Skip to main content
Log in

The Origins of Euler's Variational Calculus

  • Published:
Archive for History of Exact Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Barbeau, E. J., & Leah, P. J., 1976. “Euler's 1760 paper on divergent series”, Historia Mathematica 3, pp. 141–160.

    Google Scholar 

  • Bernoulli, Jakob. 1697. “Solutio problematum fraternorum, peculiari programmate cal. Jan. 1697 Groningae, nec non Actorum Lips. mense Jun. & Dec. 1696, & Febr. 1697 propositorum: una cum propositione reciproca aliorum”, in Acta eruditorum, pp. 211–217. Published in Jakob's Opera (1744), pp. 768–778. Reproduced in [Bernoulli, Jakob and Johann, 1991], pp. 271–282.

  • Bernoulli, Jakob. 1701. “Analysis magni problematis isoperimetrici”, Acta eruditorum, pp. 213–228. Published in Jakob's Opera (1744),pp. 895–920, and in Johann's Opera V. 2 (1742), pp. 219–234. Reproduced in [Bernoulli, Jakob and Johann, 1991].

  • Bernoulli, Jakob. 1744. Jacobi Bernoulli Basileensis opera, 2 volumes. Ed. Gabriel Cramer. Geneva.

  • Bernoulli, Johann. 1719. “Remarques sur ce qu'on a donné jusqu'ici de solutions des Problêmes sur les Isoperimetres, avec une nouvelle methode courte & facile de les resoudre sans calcul, laquelle s'étend aussi à d'autres problêmes qui ont rapport à ceux-là”, Mémoires de l'Académie Royale des Sciences 1718, pp. 100–138. Reproduced in [Bernoulli, Jakob and Johann, 1991], pp. 527–568.

  • Bernoulli, Jakob. 1742. Johannis Bernoulli opera omnia. 4 volumes. Ed. Gabriel Cramer. Lausanne and Geneva.

  • Bernoulli, Jakob & Bernoulli, Johann. 1991. Die Streitschriften von Jacob und Johann Bernoulli Variationsrechnung. Edited by H. H. Goldstine with the assistance of P. Radelet-de Grave. Introduction by Goldstine, pp. 4–113. Published by the Naturforschenden Gesellschaft in Basel. Birkhäuser Verlag. Basel, Boston and Berlin. This volume contains numerous selections from the Meditationes, Jakob's scientific notebook. An early draft version of his 1701 paper will be found in Med. CCXXXIX, pp. 228–247. This selection is also reproduced by [Dietz 1959, 100–115].

    Google Scholar 

  • Bos, H. J. M. 1974. “Differentials, higher-order differentials and the derivative in the Leibnizian calculus”, Archive for History of Exact Sciences 14, pp. 1–90.

    Google Scholar 

  • Carathéodory, C. 1952. “Einführung in Eulers Arbeiten über Variationsrechnung”, in Euler's Opera Omnia, Ser. 1, V. 24, pp. viii-li.

    Google Scholar 

  • Demidov, S. S. 1982. “The study of partial differential equations of the first order in the 18th and 19th centuries”, Archive for History of Exact Sciences 26, pp. 325–350.

    Google Scholar 

  • Dietz, P.. 1959. “Die Ursprünge der Variationsrechnung bei Jakob Bernoulli”, Verhandlungen der Naturforschenden Gesellschaft in Basel V. 70 N. 2, pp. 81–146. Contains several selections from Jakob's Meditationes.

    Google Scholar 

  • Euler, L. 1726. “Constructio linearum isochronarum in medio resistente”, Acta eruditorum, pp. 361–363. In the Opera omnia Ser. 2 V. 6 (1957), pp. 1–3.

  • Euler, L. 1736. Mechanica sive motus scientia analytice exposita. Two volumes. Published in 1952 (ed. P. Stäckel) as volumes 1 and 2 of series 2 of Euler's Opera omnia.

  • Euler, L. 1738. “Problematis isoperimetrici in latissimo sensu accepti solutio generalis”, in Commentarii academiae scientiarum Petropolitanae 6, (1732/3), pp. 123–155. Reprinted in Euler's Opera omnia Ser. 1, V. 25 (1952),pp. 13–40.

    Google Scholar 

  • Euler, L. 1740. “De linea celerrimi descensus in medio quocunque resistente”, Commentant academiae scientiarum Petropolitanae 7 (1734/35), pp. 135–139. Reprinted in Opera omnia Ser. 1, V. 25 (1952), pp. 41–53.

    Google Scholar 

  • Euler, L. 1741. “Curvarum maximi minimive proprietate gaudentium inventio nova et facilis”, in Commentant academiae scientiarum Petropolitanae 8 (1736), 159–190. Reprinted in Opera omnia Ser. 1, V. 25 (1952), pp. 54–80.

    Google Scholar 

  • Euler, L. 1744. Methodus inveniendi curvas lineas maximi minimive proprietate gaudentes sive solution problematis isoperimetrici latissimo sensu accepti, Lausanne. Reprinted as Opera omnia Ser. 1, V. 24 (1952).

  • Feigenbaum, L. 1985. “Brook Taylor and the method of increments”, Archive for History of Exact Sciences 34, pp. 1–140.

    Google Scholar 

  • Feigenbaum, L. 1992. “The fragmentation of the European mathematical community”, in The investigation of difficult things: essays on Newton and the history of the exact sciences in honour of D. T. Whiteside, pp. 383–397. Cambridge University Press.

  • Fellmann, E. A., & Fleckenstein, J. O. 1970. “Bernoulli, Johann (Jean) I”, in Dictionary of scientific biography, ed. C. C. Gillispie, V. 2, pp. 51–55.

  • Fraser, C. 1985. “J. L. Lagrange's changing approach to the foundations of the calculus of variations”, Archive for History of Exact Sciences 32, pp. 151–191.

    Google Scholar 

  • Fraser, C. 1991. Review of Bernoulli, Jakob and Johann, 1991, in Centaurus 34, pp. 367–369.

    Google Scholar 

  • Fraser, C. 1992. “Isoperimetric problems in the variational calculus of Euler and Lagrange”, Historia Mathematica 19, pp. 4–23.

    Google Scholar 

  • Goldstine, H. H. 1980. A history of the calculus of variations from the 17 th through the 19 th century. Springer-Verlag.

  • Goldstine, H. H. 1991. Introduction to [Bernoulli, Jakob and Johann, 1991], pp. 1–113.

  • Hermann, J. 1729. “Theoria generalis motuum qui nascuntur a potentiis quibusvis in corpora indesinenter agentibus, sive haec corpora in vacuo ferantur sive in medio resistenti.” Commentarii academiae scientiarum imperialis Petropolitanae 2 (1727), pp. 139–173.

    Google Scholar 

  • Taylor, B. 1715. Methodus incrementorum directa & inversa. London.

  • Woodhouse, R. 1810. A treatise on isoperimetrical problems and the calculus of variations. Cambridge.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by H. Bos

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fraser, C.G. The Origins of Euler's Variational Calculus. Arch. Hist. Exact Sci. 47, 103–141 (1994). https://doi.org/10.1007/BF00394799

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00394799

Keywords

Navigation