Did Captain Kirk ever say engage?
Similarly, why does Picard say engage?
It's as if Picard uses Riker as the crew interface. Essentially the first officer is there to carry out the orders of the Captain. In this sense, giving the engage order is only an extension of the captain's order.
One may also ask, what did Captain Kirk say? His most famous line which is quoted all the time is "Beam me up, Scotty", but I'm not sure he actually ever said it exactly that way on the show.
Regarding this, did Captain Kirk say make it so?
"Make it so." One of Captain Picard's catchphrases, used to confirm a suggestion from another officer.
What is the Star Trek saying?
"Where no man has gone before" is a phrase made popular through its use in the title sequence of the original 1966-1969 Star Trek science fiction television series, describing the mission of the starship Enterprise.