Abstract A quick examination of the diagrams in the Greek manuscripts of Euclid's Elements shows that VII.28 is the only proposition which has a diagram with both horizontal and vertical lines, and it is quite similar to parallel propositions in Book X (X.15, 16). This leads to an audacious assumption that all the propositions of Book VII after it may have been added later, and their authenticity is examined by logical and linguistic analysis. In many of the propositions of Book VII after VII.28, we have found characteristics or idiosyncrasies which can be explained by the hypothesis of later addition. Moreover, some propositions can be interpreted as lemmata for conspicuous results in Book IX such as IX.20 (the number of prime numbers surpasses any given number), IX.36 (sufficient condition of a perfect number). While the prevalent view is that Book VII is a well-organized basic theory from which various arguments in the subsequent two books are developed, our examination suggests that Book VII itself contains heterogeneous components which are intended for specific arguments in subsequent books. Further investigation is needed to find out whether this heterogeneity in Book VII is the result of later intervention, or that of original compilation.

中文翻译：

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欧几里得元素算术书籍不同渊源的再考

摘要 对欧几里得几何原本希腊手稿中的图表进行快速检查表明，VII.28 是唯一一个同时具有水平线和垂直线的图表的命题，它与第十卷（X.15 16)。这导致了一个大胆的假设，即第七卷之后的所有命题可能都是后来添加的，并且它们的真实性通过逻辑和语言分析来检验。在VII.28之后的第七卷的许多命题中，我们发现了可以用后来添加的假设来解释的特征或特质。此外，有些命题可以解释为第九册中显着结果的引理，例如 IX.20（质数的数量超过任何给定数）、IX.36（完全数的充分条件）。虽然普遍的观点是，第七卷是一个组织良好的基础理论，随后两本书中的各种论点都从中发展出来，但我们的研究表明，第七卷本身包含了异类成分，这些成分旨在用于后续书籍中的特定论点。第七卷的这种异质性是后期干预的结果，还是原编的结果，还需要进一步调查。