Foundations of Science

, Volume 19, Issue 1, pp 35–51

Algebraic Collisions

Challenging Descartes with Cartesian Tools
Article

Abstract

Algebraic equations in the tradition of Descartes and Frans Van Schooten accompany Christiaan Huygens’s early work on collision, which later would be reorganized and presented as De motu corporum ex percussione. Huygens produced the equations at the same time as his announcement of his rejection of Descartes’s rules of collision. Never intended for publication, the equations appear to have been used as preliminary scaffolding on which to build his critiques of Descartes’s physics. Additionally, Huygens used algebraic equations of this form to accurately predict the speeds of bodies after collision in experiments carried out at the Royal Society. Despite their deceptive simplicity, Huygens’s algebraic equations pose significant conceptual problems both mathematically and for their physical interpretation especially for negative speeds; they may very well have been the source of a new principle, the conservation of quantity of motion with direction.

Keywords

Algebra Rules of collision Christiaan Huygens René Descartes Quantity of motion 

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References

  1. Andriesse C. D. (2005) Huygens: The Man behind the principle. Cambridge University Press, New YorkGoogle Scholar
  2. Bell, A. E. (1947). Christian Huygens and the development of science in the seventeenth century. London: St. Ann’s Press.Google Scholar
  3. Bertoloni Meli D. (2006) Thinking with objects: The transformation of mechanics in the seventeenth century. The Johns Hopkins University Press, BaltimoreGoogle Scholar
  4. Bos, H. J. M. (1980a). Christiaan huygens a biography. In H. J. M. Bos, M. J. S. Rudwick, H. A. M. Snelders, & R. P. W. Visser (Eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979. Lisse: Swets & Zeitlinger B. V.Google Scholar
  5. Bos, H. J. M. (1980b). Huygens and mathemathics. In H. J. M. Bos, M. J. S. Rudwick, H. A. M. Snelders, & R. P. W. Visser (Eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979. Lisse: Swets & Zeitlinger B. V.Google Scholar
  6. Cajori, F. (1928). A history of mathematical notations (Vol. 1). La Salle, Illinois: Open Court Publishing Co.Google Scholar
  7. Descartes R. (1954) The geometry of René Descartes with a facsimile of the first edition (D. E. Smith & M. L. Latham, Trans.). Dover Publications, New YorkGoogle Scholar
  8. Descartes R. (1983) Principles of philosophy (V. R. Miller & R. P. Miller, Trans.). Reidel, DordrechtGoogle Scholar
  9. Descartes, R., Adam, C., & Tannery, P. (1964–1976). Oeuvres de Descartes; publiées par Charles Adam & Paul Tannery, sous les auspices du Ministère de l’Instruction Publique. Paris: J. Vrin.Google Scholar
  10. Gabbey, A. (1980). Huygens and mechanics. In H. J. M. Bos, M. J. S. Rudwick, H. A. M. Snelders, & R. P. W. Visser (Eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979 (pp. 166–199). Lisse: Swets & Zeitlinger B. V.Google Scholar
  11. Galilei, G. (1974) Two new sciences, including centers of gravity and force of percussion. DS: University of Wisconsin Press.Google Scholar
  12. Garber D. (1992) Descartes’ metaphysical physics. Science and its conceptual foundations. University of Chicago Press, ChicagoGoogle Scholar
  13. Guicciardini N. (1999) Reading the principia: The debate on Newton’s mathematical methods for natural philosophy from 1687 to 1736. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  14. Hall, A. R., & Hall, M. B. (Eds.) (1965–1986). Correspondence of Henry Oldenburg (Vol. 2, 5). Madison: University of Wisconsin Press.Google Scholar
  15. Howard, N. C. (2003). Christiaan Huygens: The construction of texts and audiences. PhD thesis, Indiana University, Bloomington.Google Scholar
  16. Huygens, C. (1888–1950). Oeuvres Complétes De Christiaan Huygens. The Hague: Martinus Nijhoff.Google Scholar
  17. Huygens, C. (1995). On the motion of bodies resulting from impact, (M. S. Mahoney, Trans.).Google Scholar
  18. Mahoney M. (1980) The beginnings of algebraic thought in the seventeenth century. In: Gaukroger S. (Ed.), Descartes: Philosophy, mathematics and physics, chap. 5. The Harvester Press, HassocksGoogle Scholar
  19. Mahoney M. (1994) The mathematical career of Pierre Fermat 1601–1605. Princeton University Press, PrincetonGoogle Scholar
  20. Pycior H. M. (1997) Symbols, impossible numbers, and geometric entanglements: British algebra through the commentaries on Newton’s universal arithmetick. Cambridge University Press, New YorkCrossRefGoogle Scholar
  21. Roche J. (1998) Mathematics of measurement: A critical history. Athlone Press, LondonGoogle Scholar
  22. Roth, L. (Ed.). (1926) Correspondence of Descartes and Constantyn Huygens, 1635–1647 from manuscripts now in the Bibliothèque Nationale, formerly in the possession of the late Harry Wilmot Buxton, F. R. A. S.. Clarendon Press, OxfordGoogle Scholar
  23. Struik, D. J. (1981). The land of Stevin and Huygens: A sketch of science and technology in the Dutch Republic during the golden century, volume 7 of Studies in the History of Modern Science. Boston: Reidel Publishing Co.Google Scholar
  24. Torricelli, E., Loria, G., & Vassura, G. (1919–1944). Opere di Evangelista Torricelli, De Motu, volume 2 of Opere di Evangelista Torricelli. Stab, tipo-Lit. G. Montanavi.Google Scholar
  25. Van Maanen, J. A. (1980). Chronology. In: H. J. M. Bos, M. J. S. Rudwick, H. A. M. Snelders, & R. P. W. Visser (Eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979 (pp. 19–26). Lisse: Swets & Zeitlinger B. V.Google Scholar
  26. Van Maanen J. A. (1987) Facets of seventeenth century mathematics in the Netherlands. Drukkerij Elinkwijk BV, UtrechtGoogle Scholar
  27. Westfall R. S. (1971) Force in Newton’s physics: The science of dynamics in the seventeenth century. Elsevier Publishing Co, New YorkGoogle Scholar
  28. Westman, R. S. (1980). Huygens and the problem of cartesianism. In Bos H. J. M., M. J. S. Rudwick, H. A. M. Snelders, & R. P. W. Visser (Eds.), Studies on Christiaan Huygens: Invited papers from the symposium on the life and work of Christiaan Huygens, Amsterdam, 22–25 August 1979. Lisse: Swets & Zeitlinger B. V.Google Scholar
  29. Yoder J. (1998a) The archives of Christiaan Huygens and his editors. In: Hunter Michael (Ed.), Archives of the scientific revolution: The formation and exchange of ideas in seventeenth-century Europe. Boydell Press, Woodbridge, pp 91–108Google Scholar
  30. Yoder J. (1998b) Unrolling time: Christiaan Huygens and the mathematization of nature. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.History and Philosophy of ScienceIndiana UniversityBloomingtonUSA

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