E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Badminton
is properly a copus cup, made of claret spiced and sweetened, a favourite with the Duke of Beaufort of Badminton. As the duke used to be a great patron of the prize ring, Badminton was used as equivalent to claret as the synonym of blood.
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Also a game similar to lawn tennis, only played with shuttlecocks instead of balls.