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

The applications of this theorem are very numerous; for instance, we derive from it Pascal’s theorem of the inscribed hexagon.

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

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

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

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

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