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According to the Free Dictionary:

Jove (jv)
n. Roman Mythology
See Jupiter.
Idiom:by Jove
Used as a mild oath to express surprise or emphasis.

Jupiter -- also known as Jove in English -- was the head
of the Roman gods. Jupiter is the Roman equivalent of the
Greek god Zeus. Jupiter was a sky god who wielded bolts
of thunder.

And, in the case of Rex Harrison, above... He actually said
"By Jove! I think she's got it" because he was referring to
Eliza Dolittle (Audrey Hepburn) and her efforts to speak
English like a lady in the movie, "My Fair Lady."

So, my question is:

NOW DO YOU GET IT?