Proposition XI.3 — If two planes cut one another, their common section is a str…

Proof

Take two points

A

B

in the common section. Draw the straight line

A B

in each plane; by XI.1 each segment of

A B

lies in its plane, and uniqueness of the line forces both segments to coincide.

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Depends on (2)

XI.1Proposition XI.1A part of a straight line cannot be in the plane of reference and a part in a plane more elevated.
1Postulate 1To draw a straight line from any point to any point.

Required by (dependents) (4)

XI.6Proposition XI.6If two straight lines be at right angles to the same plane, the straight lines will be parallel.
XI.14Proposition XI.14Planes to which the same straight line is at right angles will be parallel.
XI.16Proposition XI.16If two parallel planes be cut by any plane, their common sections are parallel.
XI.38Proposition XI.38If the sides of the opposite planes of a cube be bisected, and planes be carried through the points of section, the…

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