EXCOGITATE
invent, contrive, devise, excogitate, formulate, forge
(verb) come up with (an idea, plan, explanation, theory, or principle) after a mental effort; “excogitate a way to measure the speed of light”
Source: WordNet® 3.1
Etymology
Verb
excogitate (third-person singular simple present excogitates, present participle excogitating, simple past and past participle excogitated)
To think over something carefully; to consider fully; cogitate.
To reach as a conclusion through reason or careful thought.
Source: Wiktionary
Ex*cog"i*tate v. t. [imp. & p. p. Excogitated; p. pr. & vb. n..
Excogitating.] Etym: [L. excogitatus, p. p. of excogitare to
excogitate; ex out + cogitare to think. See Cogitate.]
Definition: 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.
Ex*cog"i*tate, v. i.
Definition: To cogitate. [R.] Bacon.
Source: Webster’s Unabridged Dictionary 1913 Edition