Pascal's theorem

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.

Word History and Origins

Origin of Pascal's theorem¹

Named after Pascal

Example Sentences

We may therefore now state Pascal’s and Brianchon’s theorem thus— Pascal’s Theorem.—If a hexagon be inscribed in a conic, then the intersections of opposite sides lie in a line.

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Pascal’s Theorem.—If a solid angle of six faces be inscribed in a cone of the second order, then the intersections of opposite faces are three lines in a plane.

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

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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.

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It is convenient, in making use of Pascal’s theorem, to number the points, to indicate the order in which they are to be taken in forming a hexagon, which, by the way, may be done in 60 different ways.

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