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帕斯卡定理


PascalsTheorem

布里安숑定理的對偶定理 (Casey 1888, p. 146),由 B. 帕斯卡於 1640 年在他僅 16 歲時發現 (Leibniz 1640; Wells 1986, p. 69)。它指出,給定一個內接於圓錐曲線的(不一定是的,甚至不一定是的)六邊形,其對邊延長線的三個交點共,該線稱為帕斯卡線

1847 年, Möbius (1885) 發表了帕斯卡定理的以下推廣:如果內接於圓錐曲線的 (4n+2) 邊形的相對邊延長線的交點(可能除了一個之外)共線,那麼對於剩餘的點也成立。


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布萊肯裡奇-麥克勞林構造法, 布里安숑定理, 凱萊-巴赫拉赫定理, 圓錐曲線, 對偶原理, 六邊形, 帕普斯六邊形定理, 帕斯卡線, 斯坦納點, 斯坦納定理

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參考文獻

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.

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帕斯卡定理

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Weisstein, Eric W. "帕斯卡定理。" 來自 --一個 資源。 https://mathworld.tw/PascalsTheorem.html

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