Mathematical  Culture and Thought

Mathematical Culture and Thought

Euclid ‎and Axiomatic Geometry

Document Type : Translation

Author
Faculty of Mathematics, K. N. Toosi University of ‎Technology‎‎, ‎Iran
Abstract
In this paper, the logical development of Euclidean geometry as presented in Euclid’s Elements, has been studied. Pointing out some gaps in the Euclid arguments, the need for modern axiomatic systems has been explored.
Keywords
Subjects

Lee, John M., Axiomatic Geometry, American Mathematical Society, Providence, RI, 201‎3, ‎1-21.‎

[1]    Ball, W. W. Rouse, Mathematical Recreations and Essays, 13th ed., Dover, Mineola, NY, 1987.
[2]    Birkhoff, George D., Beatley, R., Basic Geometry, Scott, Foresman, Chicago, 1941.
[3]    Euclid, Euclid’s Elements (Dana Densmore, ed.), translated by Thomas L. Heath, Green Lion Press, Santa Fe, NM, 2002.
[4]    Greenberg, Marvin J., Euclidean and Non-Euclidean Geometries, 4th ed., W. H. Freeman, New York, 2008
[5]    Playfair, John, Elements of Geometry: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids, Bell & Bradfute and G. G. & J. Robinson, London, 1795.
[6]    Proclus, A Commentary on the First Book of Euclid’s Elements, translated by Glenn R. Morrow, Princeton University Press, Princeton, NJ, 1970.
Volume 42, Issue 2 - Serial Number 73
December 2023
Pages 83-110

  • Receive Date 16 March 2023
  • Accept Date 27 April 2023
  • Publish Date 22 December 2023