Pascal's Theorem


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 (4n+2)-gon inscribed in a conic section are collinear, then the same is true for the remaining point.

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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Pascal's Theorem

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Weisstein, Eric W. "Pascal's Theorem." From MathWorld--A Wolfram Web Resource.

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