Advertisement

Hegel on Greek Mathematics and the Modern Calculus

  • Antonio Moretto
Chapter
Part of the Archives Internationales D’Histoire Des Idées / International Archives of the History of Ideas book series (ARCH, volume 136)

Abstract

In his Lectures on the History of Philosophy. Hegel notes that even in quite recent times, Kant has maintained that since the age of Aristotle, logic — like pure geometry since Euclid’s day — has been a complete and perfect science, which has kept its place even down to the present without attaining to any further scientific improvements or alteration.1

Keywords

Pythagorean Theorem Greek Mathematic Ultimate Ratio Infinitesimal Calculus Pure Geometry 
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.

Notes

  1. 1.
    Hegel LHP II.211; Hegel MM 19.199, 229.Google Scholar
  2. 2.
    In order not to confuse our exposition by continual quotation of what has already been said about Hegel and mathematics, we refer the reader to Bonsiepen, W. 1990; Moretto, A. 1984; Id. 1986a; Id. 1986b; Id. 1988; Id. 1990; Wolff, M. 1986.Google Scholar
  3. 3.
    Hegel Encyclopedia § 254 Remark; tr. Petry 1.223, 15-16.Google Scholar
  4. 4.
    Hegel GW 21, 197-198; tr. Miller p. 206.Google Scholar
  5. 5.
    Moretto, A. 1986b.Google Scholar
  6. 6.
    Hegel GW 21, 204; tr. Miller p. 213.Google Scholar
  7. 7.
    Hegel GW 21, 205; tr. Miller p. 214.Google Scholar
  8. 8.
    Cf. Hegel LHP I, 212ff; Hegel MM 18.241ff.Google Scholar
  9. 9.
    Cf. Plato, Philebus 13D; Hegel Encyclopedia § 95.Google Scholar
  10. 10.
    Cf. Cantor, G. 1966; Moretto, A. 1984; Id. 1986a; Id. 1988; Id. 1990.Google Scholar
  11. 11.
    Hegel GW 21, 205; tr. Miller p. 214.Google Scholar
  12. 12.
    Hegel GW 21, 205; tr. Miller p. 214.Google Scholar
  13. 13.
    Hegel GW 12, 209; tr. Miller p. 794.Google Scholar
  14. 14.
    Hegel GW 12, 202; tr. Miller p. 786.Google Scholar
  15. 15.
    Hegel GW 12, 203; tr. Miller p. 787.Google Scholar
  16. 16.
    Hegel, G.W.F. 1936, pp. 288-300.Google Scholar
  17. 17.
    Hegel GW 21, 200; tr. Miller p. 209.Google Scholar
  18. 18.
    Hegel GW 21, 200; tr. Miller p. 209.Google Scholar
  19. 19.
    Hegel GW 21, 199-200; tr. Miller pp. 208-209; Archimedes. 1798, p. 4 — the book was in Hegel’s library. Cf. Archimedes. 1910-15; Archimedes, n.d., reissue of the Heath edition of 1897, p. 3.Google Scholar
  20. 20.
    Hegel GW 12, 220; tr. Miller p. 806.Google Scholar
  21. 21.
    Hegel GW 12, 221; tr. Miller p. 807.Google Scholar
  22. 22.
    Hegel GW 12, 221; tr. Miller p. 808.Google Scholar
  23. 23.
    Neuser, W. 1987.Google Scholar
  24. 24.
    Euclid, 1781; Euclid, 1807.Google Scholar
  25. 25.
    Euclid, 1781, p. 4.Google Scholar
  26. 26.
    Hegel GW 12, 222; tr. Miller p. 808.Google Scholar
  27. 27.
    Hegel GW 12, 222; tr. Miller p. 808; cf. Hegel GW 12, 104ff; tr. Miller pp. 679ff.Google Scholar
  28. 28.
    Hegel GW 12, 223-24; tr. Miller p. 810.Google Scholar
  29. 29.
    Euclid, 1781, p. 2.Google Scholar
  30. 30.
    Hegel GW 12, 224; tr. Miller p. 811.Google Scholar
  31. 31.
    Hegel GW 12, 225; tr. Miller p. 812.Google Scholar
  32. 32.
    Lagrange, J.L. 1881, pp. 238ff.Google Scholar
  33. 33.
    Lagrange, J.L. 1881, p. 239.Google Scholar
  34. 34.
    Hegel GW 21, 296; tr. Miller p. 299.Google Scholar
  35. 35.
    Lagrange, J.L. 1881, pp. 241ff.Google Scholar
  36. 36.
    Hegel GW 21, 296-97; tr. Miller p. 299.Google Scholar
  37. 37.
    Kepler, J. 1960, p. 15Google Scholar
  38. 38.
    Hegel GW 21, 297; tr. Miller p. 299.Google Scholar
  39. 39.
    Hegel GW 21, 296; tr. Miller p. 299.Google Scholar
  40. 40.
    Lagrange, J.L. 1881, p. 20.Google Scholar
  41. 41.
    Newton Horsley II. 39.Google Scholar
  42. 42.
    Schmieden, C. and Laugwitz, D., 1958; Robinson, A. 1974; Laugwitz, D. 1978.Google Scholar
  43. 43.
    Newton Horsley II. 40.Google Scholar
  44. 44.
    Newton Horsley II. 277–278.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Antonio Moretto

There are no affiliations available

Personalised recommendations