Pascal's Theorem

Theorem

Let $ABCDEF$ be a hexagon whose $6$ vertices lie on a conic section and whose opposite sides are not parallel.

Then the points of intersection of the opposite sides, when produced as necessary, all lie on a straight line.

Source of Name

This entry was named for Blaise Pascal.

Historical Note

Pascal's Theorem was discovered by Blaise Pascal when he was in his mid-teens, in the wake of his encounter with Euclid's The Elements.

He published it in his Essay pour les Coniques, which contains $400$ or so corollaries deduced from it, formed by allowing pairs of the six points involved to merge into coincidence.

James Joseph Sylvester called this theorem: