Proposition·Untested·2605.00009

Proposition XI.21

Any solid angle is contained by plane angles less than four right angles.

Proof

Cut a small polygon by a plane near the apex; the sum of the exterior angles of this polygon is less than (by I.32 / I.34 applied to the polygon). The interior face-angles at the apex are the supplements of these exterior angles, so their sum falls strictly short of .

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