# Axiom:Propositions of Incidence

## Axioms

The **propositions of incidence** are basic properties of projective geometry which are accepted as true.

It is possible to derive these propositions from the basics of linear algebra.

### Line

A (straight) line contains an infinite number of is points, and is completely determined by any two distinct points of that line.

### Plane

A plane consists of an infinite number of points, and is completely determined by any three distinct points of that plane which are not collinear.

### Line in Plane

A line defined by any two distinct points in a plane lies entirely within that plane.

### Point

Any two distinct (straight) lines lying in a plane have exactly one point in common.

### Space

A (three-dimensional) space is completely determined by any four distinct points of that space which are not coplanar.

### Plane and Line

A plane and a (straight) line which does not lie in that plane have exactly one point in common.

## Sources

- 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.2$: The projective method: The propositions of incidence