2024/04/02 by Shen, Alexander
#01A20 #FOS: Mathematics #History and Overview (math.HO)
paper · doi:10.48550/arxiv.2404.02272
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 π), 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.