欧几里得元素》中的角度比较

arXiv - MATH - History and Overview Pub Date : 2024-04-02 DOI:arxiv-2404.02272

Alexander Shen

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引用次数: 0

摘要

欧几里得的《圆》中的论述有一个明显的漏洞（似乎大多数注释者都没有注意到）：他经常比较的不只是角，而是角的*组*，同时他避免对角求和（以及考虑大于 $\pi$ 的角），也没有说明这种角组比较可能意味着什么。我们将讨论这个问题，并提出一种可能的解释，使欧几里得的论述前后一致。

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Comparing angles in Euclid's Elements

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.

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arXiv - MATH - History and Overview

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