This article suggests a novel approach to the study of the argumentative structure of Proclus’ Elements of Theology (ET). Instead of studying it through the prism of the Elements of Euclid (EG), this novel approach proposes an evaluation of ET’s argumentative structure based on Proclus’ reflections about the genre of stoicheiôsis and the methods of dialectic and geometry. Thus, I argue that studies under the suggested form of evaluation should standardize the conceptual framework of their analyses about the features of (...) ET’s argumentative structure, explicating their relevance for the interpretation of the text’s system of logical relations. Moreover, this article presents some examples of editorial enhancements made by editors of ET clarifying the argumentative structure of the text. With these examples, I will show how these enhancements help us clarify the argumentative structure of ET. (shrink)

This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius’s Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their (...) properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams. (shrink)

Over the past few decades, the question regarding the proper understanding of Diophantus’s method has attracted much scholarly attention. “Modern 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. (shrink)