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