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The mysteries of adaequare: A vindication of fermat

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Summary

The commonly accepted interpretations ofFermat's method of extreme values tell us that this is a curious method, based on an approximate equality and burdened with several contradictions withinFermat's writings. In this article, both a philological approach taking into account that there is only one manuscript written inFermat's own handwriting and a mathematical approach taking into account that brilliant mathematicians usually are not so very confused when talking about their own central mathematical ideas are combined. A new hypothesis is put forward which renders the mathematics clear and coherent and which does not need the assumption thatFermat was confused. Probably a number of words have been added byCarcavy in two ofFermat's papers.

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References

  • Andersen, K. 1980. Techniques of the Calculus 1630–1660. InFrom the Calculus to Set Theory 1630–1910. I.Grattan-Guinness, Ed., pp. 10–48. London: Duckworth.

    Google Scholar 

  • Andersen, K. 1983. The Mathematical Technique in Fermat's Deduction of the Law of Refraction.Historia Mathematica 10, 48–62.

    Google Scholar 

  • Baillet, A. 1691.La Vie de Monsieur Des-Cartes. Paris: Horthemels.

    Google Scholar 

  • Baron, M. 1968.The Origins of the Infinitesimal Calculus. Oxford, Londonetc.: Pergamon Press.

    Google Scholar 

  • Barrow, I. 1860.The Mathematical Works, second volume. Cambridge: Cambridge University Press.

    Google Scholar 

  • Belaval, Y. 1978. Note sur l'emploi par Leibniz de l'expression spinoziste d' “Idée adéquate”.Archivio di Filosofia 121–132.

  • Cajori, F. 1928.A History of Mathematical Notations, vol. 1. La Salle/Illinois: The Open Court Publishing Company.

    Google Scholar 

  • Cavalieri, B. 1635.Geometria indivisibilibus continuorum Nova quadam ratione promota, liber secundus. Bologna: Ferronius.

    Google Scholar 

  • Cavalieri, B. 1647.Exercitationes Geometricae Sex. Bologna: Jacobus Montius.

    Google Scholar 

  • Cifoletti, G. 1991.La méthode de Fermat: son statut et sa diffusion. Paris: Belin.

    Google Scholar 

  • Debeaune, F. 1661. De Aequationum Natura, Constitutione, et Limitibus Opuscula Duo. E.Bartholin, Ed., in R. Descartes:Geometria, pars secunda. F. vanSchooten, Ed., Amsterdam: Ludwig & Daniel Elsevir.

    Google Scholar 

  • Descartes, R. 1897.Oeuvres, vol. 1. Ch.Adam & P.Tannery, Ed., Paris: Léopold Cerf.

    Google Scholar 

  • Descartes, R. 1898.Oeuvres, vol. 2. Ch.Adam & P.Tannery, Ed., Paris: Léopold Cerf.

    Google Scholar 

  • Diophantus 1575.Rerum Arithmeticarum Libri sex. G.Xylander, Ed., Basel: Eusebius Episcopius & Nicolai Fr. haeredes.

    Google Scholar 

  • Diophantus 1621.Arithmeticorum libri sex. C. G.Bachet, Ed., Paris: Sebastien Cramoisy.

    Google Scholar 

  • Diophantus 1890.Die Arithmetik und die Schrift über Polygonalzahlen. G.Wertheim, Ed., Leipzig: Teubner.

    Google Scholar 

  • Diophantus 1893.Opera omnia cum graecis commentariis, vol. 1. P.Tannery, Ed., Leipzig: Teubner.

    Google Scholar 

  • Fermat, P. de 1660a.De linearum curvarum cum lineis rectis comparatione dissertatio geometrica. Toulouse: Arnaldus Colomerius.

    Google Scholar 

  • Fermat, P. de 1660b. Appendix secunda, in A. Lalouvère:Veterum geometria promota in septem de cycloide libris, et in duabus adiectis appendicibus. Toulouse: Arnaldus Colomerius, pp. 390–395.

    Google Scholar 

  • Fermat, P. de 1679.Varia opera mathematica. Toulouse: Joannes Pech.

    Google Scholar 

  • Fermat, P. de 1891.Oeuvres, vol. 1. P.Tannery & Ch.Henry, Ed., Paris: Gauthier-Vilars.

    Google Scholar 

  • Fermat, P. de 1894.Oeuvres, vol. 2. P.Tannery & Ch.Henry, Ed., Paris: Gauthier-Vilars.

    Google Scholar 

  • Fermat, P. de 1896.Oeuvres, vol. 3. P.Tannery & Ch.Henry, Ed., Paris: Gauthier-Vilars.

    Google Scholar 

  • Fermat, P. de 1922.Supplément aux Tomes I–IV. C. deWaard, Ed., Paris: Gauthier-Vilars.

    Google Scholar 

  • Gosselin, G. 1583.De Ratione discendae docendaeque mathematices repetita praelectio. No place given (Paris ?).

  • Heath, T. L. 1885.Diophantus of Alexandria. Cambridge: Cambridge University Press.

    Google Scholar 

  • Heath, T. L. 1910.Diophantus of Alexandria. Second edition. Cambridge: Cambridge University Press.

    Google Scholar 

  • Henry, Ch. 1880. Recherches sur les manuscrits de Pierre de Fermat. Extrait duBollettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche 12, 1879. Rome: Imprimerie des Sciences Mathématiques et Physiques.

    Google Scholar 

  • Henry, Ch. 1884. Pierre de Carcavy. Extrait duBollettino di Bibliografia e di Storia delle Scienze Mathematiche e Fisiche 17, 1884. Rome: Imprimerie des Sciences Mathématiques et Physiques.

    Google Scholar 

  • Hérigone, P. 1644.Cursus Mathematici Tomus Sextus Ac Ultimus sive Supplementum. Paris: Simeon Piget.

    Google Scholar 

  • Hoffmeister, J. 1955.Wörterbuch der philosophischen Begriffe. Second edition. Hamburg: Meiner.

    Google Scholar 

  • Huygens, Ch. 1693. Demonstratio regulae de maximis et minimis. InDivers Ouvrages de Mathématique et de Physique Par Messieurs de l'Académie des Sciences, pp. 326–335. Paris: Imprimerie Royale.

    Google Scholar 

  • Huygens, Ch. 1888.Oeuvres complètes, vol. 1. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Huygens, Ch. 1889.Oeuvres complètes, vol. 2. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Huygens, Ch. 1890.Oeuvres complètes, vol. 3. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Huygens, Ch. 1901.Oeuvres complètes, vol. 9. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Huygens, Ch. 1908.Oeuvres complètes, vol. 11. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Huygens, Ch. 1910.Oeuvres complètes, vol. 12. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Huygens, Ch. 1940.Oeuvres complètes, vol. 20. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Itard, J. 1948. Fermat, précurseur du Calcul différentiel.Archives Internationales d'Histoire des Sciences 27, 589–610.

    Google Scholar 

  • Itard, J. 1975. La lettre de Torricelli à Roberval d'octobre 1643.Revue d'Histoire des Sciences 28, 113–124.

    Google Scholar 

  • Leibniz, G. W. 1880.Die philosophischen Schriften, vol. 4. C. I.Gerhardt, Ed., Berlin: Weidmann.

    Google Scholar 

  • Leibniz, G. W. 1890.Die philosophischen Schriften, vol. 7. C. I.Gerhardt, Ed., Berlin: Weidmann.

    Google Scholar 

  • Mahoney, M. S. 1973.The Mathematical Career of Pierre de Fermat. Princeton: Princeton University Press.

    Google Scholar 

  • Mersenne, M. 1955.La Correspondance, vol. 4. C. deWaard, Ed., Paris: Presses Universitaire de France.

    Google Scholar 

  • Oxford Latin Dictionary 1982. Oxford: Clarendon Press.

  • Pascal, B. 1658.Lettre de A. Dettonville à Monsieur A.D.D.S. en Luy envoyant La Demonstration à la manière des Anciens de l'Egalité des Lignes Spirale et Parabolique. Paris: Desprez.

    Google Scholar 

  • Schooten, F. van 1659. In Geometriam Renati des Cartes Commentarii. In R. Descartes:Geometria. F. vanSchooten, Ed., Amsterdam: Ludwig & Daniel Elsevir.

    Google Scholar 

  • Spinoza, B. de 1925.Opera. 4 volumes. C.Gebhardt, Ed., Heidelberg: Carl Winter.

    Google Scholar 

  • Strømholm, P. 1968/69. Fermat's Methods of Maxima and Minima and of Tangents.Archive for History of Exact Sciences 5, 47–69.

    Google Scholar 

  • Thesaurus Linguae Latinae 1900, vol. 1. Leipzig: Teubner.

  • Thesaurus Graecae Linguae 1842–1847, vol 6. Paris: Firmin Didot.

  • Toulouse Bibliothèque Municipale. Manuscript 1531: Fermat: Miscellanea di cose mathematiche. Copies du XVIIe siècle d'oeuvres de divers savants dont Fermat, Descartes, Michel Angelo Ricci auteur de ces copies.

  • Viète, F. 1646.Opera Mathematica. F. vanSchooten, Ed., Leiden: Bonaventura & Abraham Elzevir.

    Google Scholar 

  • Wallis, J. 1658.Commercium epistolicum de Quaestionibus quibusdam Mathematicis nuper habitum. Oxford: Robinson.

    Google Scholar 

  • Wieleitner, H. 1929. Bemerkungen zu Fermats Methode der Aufsuchung von Extremwerten und der Bestimmung von Kurventangenten.Jahresbericht der Deutschen Mathematiker-Vereinigung 38, 24–35.

    Google Scholar 

  • Zeuthen, H. G. 1903.Geschichte der Mathematik im 16. und 17. Jahrhundert. Leipzig: Teubner.

    Google Scholar 

Download references

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  1. Leibniz Archive, D-30169, Hannover, Germany

    Herbert Breger

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Breger, H. The mysteries of adaequare: A vindication of fermat. Arch. Hist. Exact Sci. 46, 193–219 (1994). https://doi.org/10.1007/BF01686277

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