Principle of Duality in Space

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 plane

$(2) \quad$ the terms lie on and intersect at

and so on.

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

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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