The Collaborative International Dictionary of English v.0.48:

Quadrel \Quad"rel\, n. [It. quadrello, LL. quadrellus, fr. L.
   quadrus square. See Quadrate, and cf. Quarrel an arrow.]
   1. A square piece of turf or peat. [Prov. Eng.]
      [1913 Webster]

   2. A square brick, tile, or the like.
      [1913 Webster]