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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]