Περίληψη:
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.
