The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic
section , the lines joining opposite polygon vertices
(polygon diagonals ) meet in a single point.
In 1847, Möbius (1885) gave a statement which generalizes Brianchon's theorem: if all lines (except possibly one) connecting two opposite vertices of a (
See also Duality Principle ,
Pascal's
Theorem
Explore with Wolfram|Alpha
References 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. Coxeter, H. S. M.
and Greitzer, S. L. "Brianchon's Theorem." §3.9 in Geometry
Revisited. 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. Graustein, W. C. Introduction
to Higher Geometry. Johnson,
R. A. §387 in Modern
Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Möbius, F. A.
Gesammelte
Werke, Vol. 1 Ogilvy, C. S. Excursions
in Geometry. Smogorzhevskii,
A. S. The
Ruler in Geometrical Constructions. Wells, D. The
Penguin Dictionary of Curious and Interesting Geometry. Referenced on Wolfram|Alpha Brianchon's Theorem
Cite this as:
Weisstein, Eric W. "Brianchon's Theorem."
From MathWorld https://mathworld.wolfram.com/BrianchonsTheorem.html
Subject classifications More... Less...
)-gon circumscribed on a conic section meet in one point,
then the same is true for the remaining line.
