Theory of ratios in Nicomachus' Arithmetica and series of arithmetical problems in Pachymeres' Quadrivium
Reflections about a possible relationship
Bibliographic Data
| ID | 11745533 |
|---|---|
| Authors | Athanasia Megremi (National and Kapodistrian University of Athens, corresponding author), Jean Christianidis (0000-0002-9184-5126, National and Kapodistrian University of Athens) |
| Editors | A Bernard (0000-0001-7388-4562) |
| Year | 2015 |
| Volume | 22 |
| Pages | 00006-00006 |
| Publication date | 2015-01-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | SHS Web of Conferences (JOURNAL) |
| Journal identifiers | ISSN: 2261-2424 • E-ISSN: 2416-5182 |
| Publisher | EDP Sciences (PUBLISHER • FR) |
| DOI | 10.1051/shsconf/20152200006 |
| OpenAlex | W2198700923 |
| Language | EN |
| Citations received | 2 |
| References cited | 6 |
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
Algebra over a field · Arithmetic function · Diophantine equation · Discrete mathematics · Pure mathematics · Series (stratigraphy · Computer Science · Historical and Literary Studies · Historical, Religious, and Philosophical Studies · History and Theory of Mathematics · Mathematics
| Citations per year | 0.18 |
|---|---|
| Citation span | 2015 - 2015 (1) |
| Highly cited | No |