# Duality Principle (Projective Geometry)

## Theorem

### Principle of Duality in the Plane

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.

### Principle of Duality in Space

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.