메뉴 건너뛰기




Volumn 29, Issue 4, 2002, Pages 395-426

Symbolical algebra as a foundation for calculus: D. F. Gregory's contribution

Author keywords

Abstract algebra; Gregory; Murphy; Power series; Separation of symbols; Servois; Symbolic algebra

Indexed keywords


EID: 0036858645     PISSN: 03150860     EISSN: None     Source Type: Journal    
DOI: 10.1006/hmat.2002.2358     Document Type: Article
Times cited : (16)

References (55)
  • 1
    • 85031357290 scopus 로고    scopus 로고
    • The Development of British Symbolical Algebra ⋯
    • Ann Arbor: UMI Dissertation Services
    • Allaire, P.R. 1997. The Development of British Symbolical Algebra μe. Ann Arbor: UMI Dissertation Services.
    • (1997)
    • Allaire, P.R.1
  • 2
    • 0004186620 scopus 로고
    • Du calcul des dérivations
    • Strasbourg: LeVrault Frères
    • Arbogast, L. F A. 1800. Du calcul des dérivations. Strasbourg: LeVrault Frères.
    • (1800)
    • Arbogast, L.FA.1
  • 3
    • 0011904685 scopus 로고
    • A History of the Study of Mathematics at Cambridge
    • Cambridge, UK: Cambridge Univ. Press
    • Ball, W. W. R. 1889. A History of the Study of Mathematics at Cambridge. Cambridge, UK: Cambridge Univ. Press.
    • (1889)
    • Ball, W.W.R.1
  • 4
    • 84956830670 scopus 로고
    • A New Mathematical and Philosophical Dictionary
    • London: Whittingham & Roland
    • Barlow, P. 1814. A New Mathematical and Philosophical Dictionary. London: Whittingham & Roland.
    • (1814)
    • Barlow, P.1
  • 5
    • 0011834015 scopus 로고
    • Woodhouse, Babbage, Peacock, and modern algebra
    • Becher, H. W. 1980. Woodhouse, Babbage, Peacock, and modern algebra. Hist. Math. 7, 389-400.
    • (1980) Hist. Math. , vol.7 , pp. 389-400
    • Becher, H.W.1
  • 6
    • 0011884196 scopus 로고
    • On the integration of linear differential equations with constant coefficients
    • Boole, G. 1840. On the integration of linear differential equations with constant coefficients. Cambridge J. Math. 2, 114-119.
    • (1840) Cambridge J. Math. , vol.2 , pp. 114-119
    • Boole, G.1
  • 7
    • 0011873014 scopus 로고
    • On a general method in analysis
    • Boole, G. 1844. On a general method in analysis, Phil. Trans. R. Soc. London 134, 225-287.
    • (1844) Phil. Trans. R. Soc. London , vol.134 , pp. 225-287
    • Boole, G.1
  • 8
    • 0004260199 scopus 로고
    • The Mathematical Analysis of Logic
    • Cambridge, UK: Macmillan, Barclay, & Macmillan. Reprinted 1948, New York: Philosophical Library. Page references are from the reprinted volume
    • Boole, G. 1847. The Mathematical Analysis of Logic. Cambridge, UK: Macmillan, Barclay, & Macmillan. Reprinted 1948, New York: Philosophical Library. Page references are from the reprinted volume.
    • (1847)
    • Boole, G.1
  • 9
    • 0003451567 scopus 로고
    • An Investigation of the Laws of Thought
    • Reprinted 1952, New York: Dover. Page references are from the reprinted volume
    • Boole, G. 1854. An Investigation of the Laws of Thought. Reprinted 1952, New York: Dover. Page references are from the reprinted volume.
    • (1854)
    • Boole, G.1
  • 10
    • 0011828350 scopus 로고
    • Cambridge, UK. 5th ed., New York: Chelsea, 1959. Page references are from the fifth edition
    • Boole, G. 1859. A Treatise on Differential Equations. Cambridge, UK. 5th ed., New York: Chelsea, 1959. Page references are from the fifth edition.
    • (1859) A Treatise on Differential Equations
    • Boole, G.1
  • 11
    • 84887509105 scopus 로고
    • Le mathématicien franc-comtois François-Joseph Servois
    • Boyer, J. 1894. Le mathématicien franc-comtois François-Joseph Servois. Mém. Soc. Émulation Doubs 9, 305-328.
    • (1894) Mém. Soc. Émulation Doubs , vol.9 , pp. 305-328
    • Boyer, J.1
  • 12
    • 0011910967 scopus 로고    scopus 로고
    • The origins of linear operator theory in the work of François-Joseph Servois
    • to appear
    • Bradley, R. E. 2002. The origins of linear operator theory in the work of François-Joseph Servois. Proc. Can. Soc. Hist. Phil. Math. 14, to appear.
    • (2002) Proc. Can. Soc. Hist. Phil. Math. , vol.14
    • Bradley, R.E.1
  • 13
    • 85031347024 scopus 로고    scopus 로고
    • Cambridge Math. J. 1841-1845 [4 vols.].
    • Cambridge Math. J. , vol.4 , pp. 1841-1845
  • 14
    • 85031364694 scopus 로고
    • Edinburgh. London: Hamish Hamilton
    • Daiches, D. 1978. Edinburgh. London: Hamish Hamilton.
    • (1978)
    • Daiches, D.1
  • 16
    • 0011873316 scopus 로고
    • The Differential and Integral Calculus
    • London: Baldwin & Craddock
    • De Morgan, A. 1842. The Differential and Integral Calculus. London: Baldwin & Craddock.
    • (1842)
    • De Morgan, A.1
  • 18
    • 0011910969 scopus 로고
    • Memoir of Augustus De Morgan. By His Wife Sophia Elizabeth De Morgan, with Selections from His Letters. London: Longmans Green
    • De Morgan, S. E. 1882. Memoir of Augustus De Morgan. By His Wife Sophia Elizabeth De Morgan, with Selections from His Letters. London: Longmans Green.
    • (1882)
    • De Morgan, S.E.1
  • 19
    • 0004230658 scopus 로고
    • L. Stephen and S. Lee, Eds. London: Oxford University
    • Dictionary of National Biography 1921. L. Stephen and S. Lee, Eds. London: Oxford University.
    • (1921) Dictionary of National Biography
  • 20
    • 0004000254 scopus 로고
    • C. C. Gillespie, Ed. New York: Scribner
    • Dictionary of Scientific Biography 1972. C. C. Gillespie, Ed. New York: Scribner.
    • (1972) Dictionary of Scientific Biography
  • 21
    • 0011881017 scopus 로고
    • Babbage, Peacock and modern algebra
    • Dubbey, J. M. 1977. Babbage, Peacock and modern algebra. Hist. Math. 4, 295-302.
    • (1977) Hist. Math. , vol.4 , pp. 295-302
    • Dubbey, J.M.1
  • 22
    • 0346833650 scopus 로고
    • Biographical memoir of Duncan Farquharson Gregory
    • Ellis, R. L. 1845. Biographical memoir of Duncan Farquharson Gregory. Cambridge Math. J 4, 145-151.
    • (1845) Cambridge Math. J. , vol.4 , pp. 145-151
    • Ellis, R.L.1
  • 23
    • 85031363649 scopus 로고    scopus 로고
    • Obituary notice of Duncan F. Gregory, Esq
    • The Gentlemen's Magazine
    • The Gentlemen's Magazine. Obituary notice of Duncan F. Gregory, Esq. The Gentlemen's Magazine 21, 657.
    • The Gentlemen's Magazine , vol.21 , pp. 657
  • 24
    • 85031351791 scopus 로고
    • 1882, 1885, Dublin: Hodges, Figgis. Reprint 1975, New York: Arno. Page references are from the reprinted volume
    • Graves, R. P. 1882, 1885, 1889. Life of Sir William Rowan Hamilton, 3 vols. Dublin: Hodges, Figgis. Reprint 1975, New York: Arno. Page references are from the reprinted volume.
    • (1889) Life of Sir William Rowan Hamilton , vol.3
    • Graves, R.P.1
  • 25
    • 0011833714 scopus 로고
    • On the use of negative quantities in the solution of problems by algebraic equations
    • Greenfield, W. 1788. On the use of negative quantities in the solution of problems by algebraic equations. Trans. R. Soc. Edinburgh 1, 131-45.
    • (1788) Trans. R. Soc. Edinburgh , vol.1 , pp. 131-145
    • Greenfield, W.1
  • 26
    • 85031354790 scopus 로고
    • Letter to Archibald Smith, November 23, 1836, Archibald Smith Collection TD1/476, Glasgow City Archives
    • Gregory, D. F. 1836. Letter to Archibald Smith, November 23, 1836, Archibald Smith Collection TD1/476, Glasgow City Archives.
    • (1836)
    • Gregory, D.F.1
  • 28
    • 85031355625 scopus 로고
    • Letter to S. S. Greatheed, July 7, 1839. Trinity College Library, Add Ms C 1 138, Cambridge
    • Gregory, D. F. 1839. Letter to S. S. Greatheed, July 7, 1839. Trinity College Library, Add Ms C 1 138, Cambridge.
    • (1839)
    • Gregory, D.F.1
  • 29
    • 0011873317 scopus 로고
    • On the real nature of symbolical algebra
    • Also in [Gregory 1865, pp. 1-13]. Page references are to the reprinted version in [Gregory 1865]
    • Gregory, D. F. 1840. On the real nature of symbolical algebra. Trans. R. Soc. Edinburgh 14, 208-216. Also in [Gregory 1865, pp. 1-13]. Page references are to the reprinted version in [Gregory 1865].
    • (1840) Trans. R. Soc. Edinburgh , vol.14 , pp. 208-216
    • Gregory, D.F.1
  • 30
    • 0011884199 scopus 로고
    • Examples of the Processes of the Differential and Integral Calculus
    • Cambridge: J. & J.J. Deighton
    • Gregory, D. F. 1841a. Examples of the Processes of the Differential and Integral Calculus. Cambridge: J. & J.J. Deighton.
    • (1841)
    • Gregory, D.F.1
  • 31
    • 85031354212 scopus 로고
    • Letter to James Thomson, March 6, 1841. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/G182. Cambridge University Library, Cambridge
    • Gregory, D. F. 1841b. Letter to James Thomson, March 6, 1841. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/G182. Cambridge University Library, Cambridge.
    • (1841)
    • Gregory, D.F.1
  • 34
    • 85031347027 scopus 로고
    • George Boole, F. R. S. Brit. Quart. R. July 1866. Reprinted in Boole, G. 1952, La Salle: Open Court, References are to the reprinted version
    • Harley, R. 1866. George Boole, F. R. S. Brit. Quart. R. July 1866. Reprinted in Boole, G. 1952, Studies in Logic and Probability. La Salle: Open Court, 425-472. References are to the reprinted version.
    • (1866) Studies in Logic and Probability , pp. 425-472
    • Harley, R.1
  • 35
    • 0011828351 scopus 로고
    • London: J. Johnson. New edition, London: F. C. & J. Rivington 1815
    • Hutton, C. 1795. Mathematical and Philosophical Dictionary. London: J. Johnson. New edition, London: F. C. & J. Rivington, 1815.
    • (1795) Mathematical and Philosophical Dictionary
    • Hutton, C.1
  • 36
    • 0011827989 scopus 로고
    • The calculus of operations and the rise of abstract algebra
    • Koppelman, E. 1971. The calculus of operations and the rise of abstract algebra. Arch. Hist. Exact Sci. 8, 155-242.
    • (1971) Arch. Hist. Exact Sci. , vol.8 , pp. 155-242
    • Koppelman, E.1
  • 37
    • 0004317660 scopus 로고    scopus 로고
    • An Elementary Treatise on the Differential and Integral Calculus
    • Charles Babbage, William Herschel, George Peacock, Transls. Cambridge, UK: J. Deighton and Sons
    • Lacroix, S. F., An Elementary Treatise on the Differential and Integral Calculus. Charles Babbage, William Herschel, George Peacock, Transls. Cambridge, UK: J. Deighton and Sons.
    • Lacroix, S.F.1
  • 38
    • 84957435799 scopus 로고
    • Sur une nouvelle espèe de calcul relatif à la différentiation et a l'intégration des quantités variables
    • J. A. Serret, Ed. Paris
    • Lagrange, J. L., Sur une nouvelle espèe de calcul relatif à la différentiation et a l'intégration des quantités variables. In Oeuvres de Lagrange, J. A. Serret, Ed. Paris, 1867-1892, III: 441-476.
    • (1867) Oeuvres De Lagrange , vol.3 , pp. 441-476
    • Lagrange, J.L.1
  • 39
    • 0011900343 scopus 로고
    • Les premières étapes du calcul symbolique
    • Lusternik, L. A., & Petrova, S. S. 1972. Les premières étapes du calcul symbolique. Rev. Hist. Sci. 25, 201-206.
    • (1972) Rev. Hist. Sci. , vol.25 , pp. 201-206
    • Lusternik, L.A.1    Petrova, S.S.2
  • 40
    • 0011830769 scopus 로고
    • Petrova, From the history of symbolic calculus
    • [Russian]
    • Lusternik, L. A., & Petrova, S. S. 1977. Petrova, From the history of symbolic calculus [Russian]. Isto.-Mat. Issled. Vyp. 22, 85-101.
    • (1977) Isto.-Mat. Issled. Vyp. , vol.22 , pp. 85-101
    • Lusternik, L.A.1    Petrova, S.S.2
  • 41
    • 85020093011 scopus 로고
    • A Dictionary of the Mathematical and Physical Sciences, According to the Latest Improvements and Discoveries
    • London: Whittaker
    • Mitchell, J. 1823. A Dictionary of the Mathematical and Physical Sciences, According to the Latest Improvements and Discoveries. London: Whittaker.
    • (1823)
    • Mitchell, J.1
  • 42
    • 0011913530 scopus 로고
    • First memoir on the theory of analytic operations
    • Murphy, R. 1837. First memoir on the theory of analytic operations. Phil. Trans. R. Soc. London 127, 179-210.
    • (1837) Phil. Trans. R. Soc. London , vol.127 , pp. 179-210
    • Murphy, R.1
  • 43
    • 34548003409 scopus 로고
    • Scottish and English Schools
    • Pittsburgh: Univ. of Pittsburgh Press
    • Osborne, G. S. 1967. Scottish and English Schools. Pittsburgh: Univ. of Pittsburgh Press.
    • (1967)
    • Osborne, G.S.1
  • 44
    • 0011834752 scopus 로고
    • Collection of'Examples of the Applications of the Differential and Integral Calculus
    • Cambridge, UK: J. Deighton and Sons
    • Peacock, G. 1820. Collection of'Examples of the Applications of the Differential and Integral Calculus. Cambridge, UK: J. Deighton and Sons.
    • (1820)
    • Peacock, G.1
  • 45
    • 0011887587 scopus 로고
    • A Treatise on Algebra
    • Cambridge, UK: J. & J. J. Deighton
    • Peacock, G. 1830. A Treatise on Algebra. Cambridge, UK: J. & J. J. Deighton.
    • (1830)
    • Peacock, G.1
  • 46
    • 0011869495 scopus 로고
    • The origin of linear operator theory in the works of Servois and Murphy
    • [Russian] Moscow
    • Petrova, S. S. 1978. The origin of linear operator theory in the works of Servois and Murphy [Russian]. In History and Methodology of the Natural Sciences XX, pp. 122-128. Moscow.
    • (1978) History and Methodology of the Natural Sciences XX , pp. 122-128
    • Petrova, S.S.1
  • 47
    • 85031354684 scopus 로고
    • Announcement of the regulations for awarding Royal Medals
    • Royal Society of London Announcement of awarding of Royal Medal to George Boole, Phil. Trans. 134, 329
    • Royal Society of London 1844. Announcement of the regulations for awarding Royal Medals, Phil. Trans. 134, vii-viii. Announcement of awarding of Royal Medal to George Boole, Phil. Trans. 134, 329.
    • (1844) Phil. Trans. , vol.134
  • 48
    • 0002787151 scopus 로고
    • Essai sur un nouveau d'exposition des principes do calcul diff\érentiel
    • Servois, F. J. 1814a. Essai sur un nouveau d'exposition des principes do calcul différentiel. Ann. Math. Pures Appl. 5, 93-140.
    • (1814) Ann. Math. Pures Appl. , vol.5 , pp. 93-140
    • Servois, F.J.1
  • 49
    • 0002787151 scopus 로고
    • Reflexions sur les divers systèmes d'exposition des principes du calcul différentiel, et, en particulier, sur la doctrine des infiniment petits
    • Servois, F. J. 1814b. Reflexions sur les divers systèmes d'exposition des principes du calcul différentiel, et, en particulier, sur la doctrine des infiniment petits. Ann. Math. Pures Appl. 5, 141-170.
    • (1814) Ann. Math. Pures Appl. , vol.5 , pp. 141-170
    • Servois, F.J.1
  • 50
    • 85031348910 scopus 로고
    • Robert Murphy, Monograph 31. Department of Mathematics, Monash University, Clayton, Australia
    • Smith, G. C. 1984. Robert Murphy, Monograph 31. Department of Mathematics, Monash University, Clayton, Australia.
    • (1984)
    • Smith, G.C.1
  • 52
    • 85031353943 scopus 로고
    • Letter to D. F. Gregory, March 9, 1841. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/G183, Cambridge University Library, Cambridge
    • Thomson, J. 1841. Letter to D. F. Gregory, March 9, 1841. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/G183, Cambridge University Library, Cambridge.
    • (1841)
    • Thomson, J.1
  • 53
    • 85031352308 scopus 로고
    • Letter to William Thomson, October 24, 1843. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/T250, Cambridge University Library, Cambridge
    • Thomson, J. 1843. Letter to William Thomson, October 24, 1843. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/T250, Cambridge University Library, Cambridge.
    • (1843)
    • Thomson, J.1
  • 54
    • 85031362972 scopus 로고
    • Draft of a letter to D. F. Gregory, February, 1841. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/G179, Cambridge University Library, Cambridge
    • Thomson, W. 1841. Draft of a letter to D. F. Gregory, February, 1841. William Thomson, Lord Kelvin Papers: Add. Ms. 7342/G179, Cambridge University Library, Cambridge.
    • (1841)
    • Thomson, W.1
  • 55
    • 0011867246 scopus 로고
    • Alumni Cantabrigiensis: A Biographical List of All Known Students, Graduates and Holders of Office at the University of Cambridge, from the Earliest Times to 1900. Cambridge, UK: Cambridge Univ. Press
    • Venn, J., & Venn, J. A. 1922. Alumni Cantabrigiensis: A Biographical List of All Known Students, Graduates and Holders of Office at the University of Cambridge, from the Earliest Times to 1900. Cambridge, UK: Cambridge Univ. Press.
    • (1922)
    • Venn, J.1    Venn, J.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.