The Limits of Text in Greek Mathematics

Abstract

This article argues for a limited role of the text in Greek mathematics, in two senses of “text”: the verbal as opposed to the visual; and the literate as opposed to the “oral” (understood in a wide sense). The Greek mathematical argument proceeds not within the confines of the verbal alone, but essentially relies upon diagrams. On the other hand, it does not use other specific techniques, such as those of the modern cross-reference, relying instead upon verbal echoes. The two, taken together, suggest a model of scientific writing radically different from what we associate with our own mathematics. In methodological terms, the article surveys its evidence in detail, and makes comments concerning the methodology of studying ancient texts through the evidence of those texts alone.