Advertisement

Archive for History of Exact Sciences

, Volume 70, Issue 2, pp 175–204 | Cite as

A new reading of Archytas’ doubling of the cube and its implications

  • Ramon Masià
Article

Abstract

The solution attributed to Archytas for the problem of doubling the cube is a landmark of the pre-Euclidean mathematics. This paper offers textual arguments for a new reading of the text of Archytas’ solution for doubling the cube, and an approach to the solution which fits closely with the new reading. The paper also reviews modern attempts to explain the text, which are as complicated as the original, and its connections with some xvi-century mathematical results, without any documented relation to Archytas’ doubling the cube.

Keywords

Initial Configuration Great Circle Final Configuration Textual Evidence Geometrical Element 
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.

References

  1. Acerbi, Fabio. 2012. I codici stilistici della matematica greca: Dimostrazioni, procedure, algoritmi. Quaderni Urbinati di Cultura Classica 101: 167–216.Google Scholar
  2. Archimedes. 1910–1915. Archimedis Opera Omnia, cum Commentariis Eutocii, iterum edidit I.L. Heiberg. 3 vol. Leipzig, B.G: Teubner (reprint: Stuttgart und Leipzig: B.G. Teubner 1972).Google Scholar
  3. Becker, Oskar. 1966. Das Mathematische Denken Der Antike. Göttingen: Vandenhoeck & Ruprecht.Google Scholar
  4. Burkert, Walter. 1972. Lore and Science in Ancient Pythagoreanism. Cambridge: Harvard University Press.Google Scholar
  5. Clagett, Marshall. 1964–1984. Archimedes in the Middle Ages. 5 vol. in 10 tomes. Vol. 1. The Arabo-Latin Tradition. Madison: The University of Wisconsin Press 1964; Vol. 2. The Translations from the Greek by William of Moerbeke. Memoirs 117. 2 tomes. Philadelphia: American Philosophical Society 1976; Vol. 3. The Fate of the Medieval Archimedes 1300--1565. Memoirs 125. 3 tomes. Philadelphia: American Philosophical Society 1978; Vol. 4. A Supplement on the Medieval Latin Traditions of Conic Sections (1150--1566). Memoirs 137. 2 tomes. Philadelphia: American Philosophical Society 1980; Vol. 5. Quasi-Archimedean Geometry in the Thirteenth Century. Memoirs 157. 2 tomes. Philadelphia: American Philosophical Society 1984.Google Scholar
  6. Euclide. 2007. Tutte le Opere. Introduzione, traduzione, note e apparati di Fabio Acerbi. Milano: Bompiani (reprint: 2008).Google Scholar
  7. Heath, Thomas Little. 1921. A history of greek mathematics, 2. vol. Oxford: Oxford University Press. (reprint: New York: Dover Publications, Inc. 1981).Google Scholar
  8. Kepler, Johannes. 1609. Astronomia Nova. Heidelberg: Voegelin. Web e-rara. doi: 10.3931/e-rara-558.
  9. Knorr, Wilbur Richard. 1986. The ancient tradition of geometric problems. Basel: Birkhäuser.Google Scholar
  10. Knorr, Wilbur Richard. 1989. Textual studies in ancient and medieval geometry. Basel: Birkhäuser.CrossRefzbMATHGoogle Scholar
  11. Loria, Gino. 1902. Spezielle algebraische und transscendente Ebene Kurven: Theorie und Geschichte. Leipzig: Teubner. Web Internet Archive. https://archive.org/stream/speziellealgebr00lorigoog#page/n4/mode/2up.
  12. Masià, Ramon. 2012. La llengua d’Arquimedes a De Sphaera et De Cylindro, Ph.D. Thesis. http://diposit.ub.edu/dspace/handle/2445/46868.
  13. Netz, Reviel. 1999. Proclus’ division of the mathematical proposition into parts: How and why was it formulated? Classical Quarterly 49(1): 282–303.CrossRefMathSciNetGoogle Scholar
  14. Prado, Jerónimo, Villalpando, Juan Bautista. 1596–1604. In Ezechielem explanationes et apparatus urbis, ac templi Hierosolymitani commentariis et imaginibus illustratus. Opus tribus tomis distinctum. Roma: ex typographia Aloysii Zannetii. Web e-rara. http://www.e-rara.ch/zut/content/titleinfo/3799530.
  15. Tannery, Paul. 1912–1915. Mémoires Scientifiques, v. i. Paris: Éditions Jacques Gabay (reprint: 1995).Google Scholar
  16. Thomas, Ivor. 1951. Greek mathematical works, v. ii. Cambridge, MA: Harvard University Press. (reprint: 2000).Google Scholar
  17. van der Waerden, Bartel Leendert. 1954. Science awakening. Groningen: Noordhoff.zbMATHGoogle Scholar
  18. Viviani, Vincenzio. 1674. Diporto Geometrico. In Quinto libro degli Elementi d’Euclide, ovvero, Scienza universale delle proporzioni spiegata colla dottrina del Galileo. Firenze: alla Condotta. Web Museo Galileo. http://193.206.220.110/Teca/Viewer?an=300943.

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Universitat Oberta de CatalunyaBarcelonaSpain

Personalised recommendations