173. Joseph and Frances Gies, Leonard of Pisa and the New Mathematics of the Middle Ages Leonard of Pisa and the New Mathematics of the Middle Ages, New York, 1969, p. 58. An edition of Liber abaci Liber abaci (in the original Latin) was published in Rome, in (in the original Latin) was published in Rome, in Scritti di Leonardo Pisano Scritti di Leonardo Pisano, edited by Balda.s.sarre Boncompagni (18571864). Leonardo's Liber quadratorum Liber quadratorum (Book of square numbers) was translated into French in 1952 by Paul Ver Eecke, as (Book of square numbers) was translated into French in 1952 by Paul Ver Eecke, as Le Livre des nombres carres Le Livre des nombres carres.

174. J. and F. Gies, Leonard of Pisa Leonard of Pisa, pp. 7784.

175. Ibid., pp. 6263.

176. James Gairdner, ed., The Paston Letters, 14221509 The Paston Letters, 14221509, London, 1904, vol. VI, p. 22.

177. Singer, "Epilogue," in Singer, II, p. 767.

178. Crombie, Medieval and Early Modern Science Medieval and Early Modern Science, vol. I, p. 97.

179. Stiefel, "'Impious Men,'" p. 212.

180. Dales, Scientific Achievement Scientific Achievement, pp. 6370.

181. B. Gille, "Techniques of a.s.sembly," in Daumas, II, p. 97.

182. Dales, Scientific Achievement Scientific Achievement, p. 61.

183. Haskins, Renaissance of the Twelfth Century Renaissance of the Twelfth Century, p. 310.

184. Nicholas H. Steneck, "The Relevance of the Middle Ages to the History of Science and Technology," in Long, Science and Technology Science and Technology, p. 22.

185. Forbes and Dijksterhuis, p. 97.

186. Ibid., p. 98.

187. Benton, "Ideas of Order," p. 22; Richard C. Dales, "Robert Grosseteste's View on Astrology," Medieval Studies Medieval Studies 29 (1967), pp. 35763. 29 (1967), pp. 35763.

188. Chaucer, Canterbury Tales Canterbury Tales, trans. Neville Coghill, Baltimore, 1952, p. 28 (Prologue, II, lines 411 ff.).

189. Crombie, Medieval and Early Modern Science Medieval and Early Modern Science, I, p. 227.

190. Ibid., p. 96.

191. B. Gille, "Technology and Civilization of the Medieval West," in Daumas, I, p. 571.

192. White, Medieval Religion and Technology Medieval Religion and Technology, p. 39.

193. Haskins, Renaissance of the Twelfth Century Renaissance of the Twelfth Century, p. 333.

194. Crombie, Medieval and Early Modern Science Medieval and Early Modern Science, I, p. 182.

195. Samuel Eliot Morison, The European Discovery of America: The Southern Voyages, A.D. 14921616 The European Discovery of America: The Southern Voyages, A.D. 14921616, New York, 1974, pp. 27, 39.

196. Charles Homer Haskins, Studies in Mediaeval Culture Studies in Mediaeval Culture, Oxford, 1929, p. 25.

7: LEONARDO AND COLUMBUS: THE END OF THE MIDDLE AGES.

1. Lopez, "Still Another Renaissance?" p. 2.

2. Haskins, Renaissance of the Twelfth Century Renaissance of the Twelfth Century.

3. Bert S. Hall, "The New Leonardo," Isis Isis 67 (1976), p. 475. In his review of 67 (1976), p. 475. In his review of Leonardo da Vinci, the Madrid Codices Leonardo da Vinci, the Madrid Codices, Hall quotes an "offhand remark" of Ladislao Reti, the editor of the Codices, on Leonardo's two metiers: "At last people will start believing me when I tell them that Leonardo da Vinci was an engineer who occasionally painted a picture when he was broke" (p. 475).

4. William of Malmesbury, Chronicle of the Kings of England Chronicle of the Kings of England, pp. 25152; Lynn White, "Eilmer of Malmesbury, an Eleventh-Century Aviator: A Case Study of Technological Innovation, Its Context and Tradition," Technology and Culture Technology and Culture 2 (1961), pp. 97111. 2 (1961), pp. 97111.

5. Robert Brun, "Notes sur le commerce des objets d'art en France et princ.i.p.alement a Avignon a la fin du XIVe siecle," Bibliotheque de l'Ecole des Chartes Bibliotheque de l'Ecole des Chartes 95 (1934), pp. 32746. 95 (1934), pp. 32746.

6. Phillips, Medieval Expansion of Europe Medieval Expansion of Europe, p. 154.

7. Audin, "Printing," in Daumas, II, pp. 63940.

8. Ibid., pp. 62223; B. Gille, "Techniques of a.s.sembly," in Daumas, II, pp. 99101; Derry and Williams, p. 235.

9. Audin, "Printing," in Daumas, II, pp. 63234.

10. A. Rupert Hall, "Early Modern Technology to 1600," in Melvin Kranzberg and Carroll W. Pursell, Jr., eds., Technology in Western Civilization Technology in Western Civilization, vol. I, The Emergence of Modern Industrial Society, Earliest Times to 1900 The Emergence of Modern Industrial Society, Earliest Times to 1900, New York, 1967, p. 101.

11. Audin, "Printing," in Daumas, II, p. 638.

12. B. Gille, "Techniques of a.s.sembly," in Daumas, II, p. 100.

13. Ibid., pp. 99100.

14. Ibid., p. 101; Derry and Williams, p. 239.

15. Derry and Williams, p. 239.

16. Ibid., p. 237.

17. Ibid., p. 236; Hall, "Early Modern Technology," p. 101; Forbes and Dijksterhuis, p. 145.

18. Cymbeline Cymbeline, I, i.

19. Derry and Williams, p. 236; B. Gille, "Techniques of a.s.sembly," in Daumas, II, p. 101; Audin, "Printing," in Daumas, II, pp. 64647.

20. Elizabeth E. Eisenstein, The Printing Press as an Agent of Change The Printing Press as an Agent of Change, Cambridge, 1979, vol. I, p. 54.

21. Ivor B. Hart, The World of Leonardo da Vinci, Man of Science, Engineer, and Dreamer of Flight The World of Leonardo da Vinci, Man of Science, Engineer, and Dreamer of Flight, New York, 1962, p. 61.

22. Eisenstein, Printing Press Printing Press, I, p. 46.

23. Audin, "Printing," in Daumas, II, pp. 64344.

24. Eisenstein, Printing Press Printing Press, I, p. 55.

25. Derry and Williams, p. 240.

26. Hart, World of Leonardo da Vinci World of Leonardo da Vinci, p. 62.

27. Samuel Eliot Morison, The European Discovery of America: The Northern Voyages The European Discovery of America: The Northern Voyages, A.D. 5001600, New York, 1971, p. 105.

28. A. C. Crombie, Medieval and Early Modern Science Medieval and Early Modern Science, vol. II, Science in the Later Middle Ages and Early Modern Times, XIIIXVII Centuries Science in the Later Middle Ages and Early Modern Times, XIIIXVII Centuries, New York, 1959 (first pub. in 1952), pp. 11112.

29. Derry and Williams, p. 235.

30. Contamine, War in the Middle Ages War in the Middle Ages, p. 145.

31. Jules Quicherat, ed., Proces de cond.a.m.nation et de rehabilitation de Jeanne d'Arc, dite la pucelle Proces de cond.a.m.nation et de rehabilitation de Jeanne d'Arc, dite la pucelle, Paris, 18411849, vol. III, p. 211, cited in Frances Gies, Joan of Arc: The Legend, the Reality Joan of Arc: The Legend, the Reality, New York, 1981, p. 77.

32. Ritchie Calder, Leonardo and the Age of the Eye Leonardo and the Age of the Eye, New York, 1970, p. 94.

33. Contamine, War in the Middle Ages War in the Middle Ages, pp. 14243; Forbes and Dijksterhuis, p. 140.

34. Cipolla, European Culture European Culture, p. 75.

35. Paul Gille, "Military Techniques," in Daumas, II, pp. 47475.

36. Bertrand Gille, "Military Techniques," in Daumas, II, p. 107.

37. P. Gille, "Military Techniques," in Daumas, II, p. 477.

38. B. Gille, "Military Techniques," in Daumas, II, p. 103.

39. Cipolla, European Culture European Culture, p. 38.

40. B. Gille, "Military Techniques," in Daumas, II, p. 114.

41. Needham, Science and Civilization Science and Civilization, vol. V, pt. 7, pp. 1618.

42. B. Gille, Renaissance Engineers Renaissance Engineers, p. 58.

43. Honore Bonet, The Tree of Battles The Tree of Battles, trans. G. W. Coopland, Cambridge, Ma.s.s., 1949.

44. A. E. Housman, "Epitaph on an Army of Mercenaries," verse 37, Last Poems Last Poems (1922). (1922).

45. B. Gille, Renaissance Engineers Renaissance Engineers, p. 63.

46. Ibid., p. 12.

47. Maurice Daumas and Andre Garanger, "Industrial Mechanization," in Daumas, II, p. 271.

48. Calder, Leonardo Leonardo, p. 255, quoting MS. Trattato della pittura Trattato della pittura, in the Vatican Library.

49. Bert S. Hall, "Der Meister sol auch kennen schreiben und lesen: Writings About Technology, ca. 14001600 A.D. A.D., and Their Cultural Implications," in Denise Schmant-Besserat, ed., Early Technologies Early Technologies, Malibu, Calif., 1979, p. 48.

50. B. Gille, Renaissance Engineers Renaissance Engineers, p. 92; Calder, Leonardo Leonardo, p. 51.

51. Hall, "Der Meister," p. 53.

52. Bertrand Gille, "Engineers and Technicians of the Renaissance," in Daumas, II, p. 24.

53. Frank D. Prager and Gustina Scaglia, Mariano Toccola and His Book, "De ingeniis Mariano Toccola and His Book, "De ingeniis," Cambridge, 1972; B. Gille, Renaissance Engineers Renaissance Engineers, pp. 8386; B. Gille, "Engineers and Technicians of the Renaissance," in Daumas, II, p. 25.

54. Hill, History of Engineering History of Engineering, p. 73.

55. B. Gille, Renaissance Engineers Renaissance Engineers, p. 71.

56. Ibid., p. 56; B. Gille, "Engineers and Technicians of the Renaissance," in Daumas, II, p. 23.

57. Morison, European Discovery: The Southern Voyages European Discovery: The Southern Voyages, p. 27; Phillips, Medieval Expansion of Europe Medieval Expansion of Europe, p. 233; Hart, World of Leonardo da Vinci World of Leonardo da Vinci, pp. 2930.

58. Cited in Hart, World of Leonardo da Vinci World of Leonardo da Vinci, p. 142.

59. B. Gille, Renaissance Engineers Renaissance Engineers, pp. 9293; B. Gille, "Engineers and Technicians of the Renaissance," in Daumas, II, p. 26.

60. B. Gille, Renaissance Engineers Renaissance Engineers, pp. 8789; Calder, Leonardo Leonardo, pp. 9799; Hart, World of Leonardo da Vinci World of Leonardo da Vinci, p. 167; White, Medieval Technology and Social Change Medieval Technology and Social Change, p. 114.

61. Hart, World of Leonardo da Vinci World of Leonardo da Vinci, p. 139.

62. B. Gille, Renaissance Engineers Renaissance Engineers, p. 139.

63. Ibid., pp. 10614; B. Gille, "Engineers and Technicians of the Renaissance," in Daumas, II, p. 29.

64. B. Gille, "Engineers and Technicians of the Renaissance," in Daumas, II, pp. 4344.

65. Ibid., pp. 4950.

66. Hart, World of Leonardo da Vinci World of Leonardo da Vinci, p. 30.

67. Pacey, Maze of Ingenuity Maze of Ingenuity, p. 57.

68. Hart, World of Leonardo da Vinci World of Leonardo da Vinci, pp. 3031; Charles Singer, quoted in Hart, p. 24.

69. Ibid., p. 18.

70. B. Gille, Renaissance Engineers Renaissance Engineers, p. 138.

71. B. Gille, "Machines," in Singer, II, p. 654.

72. Calder, Leonardo Leonardo, pp. 13738.

73. Ibid., p. 132; B. Gille, "Machines," in Singer, II, pp. 65256.

74. B. Gille, "Machines," in Singer, II, p. 656; Hart, World of Leonardo da Vinci World of Leonardo da Vinci, pp. 22425.

75. Calder, Leonardo Leonardo, p. 122.