Is Mathematics to Be Useful? The Case of de la Hire, Fontenelle, and the Epicycloid

  • Christopher BaltusEmail author
Conference paper
Part of the Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques book series (PCSHPM)


The epicycloid is the path of a point on a circle rolling on another circle. Philippe de la Hire (1640–1718) developed mathematical properties of the epicycloid in a 1694 work. Further, according to Bernard de Fontenelle’s Eloge de M. de la Hire, where the shape of gear teeth had earlier been “abandoned to the fantasies of workmen,” M. de la Hire showed “that these teeth, in order to have all the perfection possible, should be in the form of an arc of the epicycloid.” However, despite words praising the utility of mathematics, La Hire’s work itself suggests a mathematician with a solution in search of a problem as much as the reverse motivation. La Hire’s mathematics is examined, together with the views of Fontenelle and de la Hire on the role of science and mathematics.


Gear Tooth Base Circle Companion Curve Simple Worker Greek Geometry 
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  1. de Fontenelle, B. (1718). Eloge de M. de la hire (pp. 76–89). Histoire de l’Académie Royale de Sciences.Google Scholar
  2. de Fontenelle, B. (1727). Eloge de M. Neuton (pp. 151–172). Histoire de l’Académie Royale de Sciences.Google Scholar
  3. de Roberval, G. P. (1693). Divers ouvrages de M. de Roberval. Paris: Académie Royale des Sciences.Google Scholar
  4. La Hire, P. (1676). De cycloide, Paris (author’s date)Google Scholar
  5. La Hire, P. (1694). Traité des epicycloides, et de leur usage dans les méchaniques. In Mémoires de Mathematique et de Physique. Paris: Imprimerie Royale.Google Scholar
  6. Schwamb, P., & Merrill, A. (1908). Elements of mechanism (2nd ed.). New York: Wiley.Google Scholar
  7. Whitman, E. A. (1943). Some historical notes on the cycloid. American Mathematical Monthly, 50(5), 309–315.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsSUNY College at OswegoOswegoUSA

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