The calculus as algebraic analysis: Some observations on mathematical analysis in the 18th century

D'Alembert, Jean. 1743. Traité de dynamique. Paris.

D'Alembert, Jean. 1754. Différentiel. Encyclopédie ou dictionnaire raisonée des sciences, des arts et des métiers Volume 4, pp. 985–989. Paris.

D'Alembert, Jean. 1757. Fonction. Enyclopédie ou ... métiers Volume 7, p. 50. Paris.

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

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

Bottazzini, Umberto. 1986. The higher calculus: A history of real and complex analysis from Euler to Weierstrass. New York: Springer-Verlag.

Boyer, Carl B. 1969. The history of the calculus and its conceptual development. New York: Dover. Originally published in 1949 under the title The concepts of the calculus, a critical and historical discussion of the derivative and the integral.

Burkhardt, H. 1908. Entwicklungen nach oscillirenden Funktionen und Integration der Differentialgleichungen der mathematischen Physik. Jahresbericht der Deutschen Mathematiker-Vereinigung 10, 1–1804.

Cantor, Moritz. 1901. Vorlesungen űber Geschichte der Mathematik Dritter Band 1668–1758. Reprinted 1965 by the Johnson Reprint Corporation, New York.

Cantor, Moritz. 1908. Überlick über die Zeit von 1758 bis 1799. Vorlesungen űber Geschichte der Mathematik Vierter Band 1759–1799, pp. 1075–1096.

Cauchy, Augustin Louis. 1821. Cours de l'analyse de l'École Polytechnique. Première partie: analyse algébrique. Paris. Reprinted as Oeuvres (2)3.

Cauchy, Augustin Louis. 1823. Resumé des leçons données a l'École Polytechnique sur le calcul infinitésimal. Tome premier. Paris. Reprinted in Oeuvres (2)4, 5–261.

Cauchy, Augustin Louis. 1829. Leçons sur le calcul différentiel. Paris: Reprinted in Oeuvres (2)4, 263–609.

Cauchy, Augustin Louis. 1882. Oeuvres complètes. Paris: Gauthier-Villars.

Engelsman, Steven B. 1984. Families of curves and the origins of partial differentiation. Amsterdam: North-Holland.

Euler, Leonhard. 1740. De infinitis curvis eiusdem generis seu methodus inveniendi aequationes pro infinitis curvis eiusdem generis. Commentarii academiae scientiarum Petropolitanae 7 (1734–5), 174–189, 180–183. (Pages 190–199 were incorrectly numbered as 180–189.) In Opera (1)22, 36–56.

Euler, Leonhard. 1744. Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti. Lausanne and Geneva. Reprinted as Opera (1)24, (C. Carathéodory, Ed.).

Euler, Leonhard. 1748. Introductio in analysin infinitorum, Volume 1. Reprinted as Opera (1)8.

Euler, Leonhard. 1751. De la controverse entre Mrs. Leibniz et Bernoulli sur les logarithmes des nombres negatifs et imaginaires. Mémoires de l'académie des sciences de Berlin 5 (1749), 139–171. In Opera (1)17, 195–232.

Euler, Leonhard. 1755. Institutiones calculi differentialis. St. Petersburg. Reprinted as Opera (1)10.

Euler, Leonhard. 1760. De seriebus divergentibus. Novi commentarii academiae scientarum Petropolitanae 5 (1754–55), 205–237. In Opera (1)14, 485–617.

Euler, Leonhard. 1768–1770. Institutiones calculi integralis. 3 volumes. St. Petersburg. Reprinted as Opera (1) 11–13.

Euler, Leonhard. 1911–1975. Leonhardi Euleri opera omnia. Series 1: Opera mathematica. Bern.

Flett, P. M. 1974. Some historical notes and speculations concerning the mean-value theorem of the differential calculus. Bulletin of the Institute of Mathematics and Its Applications 10, 66–72.

Fraser, Craig G. 1985a. D'Alembert's principle: The original formulation and application in Jean D'Alembert's Traité de dynamique (1743). Centaurus 28, 31–61, 145–159.

Fraser, Craig G. 1985b. J. L. Lagrange's changing approach to the foundations of the calculus of variations. Archive for History of Exact Sciences 32, 151–191.

Fraser, Craig G. 1987. Joseph Louis Lagrange's algebraic vision of the calculus. Historia Mathematica 14, 38–53.

Freudenthal, Hans. 1971. Did Cauchy plagiarize Bolzano? Archive for History of Exact Sciences 7, 375–392.

Freudenthal, Hans. 1973. Review of Grattan-Guinness [1970b] in Centaurus 18: 90–91.

Fuss, Paul Heinrich von. 1843. Correpondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle. Two volumes. Reprinted in 1967 by Johnson Reprint Corporation.

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

Grabiner, Judith V. 1974. Is mathematical truth time-dependent? American Mathematical Monthly 81, 354–365.

Grabiner, Judith V. 1981. The origins of Cauchy's rigorous calculus. Cambridge, MA: M.I.T. Press.

Grattan-Guinness, Ivor. 1970a. Bolzano, Cauchy and the “new analysis” of the early 19th century. Archive for History of Exact Sciences 6, 372–400.

Grattan-Guinness, Ivor. 1970b. The development of the foundations of mathematical analysis from Euler to Riemann. Cambridge, MA: M.I.T. Press.

Guisnée. 1733. Application de l'algèbre à la géometre ou méthode de demontrer par l'algèbre, les theorêmes de géométrie, et d'en résoudre et construire tous les problêmes. Second edition. Paris. (The first edition appeared in 1705.)

Jourdain, Philip E. B. 1905. The theory of functions with Cauchy and Gauss. Biblioteca Mathematica (3) 6, 190–207.

Jourdain, Philip E. B. 1913. The origin of Cauchy's conceptions of a definite integral and of the continuity of a function. Isis 1, 661–703.

Katz, Victor J. 1987. Calculus of the trigonometric functions. Historia Mathematica 14: 311–324.

Kline, Morris. 1972. Mathematical thought from ancient to modern times. New York: Oxford University Press.

Lagrange, Joseph Louis. 1773. Sur l'attraction des sphéroïdes elliptiques. Nouveaux mémoires de l'académie royale des sciences et belles-lettres de Berlin, année 1773, 121–148. In Oeuvres 3, 619–649.

Lagrange, Joseph Louis. 1788. Méchanique analitique. Paris. The second edition appeared in two volumes as the Mécanique analytique (1811, 1815) and is reprinted as Oeuvres 11 and 12.

Lagrange, Joseph Louis. 1797. Théorie des fonctions analytiques. Paris. The second edition appeared in 1813 and is reprinted as Oeuvres 9.

Lagrange, Joseph Louis. 1801. Leçons sur le calcul des fonctions. Paris. Reissued in 1804 in Journal de l'École Polytechnique, 12 cahier, tome 5.

Lagrange, Joseph Louis. 1806. Leçons sur le calcul des fonctions. Nouvelle edition. Paris. This edition includes additions and “un traité complet du calcul des variations.” Reprinted as Oeuvres 10.

Lagrange, Joseph Louis. 1867–1892. Oeuvres de Lagrange. 14 volumes. Paris: Gauthier-Villars.

Langer, Rudolph E. 1947. Fourier series, the evolution and genesis of a theory. American Mathematical Monthly 54, pt. II, 1–86.

Lützen, Jesper. 1983. Euler's vision of a general partial differential calculus for a generalized kind of function. Mathematics Magazine 56, 299–306.

Mahoney, Michael S. 1984. Changing canons of mathematical and physical intelligibility in the later 17th century. Historia Mathematica 11, 417–423.

Ovaert, J. L. 1976. La thèse de Lagrange et la transformation de l'analyse. In Philosophie et calcul de l'infini, Christian Houzel et al., Eds., pp. 157–222. Paris: François Maspero.

Ravetz, J. R. 1961. Vibrating strings and arbitrary functions. In The logic of personal knowledge, Essays presented to Michael Polyani on his seventieth birthday, pp. 71–88. London: Routledge & Kegan Paul.

Smithies, F. 1986. Cauchy's conception of rigour in analysis. Archive for History of Exact Sciences 36, 41–61.

Stäckel, P. G. 1900. Integration durch imaginäres Gebiet. Ein Beitrag zur Gechichte der Funktionentheorie. Bibliotheca Mathematica (3) 1, 100–128.

Taylor, Angus E. 1955. Advanced Calculus. Waltham, MA: Xerox Publishing.

Truesdell, Clifford. 1960. The rational mechanics of flexible or elastic bodies, 1638–1788. Published as Euler's Opera Omnia Ser. 2 11(2).

Vivanti, G. 1908. Infinitesimalrechnung. In [Cantor 1908, 639–869].

Volkert, Klaus. 1987. Die Geschichte der pathologischen Funktionen — Ein Beitrag zur Entstehung der mathematischen Methodologie. Archive for History of Exact Sciences 37, 193–232.

Wallner, C. R. Totale und partielle Differentialgleichungen. Differenzen- und Summenrechnung. Variationsrechnung. In [Cantor 1908, 871–1074].

Wilson, Curtis. 1985. The great equality of Jupiter and Saturn: from Kepler to Laplace. Archive for History of Exact Sciences 33, 15–290.

Youschkevitch, A. P. 1976. The concept of the function up to the middle of the 19th century. Archive for History of Exact Sciences 16, 37–85.