# Plane contains Infinite Number of Lines

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## Theorem

A plane contains an infinite number of distinct lines.

## Proof

A plane contains an infinite number of points.

Not all these points are collinear.

From Propositions of Incidence: Line in Plane, any two points determine a line.

Hence the result.

$\blacksquare$

## Sources

- 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): $1.2$: The projective method