# Meaning of the word “conjugate” across mathematics?

Clearly, the word conjugate or conjugation is used for a myriad of different concepts across mathematics and even in science (see the Wikipedia page).

Its meaning can range from the fraction used to rationalize a denominator in pre-algebra, to the $gNg^{-1}$ action in group theory. Complex numbers have conjugates, and harmonic functions can have “harmonic conjugates”.

Surprisingly, I can’t find an explanation of the origin of the word “conjugate” to describe all these cases, nor an explicit meaning or mathematical definition of the word itself.

What is the history of this word, and what (if any) unifying concepts tie the examples together?