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 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

But by Pascal’s theorem D1 and D2 will always lie in a line with S, so that the rows described by D1 and D2 are perspective.

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

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

Pascal's theorem thus affords a ready method of drawing the tangent line to a conic at a given point.

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