References for: The real numbers: Pythagoras to Stevin

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  1. B Artmann, Euclid : The creation of mathematics (Springer, New York, Berlin, 1999).
  2. B Artmann, The concept of number (Wiley, Chichester, 1988).
  3. J N Crossley, The emergence of number (Upside Down A Book Company, Yarra Glen, 1980).
  4. H N Jahnke (ed.), A history of analysis (American Mathematical Society, Providence, R.I., 2003).
  5. C J Scriba, The concept of number (Mannheim-Zurich, 1968).
  1. R P Coelho, Old and new aspects of the theory of real numbers. I (Portuguese), in Proceedings of the First Spanish- Portuguese Mathematical Conference, Madrid, 1973, Consejo Sup. Inv. Cient. (Madrid, 1977), 168-181.
  2. J N Crossley, Number. I. Irrational numbers. Part 1, Austral. Math. Soc. Gaz. 4 (3) (1977), 73-85.
  3. J N Crossley, Number. I. Irrational numbers. Part 2, Austral. Math. Soc. Gaz. 5 (1) (1978), 1-14.
  4. S Giuntini, A discussion concerning the nature of zero and the relation between imaginary and real numbers (Italian), Boll. Storia Sci. Mat. 4 (1) (1984), 25-63.
  5. I Grattan-Guinness, Numbers, ratios, and proportions in Euclid's Elements : How did he handle them?, Historia Mathematica 23 (1996), 355-375.
  6. A Heimonen, How were the irrational numbers discovered? (Finnish), Arkhimedes (6) (1997), 10-16.
  7. M Lopez Pellicer, Constructions of real numbers (Spanish), in History of mathematics in the XIXth century, Part 2 (Spanish), Madrid, 1993, Real Acad. Cienc. Exact. Fís. Natur. (Madrid, 1994), 11-33.
  8. L C Mejlbo, Addendum to: "Some fundamental theorems about real numbers and their history" (Danish), Nordisk Mat. Tidskr. 25/26 (3-4) (1978), 120; 208.
  9. L C Mejlbo, Some fundamental theorems about real numbers and their history (Danish), Nordisk Mat. Tidskr. 25/26 (2) (1978), 57-69; 111.
  10. M Pihl, The place of Theodoros in Plato's "Theaitetos" and the earliest history of irrational numbers (Danish), Mat. Tidsskr. A. 1951 (1951), 19-38.
  11. J Simsa, Development of the concept of real numbers (Czech), in Mathematics in the 16th and 17th centuries (Czech), Jevícko, 1997 (Prometheus, Prague, 1999), 259-282.
  12. J E Snow, Views on the real numbers and the continuum, Rev. Mod. Log. 9 (1-2) 2001/03), 95-113.
  13. K von Fritz, The discovery of incommensurability by Hippasos of Metapontum, Ann. Math. 46 (1945), 242-264.

JOC/EFR October 2005

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