr. & vb. n.. Excogitating.] [L. excogitatus, p. p. of excogitare to excogitate; ex out + cogitare to think. See Cogitate.] To think out; to find out or discover by thinking; to devise; to contrive. "Excogitate strange arts." --Stirling. [1913 Webster] This evidence . . . thus excogitated out of the general theory. --Whewell. [1913 Webster]