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Harmonic properties of the complete quadrilateral and quadrangle.

A figure formed by four lines in a plane is called a complete quadrilateral, or, shorter, a four-side.

The harmonic property of the complete quadrilateral is: Any diagonal or harmonic line is harmonically divided by the other two; and of a complete quadrangle: The angle at any harmonic point is divided harmonically by the joins to the other harmonic points.

A four-side is usually called a complete quadrilateral, and a four-point a complete quadrangle.

The method which has been used in Chapter II to develop the notion of four harmonic points by means of the complete quadrilateral is due to Von Staudt.