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]

The Collaborative International Dictionary of English v.0.48:

Excogitate \Ex*cog"i*tate\, v. i.
   To cogitate. [R.] --Bacon.
   [1913 Webster]

WordNet (r) 3.0 (2006):

excogitate
    v 1: come up with (an idea, plan, explanation, theory, or
         principle) after a mental effort; "excogitate a way to
         measure the speed of light" [syn: invent, contrive,
         devise, excogitate, 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, excogitate, contemplate,
       muse, reflect, mull, mull over, ruminate,
       speculate]

Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "excogitate":
   cogitate, contemplate, contrive, develop, educe, evolve,
   give thought to, invent, mind, perpend, ponder, puzzle out,
   reason out, sort out, study, think about, think out, think over,
   think through, think up, weigh