Axiom:Propositions of Incidence

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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 is completely determined by any two distinct points of that line.


Plane

A plane 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