1911 Encyclopædia Britannica/Infinitesimal Calculus/Bibliography

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III. Outlines of the Infinitesimal Calculus (§47-56) Infinitesimal Calculus

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 Calculus (Cambridge, 1820); A. L. Cauchy, Résumé des leçons . . . sur le calcul infinitésimale (Paris, 1823), and Leçons sur 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); É. 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); É. 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); W. 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.)