The “logic” of diagrams in the Spherics of Theodosios

Abstract

This paper provides a semiotic reading of the relationship between the text and the diagram in Theodosios’ Spherics, focusing on Sph. II.4 and II.5. This analysis provides a detailed explanation of what the inferences in the text imply for the mathematical objects and for the diagram, and argues that these are independent. It argues that the objects, and in particular the letters that name them, function in semiotically different ways in the text and in the diagram, but that the role of the objects in the text is meant to be mathematically and logically prior. It then argues that many places in which the diagram seems to contain information that is not included in the text are best explained by errors of the editing process or of the transmission; but that there do remain a few places that require direct inferences from the diagram.