English

Comparing angles in Euclid's Elements

History and Overview 2024-04-04 v1

Abstract

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\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.

Cite

@article{arxiv.2404.02272,
  title  = {Comparing angles in Euclid's Elements},
  author = {Alexander Shen},
  journal= {arXiv preprint arXiv:2404.02272},
  year   = {2024}
}
R2 v1 2026-06-28T15:42:18.968Z