# Principle of Duality in Space

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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:

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