The rhetoric of utility: Avoiding occult associations for mathematics through profitability and pleasure

History of Science

Volumn 37, Issue 2, 1999, Pages 151-178

  Neal, Katherine ^a  

^a NONE

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EID: 0347595500     PISSN: 00732753     EISSN: None     Source Type: Journal    
DOI: 10.1177/007327539903700202     Document Type: Article

References (159)

1. Philip Davis and Reubin Hersh, "Rhetoric and mathematics", in J. S. Nelson, A. Megill and D. N. McCloskey (eds), The rhetoric of the human sciences: Language and argument in scholarship and public affairs (Madison, 1987), 53-68.
2. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
3. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
4. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
5. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
6. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
7. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
8. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
9. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
10. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
11. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
12. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
13. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
14. th-century England", in Irmgard Hantsche (ed.), Der 'mathematicus': Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Bochum, 1996), 93-120; Frances Willmoth, Sir Jonas Moore: Practical mathematics and Restoration science (Woodbridge, Suffolk, 1993); W. R. Laird, "Patronage of mechanics and theories of impact in sixteenth century Italy", in Bruce Moran (ed.), Patronage and institutions: Science, technology and medicine at the European court, 1500-1750 (Woodbridge, Suffolk, 1991), 51-66.
15. Johnston, op. cit. (ref. 2, 1991), focuses on how mathematical practitioners used instruments as another tool to "negotiate the character and status of the mathematicalls".
16. Johnston, op. cit. (ref. 2, 1996), provides an important summary of diversity of mathematical practice.
17. E. G. R. Taylor, The mathematical practitioners of Tudor and Stuart England (3rd edn, Cambridge, 1968). See also David Waters, The art of navigation in England in Elizabethan and early Stuart times (London, 1958).
18. E. G. R. Taylor, The mathematical practitioners of Tudor and Stuart England (3rd edn, Cambridge, 1968). See also David Waters, The art of navigation in England in Elizabethan and early Stuart times (London, 1958).
19. Bennett, op. cit. (ref. 2, 1991), and op. cit. (ref. 2, 1986), 11.
20. Johnston, op. cit. (ref. 2, 1991).
21. Ivor Grattan-Guinness (ed.), Companion encyclopedia of the history and philosophy of the mathematical sciences (2 vols, London and New York, 1994).
22. John Henry, "Magic and science in the sixteenth and seventeenth centuries", in R. C. Olby, G. N. Cantor, J. R. R. Christie, and M. J. S. Hodge (eds), Companion to the history of modern science (London and New York, 1990).
23. Peter Zetterberg, "The mistaking of 'the mathematicks' for magic in Tudor and Stuart England", Sixteenth century journal, xi (1980), 83-97, p. 83; see also William Eamon, "Technology as magic in the late Middle Ages and the Renaissance", Janus, lxx (1983), 171-212, and Frances A. Yates, "The Hermetic tradition in Renaissance science", in Charles S. Singleton (ed.), Ideas and ideals in the North European Renaissance: Collected essays (3 vols, Baltimore, 1967), iii, 227-46, p. 230.
24. Peter Zetterberg, "The mistaking of 'the mathematicks' for magic in Tudor and Stuart England", Sixteenth century journal, xi (1980), 83-97, p. 83; see also William Eamon, "Technology as magic in the late Middle Ages and the Renaissance", Janus, lxx (1983), 171-212, and Frances A. Yates, "The Hermetic tradition in Renaissance science", in Charles S. Singleton (ed.), Ideas and ideals in the North European Renaissance: Collected essays (3 vols, Baltimore, 1967), iii, 227-46, p. 230.
25. Peter Zetterberg, "The mistaking of 'the mathematicks' for magic in Tudor and Stuart England", Sixteenth century journal, xi (1980), 83-97, p. 83; see also William Eamon, "Technology as magic in the late Middle Ages and the Renaissance", Janus, lxx (1983), 171-212, and Frances A. Yates, "The Hermetic tradition in Renaissance science", in Charles S. Singleton (ed.), Ideas and ideals in the North European Renaissance: Collected essays (3 vols, Baltimore, 1967), iii, 227-46, p. 230.
26. Eamon, "Technology as magic" (ref. 10). See also A. George Molland, "Cornelius Agrippa's mathematical magic", in Cynthia Hay (ed.), Mathematics from manuscript to print 1300- 1600 (Oxford, 1988), 209-19.
27. Eamon, "Technology as magic" (ref. 10). See also A. George Molland, "Cornelius Agrippa's mathematical magic", in Cynthia Hay (ed.), Mathematics from manuscript to print 1300-1600 (Oxford, 1988), 209-19.
28. Mordechai Feingold, "The occult tradition in the English universities of the Renaissance: A reassessment", in Brian Vickers (ed.), Occult and scientific mentalities in the Renaissance (Cambridge, 1984), 73-91, p. 79.
29. For Dee, see William H. Sherman, John Dee: The politics of reading and writing in the English Renaissance (Amherst, 1995); Nicholas H. Clulee, John Dee's natural philosophy: Between science and religion (London, 1988); idem, "At the crossroads of magic and science: John Dee's Archemastrie", in Vickers (ed.), op. cit. (ref. 12), 57-71; James Crossley (ed.), The autobiographical tracts of Dr. John Dee (Manchester, 1851).
30. For Dee, see William H. Sherman, John Dee: The politics of reading and writing in the English Renaissance (Amherst, 1995); Nicholas H. Clulee, John Dee's natural philosophy: Between science and religion (London, 1988); idem, "At the crossroads of magic and science: John Dee's Archemastrie", in Vickers (ed.), op. cit. (ref. 12), 57-71; James Crossley (ed.), The autobiographical tracts of Dr. John Dee (Manchester, 1851).
31. For Dee, see William H. Sherman, John Dee: The politics of reading and writing in the English Renaissance (Amherst, 1995); Nicholas H. Clulee, John Dee's natural philosophy: Between science and religion (London, 1988); idem, "At the crossroads of magic and science: John Dee's Archemastrie", in Vickers (ed.), op. cit. (ref. 12), 57-71; James Crossley (ed.), The autobiographical tracts of Dr. John Dee (Manchester, 1851).
32. For Dee, see William H. Sherman, John Dee: The politics of reading and writing in the English Renaissance (Amherst, 1995); Nicholas H. Clulee, John Dee's natural philosophy: Between science and religion (London, 1988); idem, "At the crossroads of magic and science: John Dee's Archemastrie", in Vickers (ed.), op. cit. (ref. 12), 57-71; James Crossley (ed.), The autobiographical tracts of Dr. John Dee (Manchester, 1851).
33. No exhaustive study of the literature is intended. As examples I have selected the prefaces and popular works of the mathematicians such as Robert Recorde, Edmund Wingate, John Tapp, Thomas Blundeville, Richard Witt, and sundry non-mathematical works where mathematics is discussed.
34. Zetterberg, op. cit. (ref. 10); Keith Thomas, Religion and the decline of magic (New York, 1971), 362-3.
35. Zetterberg, op. cit. (ref. 10); Keith Thomas, Religion and the decline of magic (New York, 1971), 362-3.
36. John Aubrey, 'Brief Lives', chiefly of contemporaries, set down by John Aubrey, between the years 1669 and 1696, ed. by Andrew Clark (2 vols, Oxford, 1898), i, 27.
37. Allen left his watch in a chamber of his room when he was visiting Mr John Scudamore in Herefordshire. The maid, when she heard it ticking, concluded it was the devil and threw it into the moat. The watch, however, was attached to a string, and was caught on a branch, confirming its association with the devil.
38. The famous story alleges that when Dee left Mortlake privately in 1583 to embark for Holland, a mob, believing him to be a magician, broke into his house and destroyed a great part of his furniture and books, and also his mathematical instruments, has been conclusively demolished. See the article on Dee in DNB, xiv, 275 for the original story, and Julian Roberts and Andrew G. Watson (eds), John Dee's library catalogue (London, 1990), for a refutation.
39. The famous story alleges that when Dee left Mortlake privately in 1583 to embark for Holland, a mob, believing him to be a magician, broke into his house and destroyed a great part of his furniture and books, and also his mathematical instruments, has been conclusively demolished. See the article on Dee in DNB, xiv, 275 for the original story, and Julian Roberts and Andrew G. Watson (eds), John Dee's library catalogue (London, 1990), for a refutation.
40. Aubrey, op. cit. (ref. 16), 109, 213.
41. As quoted in Zetterberg, op. cit. (ref. 10), 85.
42. Aubrey, op. cit. (ref. 16), 108, 153.
43. l.
44. r.
45. Francis Osborne, Advise to a son (Oxford, 1656), 7-8.
46. Historical Manuscripts Commission, Various collections (Westminster, 1909), v, 246, as quoted in Feingold, "The occult tradition" (ref. 12), 79.
47. Historical Manuscripts Commission, Various collections (Westminster, 1909), v, 246, as quoted in Feingold, "The occult tradition" (ref. 12), 79.
48. Henry Cornelius Agrippa, De occulta philosophia II. 1 (Opera, i, 53); see also Molland, op. cit. (ref. 11).
49. Henry Cornelius Agrippa, De occulta philosophia II. 1 (Opera, i, 53); see also Molland, op. cit. (ref. 11).
50. Yates, "The Hermetic tradition" (ref. 10), 230.
51. Feingold, "The occult tradition" (ref. 12), 81.
52. Quoted in Eamon, "Technology as magic" (ref. 11), 201.
53. William Eamon, Science and the secrets of nature: Books of secrets in medieval and early modern culture (Princeton, N.J., 1994), 39-44.
54. Yates, op. cit. (ref. 10), 230.
55. Molland, op. cit. (ref. 11), 210.
56. Richard Dunn, "The true place of astrology among the mathematical arts of late Tudor England", Annals of science, li (1994), 151-63.
57. Thomas, op. cit. (ref. 15), 358-68.
58. Eamon, "Technology as magic" (ref. 11), 201; see also Paul Rose, Italian renaissance of mathematics (Droz, 1975), chap. 1.
59. Eamon, "Technology as magic" (ref. 11), 201; see also Paul Rose, Italian renaissance of mathematics (Droz, 1975), chap. 1.
60. Thomas, op. cit. (ref. 34), 363.
61. Richard Kieckhefer, Magic in the Middle Ages (Cambridge, 1989), 47-49.
62. Thomas, op. cit. (ref. 15), 363.
63. Roger Ascham, The scholemaster, ed. by John E. B. Mayor (London, 1863; rpr. New York, 1967), 14-15. Ascham's text was printed in 1570, with two more editions in 1571, one edition in 1573, and one edition in 1589.
64. For Ascham's career as a mathematical lecturer, see P. L. Rose, "Erasmians and mathematics at Cambridge in the early sixteenth century", Sixteenth century journal, viii, supplement (1977), 47-59, p. 56. Ascham also advised against studying mathematics too intensely in a 1564 letter to the Earl of Leicester, stating "I think you did yourself injury in changing Tully's wisdom with Euclid's pricks and lines" (in J. A. Giles (ed.). The whole works of Roger Ascham (3 vols, London, 1864-65), ii, 103).
65. For Ascham's career as a mathematical lecturer, see P. L. Rose, "Erasmians and mathematics at Cambridge in the early sixteenth century", Sixteenth century journal, viii, supplement (1977), 47-59, p. 56. Ascham also advised against studying mathematics too intensely in a 1564 letter to the Earl of Leicester, stating "I think you did yourself injury in changing Tully's wisdom with Euclid's pricks and lines" (in J. A. Giles (ed.). The whole works of Roger Ascham (3 vols, London, 1864-65), ii, 103).
66. Stephen Shapin, A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994); Peter Dear, "Totius in verba: Rhetoric and authority in the early Royal Society", Isis, lxxvi (1985), 145-61. See also Marello Pera and William Shea (eds), Persuading science (Canton, Mass., 1991) and Peter Dear (ed.) The literary structure of scientific argument: Historical studies (Philadelphia, 1991).
67. Stephen Shapin, A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994); Peter Dear, "Totius in verba: Rhetoric and authority in the early Royal Society", Isis, lxxvi (1985), 145-61. See also Marello Pera and William Shea (eds), Persuading science (Canton, Mass., 1991) and Peter Dear (ed.) The literary structure of scientific argument: Historical studies (Philadelphia, 1991).
68. Stephen Shapin, A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994); Peter Dear, "Totius in verba: Rhetoric and authority in the early Royal Society", Isis, lxxvi (1985), 145-61. See also Marello Pera and William Shea (eds), Persuading science (Canton, Mass., 1991) and Peter Dear (ed.) The literary structure of scientific argument: Historical studies (Philadelphia, 1991).
69. Stephen Shapin, A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994); Peter Dear, "Totius in verba: Rhetoric and authority in the early Royal Society", Isis, lxxvi (1985), 145-61. See also Marello Pera and William Shea (eds), Persuading science (Canton, Mass., 1991) and Peter Dear (ed.) The literary structure of scientific argument: Historical studies (Philadelphia, 1991).
70. See Frederic L. Holmes, "Argument and narrative in scientific writing", in Pera and Shea (eds), Persuading science (ref. 41 ), 164-94, for an exploration of the method of obtaining consensus used by the Academicians.
71. Shapin, op. cit. (ref. 41), 337. See also Shapin, "Robert Boyle and mathematics: Reality, representation, and experimental practice", Science in context, ii (1988), 23-58.
72. Shapin, op. cit. (ref. 41), 337. See also Shapin, "Robert Boyle and mathematics: Reality, representation, and experimental practice", Science in context, ii (1988), 23-58.
73. Dear, "Totius in verba" (ref. 41), 159.
74. Geoffrey Cantor, "The rhetoric of experiment", in David Gooding, Trevor Pinch and Simon Schaffer (eds), The uses of experiment: Studies in the natural sciences (Cambridge, 1989), 159-80. Cantor discusses the rhetoric of experimental reports. See also Michael Hunter's Science and society in Restoration England (Cambridge, 1981), especially chap. 5, for a discussion of the role of utility in Restoration science.
75. Geoffrey Cantor, "The rhetoric of experiment", in David Gooding, Trevor Pinch and Simon Schaffer (eds), The uses of experiment: Studies in the natural sciences (Cambridge, 1989), 159-80. Cantor discusses the rhetoric of experimental reports. See also Michael Hunter's Science and society in Restoration England (Cambridge, 1981), especially chap. 5, for a discussion of the role of utility in Restoration science.
76. Philip Kitcher, "Persuasion", in Pera and Shea (eds), Persuading science (ref. 41), 3-27.
77. Johnston, op. cit. (ref. 4), 108.
78. Shapin, A social history of truth (ref. 41), 222, 236.
79. Taylor, op. cit. (ref. 5), 205.
80. r.
81. Ibid.
82. John Tapp, The path-way to knovvledge; Containing the whole art of arithmeticke ... (London, 1613).
83. Taylor, op. cit. (ref. 5), 173. Waters, op. cit. (ref. 5), 569.
84. l.
85. l.
86. Fernand Braudel, The wheels of commerce: Civilization and capitalism 15th-18th century, transl. by Siân Reynolds (2 vols, New York, 1986), ii, 448.
87. For more details on the problems of audience, see Johnston, "Mathematical practitioners" (ref. 3), 342.
88. th centuries (2nd edn, Newton Abbot, 1972); R. Brenner, "The social basis of English commercial expansion 1550- 1650", Journal of economic history, xxxii (1972), 361-441.
89. th centuries (2nd edn, Newton Abbot, 1972); R. Brenner, "The social basis of English commercial expansion 1550-1650", Journal of economic history, xxxii (1972), 361-441.
90. Robert Brenner, Merchants and revolution: Commercial change, political conflict, and London's overseas traders, 1550-1653 (Cambridge, 1993), 5.
91. Brenner, op. cit. (ref. 58), 12-14.
92. Taylor, op. cit. (ref. 5), 33, 171.
93. Waters, op. cit. (ref. 5), 542-3.
94. Waters, op. cit. (ref. 5), 558.
95. Davis, op. cit. (ref. 57), 125.
96. Lisa Jardine, Francis Bacon: Discovery and the art of discourse (Cambridge, 1974), 69-71.
97. See A. J. Turner's "Mathematical instruments and the education of gentlemen", Annals of science, xxx (1973), 51-88 for a detailed explanation of why these skills became necessary.
98. Sir Thomas Elyot, The boke named the Governour (ed. from 1st edn of 1531 by Henry Herbert Stephen Croft; 2 vols, New York, 1968, reprint of 1883 edn), 28.
99. Elyot, op. cit. (ref. 66), 45-46.
100. Sir Humphrey Gilbert, "Queene Elizabethes Academy", in F. J. Funivell (ed.), Queene Elizabethes Academy (by Sir Humphrey Gilbert). A booke of precedence, The ordering of a funerall, &c. Varying versions of the good wife, The wise man, &c. Maxims, Lydgate's order of fools, A poem on heraldry, Occleve on Lords' men &c (London, 1969), 4-5.
101. Henry Percy, Advice to his son, ed. by G. B. Harrison (London, 1930), 67-72.
102. British Library, Add MS 27,606 (The design and method of Mr Crow's studies).
103. Henry Peacham, The compleat gentleman (London, 1622).
104. Peacham, op. cit. (ref. 71), 72.
105. Turner, "Mathematical instruments" (ref. 65), 51.
106. T. S. Willan, The Muscovy merchants of 1555 (Manchester, 1953), 5-10.
107. Willan, op. cit. (ref. 74), 7.
108. Kenneth Andrews, Trade, plunder and settlement: Maritime enterprise and the genesis of the British Empire 1480-1630 (Cambridge, 1984), 8.
109. Andrews, op. cit. (ref. 76), 33, for an excellent review of the rhetoric used by the literature advocating voyages of discovery, new trades, and the colonies.
110. r.
111. r.
112. See Johnston, op. cit. (ref. 2, 1996), 112, on this point.
113. r.
114. l.
115. Robert Recorde, Pathway of knowledge (London, 1551), Preface sig. i.
116. r.
117. Stephen Johnston, "Making mathematical practice: Gentlemen, practitioners and artisans in Elizabethan England", Ph.D.dissertation, Cambridge University, 1994, provides a lucid explanation of the connections between Digges's shift in orientation and a highly nuanced conception of patronage as social credit. By contrast, see also Mordechai Feingold, The mathematicians' apprenticeship: Science, universities and society in England 1560-1640 (Cambridge, 1984), 186, and cf. 206-7.
118. Stephen Johnston, "Making mathematical practice: Gentlemen, practitioners and artisans in Elizabethan England", Ph.D.dissertation, Cambridge University, 1994, provides a lucid explanation of the connections between Digges's shift in orientation and a highly nuanced conception of patronage as social credit. By contrast, see also Mordechai Feingold, The mathematicians' apprenticeship: Science, universities and society in England 1560-1640 (Cambridge, 1984), 186, and cf. 206-7.
119. l.
120. r.
121. Taylor, op. cit. (ref. 5), 337.
122. John Tapp, The path-way to knowledge (London, 1613), 10-11.
123. Tapp, op. cit. (ref. 89), 49.
124. Tapp, op. cit. (ref. 89), 305-6.
125. l-r.
126. Robert Recorde, Whetstone of witte (London, 1557), sig. Miir.
127. John Blagrave, The mathematical iewel (London, 1585), title-page.
128. See Katherine Hill, "'Juglers or Schollers': Negotiating the role of a mathematical practitioner", The British journal for the history of science, in press.
129. Johnston, "Mathematical practitioners" (ref. 3).
130. John Parker, Books to build an empire: Bibliographical history of English overseas interest to 1620 (Amsterdam, 1965), 55-56.
131. Recorde, Whetstone of witte (ref. 93), fol. Aiii. See also Willan, The Muscovy merchants of 1555 (ref. 74), 23; E. G. R. Taylor, The haven-finding art: A history of navigation from Odysseus to Captain Cook (London, 1957), 197; Waters, op. cit. (ref. 5), 94-95.
132. Recorde, Whetstone of witte (ref. 93), fol. Aiii. See also Willan, The Muscovy merchants of 1555 (ref. 74), 23; E. G. R. Taylor, The haven-finding art: A history of navigation from Odysseus to Captain Cook (London, 1957), 197; Waters, op. cit. (ref. 5), 94-95.
133. Recorde, Whetstone of witte (ref. 93), fol. Aiii. See also Willan, The Muscovy merchants of 1555 (ref. 74), 23; E. G. R. Taylor, The haven-finding art: A history of navigation from Odysseus to Captain Cook (London, 1957), 197; Waters, op. cit. (ref. 5), 94-95.
134. Recorde, Whetstone of witte (ref. 93), fol. Aiii. See also Willan, The Muscovy merchants of 1555 (ref. 74), 23; E. G. R. Taylor, The haven-finding art: A history of navigation from Odysseus to Captain Cook (London, 1957), 197; Waters, op. cit. (ref. 5), 94-95.
135. 3.
136. r.
137. Taylor, op. cit. (ref. 5), 193.
138. Andrews, op. cit. (ref. 76), 20.
139. l.
140. Waters, op. cit. (ref. 5).
141. Taylor, The haven-finding art (ref. 98).
142. See Luke Foxe, North-West Fox, or, Fox from the North-West Passage (London, 1635).
143. v.
144. Thomas Rundall (ed.), Narratives of voyages towards the north-west in search of a passage to Cathay and India 1496 to 1631 (London, 1869), 205.
145. Foxe not only managed not to lose a man, but also to sail much further north, and was at least able to discount earlier suggestions as to the possible location of the passage.
146. William Borough, A discourse of the variation of the cumpas (London, 1581). He suggests that all seamen who wished to excel at their profession should learn arithmetic and geometry, but he urged this course so that they could design their own instruments and not depend upon outside advice.
147. r.
148. r-l.
149. James does not mention very precisely which books he brought with him, stating merely "A Chest full of the best and choicest Mathematicall bookes that could be got for money in England; as likewise Master Hackkluite and Master Purchas, and other books of Iournals and Histories". He did, however, supply a list of instruments, including "glasses, logg-line, meridian-line, plumb-lines, globes, semi-circles, meridian compasses, loade-stone,
150. r). In the end, he assumed that the more skilful sailors would accept his suggestions.
151. r). Additionally, he claimed that astrology and astronomy were in fact the same thing (sig. A1r), and also maintained that he was only defending 'proper' astrologers who "contain themselves within the bounds of naturall Philosophie".
152. r). Additionally, he claimed that astrology and astronomy were in fact the same thing (sig. A1r), and also maintained that he was only defending 'proper' astrologers who "contain themselves within the bounds of naturall Philosophie".
153. Stuart Clark, "The rational witchfinder: Conscience, demonological naturalism and popular superstitions", in Pumfrey, Rossi and Slawinski (eds), op. cit. (ref. 2), 222-48; idem, "The scientific status of demonology", in Vickers (ed.), op. cit. (ref. 12), 351-74; and John Henry, "'The touch of cold philosophy? ...'; The fragmentation of Renaissance occultism and the origin of the Enlightenment", unpublished manuscript. I thank John Henry for letting me read this work.
154. Stuart Clark, "The rational witchfinder: Conscience, demonological naturalism and popular superstitions", in Pumfrey, Rossi and Slawinski (eds), op. cit. (ref. 2), 222-48; idem, "The scientific status of demonology", in Vickers (ed.), op. cit. (ref. 12), 351-74; and John Henry, "'The touch of cold philosophy? ...'; The fragmentation of Renaissance occultism and the origin of the Enlightenment", unpublished manuscript. I thank John Henry for letting me read this work.
155. Stuart Clark, "The rational witchfinder: Conscience, demonological naturalism and popular superstitions", in Pumfrey, Rossi and Slawinski (eds), op. cit. (ref. 2), 222-48; idem, "The scientific status of demonology", in Vickers (ed.), op. cit. (ref. 12), 351-74; and John Henry, "'The touch of cold philosophy? ...'; The fragmentation of Renaissance occultism and the origin of the Enlightenment", unpublished manuscript. I thank John Henry for letting me read this work.
156. John Henry, The Scientific Revolution and the origin of modern science (London, 1997), 47.
157. Paolo Rossi, Francis Bacon: From magic to science (Chicago, 1968); and Henry, opera cit. (refs 9 and 117).
158. William London, A catalogue of the most vendible books in England, sig. Dd2r-Dd31.
159. Katherine Hill, "Mathematics as a tool for social change: Educational reform in seventeenth-century England", The seventeenth century, xii (1997), 23-36.