Advertisement

On the History of Indeterminate Problems of the First Degree in Greek Mathematics

  • Jean Christianidis
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 151)

Abstract

One of the most interesting issues in the early history of algebra is that of the formation of the methods for solving the first-degree indeterminate equations. In the traditional historiography such methods are primarily associated with the Chinese and the Indian mathematical traditions. The fact that the Remainder Theorem is commonly called “Chinese Remainder Theorem” in almost all the textbooks on Number Theory, strikingly expresses the traditional viewpoint. The same holds about the so called problem of the “hundred fowls”, the origins of which are also reduced to the Chinese mathematical tradition.1

Keywords

Diophantine Equation Chinese Remainder Theorem Proper Number Euclidean Algorithm Mathematical Tradition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Athenaeus, 1961, The Deipnosophists (Ed. Ch. Barton Gulick) 7 vols. (The Loeb Classical Library ). First printed 1927–1941.Google Scholar
  2. Baillet, J. (Ed.), 1892, Le papyrus mathématique d’ Akhmîm. Mémoires publiés par les membres de la Mission Archéologique Française au Caire, vol. IX, fasc. 1. Paris: Ernest Leroux.Google Scholar
  3. Diophantus, 1893–1895, Diophantus Alexandrinus Opera Omnia (Ed. P. Tannery) 2 vols. Leipzig: Teubner.Google Scholar
  4. Eganyan, A. M., 1972, Grescheskajia Logistika. Erevan: Aiastan.Google Scholar
  5. Fowler, D. H., 1980/1981, Archimedes’ Cattle Problem and the Pocket Calculating Machine. Coventry: University of Warwick, Math. Institute Preprint.Google Scholar
  6. Fowler, D. H., 1990, The Mathematics of Plato’s Academy. A New Reconstruction. Oxford: The Clarendon Press. First printed in hardback 1987.Google Scholar
  7. Heath, T. L., 1897, The Works of Archimedes. Cambridge: University Press.Google Scholar
  8. Heath, T. L., 1981, A History of Greek Mathematics, 2 vols. New York: Dover. First printed 1921.Google Scholar
  9. Hunger, H. and Vogel, K. (Eds.), 1963, Ein Byzantinisches Rechenbuch des 15. Jahrhunderts. österreichische Akademie der Wissenschaften. Philosophisch-Historische Klasse. Denkschriften, Bd 78, Abh. 2. Wien.Google Scholar
  10. Iamblichus, 1894, In Nicomachi Arithmeticam Introductionem liber (Ed. H. Pistelli). Leipzig: Teubner.Google Scholar
  11. Knorr, W. R., 1982, Techniques of fractions in ancient Egypt and Greece. Historia Mathematica 9, 133–171.CrossRefGoogle Scholar
  12. Libbrecht, U., 1973, Chinese Mathematics in the Thirteenth Century. Cambridge: The M.I.T. Press.Google Scholar
  13. Nicomachus, 1866, Nicomachi Geraseni Pythagorei Introductionis Arithmeticae libri II (Ed. R. Hoche). Leipzig: Teubner.Google Scholar
  14. Paton, W. R. (Ed.), 1960, The Greek Anthology, 5 vols. ( The Loeb Classical Library ). First printed 1916–1918.Google Scholar
  15. Tannery, P., 1912, La perte des sept livres de Diophante. Mémoires Scientifiques (Eds. J.-L. Heiberg and H.-G. Zeuthen ) 2, 73–90.Google Scholar
  16. Toulouse: E. Privat and Paris: Gauthier-Villars. First printed in Bulletin des Sciences Mathématiques 8 (1884), 192–206.Google Scholar
  17. Van der Waerden, B. L., 1983, Geometry and Algebra in Ancient Civilizations. Berlin/Heidelberg/New York/Tokio: Springer-Verlag.CrossRefGoogle Scholar
  18. Winter, J. G. (Ed.), 1936, Papyri in the University of Michigan collection. Miscellaneous papyri. Michigan Papyri, vol. 3. Ann Arbor: University of Michigan Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Jean Christianidis
    • 1
  1. 1.Greek Naval AcademyAthensGreece

Personalised recommendations