Bulletin (New Series) of the American Mathematical Society

“La croix des mathématiciens”: The Euclidean theory of irrational lines

Wilbur Knorr

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 9, Number 1 (1983), 41-69.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183550975

Mathematical Reviews number (MathSciNet)
MR699316

Zentralblatt MATH identifier
0538.01003

Subjects
Primary: 01A20: Greek, Roman

Citation

Knorr, Wilbur. “La croix des mathématiciens”: The Euclidean theory of irrational lines. Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 1, 41--69. https://projecteuclid.org/euclid.bams/1183550975


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References

  • Euclid (1969-73), Elementa, (J. L. Heiberg (ed.)), rev. E. Stamatis, 4 vols., Leipzig (based on the first Heiberg edition, 4 vols., 1883-85).
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  • Heath, T. L. (1926), The thirteen books of Euclid's Elements, 2nd ed., 3 vols., Cambridge.
  • Heath, T. L. (1949), Mathematics in Aristotle, Oxford. Junge, see Pappus (1930).
  • Knorr, W. R. (1975), The evolution of the Euclidean Elements, Dordrecht, Netherlands.
  • Knorr, W. R. (1978), Archimedes and the pre-Euclidean proportion theory, Arch. Internat. Hist. Sci., 28, 183-244.
  • Knorr, W. R. (1981), Aristotle and incommensurability, Arch. Hist. Exact Sci., 24, 1-9.
  • Maracchia, S. (1980), Aristotele e l'incommensurabilità, Arch. Hist. Exact Sci., 21, 201-228.
  • Mueller, I. (1981), Philosophy of mathematics and deductive structure in Euclid's Elements, Cambridge, Mass.
  • Neugebauer, O. (1957), The exact sciences in antiquity, 2nd ed., Providence, R. I.
  • Pappus (1876-78), Collectionis quae supersunt (F. Hultsch (ed.)), 3 vols., Berlin.
  • Pappus (1930), The commentary of Pappus on Book X of Euclid's Elements (text and translation by W. Thomson; notes and introduction by G. Junge), Cambridge, Mass.
  • Proclus (1873), In primum Euclidis Elementorum librum commentarii (G. Friedlein (ed.)), Leipzig. Thomson, see Pappus (1930).
  • van der Waerden, B. L. (1963), Science awakening, rev. ed., New York.
  • Zeuthen, H. G. (1896), Die geometrische Konstruktion als 'Existenzbeweis' in der antiken Geometrie, Math. Ann., 47, 222-228.

See also

  • Errata: Erratum. Bull. Amer. Math. Soc. (N.S.), Volume 10, Number 2 (1984), 351--351.