, Volume 186, Issue 1, pp 257-288

First online:

Diagrams in the theory of differential equations (eighteenth to nineteenth centuries)

  • Dominique TournèsAffiliated withLIM, EA 2525, University of La RéunionSPHERE, UMR 7219, CNRS, University Paris Diderot Email author 

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Diagrams have played an important role throughout the entire history of differential equations. Geometrical intuition, visual thinking, experimentation on diagrams, conceptions of algorithms and instruments to construct these diagrams, heuristic proofs based on diagrams, have interacted with the development of analytical abstract theories. We aim to analyze these interactions during the two centuries the classical theory of differential equations was developed. They are intimately connected to the difficulties faced in defining what the solution of a differential equation is and in describing the global behavior of such a solution.


Differential equation Diagram Geometric intuition Visual thinking Integral curve Tractional motion Qualitative integration Graphical integration