Source — Euclid's Elements, encoded as an rrxiv paper

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XI.20 Proposition XI.20

If a solid angle be contained by three plane angles, any two, taken together in any manner, are greater than the remaining one.

Proof

Suppose the largest face-angle is

∠ B A C

. Within

∠ B A C

construct

∠ B A D

equal to

∠ B A E

(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.

lines 74–74 in main.tex