Pascal's theorem

American  

noun

Geometry.

1. the theorem that the lines joining adjacent vertices of a hexagon intersect the same straight line if alternate vertices lie on two intersecting straight lines.

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Etymology

Origin of Pascal's theorem

Named after Pascal

Example Sentences

Pascal's theorem furnishes an elegant solution of the problem of drawing a conic through five given points.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

This acknowledgment led Descartes to believe that Pascal's theorem should also be credited to Desargues.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

Pascal's theorem, then, may be stated as follows: The three pairs of opposite sides of a hexagon inscribed in a point-row of the second order meet in three points on a line.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

Also a conic can be defined as the locus of the points found by the usual construction, based upon Pascal’s theorem, for points on the conic through five given points.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various

Pascal's theorem then indicates that L = AB-CD, M = AD-BC, and N, which is the intersection of the tangents at A and C, are all on a straight line u.

From An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman