The function of diorism in ancient Greek analysis

Ken Saito, Nathan Sidoli

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This paper is a contribution to our knowledge of Greek geometric analysis. In particular, we investigate the aspect of analysis know as diorism, which treats the conditions, arrangement, and totality of solutions to a given geometric problem, and we claim that diorism must be understood in a broader sense than historians of mathematics have generally admitted. In particular, we show that diorism was a type of mathematical investigation, not only of the limitation of a geometric solution, but also of the total number of solutions and of their arrangement. Because of the logical assumptions made in the analysis, the diorism was necessarily a separate investigation which could only be carried out after the analysis was complete.

Original languageEnglish
Pages (from-to)579-614
Number of pages36
JournalHistoria Mathematica
Volume37
Issue number4
DOIs
Publication statusPublished - 2010 Nov 1

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Keywords

  • Ancient Greek analysis
  • Apollonius
  • Archimedes
  • Diorism
  • Pappus

ASJC Scopus subject areas

  • Mathematics(all)
  • History

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