From The Collaborative International Dictionary of English v.0.48:

Quarterstaff \Quar"ter*staff`\, n.; pl. Quarterstaves.
   A long and stout staff formerly used as a weapon of defense
   and offense; -- so called because in holding it one hand was
   placed in the middle, and the other between the middle and
   the end.
   [1913 Webster] Quartet
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