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

We may therefore state the required condition, together with the reciprocal one, as follows:— 697 Pascal’s Theorem.—If a hexagon be inscribed in a curve of the second order, then the intersections of opposite sides are three points in a line.

From Project Gutenberg

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 Project Gutenberg

Pascal’s theorem may be used when five points are given to find more points on the curve, viz. it enables us to find the point where any line through one of the given points cuts the curve again.

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

If the points 1 2 3 4 5 are given, and we want a 6th point on a line drawn through 1, we know all the sides of the hexagon with the exception of 5 6, and this is found by Pascal’s theorem.

From Project Gutenberg