quadrature of the moon

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.
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   2. A quadrate; a square. --Milton.
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   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.
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   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.
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   {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.
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