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excogitate\ eks-KOJ-i-teyt\ , verb;
1.To think out; devise; invent.
2.To study intently and carefully in order to grasp or comprehend fully.
Quotes:
But observe the singular phenomenon — on approximately the same date several thousand men and women of letters retire to secluded corners to excogitate a thing described as "charm"; each cudgeling his or her head for some variety which can possibly be regarded as original...
-- Upton Sinclair,Money Writes!
I preferred to relate aloud, to excogitate in a lively, external manner, with a flow of invention as useless as was my declamation of it, a whole novel crammed with adventure, in which the Duchess, fallen upon misfortune…
-- Marcel Proust,Swann's Way
Origin:
Excogitate is related to the wordcogitate which means "to think." The prefixex- typically means "out of", but in this case it means "thoroughly."