'Juglers or Schollers?': Negotiating the role of a mathematical practitioner

British Journal for the History of Science

Volumn 31, Issue 3, 1998, Pages 253-274

  Hill, Katherine ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347722676     PISSN: 00070874     EISSN: None     Source Type: Journal    
DOI: 10.1017/S000708749800329X     Document Type: Review

References (155)

1. J. A. Bennett, 'The mechanics' philosophy and the mechanical philosophy', History of Science (1986), 24, 1-28; Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution, Chicago, 1995; Robert Westman, 'The astronomer's role in the sixteenth century: a preliminary study', History of Science (1980), 18, 105-47. J. A. Bennett's valuable research, for example, makes important contributions both to the investigation of the role of mathematical instruments in the remarkable growth of the mathematical sciences in England and in establishing the image of the subject.
2. J. A. Bennett, 'The mechanics' philosophy and the mechanical philosophy', History of Science (1986), 24, 1-28; Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution, Chicago, 1995; Robert Westman, 'The astronomer's role in the sixteenth century: a preliminary study', History of Science (1980), 18, 105-47. J. A. Bennett's valuable research, for example, makes important contributions both to the investigation of the role of mathematical instruments in the remarkable growth of the mathematical sciences in England and in establishing the image of the subject.
3. J. A. Bennett, 'The mechanics' philosophy and the mechanical philosophy', History of Science (1986), 24, 1-28; Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution, Chicago, 1995; Robert Westman, 'The astronomer's role in the sixteenth century: a preliminary study', History of Science (1980), 18, 105-47. J. A. Bennett's valuable research, for example, makes important contributions both to the investigation of the role of mathematical instruments in the remarkable growth of the mathematical sciences in England and in establishing the image of the subject.
4. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
5. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
6. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
7. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
8. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
9. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
10. Several papers discuss various aspects of the priority dispute. A. J. Turner, 'William Oughtred, Richard Delamain and the horizontal instrument in seventeenth century England', Annali Dell'Instituto e Museo di Storia della Scienza di Firenze (1981), 6, 99-125, provides a detailed account of the conflict, and his 'Mathematical instruments and the education of gentlemen', Annals of Science (1973), 30, 55-88 also discusses the controversy as well as supplying vital contextual information. Frances Willmoth, Sir Jonas Moore: Practical Mathematics and Restoration Science, Woodbridge, Suffolk, 1993, contains the first discussion, to my knowledge, of this dispute in the context of the unravelling of consensus over mathematical boundaries. For a discussion of several of the educational aspects of the controversy see Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, and D. J. Bryden, 'A didactic introduction to arithmetic, Sir Charles Cotterell's "Instrument for Arithmeticke" of 1667', History of Education (1973), 2, 5-18, especially 14-15. For a clear account of the difficulties in dating Delamain's work see D. J. Bryden, '"A patchery and confusion of disjointed stuffe": Richard Delamain's Grammelogia of 1631/3', Transactions of the Cambridge Bibliographical Society (1978), 6, 158-66, and for the dating of Oughtred's work see P. J. Wallis, 'William Oughtred's "Circles of Proportion" and "Trigonometries"', ibid. (1968), 4, 372-82.
11. Bennett, op. cit. (1), 6; Willmoth, op. cit. (2), 1-4; Mario Biagioli, 'The social status of Italian mathematicians, 1450-1600', History of Science (1989), 37, 41-95, is a subtle account of the social status of Italian mathematicians; for example, he investigates how claims to a 'theoretical' orientation were utilized to close the doors to certain groups of 'lower-class' mathematicians.
12. Bennett, op. cit. (1), 6; Willmoth, op. cit. (2), 1-4; Mario Biagioli, 'The social status of Italian mathematicians, 1450-1600', History of Science (1989), 37, 41-95, is a subtle account of the social status of Italian mathematicians; for example, he investigates how claims to a 'theoretical' orientation were utilized to close the doors to certain groups of 'lower-class' mathematicians.
13. Bennett, op. cit. (1), 6; Willmoth, op. cit. (2), 1-4; Mario Biagioli, 'The social status of Italian mathematicians, 1450-1600', History of Science (1989), 37, 41-95, is a subtle account of the social status of Italian mathematicians; for example, he investigates how claims to a 'theoretical' orientation were utilized to close the doors to certain groups of 'lower-class' mathematicians.
14. Stephen Johnston, 'Mathematical practitioners and instruments in Elizabethan England', Annals of Science (1991), 48, 319-44, especially 319-20.
15. Descriptions of vernacular mathematical works are examined in E. G. R. Taylor, The Mathematical Practitioners of Tudor and Stuart England, Cambridge, 1954, and H. S. Bennet, English Books and Readers, 1475-1603, Cambridge, 1952.
16. Descriptions of vernacular mathematical works are examined in E. G. R. Taylor, The Mathematical Practitioners of Tudor and Stuart England, Cambridge, 1954, and H. S. Bennet, English Books and Readers, 1475-1603, Cambridge, 1952.
17. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
18. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
19. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
20. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
21. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
22. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
23. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
24. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
25. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
26. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
27. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
28. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
29. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
30. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
31. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
32. Fuller detail's of Recorde's life are included in: F. M. Clark, 'New light on Robert Recorde', Isis (1926), 8, 50-70; E. Kaplan, 'Robert Recorde: Studies in the Life and Works of a Tudor Scientist', PhD dissertation, New York University, 1960. 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; James Crossley (ed.), The Autobiographical Tracts of Dr. John Dee, Manchester, 1851. Taylor, op. cit. (5), 167, 170; See, for details of Robert Recorde's career, Geoffrey Howson, A History of Mathematical Education in England, Cambridge, 1982, 6-27; P. Bockstaele, 'Notes on the first arithmetics printed in Dutch and English', Isis (1960), 51, 315-21; and also F. R. Johnson, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, (1935), 7, 59-87. For Digges, see Stephen Johnston, 'Making Mathematical Practice; Gentlemen, Practitioners and Artisans in Elizabethan England', PhD dissertation, University of Cambridge, 1994, ch. 2 'Thomas Digges: gentleman and mathematician', 50-106; for Digges's astronomy, see Francis R. Johnsoin and Sanford V. Larkey, 'Thomas Digges, the Copernican system, and the idea of the infinity of the universe in 1576', Huntington Library Bulletin (1934), 5, 69-117; Francis Johnson, Astronomical Thought in Renaissance England: A Study of English Scientific Writings from 1500 to 1645, Baltimore, 1957. For navigation, surveying and artillery: D. W. Waters, The Art of Navigation in Elizabethan and Early Stuart Times, London, 1958; A. W. Richeson, English Land Measuring to 1800: Instruments and Practices, Cambridge, MA, 1966; A.R. Hall, Ballistics in the Seventeenth Century, Cambridge, 1952.
33. The Grounde of Artes first appeared in 1543, and forty-five editions of this work were printed under various editors; The Pathway to Knowledge, London, 1551 (also in 1574 and 1620); The Castle of Knowledge, London, 1556 (reprinted 1596); The Whetstone of Witte, London, 1557.
34. The Grounde of Artes first appeared in 1543, and forty-five editions of this work were printed under various editors; The Pathway to Knowledge, London, 1551 (also in 1574 and 1620); The Castle of Knowledge, London, 1556 (reprinted 1596); The Whetstone of Witte, London, 1557.
35. The Grounde of Artes first appeared in 1543, and forty-five editions of this work were printed under various editors; The Pathway to Knowledge, London, 1551 (also in 1574 and 1620); The Castle of Knowledge, London, 1556 (reprinted 1596); The Whetstone of Witte, London, 1557.
36. r. Indeed, he listed twenty-seven practical and mechanical sciences that benefit from the use of Euclidean geometry.
37. Sherman, op. cit. (6), 95.
38. r-v.
39. See Johnston, op. cit. (6), for an interesting interpretation of this passage.
40. John Aubrey, Brief Lives by John Aubrey (ed. Richard Barber), London, 1975, 274. However, Willmoth, op. cit. (2), 2, quite correctly points out that this tale was written down at least half a century after the events and Bishop Ward was actively involved in restricting the style of university mathematics. See also Johnston, op. cit. (4), 342.
41. John Aubrey, Brief Lives by John Aubrey (ed. Richard Barber), London, 1975, 274. However, Willmoth, op. cit. (2), 2, quite correctly points out that this tale was written down at least half a century after the events and Bishop Ward was actively involved in restricting the style of university mathematics. See also Johnston, op. cit. (4), 342.
42. John Aubrey, Brief Lives by John Aubrey (ed. Richard Barber), London, 1975, 274. However, Willmoth, op. cit. (2), 2, quite correctly points out that this tale was written down at least half a century after the events and Bishop Ward was actively involved in restricting the style of university mathematics. See also Johnston, op. cit. (4), 342.
43. Christopher Hill, The Intellectual Origins of the English Revolution, Oxford, 1965, 37-51; Miller Christy (ed.) The Voyages of Captain Luke Foxes and Thomas James of Bristol, 2 vols., London, 1894. Also see Briggs's tract on a north-west passage that was published together with Edward Waterhouse's, A Declaration of the State of the Colony and Affaires in Virginia ..., London, 1622; this work was clearly meant to encourage the settlement of Virginia and further exploration.
44. Christopher Hill, The Intellectual Origins of the English Revolution, Oxford, 1965, 37-51; Miller Christy (ed.) The Voyages of Captain Luke Foxes and Thomas James of Bristol, 2 vols., London, 1894. Also see Briggs's tract on a north-west passage that was published together with Edward Waterhouse's, A Declaration of the State of the Colony and Affaires in Virginia ..., London, 1622; this work was clearly meant to encourage the settlement of Virginia and further exploration.
45. Christopher Hill, The Intellectual Origins of the English Revolution, Oxford, 1965, 37-51; Miller Christy (ed.) The Voyages of Captain Luke Foxes and Thomas James of Bristol, 2 vols., London, 1894. Also see Briggs's tract on a north-west passage that was published together with Edward Waterhouse's, A Declaration of the State of the Colony and Affaires in Virginia ..., London, 1622; this work was clearly meant to encourage the settlement of Virginia and further exploration.
46. See the extensive bibliographical research of E. G. R. Taylor, op. cit. (5). Amir Alexander provides a detailed example in his paper on Thomas Harriot, 'The imperialist space of Elizabethan mathematics', Studies in the History and Philosophy of Science (1995), 26, 559-92.
47. See the extensive bibliographical research of E. G. R. Taylor, op. cit. (5). Amir Alexander provides a detailed example in his paper on Thomas Harriot, 'The imperialist space of Elizabethan mathematics', Studies in the History and Philosophy of Science (1995), 26, 559-92.
48. William Oughtred, The Circles of Proportion (tr. W. Forster), London, 1632. The 1633 edition includes To the English Gentrie ... The Just Apologie of Wil. Oughtred, Against the Slaunderous Insimulations of Richard Delamain. A. J. Turner, 'William Oughtred', op. cit. (2), 99-125, provides a description of the instruments involved in the dispute as well as a very detailed account of the controversy itself.
49. William Oughtred, The Circles of Proportion (tr. W. Forster), London, 1632. The 1633 edition includes To the English Gentrie ... The Just Apologie of Wil. Oughtred, Against the Slaunderous Insimulations of Richard Delamain. A. J. Turner, 'William Oughtred', op. cit. (2), 99-125, provides a description of the instruments involved in the dispute as well as a very detailed account of the controversy itself.
50. Turner, 'William Oughtred', op. cit. (2), 105-6, states that little is known of Forster. He proposes as a likely possibility the William Foster who matriculated as a pensioner at Trinity College, Cambridge, in Easter 1627. In the Circles, Foster describes himself as a teacher of mathematics 'at the Red Bull over against the St Clements Churchyard without Temple Bar'. Taylor, op. cit. (5), 212, identifies him as a surveyor and a friend of William Leybourne.
51. r.
52. 1.
53. r.
54. v.
55. r.
56. v.
57. r. Oughtred seems dismayed that Delamain wanted him to stick to his own occupation and stay out of his.
58. r.
59. Turnet, 'Mathematical instruments', op. cit. (2), 56.
60. Johnston, op. cit. (4), 320.
61. Frances Willmoth, in a personal communication, pointed out to me that this is likely to be merely part of Oughtred's pose after his quarrel with Delamain. She convinced me that Oughtred did his Cambridge tutoring for money, as was customary, and that he probably also received a nominal payment for tutoring the Earl of Arundel's son.
62. r.
63. Florian Cajori, William Oughtred: A Great Seventeenth Century Teacher of Mathematics, Chicago, 1916, discusses Oughtred's ideas about teaching mathematics in ch. 5.
64. r. This tract is usually found bound with The Circles of Proportion. 30 On this point, see Willmoth, op. cit. (2), 4.
65. r. This tract is usually found bound with The Circles of Proportion. 30 On this point, see Willmoth, op. cit. (2), 4.
66. r.
67. This quote is taken from R. Malcolm Smuts, Court Culture and the Origins of a Royalist Tradition in Early Stuart England, Philadelphia, 1987, 147.
68. 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.
69. Elyot, op. cit. (33), 45-6.
70. Henry Percy, Advice to his Son (ed. from 1st edn of 1609 by G. B. Harrison), London, 1930, 67-8.
71. Henry Peacham, The Compleat Gentleman, London, 1622, 72.
72. Peacham, op. cit. (36), 76-7.
73. Peacham, op. cit. (36), 73.
74. Sir Humphrey Gilbert, Queene Elizabethes Academy (ed. F. J. Furnivall), London, 1869, 4-5.
75. On this point see the detailed study by A. J. Turner, 'Mathematical instruments', op. cit. (2) 55-88. He points out that there was a 'gap between what the gentlemen wanted, the interests of the mathematicians, the views of educational writers and the commercial interests of the mathematical artisans', 61.
76. Johnston, op. cit. (4), 320.
77. Kevin Sharpe, The Personal Rule of Charles I, New Haven, 1992, 182; Smuts, op. cit. (32), 153; Gervas Huxley, Endymion Porter: The Life of a Courtier, 1598-1649, London, 1959, 167. Charles I's early interest may be traced through The Calendar of the State Papers Domestic (hereafter CSPD) for the years 1611-18, 383, 385, 398, 399. Even at this stage there seem to have been difficulties about receiving payment.
78. Kevin Sharpe, The Personal Rule of Charles I, New Haven, 1992, 182; Smuts, op. cit. (32), 153; Gervas Huxley, Endymion Porter: The Life of a Courtier, 1598-1649, London, 1959, 167. Charles I's early interest may be traced through The Calendar of the State Papers Domestic (hereafter CSPD) for the years 1611-18, 383, 385, 398, 399. Even at this stage there seem to have been difficulties about receiving payment.
79. Kevin Sharpe, The Personal Rule of Charles I, New Haven, 1992, 182; Smuts, op. cit. (32), 153; Gervas Huxley, Endymion Porter: The Life of a Courtier, 1598-1649, London, 1959, 167. Charles I's early interest may be traced through The Calendar of the State Papers Domestic (hereafter CSPD) for the years 1611-18, 383, 385, 398, 399. Even at this stage there seem to have been difficulties about receiving payment.
80. Kevin Sharpe, The Personal Rule of Charles I, New Haven, 1992, 182; Smuts, op. cit. (32), 153; Gervas Huxley, Endymion Porter: The Life of a Courtier, 1598-1649, London, 1959, 167. Charles I's early interest may be traced through The Calendar of the State Papers Domestic (hereafter CSPD) for the years 1611-18, 383, 385, 398, 399. Even at this stage there seem to have been difficulties about receiving payment.
81. William Perrinchief, Royal Martyr, London, 1676, 253.
82. Smuts, op. cit. (32), 153.
83. Lesley Cormack, 'Twisting the lion's tail: practice and theory at the court of Henry Prince of Wales', in Patronage and Institutions: Science, Technology, and Medicine at the European Court 1500-1750 (ed. Bruce Moran), Rochester NY, 1991, 67-83.
84. J. V. Field, 'What is scientific about a scientific instrument?', Istituto Museo di Storia della Scienza Firenze Nuncius Annali di Storia della Scienza (1988), 3, pt 2, 3-26, on 3, points out that the value of the instruments was often decorative and practical, not scientific.
85. For example, Robert Austin seems to have sent Oughtred several books (Harvey and Gassendus) in exchange for one of Oughtred's works and his advice. See Correspondence of Scientific Men of the Seventeenth Century (ed. Stephen Jordan Rigaud), 2 vols., Hildesheim, 1965, 73. Early in his career he taught mathematics to Gerald, the son of Sir Francis Aungier, the MP for Haslemere and later Baron Longford, and the Earl of Arundel is said to have heard of his mathematical talent through a local intermediary. See Willmoth, op. cit. (2), 45.
86. For example, Robert Austin seems to have sent Oughtred several books (Harvey and Gassendus) in exchange for one of Oughtred's works and his advice. See Correspondence of Scientific Men of the Seventeenth Century (ed. Stephen Jordan Rigaud), 2 vols., Hildesheim, 1965, 73. Early in his career he taught
87. J. F. Scott, 'William Oughtred', DSB, 254-5.
88. See Willmoth, op. cit. (2), 45, for Oughtred's early patrons among the local Surrey gentry.
89. Aubrey, op. cit. (11), 236.
90. Rigaud, op. cit. (47), 11.
91. v. Delamain, of course, was also originally said to be a joiner. Joiners were considered to be a step above carpenters, but still had low social status. The difference between Oughtred's and Delamain's status might be compared to the differences between Cardano and Tartaglia. See Biagioli, op. cit. (3), 50, 55.
92. v. Delamain, of course, was also originally said to be a joiner. Joiners were considered to be a step above carpenters, but still had low social status. The difference between Oughtred's and Delamain's status might be compared to the differences between Cardano and Tartaglia. See Biagioli, op. cit. (3), 50, 55.
93. r.
94. r.
95. See, for example, the Latin phrase inserted in the title page of Delamain's The Making, Description, and Use ... [of a] Horizontal Quadrant, London, 1639?. Delamain in this work styles himself 'Student and Teacher of the Mathematickes'. At times, practitioners with questionable status, like John Babington, who was a gunner, referred to themselves as being 'students' in order to shield themselves from criticism. See John Babington, A Short Treatise of Geometrie, London, 1636, especially the title page and dedication to Sir John Heydon.
96. See, for example, the Latin phrase inserted in the title page of Delamain's The Making, Description, and Use ... [of a] Horizontal Quadrant, London, 1639?. Delamain in this work styles himself 'Student and Teacher of the Mathematickes'. At times, practitioners with questionable status, like John Babington, who was a gunner, referred to themselves as being 'students' in order to shield themselves from criticism. See John Babington, A Short Treatise of Geometrie, London, 1636, especially the title page and dedication to Sir John Heydon.
97. See, for example, CSPD, Historical Manuscripts Commission 9 Calendar of Manuscripts of the Most Honorable The Marquess of Salisbury part XXII (A.D. 1612-1688) (ed, G. Dyfnallt Owen), London, 1971; Public Record Office (Kew) (hereafter PRO), PRO C 66/2631, PRO C 274/29, PRO C 66/2799, PRO C 274/32; Sixth Report of the Royal Commission on Historical Manuscripts, The Journal of the House of Commons; and Journal of the House of Commons.
98. See, for example, CSPD, Historical Manuscripts Commission 9 Calendar of Manuscripts of the Most Honorable The Marquess of Salisbury part XXII (A.D. 1612-1688) (ed, G. Dyfnallt Owen), London, 1971; Public Record Office (Kew) (hereafter PRO), PRO C 66/2631, PRO C 274/29, PRO C 66/2799, PRO C 274/32; Sixth Report of the Royal Commission on Historical Manuscripts, The Journal of the House of Commons; and Journal of the House of Commons.
99. The Clavis appeared in five Latin editions, the first in 1631 and the last in 1698. There were also two independent English editions. The first English edition, London, 1647, was translated by Robert Wood.
100. v.
101. r.
102. Willmoth, op. cit. (2), 4; Rigaud, op. cit. (47), 11.
103. Willmoth, op. cit. (2), 4; Rigaud, op. cit. (47), 11.
104. Rigaud, op. cit. (47), 27.
105. Rigaud, op. cit. (47), 27.
106. Rigaud, op. cit. (47), 10.
107. Cajori, op. cit. (2), 60. Willmoth, op. cit. (2), 44, points out that it should be kept in mind Cajori accepted post-Restoration stories about grateful pupils, and failed to question their basis in pre-Restoration fact. Ward might have simply cultivated the association for 'glamour of it', or for practical advice on how to use the Clavis as a teaching text.
108. Cajori, op. cit. (2), 60. Willmoth, op. cit. (2), 44, points out that it should be kept in mind Cajori accepted post-Restoration stories about grateful pupils, and failed to question their basis in pre-Restoration fact. Ward might have simply cultivated the association for 'glamour of it', or for practical advice on how to use the Clavis as a teaching text.
109. Willmoth, op. cit. (2), 48-9.
110. Rigaud, op. cit. (47), 61.
111. Robinson refers to the Earl of Arundel, Rigaud, op. cit. (47), 15.
112. David Howarth, Lord Arundel and His Circle, New Haven, 1985, 124. Arundel is usually described quite unproblematically as Oughtred's patron, as, for example, in Mary Hervey's Correspondence and Collections of Thomas Howard Earl of Arundel 'Father of Vertu in England', Cambridge, 1921, 346.
113. David Howarth, Lord Arundel and His Circle, New Haven, 1985, 124. Arundel is usually described quite unproblematically as Oughtred's patron, as, for example, in Mary Hervey's Correspondence and Collections of Thomas Howard Earl of Arundel 'Father of Vertu in England', Cambridge, 1921, 346.
114. Stephen Greenblatt, Renaissance Self-Fashioning, Chicago, 1980. Lesley Cormack (op. cit. (45), 68) makes a similar point for images and descriptions of the world.
115. Stephen Greenblatt, Renaissance Self-Fashioning, Chicago, 1980. Lesley Cormack (op. cit. (45), 68) makes a similar point for images and descriptions of the world.
116. Sharpe, op. cit. (42), 205.
117. PRO C 66/2631, no. 19.
118. See Sharpe, op. cit. (42), 10.5, 124. Malcolm Smuts, 'The political failure of Stuart cultural patronage', in Patronage in the Renaissance (ed. Guy Fitch Lytle and Stephan Orgal), Princeton, 1981, 165-87, especially 174-5.
119. See Sharpe, op. cit. (42), 10.5, 124. Malcolm Smuts, 'The political failure of Stuart cultural patronage', in Patronage in the Renaissance (ed. Guy Fitch Lytle and Stephan Orgal), Princeton, 1981, 165-87, especially 174-5.
120. Smuts, op. cit. (32), 56, 57.
121. Smuts, op. cit. (32), 59-60. Although there are many studies of court patronage in this period, they concentrate on artists and do not discuss figures such as Delamain.
122. Calendar, op. cit. (56), 10. Delamain was paid £10 for instructing the children for five months and £3 6s for the 'gift' of a sphere. See CSPD 1629-31, 138, for Endymion Porter, and CSPD 1637-38, 121, for Sir John Heydon.
123. See Linda Levy Peck, '"For a King not to be bountiful were a fault"; perspectives on court patronage in early Stuart England', Journal of British Studies (1986), 25, 31-61, for an important study of patronage in this period.
124. Paula Findlen, 'Economy of scientific exchange in early modern Italy', in Moran, op. cit. (45), 5-24, especially 6-7; William Eamon, 'Court, academy, and printing house: patronage and scientific careers in late Renaissance Italy', ibid., 25-50, especially 39; Mario Biagioli, Galileo Courtier: The Practice of Science in the Culture of Absolutism, Chicago, 1993.
125. Paula Findlen, 'Economy of scientific exchange in early modern Italy', in Moran, op. cit. (45), 5-24, especially 6-7; William Eamon, 'Court, academy, and printing house: patronage and scientific careers in late Renaissance Italy', ibid., 25-50, especially 39; Mario Biagioli, Galileo Courtier: The Practice of Science in the Culture of Absolutism, Chicago, 1993.
126. Paula Findlen, 'Economy of scientific exchange in early modern Italy', in Moran, op. cit. (45), 5-24, especially 6-7; William Eamon, 'Court, academy, and printing house: patronage and scientific careers in late Renaissance Italy', ibid., 25-50, especially 39; Mario Biagioli, Galileo Courtier: The Practice of Science in the Culture of Absolutism, Chicago, 1993.
127. Richard Delamain, Grammelogia or, Mathematical Ring, London, 1633, Sig. S3i. According to Bryden this was the last edition printed.
128. CSPD, 1629-31, 138.
129. CSPD, 1629-33, 84.
130. See also, A Companion to Arber (ed. W. W. Greg), Oxford, 1967, 250-3, for the complete texts.
131. Delamain received sporadic payments of £10 for unspecified services, CSPD, 1635, 134, 268, 467. For the grant, see PRO C 66/2631. I would like to thank Dr Sean Cunningham of the Public Records Office for help in locating this reference.
132. CSPD, 1637-38, 282. For Charles receiving his personal petition, see Sharpe, op. cit. (42), 205.
133. CSPD, 1637-38, 121.
134. Sixth Report of the Royal Commission on Historical Manuscripts. Part I Report and Appendix, London, 1877, 82.
135. He wanted Peter Burr's place and fee as the position of engineer of fortifications had been void for more than seven years. When phrasing his request for payment for the instrument, he often asked simply for money for the workmen, implying that he was donating his own expenses, CSPD, 1637-38, 121.
136. CSPD, 1637-38, 282.
137. Anthony Wood, Athenae Oxonienses, 2 vols., London, 1691/92, 525. Also see Sir Thomas Herbert's Memoirs, London, 1711, 130.
138. Anthony Wood, Athenae Oxonienses, 2 vols., London, 1691/92, 525. Also see Sir Thomas Herbert's Memoirs, London, 1711, 130.
139. l.
140. r.
141. Sixth Report, op cit. (85), 82;
142. Journal of the House of Lords (1644/45), 7, 657;
143. The Journal of the House of Commons (1644/45), 4, 197.
144. See for Richard Delamain: Imposter Magnus, or The Legerdemain of Richard Delamain ..., London, 1654; it refers to him as a 'wicked son of a good Father' and claims that he did not know as much mathematics as one might expect, 3, 13.
145. See Katherine Hill, 'Mathematics as a tool for social change: educational reform in seventeenth-century England', Seventeenth Century (1997), 12, 23-36, for a brief outline of the positions taken in the arguments over educational reform.
146. Rigaud, op. cit. (47), 479-80 (John Collin's letter to John Wallis).
147. 1.
148. Oughtred was, however, willing to help others. For example, he designed a gauging rod at Elias Allen's request for the Master of the Vintner's Company in 1633. In general, he had a substantial collaboration with Allen. See Taylor, op. cit. (5), 348-9. Additionally, he included a more practically oriented work with the second and third editions of the Clavis that included topics such as commercial arithmetic and fortifications.
149. Rigaud, op. cit. (47), 16-17.
150. Rigaud, op. cit. (47), 67.
151. Hill, op. cit. (92); Willmoth, op. cit. (2), 4-10.
152. Hill, op. cit. (92); Willmoth, op. cit. (2), 4-10.
153. Steven Shapin, A Social History of Truth: Civility and Science in Seventeenth-Century England, Chicago, 1994, see ch. 5 'Epistemological decorum'.
154. Rob Iliffe, '"In the warehouse": privacy, property and priority in the early Royal Society' History of Science (1992), 30, 29-68.
155. Steven Shapin, 'Discipline and bounding: the history and sociology of science as seen through the externalism-internalism debate', History of Science (1992), 30, 333-69, especially 335.