[dr_lew]

The diagram illustrates the defining angles of the (angular) sides of a spherical triangle, and the angles betweeen them, which are dihedrals.

These definitions were unknown to Euclid, as trigonometry was a much later development.

However I did learn recently that the "law of cosines" of plane trigonometry is to be found in essence in Euclid Book II Prop. 12, so I think we can give the cartoon a pass.

[oh8eleven]

so I think we can give the cartoon a pass.
Whew, I was worried there for a minute :)