What is "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.

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

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.

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.

   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.