Analytical Reasoning and Problem-Solving in Diophantus’s Arithmetica : Two Different Styles of Reasoning in Greek Mathematics

Abstract

Over the past few decades, the question regarding the proper understanding of Diophantus’s method has attracted much scholarly attention. “Modern (i.e., post-Vietan) algebra”, “algebraic geometry”, “arithmetic”, “analysis and synthesis”, have been suggested by historians as suitable contexts for describing Diophantus’s resolutory procedures, while the category of “premodern algebra” has recently been proposed by other historians to this end. The aim of this paper is to provide arguments against the idea of contextualizing Diophantus’s modus operandi within the conceptual framework of the ancient analysis and to examine the few instances, in the preserved books of the Arithmetica, which might be regarded as linked to practices belonging to the field of analysis.