Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-09T06:20:18.092Z Has data issue: false hasContentIssue false
  • English
  • Français

Intertextual Reference in Nineteenth-Century Mathematics

Published online by Cambridge University Press:  26 September 2008

John O'Neill
John O'Neill
Affiliation:
School of Social Sciences, Sussex University
Get access Rights & Permissions [Opens in a new window]

Abstract

A scientific work presupposes a body of texts that are a condition for its intelligibility. This paper shows that the study of intertextual reference — of the ways a text indicates its relation to other texts — provides a fruitful perspective in the study of science that deserves more attention than it has hitherto received. The paper examines intertextual reference in early nineteenth-century mathematics, first surveying a variety of mathematical texts in the period and then examining in detail W.R. Hamilton's work on quaternions.

Three questions are addressed: (1) What forms of intertextual reference are employed? (2) What is the range of intertextual reference? (3) What are the functions of intertextual reference? The answers to the first two questions provide an unexplored perspective on the institutional changes in science during the period. The transitional status of the period in the development of later professional science is reflected in the relative openness in the forms of intertextual reference employed and the range of texts to which reference was made. In virtue of these features the period is particularly fruitful in the study of the functions of intertextual reference. With some major qualifications, the paper defends a Mertonian view that intertextual reference needs to be understood in terms of the claim to intellectual property rights.

Type
Article
Information
Science in Context , Volume 6 , Issue 2 , Autumn 1993 , pp. 435 - 468
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Babbage, C. 1815. “An Essay towards the Calculus of Functions.” Philosophical Transactions of the Royal Society 105:391–93.Google Scholar
Babbage, C. 1816. “An Essay towards the Calculus of Functions: Part II.” Philosophical Transactions of the Royal Society 106:106–256.Google Scholar
Babbage, C. 1820. “Observations on the Notation Employed in the Calculus of Functions.” Transactions of the Cambridge Philosophical Society 1:67–78.Google Scholar
Babbage, C. 1824. “On the Determination of the General Term of a New Class of Infinite Series.” Transactions of the Cambridge Philosophical Society 2:217–25.Google Scholar
Burke, F. 1810. “Essays on Powers and Their Differences.” Transactions of the Royal Irish Academy 11:131–210.Google Scholar
Cayley, A. 1845. “On Jacobi's EllipticalFunctions and on Quaternions.” Philosophical Magazine 36:208–11.Google Scholar
Davies, T. S. 1825. “Thoughts on the Demonstration of Certain Formulae.” Philosophical Magazine 66:115–21.CrossRefGoogle Scholar
De Morgan, A. 1830. “On the General Equation of Curves of the Second Degree: Part I.” Transactions of the Cambridge Philosophical Society 4:71–78.Google Scholar
De Morgan, A. 1832. “On the General Equation of Surfaces of the Second Degree: Part II.” Transactions of the Cambridge Philosophical Society 5:77–94.Google Scholar
De Morgan, A. 1836. “Sketch of a Method of Introducing Discontinuous Constants into the Arithmetical Expressions for Infinite Series, in Cases Where They Admit of Several Values. In a letter to the Rev. George Peacock, &c &c.” Transactions of the Cambridge Philosophical Society 6:185–219.Google Scholar
De Morgan, A. 1839. “On the Foundation of Algebra.” Transactions of the Cambridge Philosophical Society 7:173–85.Google Scholar
De Morgan, A. 1841. “On the Foundation of Algebra: No. II.” Transactions of the Cambridge Philosophical Society 7:287–300.Google Scholar
De Morgan, A. 1843. “On the Foundation of Algebra: No. III.” Transactions of the Cambridge Philosophical Society 8:141–42.Google Scholar
De Morgan, A. 1844. “On the Foundation of Algebra: No. IV.” Transactions of the Cambridge Philosophical Society 8:241–54.Google Scholar
Graves, J. 1828. “An Attempt to Rectify the Inaccuracy of Some Logarithmic formulae.” Philosophical Transactions of me Royal Society 108:171–86.Google Scholar
Graves, J. 1845. “On the Theory of Couples.” Philosophical Magazine 36:315–20.Google Scholar
Hamilton, W. 1835. “Theory of Conjugate Functions, or Algebraic Couples: With a Preliminary and Elementary Essay on Algebra as the Science of Pure Time.” Transactions of the Royal Irish Academy 17:243–482.Google Scholar
Hamilton, W. 1844a. “On a New Species of Imaginary Quantities Connected with the Theory of Quaternions.” Proceedings of the Royal Irish Academy 2:424–34.Google Scholar
Hamilton, W. 1844b. “On Quaternions: Or on a New System of Imaginaries in Algebra.” Philosophical Magazine 25: 10–13, 241–46.Google Scholar
Hamilton, W. 1844c. “On Quaternions: Or on a New System of Imaginaries in Algebra.” Philosophical Magazine 25:489–95.Google Scholar
Hamilton, W. 1846. “On a Proof of Pascal's Theorem by Means of Quaternions; and on Some Connected Subjects.” Proceedings of the Royal Irish Academy 3:273–92.Google Scholar
Hamilton, W. 1847. “On Quaternions, or on a New System of Imaginaries in Algebra, with Some Geometrical Illustrations.” Proceedings of the Royal Irish Academy 3:1–16.Google Scholar
Hamilton, W. 1848. “Research Respecting Quaternions.” Transactions of the Royal Irish Academy 21:199–203.Google Scholar
Hamilton, W. 1853a. “A Generalization of Pascal's Theorem.” Proceedings of the Royal Irish Academy 5: 100–101.Google Scholar
Hamilton, W. 1853b. Lectures on Quaternions. Dublin: Hodges and Smith.Google Scholar
Hamilton, W. 1853c. “On a Proof from Quaternions of the Celebrated Theorem of Joachimsthal.” Proceedings of the Royal Irish Academy 5:71.Google Scholar
Hamilton, W. 1858. “On the Celebrated Theorem of Dupin.” Proceedings of the Royal Irish Academy 6:86–88.Google Scholar
Hamilton, W. [1866] 1969. Elements of Quaternions, 3rd ed. New York: Chelsea.Google Scholar
Herapath, J. 1825. “On the Binomial Theorem and the Application of Some Properties of Δm. Onto the General Differentiation and Integration.” Philosophical Magazine 65:321–32.Google Scholar
Herschel, J. 1814. “Consideration of Various Points of Analysis.” Philosophical Transactions of the Royal Society 104:440–68.Google Scholar
Herschel, J. 1820–21. “On the Reductionof Certain Classes of Functional Equations to Equations of Finite Differences.” Transactions of the Cambridge Philosophical Society 1:77–88.Google Scholar
Herschel, J. 1832. “Description of a Machine for Resolving by Inspection Certain Important Forms of Transcendental Equations.” Transactions of the Cambridge Philosophical Society 4:425–40.Google Scholar
Horner, W. 1838. “New Demonstration of an Original Proposition in the Theory of Number.” Philosophical Magazine, 3rd series, vol. 12:456–60.Google Scholar
Jarrett, T. 1827. “On Algebraic Notation.” Transactions of theCambridge Philosophical Society 3:65–104.Google Scholar
Memoirs of the Analytical Society. 1813. Cambridge: Smith.Google Scholar
Meredith, T. 1800. “A New Method for Resolving Cubic Equations.” Transactions of the Royal Irish Academy 7:69–78.Google Scholar
Moore, A. 1837. “On the Explanation of a Difficulty in Analysis Noted by Sir William Hamilton.” Transactions of the Cambridge Philosophical Society 6:317–22.Google Scholar
Murphy, R. 1827–30. “On the General Properties of Definite Integrals.” Transactions of the Cambridge Philosophical Society 3:429–43.Google Scholar
Murphy, R. 1831. “On the Resolution of Algebraic Equations.” Transactions of the Cambridge Philosophical Society 4:125–53.Google Scholar
Murphy, R. 1832a. “On the Elimination betweenan Indefinite Number of Unknown Quantities.” Transactions ofthe Cambridge Philosophical Society 5:65–75.Google Scholar
Murphy, R. 1832b. “On the Inverse Method of Definite Integrals with Physical Applications.” Transactions of the Cambridge Philosophical Society 4:353–408.Google Scholar
Murphy, R. 1833. “Second Memoir on the Inverse Method of Definite Integrals.” Transactions of the Cambridge Philosophical Society 5:113–48.Google Scholar
Murphy, R. 1835a. “On the Resolution of Equations in Finite Difference.” Transactions of the Cambridge Philosophical Society 6:91–106.Google Scholar
Murphy, R. 1835b. “Third Memoir on the Inverse Method of Definite Integrals.” Transactions of the Cambridge Philosophical Society 5:315–94.Google Scholar
Murphy, R. 1837. “On a New Theorem in Analysis.” Philosophical Magazine, 3rd series, vol.10:28–32.Google Scholar
Murray, D. 1803. “On Doctor Halley's Series for the Calculation of Logarithms.” Transactions of the Royal Irish Academy 9:3–19.Google Scholar
Nicholson, P. 1820. “An Entirely New Method of Extracting the Cube Root in Numbers.” Philosophical Magazine 56:360–62.CrossRefGoogle Scholar
Smith, A. 1835. “Investigation of the Equation to Fresnel's Wave Surface.” Transactions of the Cambridge Philosophical Society 6:85–90.Google Scholar
Sylvester, J. 1838. “Notes to Analytical Development &c' Philosophical Magazine, 3rd series, 12:341–47.Google Scholar
Toplis, J. 1805. “Concerning the Analytical and Synthetical Modes of Reasoning Made Use of in Mathematics and Other Sciences.” Philosophical Magazine 20:193–202.Google Scholar
Vince, S. 1815. “On Certain Properties of Numbers.” Transactions of the Royal Irish Academy 12:34–38.Google Scholar
Walker, Arnott G. A. 1817. “Observation on the Solution of Exponential Equations.” Philosophical Magazine 49:321–29.Google Scholar
Warren, J. 1829. “Consideration of the Objections Raised against the Geometrical Representation of the Square Roots of Negative Quantities.” Philosophical Transactions of the Royal Society 119:21.Google Scholar
Woodhouse, R. 1801. “On the Necessary Truth of Certain Conclusions Obtained by Means of Imaginary Quantities.” Philosophical Transactions of the Royal Society 91:89–119.Google Scholar
Woodhouse, R. 1803. The Principles of Analytical Calculation. Cambridge: Cambridge University Press.Google Scholar
Young, J. 1837. “Investigation of Formulae for the Summation of Certain Classes of Infinite Series.” Philosophical Magazine 10:121–24.Google Scholar
Young, J. 1845–57. “An Extension ofa Theorem of Euler with a Determination of the Limit beyond Which It Fails.” Proceedings of the Royal Irish Academy 2.Google Scholar
Becher, W. 1980. “William Whewell and Cambridge Mathematics.” Historical Studies in the Physical Sciences 11:1–48.Google Scholar
Bloor, D. 1981. “Hamilton and Peacock and the Essence of Algebra.” In Mehrtens et al. 1981,CrossRefGoogle Scholar
Bork, A. 1966. “Vectors versus Quaternions.” American Journal of Physics 34:257–66.Google Scholar
Brown, P., and Levinson, S. 1987. Politeness. Cambridge: Cambridge University Press.Google Scholar
Cohen, G. A. 1978. Karl Marx's Theory of History. Oxford: Oxford University Press.Google Scholar
Cohen, G. A. 1982. “Functional Explanation, Consequence Explanation, and Marxism.” Inquiry 25:27–56.Google Scholar
Crowe, M. 1968. A History of Vector Analysis. Ind.:Notre Dame University Press.Google Scholar
Culler, J. 1981. The Pursuit of Signs. London: Routledge and Kegan Paul.Google Scholar
Elster, J. 1982. “Marxism, Functionalism and Game Theory.” Theory and Society 11:453–82.Google Scholar
Elster, J. 1985. Making Sense of Marx. Cambridge: Cambridge University Press.Google Scholar
Enros, P. 1981. “Cambridge University and the Adoption of Analytics in Early Nineteenth-Century England. ” In Mehrtens et al. 1981,CrossRefGoogle Scholar
Gilbert, G. 1977. “Referencing as Persuasion.” Social Studies of Science 7:113–22.Google Scholar
Graves, R. 1882. Life of Sir William Rowan Hamilton, vol. 1. Dublin: Hodges, Figgis.Google Scholar
Graves, R. 1885. Life of Sir William Rowan Hamilton, vol. 2. Dublin: Hodges, Figgis.Google Scholar
Graves, R. 1892. Life of Sir William Rowan Hamilto, vol. 3. Dublin: Hodges, Figgis.Google Scholar
Gross, A. 1990. The Rhetoric of Science. Cambridge, Mass.: Harvard University Press.Google Scholar
Halberstam, H., and Ingram, R, eds. 1967. The Mathematical Papers of Sir William Rowan Hamilton, vol. 3. Cambridge: Cambridge University Press.Google Scholar
Halliday, M. 1978. Language as Social Semiotic. London: Edward Arnold.Google Scholar
Halliday, M., and Hasan, R. 1976. Cohesion in English. London: Longman.Google Scholar
Halliday, M., 1985. Language, Context and Text.Geelong: Deakin University Press.Google Scholar
Hankins, T. 1980. Sir William Rowan Hamilton. Baltimore: Johns Hopkins University Press.Google Scholar
Jenny, L. 1982. “The Strategy of Form.” In French Literary Theory Today, edited by Todorov, T, 34–63. Cambridge: Cambridge University Press.Google Scholar
Kristeva, J. 1987. The Kristeva Reader, edited by Moi, Toril. Oxford: Blackwell.Google Scholar
Kronick, D. 1976. A History of Scienfic and Technical Periodicals, 2nd ed. New York: Scarecrow Press.Google Scholar
Latour, B. 1987. Science in Action.Milton Keynes: Open University Press.Google Scholar
Mehrtens, H., Bos, H. and Schneider, I., eds. 1981. Social History of Nineteenth Century Mathematics. Boston: Birkhauser.Google Scholar
Merton, R. 1957. “Priorities in Scientific Discovery.” American Sociological Review 22:635–59.Google Scholar
Merton, R. 1968. Social Theory and Social Structure.. New York: Free Press.Google Scholar
Moravcisk, M., and Murgesan, P. 1975. “Some Results on the Function and Quality of Citations.” Social Studies of Science 5:86–92.Google Scholar
Myers, G. 1989. “The Pragmatics of Politeness in Scientific Articles.” Applied Linguistics 10:1–35.Google Scholar
O'Donnell, S. 1983. William Rowan Hamilton. Dublin: Boole Press.Google Scholar
O'Neill, J. 1986. “Formalism, Hamilton and Complex Numbers.” Studies in History and Philosophy of Science 17:351–72.Google Scholar
O'Neill, J. 1988. Six Presentations of a Mathematical Discovery. Lancaster: Lancaster University.Google Scholar
O'Neill, J. 1990. “Property in Science and the Market.” The Monist 73:601–20.Google Scholar
O'Neill, J. 1991. Worlds without Content: Against Formalism. London: Routledge.Google Scholar
Ravetz, J. 1973. Scientific Knowledge and Its Social Problems. London: Penguin.Google Scholar
Riffaterre, M. 1978. Semiotics of Poetry. London: Methuen.Google Scholar
Rotman, B. 1977. Piaget: Psychologist of the Real. Brighton: Harvester.Google Scholar
Small, H. 1978. “Cited Documents as Concept Symbols.” Social Studies of Science 8:327–40.Google Scholar
Solomon, Y. 1989. The Practice of Mathematics. London: Routledge.Google Scholar
Stephenson, R. 1966. “The Development of Vector Analysis from Quaternions.” American Journal of Physics 34:194–201.Google Scholar
Worton, M., and Still, J. 1990. Intertextuality: Theories and Practice. Manchester: Manchester University Press.Google Scholar