| 单词 | Complete Quadrilateral |
| 释义 | Complete QuadrilateralThe figure determined by four lines and their six points of intersection (Johnson 1929, pp. 61-62). Note that this isdifferent from a Complete Quadrangle. The midpoints of the diagonals of a complete quadrilateral areCollinear (Johnson 1929, pp. 152-153). A theorem due to Steiner (Mention 1862, Johnson 1929, Steiner 1971) states that in a complete quadrilateral, the bisectors ofangles are Concurrent at 16 points which are the incenters and Excenters of the fourTriangles. Furthermore, these points are the intersections of two sets of four Circleseach of which is a member of a conjugate coaxal system. The axes of these systems intersect at the point common to theCircumcircles of the quadrilateral. See also Complete Quadrangle, Gauss-Bodenmiller Theorem, Polar Circle
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 230-231, 1969. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 61-62, 149, 152-153, and 255-256, 1929. Mention, M. J. ``Démonstration d'un Théorème de M. Steiner.'' Nouv. Ann. Math., 2nd Ser. 1, 16-20, 1862. Mention, M. J. ``Démonstration d'un Théorème de M. Steiner.'' Nouv. Ann. Math., 2nd Ser. 1, 65-67, 1862. Steiner, J. Gesammelte Werke, 2nd ed, Vol. 1. New York: Chelsea, p. 223, 1971. |
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