The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just
16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a (not
necessarily regular, or even
convex) hexagon inscribed in a conic
section, the three pairs of the continuations of opposite sides meet on a straight
line, called the Pascal line.
In 1847, Möbius (1885) published the following generalization of Pascal's theorem: if all intersection points (except possibly one) of the lines prolonging two opposite
sides of a  -gon inscribed in a conic section
are collinear, then the same is true for the remaining point.
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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