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Latin word cogito comes from Latin con (together) and Latin agitare (turn over, consider)
con- (Latin)
Used in compounds to indicate a being or bringing together of several objects. Used in compounds to indicate the completeness, perfecting of any act, and thus gives intensity to the signification of the simple word.
agitare (Latin)
Turn over, consider
cogito (Latin)
I consider, ponder. I think.