The Meaning of Hypostasis in Diophantus’ Arithmetica

Abstract

Historians of ancient philosophy and theological writers often come up against the puzzling issue of understanding the meaning of the term hypostasis used by different ancient authors. One could hardly expect that the same issue would be of interest for historians of ancient mathematics. Indeed, altogether absent from the works of Euclid, Archimedes, and Apollonius, and scarcely appearing in a nonmathematical context in the works of Heron and Nicomachus, the term hypostasis and its cognates appear 127 times in the six books of Diophantus’ Arithmetica preserved in Greek. This chapter examines Diophantus’ use of the term hypostasis and argues in favour of interpreting it as a term for numbers qua specific, individual entities. It is composed of three parts. The first part discusses the different statuses of numbers in a worked-out problem according to Diophantus’ general method, and the relevant issue of the Diophantine conception of an arithmetical problem; the second part investigates all instances of the term within Diophantus’ text; and the third part surveys briefly the testimonies of the Byzantine commentators of the Arithmetica, which provide further evidence supporting the interpretation proposed in this paper.