Leibnitz and his school, especially the Bernouillis poured forth memoirs abundantly. Leibnitz' first, 'Nova Methodus pro maximis et minimis, itemque tangentibus, etc.,' appeared in the Leipzig Acta Eruditorum, 1684. Newton gave his method of prime and ultimate ratios in geometric form in his 'Philo sophim Naturalis Principia Mathematica,' 1687. Johann Bernouilli's 'Lectiones Mathematicz> was the first textbook of the Integral Calculus, composed at Paris 1691-92, published 1742; Taylor, incrementorum directa et inversa' (1715) ; D'Alembert, sur le calcul integral' (1739) ; Maclaurin, (A Treatise on Fluxions> (1742) ; Euler, (Introductio in Analysin Infinitorum) (1748)— resuming and expanding all knowledge on the subject, tone of the most contentful, beautiful, and fruitful works that ever left the press,°— (Institutiones Calculi (1768-70) ; Cramer, a l'analyse des lignes courbes algebriques' (1750); Lacrobq 'Traits du calcul dif. et du cal. int.' (1797) ; Lagrange, des fonctions analytiques' (1797) ; Cauchy, Tours d'analyse' (1821), sur le calcul differentia) (1829); Duhamel, (Cours d'analyse) (1840), third edition, by Bertrand (1874-75) ; De Morgan, and Int. Calculus' (1842) ; 'i'odhunter, and Int. Calculus' (1852) • Price, (Infinitesinial Calculus' (1854) ; Gerhardt, 'Die Entdeckung der hoheren Anal ysis> (1855) ; Bertrand, 'Traits du Cal. Diff. et du Cal. Int.) (1864-70) ; Hermite, Tours d'Ana lyse' (1873) ,• Williamson, 'Dif. and Int. Cal culus' (1872-74) ; Meyer, der bestimm ten Integra10—nach Lejeune-Dirichlet (1875) ; Lipschitz, 'Lehrbuch der Analysis' (1877-80); Hovel, 'Coors de Calcul Infinitesimal' (1878. 79); Dini, 'Analisi Infinitesimale' (1877-78), 'Fondamenti per la teorica delle funzioni di variabili reali' (1878) ; Harnack, (Die Elemente der Dif.-und Int. Rechung' (1881) ; Stolz, (All
gemeine Arithmetik> (1885--86), (Grundziige der Differential- and Integralrechnung> (1893 96-99) ; Tannery, (Introduction I la theone des fonctions dune variable' (1886) ; Laurent, 'Traits d'Analyse' (1885-92) ; Picard, 'Traite d'Analys& (1891-1903); Genocchi-Peano, (Cal colo differenziale e principii di calcolo integral& (1884, German translation 1898-99) ; Cantor, 'Geschichte der Mathematik' (1880-1900-01) ; Jordan, d'Analys0 (1893-94-96); Serret, 'Coors de Calcul dif. et int.' (1868, Harnack's German translation, 2d ed., by Bohlmann and Zermelo, 1899-1904-05) ; de la Vallee Poussin, 'Cours d'Analyse infinitesimal& (1903) ; Gour sat, (Cours d'Analyse mathematique) (1902-04) ; Humbert, 'Coors d'Analyse' (1903-04) ; Borel, 'Lecons sur les fonctions de variables (1905) ; Kiepert-Stegemann, 'Grundriss der Differential- u. Integral-rechnung' (1905).
Elementary textbooks on the calculus are legion, and of very various merits, though those in favor at American universities do not vary much from type. Those of Byerly and of Os good are perhaps as good as any. Among the older books, those of Williamson, though in many respects obsolete, give a training in the purely formal treatment of the subject that is not to be surpassed. The more advanced books generally go by the name of (Cours d'Analyse' or 'Introductions to Analysis' ; they partake equally of the nature of textbooks and of inde pendent investigations. They are only acces sible to those who already have a thorough grounding in the elements of the Calculus.