布里安숑定理的对偶定理 (Casey 1888, p. 146)，由 B. 帕斯卡于 1640 年在他仅 16 岁时发现 (Leibniz 1640; Wells 1986, p. 69)。它指出，给定一个内接于圆锥曲线的（不一定是正的，甚至不一定是凸的）六边形，其对边延长线的三个交点共线，该线称为帕斯卡线。
1847 年， Möbius (1885) 发表了帕斯卡定理的以下推广：如果内接于圆锥曲线的 
边形的相对边延长线的交点（可能除了一个之外）共线，那么对于剩余的点也成立。
帕斯卡定理
另请参阅
布莱肯里奇-麦克劳林构造法, 布里安숑定理, 凯莱-巴赫拉赫定理, 圆锥曲线, 对偶原理, 六边形, 帕普斯六边形定理, 帕斯卡线, 斯坦纳点, 斯坦纳定理在 Wolfram|Alpha 中探索
参考文献
Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 129-131, 1888.Casey, J. "Pascal's Theorem." §255 in A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 145, 328-329, and 354, 1893.Cayley, A. Quart J. 9, p. 348.Coxeter, H. S. M. and Greitzer, S. L. "L'hexagramme de Pascal. Un essai pur reconstituer cette découverte." Le Jeune Scientifique (Joliette, Quebec) 2, 70-72, 1963.Coxeter, H. S. M. and Greitzer, S. L. "Pascal's Theorem." §3.8 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 74-76, 1967.Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, p. 44, 1928.Evelyn, C. J. A.; Money-Coutts, G. B.; and Tyrrell, J. A. "Extensions of Pascal's and Brianchon's Theorems." Ch. 2 in The Seven Circles Theorem and Other New Theorems. London: Stacey International, pp. 8-30, 1974.Forder, H. G. Higher Course Geometry. Cambridge, England: Cambridge University Press, p. 13, 1931.Graustein, W. C. Introduction to Higher Geometry. New York: Macmillan, pp. 260-261, 1930.Johnson, R. A. §386 in Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 236-237, 1929.Lachlan, R. "Pascal's Theorem." §181-191 in An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 113-119, 1893.Leibniz, G. Letter to M. Périer. In Œuvres de B. Pascal, Vol. 5 (Ed. Bossut). p. 459.Möbius, F. A. Gesammelte Werke, Vol. 1. (Ed. R. Baltzer). Leipzig, Germany: S. Hirzel, pp. 589-595, 1885.Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 105-106, 1990.Pappas, T. "The Mystic Hexagram." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 118, 1989.Perfect, H. Topics in Geometry. London: Pergamon, p. 26, 1963.Salmon, G. §267 and "Notes: Pascal's Theorem, Art. 267" in A Treatise on Conic Sections, 6th ed. New York: Chelsea, pp. 245-246 and 379-382, 1960.Spieker, T. Lehrbuch der ebene Geometrie. Potsdam, Germany, 1888.Veronese. "Nuovi Teremi sull' Hexagrammum Mysticum." Real. Accad. dei Lincei. 1877.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 69, 1986.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 173, 1991.在 Wolfram|Alpha 上被引用
帕斯卡定理请引用为
Weisstein, Eric W. "帕斯卡定理。" 来自 MathWorld--一个 Wolfram Web 资源。 https://mathworld.net.cn/PascalsTheorem.html