Proposition XI.16 — If two parallel planes be cut by any plane, their common sec…

Proof

The two intersection lines lie in the cutting plane, and if they met, the meeting point would belong to both parallel planes – which is impossible.

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Full neighborhood

Depends on (2)

XI.3Proposition XI.3If two planes cut one another, their common section is a straight line.
XI.8Definition XI.8Parallel planes are those which do not meet.

Required by (dependents) (3)

XI.17Proposition XI.17If two straight lines be cut by parallel planes, they will be cut in the same ratios.
XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
XII.13Proposition XII.13If a cylinder be cut by a plane which is parallel to its opposite planes, then, as the cylinder is to the cylinder, so…

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