Theory of ratios in Nicomachus'Arithmeticaand series of arithmetical problems in Pachymeres'Quadrivium: Reflections about a possible relationship
Year: 2015
Type: conference-paper
Abstract: The voluminous Treatise of the four mathematical sciences of Georgios Pachymeres is the most renowned quadrivium produced in Byzantium. Among its specific features, historians of mathematics have pointed out, is the inclusion of Diophantus, besides Nicomachus and Euclid, in the sources for the arithmetical section and, accordingly, the incorporation of series of problems and problem-solving in its contents. The present paper investigates the “Diophantine portion” of Pachymeres' treatise and it shows that it is structured according to two criteria intrinsically characterized by seriality: on one hand, the arrangement in which the problems are presented in book I of Diophantus' Arithmetica; on the other hand, for those problems of which the enunciation involves ratio, the order in which Nicomachus discusses the kinds of ratios in his Arithmetical introduction. Furthermore, it analyses the solutions that Pachymeres offers and argues that Nicomachus' Arithmetical introduction provides the necessary tools for pursuing them.
Source: SHS Web of Conferences
Authors: Athanasia Megremi, Jean Christianidis
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2198700923