Proposition XI.22 — If there be three plane angles of which two, taken together …

Proof

The plane-angle inequality (XI.20) is precisely the triangle inequality for the joining chords; by I.22 (construction of a triangle on three given segments) the resulting triangle exists.

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Depends on (2)

I.22Proposition I.22Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is…
XI.20Proposition XI.20If a solid angle be contained by three plane angles, any two, taken together in any manner, are greater than the…

Required by (dependents) (1)

XI.23Proposition XI.23To construct a solid angle out of three plane angles, two of which, taken together in any manner, are greater than the…

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