Sophistic aspects of Pappus \textit{Collection}. (Q1566081)

This article takes up Pappus refutation of a construction of two mean proportionals between two given lines by plane means (i.e., ruler and compass) in the beginning of Book three of the \textit{Collection}, and proposes to interpret it as a sophistic argument. First, depending mainly on Philostratus, the activities of the sophists in late antiquity are described. Then the author shows that common characteristics are also found in Pappus's text. In the conclusion of the article, the author goes on to propose novel interpretations of the Greek analysis, and some of the technical terms such as ``given'' and ``problem''.