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

If five points be given, Pascal’s theorem affords a solution; if five tangents, Brianchon’s theorem is employed.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 3 "Electrostatics" to "Engis" by Various

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 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

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

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