Axiom:Propositions of Incidence/Line
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Axiom
A (straight) line contains an infinite number of is points, and is completely determined by any two distinct points of that line.
Thus, if a line determined by points $A$ and $B$ also contains the points $X$ and $Y$, then the line determined by points $X$ and $Y$ is the same line, and also contains the points $A$ and $B$.
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