Principle of Duality in the Plane
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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