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.
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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p. 173, 1991. Referenced on Wolfram|Alpha Pascal's Theorem
Cite this as:
Weisstein, Eric W. "Pascal's Theorem."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/PascalsTheorem.html
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