Interpreting Tables of the Arithmetical Introduction of Nicomachus Through Pachymeres’ Treatment of Arithmetic: Preliminary Observations

  • Athanasia MegremiEmail author
  • Jean Christianidis
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 11)


Nicomachus of Gerasa’s Arithmetical introduction, a late antique arithmeticwork that was highly appreciated for its educational value throughout Late Antiquity and the Middle Ages, is traditionally characterized by historians of mathematics as theoretical, without any practical orientation at all. In this chapter, it is argued that the textual analysis of the work suggests otherwise. More specifically, the inclusion of tables that are accompanied by meticulously detailed instructions towards reading, constructing and using them, suggests that these particular sections of the work could be viewed in the context of a certain arithmetical practice and its learning. Furthermore, we will argue that the Quadrivium of the Byzantine scholar Georgios Pachymeres provides us with a case study of how the Nicomachean tables can be interpreted as devices that could be used in arithmetical problem-solving.


Nicomachus Diophantus Pachymeres Problem-solving Arithmetic Tables 



The authors thank Jeffrey Oaks, who kindly read this paper and suggested improvements. They also thank the anonymous referees for their remarks and corrections.



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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of History and Philosophy of ScienceNational and Kapodistrian University of AthensAthensGreece
  2. 2.Centre Alexandre KoyréParisFrance

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