## References for: The real numbers: Pythagoras to Stevin

**Books:**
- B Artmann,
*Euclid : The creation of mathematics* (Springer, New York, Berlin, 1999).
- B Artmann,
*The concept of number* (Wiley, Chichester, 1988).
- J N Crossley,
*The emergence of number* (Upside Down A Book Company, Yarra Glen, 1980).
- H N Jahnke (ed.),
*A history of analysis* (American Mathematical Society, Providence, R.I., 2003).
- C J Scriba,
*The concept of number* (Mannheim-Zurich, 1968).

**Papers:**
- 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.
- J N Crossley, Number. I. Irrational numbers. Part 1,
*Austral. Math. Soc. Gaz.* **4** (3) (1977), 73-85.
- J N Crossley, Number. I. Irrational numbers. Part 2,
*Austral. Math. Soc. Gaz.* **5** (1) (1978), 1-14.
- 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.
- I Grattan-Guinness, Numbers, ratios, and proportions in Euclid's Elements : How did he handle them?,
*Historia Mathematica* **23** (1996), 355-375.
- A Heimonen, How were the irrational numbers discovered? (Finnish),
*Arkhimedes* (6) (1997), 10-16.
- 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. F’s. Natur.* (Madrid, 1994), 11-33.
- 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.
- L C Mejlbo, Some fundamental theorems about real numbers and their history (Danish),
*Nordisk Mat. Tidskr.* **25/26** (2) (1978), 57-69; 111.
- 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.
- J Simsa, Development of the concept of real numbers (Czech), in
*Mathematics in the 16th and 17th centuries (Czech), Jev’cko, 1997* (Prometheus, Prague, 1999), 259-282.
- J E Snow, Views on the real numbers and the continuum,
*Rev. Mod. Log.* **9** (1-2) 2001/03), 95-113.
- K von Fritz, The discovery of incommensurability by Hippasos of Metapontum, Ann. Math. 46 (1945), 242-264.

JOC/EFR **October 2005**
**MacTutor History of Mathematics**

[http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/Real_numbers_1.html]