The Collaborative International Dictionary
Bye \Bye\ (b[imac]), n.
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A thing not directly aimed at; something which is a secondary object of regard; an object by the way, etc.; as in on or upon the bye, i. e., in passing; indirectly; by implication. [Obs. except in the phrase by the bye.]
The Synod of Dort condemneth upon the bye even the discipline of the Church of England.
--Fuller. (Cricket) A run made upon a missed ball; as, to steal a bye.
--T. Hughes.In various sports in which the contestants are drawn in pairs, the position or turn of one left with no opponent in consequence of an odd number being engaged; as, to draw a bye in a round of a tennis tournament.
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(Golf) The hole or holes of a stipulated course remaining unplayed at the end of a match.
By the bye, in passing; by way of digression; apropos to the matter in hand. [Written also by the by.]
Wiktionary
prep.phr. (context idiomatic English) used to introduce a new topic; incidentally