Re-examination of the different origins of the arithmetical books of Euclid's \textit{Elements} (Q2001446)

Research has shown that some propositions of Euclid's \textit{Elements}, especially at the ends of certain books, may have been added to the text after its original composition. The author asserts that Book VII on arithmetic may be an example of this phenomenon. An unusual diagram in VII.28 leads to the hypothesis that VII.29--39 might be additions as well; this is verified by observations of differences in linguistic style and of the logical relations between propositions. This evidence is circumstantial, and the author leaves open the possibility that these differences may have existed already at Euclid's time; but he argues successfully that the view of Book VII as a unified treatise needs to be re-examined.