Principle of Duality in the Plane

Theorem

Let $P$ be a theorem of projective geometry proven using the propositions of incidence.

Let $Q$ be the statement created from $P$ by interchanging:

$(1): \quad$ the terms point and (straight) line

$(2): \quad$ the terms collinear (of points) and concurrent (of lines)

$(3): \quad$ the terms lie on and intersect at

and so on.

Then $Q$ is also a theorem of projective geometry.

Proof

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Sources

• 1952: T. Ewan Faulkner: Projective Geometry (2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.2$: The projective method: The principle of duality