Proof
Suppose the largest face-angle is . Within
construct equal to (one of the other
face-angles). By I.4 / I.24, the corresponding chord arcs in space
give the desired strict triangle-style inequality among the
face-angles.
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Depends on (3)
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- I.20Proposition I.20In any triangle two sides taken together in any manner are greater than the remaining one.
- I.24Proposition I.24If two triangles have the two sides equal to two sides respectively, but have the one of the angles contained by the…
Required by (dependents) (3)
- XI.21Proposition XI.21Any solid angle is contained by plane angles less than four right angles.
- XI.22Proposition XI.22If there be three plane angles of which two, taken together in any manner, are greater than the remaining one, and they…
- 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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