35. Greek Mathematics to the Time of Euclid

  1. Mary Louise Gill2 and
  2. Pierre Pellegrin3
  1. Ian Mueller

Published Online: 8 MAY 2012

DOI: 10.1002/9781444305845.ch35

A Companion to Ancient Philosophy

A Companion to Ancient Philosophy

How to Cite

Mueller, I. (2012) Greek Mathematics to the Time of Euclid, in A Companion to Ancient Philosophy (eds M. L. Gill and P. Pellegrin), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781444305845.ch35

Editor Information

  1. 2

    Brown University, USA

  2. 3

    National Center for Scientific Research (Paris), France

Author Information

  1. University of Chicago, USA

Publication History

  1. Published Online: 8 MAY 2012
  2. Published Print: 2 MAY 2012

ISBN Information

Print ISBN: 9780631210610

Online ISBN: 9781444305845

SEARCH

Keywords:

  • Greek mathematics, at the time of Euclid;
  • Euclid's Elements, formal style, gradual evolution;
  • Aristotle and Plato on first principles;
  • Euclid's plane geometry;
  • The “Pythagorean” theorem;
  • proportion, role in Greek mathematics;
  • proportionality in Aristotle;
  • incommensurability, and magnitudes;
  • Hippocrates of Chios;
  • formal deduction and first principles, “clearly perceived” truths

Summary

This chapter contains sections titled:

  • Euclid's Elements

  • First Principles

  • Aspects of Euclid's Plane Geometry

  • Proportionality

  • Greek Arithmetic and its History

  • On the History of Greek Geometry

  • Conclusion

  • Bibliography