Three Non-Collinear Planes have One Point in Common

Theorem

Three planes which are not collinear have exactly one point in all three planes.


Proof

Let $A$, $B$ and $C$ be the three planes in question.

From Two Planes have Line in Common, $A$ and $B$ share a line, $p$ say.

From Propositions of Incidence: Plane and Line, $p$ meets $C$ in one point.

$\blacksquare$


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
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