Pappus's Hexagon Theorem/Historical Note

Historical Note on Pappus's Hexagon Theorem

Pappus's Hexagon Theorem was first proved by Pappus of Alexandria in about $300$ CE.

The theorem is stated as Propositions $138$, $139$, $141$, and $143$ of Book $\text{VII}$ of Pappus's Collection.

It is noted that it is a limiting case of Pascal's Mystic Hexagram.

In $1899$ its full significance was revealed by David Hilbert, during his work on clarifying the foundations of geometry.

Sources

• 1952: T. Ewan Faulkner: Projective Geometry (2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.1$: Historical Note
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $9$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.8$: Pappus (fourth century A.D.)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $9$