Proposition XI.14 — Planes to which the same straight line is at right angles wi…

Proof

If the two planes met, the line of intersection (XI.3) would meet the common perpendicular at right angles in two distinct places – contradicting XI.13.

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Depends on (3)

XI.3Proposition XI.3If two planes cut one another, their common section is a straight line.
XI.13Proposition XI.13From the same point two straight lines cannot be set up at right angles to the same plane on the same side.
XI.8Definition XI.8Parallel planes are those which do not meet.

Required by (dependents) (1)

XI.15Proposition XI.15If two straight lines meeting one another be parallel to two straight lines meeting one another, not being in the same…

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