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.

From Project Gutenberg

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.

From Project Gutenberg

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

From Project Gutenberg

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 Project Gutenberg

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.

From Project Gutenberg