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]