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
See also Braikenridge-Maclaurin Construction ,
Brianchon's Theorem ,
Cayley-Bacharach
Theorem ,
Conic Section ,
Duality
Principle ,
Hexagon ,
Pappus's
Hexagon Theorem ,
Pascal Lines ,
Steiner
Points ,
Steiner's Theorem
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§255 in A
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Containing an Account of Its Most Recent Extensions, with Numerous Examples, 2nd
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Cambridge, England: Cambridge University Press, p. 13, 1931. Graustein,
W. C. Introduction
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R. A. §386 in Modern
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de B. Pascal, Vol. 5 (Ed. Bossut). p. 459. Möbius,
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Werke, Vol. 1. Ogilvy, C. S. Excursions
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Penguin Dictionary of Curious and Interesting Geometry. Referenced on Wolfram|Alpha Pascal's Theorem
Cite this as:
Weisstein, Eric W. "Pascal's Theorem."
From MathWorld https://mathworld.wolfram.com/PascalsTheorem.html
Subject classifications
-gon
inscribed in a conic section are collinear, then the same is true for the remaining
point.
