The Mathematical Intelligencer

, Volume 41, Issue 4, pp 29–34 | Cite as

A Relationship between the Tractrix and Logarithmic Curves with Mechanical Applications

  • Davide Crippa
  • Pietro MiliciEmail author
The “problem of exactness” consists in determining, in different historical periods, the canons of constructions deemed appropriate for mathematical problem-solving. This problem was explicitly posed, perhaps for the first time, in Descartes’s Géométrie (1637). In that work, Descartes deployed a set of criteria for deciding which curves should be accepted in geometry beyond circles and line segments. On the one hand, he presented an instrumental criterion [ 7, vol. 6, pp. 391, 393] that depended on a veritable theory of instruments for the tracing of curves. Such instruments (we may refer to them as “coordinated continuous motions” [ 4, p. 336] or “geometrical linkages” [ 11, p. 79]) were conceived as ideal machines, formed by configurations of interconnected segments, that trace curves via a unique and continuous motion in the plane, impervious to physical limitations such as velocity and friction (see Figure  1).



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université de Bretagne Occidentale CECJIBrestFrance
  2. 2.Czech Academy of Sciences Institute of PhilosophyPragueCzech Republic

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