From The Collaborative International Dictionary of English v.0.48:

Quadrature \Quad"ra*ture\, n. [L. quadratura: cf. F. quadrature.
   See Quadrate, a.]
   1. (Math.) The act of squaring; the finding of a square
      having the same area as some given curvilinear figure; as,
      the quadrature of a circle; the operation of finding an
      expression for the area of a figure bounded wholly or in
      part by a curved line, as by a curve, two ordinates, and
      the axis of abscissas.
      [1913 Webster]

   2. A quadrate; a square. --Milton.
      [1913 Webster]

   3. (Integral Calculus) The integral used in obtaining the
      area bounded by a curve; hence, the definite integral of
      the product of any function of one variable into the
      differential of that variable.
      [1913 Webster]

   4. (Astron.) The position of one heavenly body in respect to
      another when distant from it 90[deg], or a quarter of a
      circle, as the moon when at an equal distance from the
      points of conjunction and opposition.
      [1913 Webster]

   Quadrature of the moon (Astron.), the position of the moon
      when one half of the disk is illuminated.

   Quadrature of an orbit (Astron.), a point in an orbit which
      is at either extremity of the latus rectum drawn through
      the empty focus of the orbit.
      [1913 Webster]
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