Bibliography

For historical questions relating to the subject the chief authority is

• M. Cantor, Geschichte d. Mathematik (3 Bde., Leipzig, 1894-1901).

For particular matters, or special periods, the following may be mentioned:

• H. G. Zeuthen, Geschichte d. Math. im Altertum u. Mittelalter (Copenhagen, 1896) and Gesch. d. Math. im XVI. u. XVII. Jahrhundert (Leipzig, 1903)
• S. Horsley, Isaaci Newtoni opera quae exstant omnia (5 vols., London, 1779-1785)
• C. I. Gerhardt, Leibnizens math. Schriften (7 Bde., Leipzig, 1849-1863)
• Joh. Bernoulli, Opera omnia (4 Bde., Lausanne and Geneva, 1742).

Other writings of importance in the history of the subject are cited in the course of the article. A list of some of the more important treatises on the differential and integral calculus is appended. The list has no pretensions to completeness; in particular, most of the recent books in which the subject is presented in an elementary way for beginners or engineers are omitted.

• L. Euler, Institutiones calculi differentialis (Petrop., 1755) and Institutiones calculi integralis (3 Bde., Petrop., 1768—1770)
• J. L. Lagrange, Leçons sur le calcul des fonctions (Paris, 1806, Œuvres, t. x.), and Théorie des fonctions analytiques (Paris, 1797, 2nd ed., 1813, Œuvres, t. ix.)
• S. F. Lacroix, Traité de calcul diff. et de calcul int. (3 tt., Paris, 1808—1819). There have been numerous later editions; a translation by Herschel, Peacock and Babbage of an abbreviated edition of Lacroix's treatise was published at Cambridge in 1816.
• G. Peacock, Examples of the Differential and Integral Calculusii (Cambridge, 1820)
• A. L. Cauchy, Résumé des leçons . . . sue le calcul infinitesimale (Paris, 1823), and Leçons sue le calcul différentiel (Paris, 1829; Œuvres, sér. 2, t. iv.)
• F. Minding, Handbuch d. Diff. -u. Int. -Rechnung (Berlin, 1836)
• F. Moigno, Leçons sur le calcul diff. (4 tt., Paris, 1840—1861)
• A. de Morgan, Diff, and Int. Calc. (London, 1842)
• D. Gregory, Examples on the Diff. and Int. Calc. (2 vols., Cambridge, 1841—1846)
• I. Todhunter, Treatise on the Diff. Calc. and Treatise on the Int. Calc. (London, 1852), numerous later editions
• B. Price, Treatise on the Infinitesimal Calculus (2 vols., Oxford, 1854), numerous later editions
• D. Bierens de Haan, Tables d'intégrales définies (Amsterdam, 1858)
• M. Stegemann, Grundriss d. Diff. -u. Int. -Rechnung (2 Bde., Hanover, 1862) numerous later editions
• J. Bertrand, Traité de calc. diff. et int. (2 tt., Paris, 1864—1870)
• J. A. Serret, Cours de calc. diff. et int. (2 tt., Paris, 1868, 2nd ed., 1880, German edition by Harnack, Leipzig, 1884—1886, later German editions by Bohlmann, 1896, and Scheffers, 1906, incomplete)
• B. Williamson, Treatise on the Diff. Calc. (Dublin, 1872), and Treatise on the Int. Calc. (Dublin, 1874) numerous later editions of both; also the article "Infinitesimal Calculus" in the 9th ed. of the Ency. Brit.
• C. Hermite, Cours d’analyse (Paris, 1873)
• O. Schlömilch, Compendium d. höheren Analysis (2 Bde., Leipzig, 1874) numerous later editions
• J. Thomae, Einleitung in d. Theorie d. bestimmten Integrale (Halle, 1875)
• R. Lipschitz, Lehrbuch d. Analysis (2 Bde., Bonn, 1877, 1880)
• A. Harnack, Elemente d. Diff. -u. Int. -Rechnung (Leipzig, 1882, Eng. trans. by Cathcart, London, 1891)
• M. Pasch, Einleitung in d. Diff.-u. Int. -Rechnung (Leipzig, 1882)
• Genocchi and Peano, Calcolo differenziale (Turin, 1884, German edition by Bohlmann and Schepp, Leipzig, 1898, 1899)
• H. Laurent, Traité d’analyse (7 tt., Paris, 1885-1891)
• J. Edwards, Elementary Treatise on the Diff. Calc. (London, 1886), several later editions
• A. G. Greenhill, Diff. and Int. Calc. (London, 1886, 2nd ed., 1891)
• E. Picard, Traité d’analyse (3 tt., Paris, 1891-1896)
• O. Stolz, Grundzüge d. Diff.-u. Int. -Rechnung (3 Bde., Leipzig, 1893—1899)
• C. Jordan, Cours d’analyse (3 tt., Paris, 1893-1896)
• L. Kronecker, Vorlesungen ü. d. Theorie d. einfachen u. vielfachen Integrale (Leipzig, 1894)
• J. Perry, The Calculus for Engineers (London, 1897)
• H. Lamb, An Elementary Course of Infinitesimal Calculus (Cambridge, 1897)
• G. A. Gibson, An Elementary Treatise on the Calculus (London, 1901)
• E. Goursat, Cours d’analyse mathématique (2 tt., Paris, 1902-1905)
• C.-J. de la Vallée Poussin, Cours d’analyse infinitésimale (2 tt., Louvain and Paris, 1903-1906)
• A. E. H. Love, Elements of the Diff, and Int. Calc. (Cambridge, 1909)
• V. H. Young, The Fundamental Theorems of the Diff. Calc. (Cambridge, 1910).

A résumé of the infinitesimal calculus is given in the articles "Diff. -u. Int. -Rechnung" by A. Voss, and "Bestimmte Integrale" by G. Brunel in Ency. d. math. Wiss. (Bde. ii. A. 2, and ii. A. 3, Leipzig, 1899, 1900).

Many questions of principle are discussed exhaustively by

• E. W. Hobson, The Theory of Functions of a Real Variable (Cambridge,1907).

(A. E. H. L.)