Comparing angles in Euclid's Elements
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910397125099520 |
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| author | Shen, Alexander |
| author_facet | Shen, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparing angles in Euclid's Elements Shen, Alexander History and Overview 01A20 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. |
| title | Comparing angles in Euclid's Elements |
| topic | History and Overview 01A20 |
| url | https://arxiv.org/abs/2404.02272 |