  The exposition in Euclid's Elements contains an obvious gap (seemingly
unnoticed by most commentators): he often compares not just angles, but
*groups* of angles, and at the same time he avoids summing angles (and
considering angles greater than $\pi$), and does not say what such a comparison
of groups could mean. We discuss the problem and suggest a possible
interpretation that could make Euclid's exposition consistent.
