Ideas: A History from Fire to Freud

33. Vrettos, Op. cit., page 43. The originals of many of Euclid’s works have been lost and they survive only in Arabic translations, later rendered into Latin and modern languages. Among those completely lost is one which may consist of his most original idea, Porisms. It is not quite clear what a porism was to Euclid but from later commentators it appears to have been a conception intermediate between a theorem and a problem. Boyer, Op. cit., page 101.

34. Lindberg, Op. cit., page 87.

35. Vrettos, Op. cit., page 50.

36. Ettore Carruccio, Mathematics and Logic in History and Contemporary Thought, London: Faber, 1964, pages 80–83.

37. Lindberg, Op. cit., page 88. Archimedes also developed ‘the method’. This, which explained his way of working, came to light in the most colourful of fashions. It was recovered almost by accident in 1906 by the Danish historian of science, J. L. Heiberg. He had read that at Constantinople there was a palimpsest ‘of mathematical content’. Boyer, Op. cit., page 139. A palimpsest is a parchment from which the original writing has been washed away and written over with a new text. Heiberg found that on this occasion the original writing had been imperfectly removed and, with the aid of photographs, he could read the original. This turned out to be a letter written by Archimedes to Eratosthenes, mathematician and librarian at Alexandria, containing fifteen propositions outlining his way of working which included, in some cases, hanging threads as one balances weights in mechanisms, to test his calculations. In other words, The Method explains how Archimedes went from levers to more advanced maths using the same principles. Ibid., page 137.

38. Lindberg, Op. cit., page 89.

39. Vrettos, Op. cit., page 58.

40. Ibid., pages 60ff.

41. Boyer, Op. cit., pages 140ff.

42. Lindberg, Op. cit., page 97.

43. Vrettos, Op. cit., pages 163–168.

44. Ibid.

45. Ibid.

46. Ibid., page 177.

47. Ibid., page 185.

48. Ibid., page 195.

49. Lindberg, Op. cit., page 97.

50. Heinrich von Staden, ‘Body and machine: interactions between medicine, mechanics and philosophy in early Alexandria’, in: Hamma (editor), Op. cit., pages 85ff.

51. Von Staden, Op. cit., page 87.

52. Ibid., page 89.

53. Ibid., page 92.

54. Ibid., page 95.

55. Lindberg, Op. cit., page 105. In Alexandria, doctors could be divided into those using folklore remedies, practitioners who could not read and write, and literate doctors, who sought to gain experience by reading texts, and translations of texts, from all over the world, studying theories and practices that other doctors used, or said that they used, seeking authority in the past.

56. Ibid.

57. Empereur, Op. cit., page 7.

58. Ibid., page 8.

59. Richards, Op. cit., page 173.

60. Ibid., page 27.

61. John Keay, India: A History, London: HarperCollins, 2000, pages 130–133.

62. Jean S. Sedlar, India and the Greek World, Totowa, New Jersey: Rowman & Littlefield, 1980, page 65.

63. Sedlar, Op. cit., page 82.

64. Ibid., page 84.

65. Ibid., page 92–93.

66. Radhakamal Mukerjee, The Culture and Art of India, London: Allen & Unwin, 1959, page 99.

67. Ibid., page 107.

68. Sedlar, Op. cit., page 109.

69. Ibid., page 111.

70. Ibid., page 112.

71. Ibid., page 122. H. G. Keene Cie, History of India, London: W. H. Allen, 1893, pages 28–29, dismisses this, arguing that Buddha emerged out of Brahmanism, which may also have given elements to early Judaism and thence to Christianity.

72. Sedlar, Op. cit., page 180.

73. Ibid., page 176.

74. Ibid., page 180.

75. Ibid., page 187.

76. Keay, Op. cit., page 78.

77. Ibid., page 85. Chandragupta was a Jain and retired to Karnataka, at Stravana Belgola, west of Bangalore. There, in a cave in a hill, the emperor is said to have starved himself to death, ‘the ultimate act of Jain self-denial’. Apparently, the emperor, so successful in many ways, abdicated after learning of an imminent famine from a famous monk, Bhadrabahu, said to be the last Jain monk to have known the founder of the faith, Mahavira Nataputta. Ibid., page 86.

78. A. L. Basham (editor), A Cultural History of India, Oxford and New Delhi: Oxford University Press, 1975, page 42.

79. Ibid., page 88. For the Pali/Prakrit scripts, see Richard Lannoy, The Speaking Tree: A Study of Indian Culture and Society, Oxford: Oxford University Press, 1971, page 328.

80. Keay, Op. cit., page 89.