Source : Webster's Revised Unabridged Dictionary (1913)

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.

         This evidence . . . thus excogitated out of the general
         theory.                                  --Whewell.

Excogitate \Ex*cog"i*tate\, v. i.
   To cogitate. [R.] --Bacon.

Source : WordNet®

excogitate
     v 1: come up with (an idea, plan, explanation, theory, or
          priciple) after a mental effort; "excogitate a way to
          measure the speed of light" [syn: {invent}, {contrive},
          {devise}, {formulate}, {forge}]
     2: reflect deeply on a subject; "I mulled over the events of
        the afternoon"; "philosophers have speculated on the
        question of God for thousands of years"; "The scientist
        must stop to observe and start to excogitate" [syn: {chew
        over}, {think over}, {meditate}, {ponder}, {contemplate},
        {muse}, {reflect}, {mull}, {mull over}, {ruminate}, {speculate}]