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.
Proof
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Also see
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:
- a sort of cat's cradle.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{V}$: "Greatness and Misery of Man"
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.16$: Pascal ($1623$ – $1662$)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$
