The New International Encyclopædia/Euler, Leonhard

EULER, oi′lẽr, Leonhard (1707-83). A Swiss mathematician, one of the most remarkable of his century. He was born at Basel. Euler was sent to the University of Basel so early and was so proficient in his work that he received the master's degree at the age of sixteen. He studied mathematics under Johann Bernoulli at Basel, and also studied theology, the Oriental languages, and medicine. In the course of his physiological researches he wrote a treatise on the nature and propagation of sound, and he also wrote an essay on the masting of ships, which received a prize of the French Academy of Sciences in 1727. In that year Euler went to Saint Petersburg upon the invitation of Catharine I., and became an associate of the Academy of Sciences. In 1730 he was made professor of physics, and in 1733 professor of higher mathematics. In 1740 he became inspector of the geographical department, and in the following year was called to Berlin by Frederick II. to take the chair of mathematics in the Academy of Sciences, from which he was not long afterwards advanced to the position of director of the mathematical class. In 1766 he was called back to Saint Petersburg, where he remained until his death. Euler lost one eye as the result of a severe illness in 1735, and soon after his return to Russia in 1766 he lost the use of the other. This did not, however, hinder his mental activity, and he contributed extensively to the science of mathematics until the day of his death.

The number no less than the value of Euler's mathematical writings was very great. He wrote, aside from his separate treatises, 473 memoirs published during his life, 200 published soon after his death, and 61 others of which the publication was undertaken by P. H. and N. Fuss in 1849. Of his more important treatises, the following may be mentioned: Mechanica sive Motus Scientia Analytice Exposita (1736; 2d ed. 1742); Tentamen Nova Theoriæ Musicæ (1739); Einleitung in die Arithmetik (1742); Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes (1744); Theoria Motuum Planetarum et Cometarum (1744; German edition 1781); Opuscula Varii Argumenti (3 vols., 1746-51); Gedanken von den Elementen der Körper (1746); Lettres à une princesse d'Allemagne sur quelques sujets de physique et de philosophie (1768-72; 2d ed. by Cournot, 1842; German edition, Stuttgart, 1853; English edition, New York, 1833). His text-books were relatively less important; they include the following: Introductio in Analysin Infinitorum (1748; French edition 1796-97; German edition, 1785-90); Institutiones Calculi Differentialis (1755; 2d ed. 1804; German edition 1790-98); Institutiones Calculi Integralis (3 vols., 1768-70; 3d ed., 4 vols., 1824-45; German edition, 4 vols., 1828-40); Anleitung zur Algebra (1771; 3d ed. 1821; French edition 1770; 2d ed. 1795, and Paris, 1807; American edition 1818, 2d ed. 1821); Dioptrica (3 vols., 1769-71); Theoria Motuum Lunæ Nova Methodo Pertractata (1772); Opuscula Analytica (1783-85). For biography of Euler, consult: Condorcet, Eloge, in Euler's Institutiones Calculi Differentialis, and in his Lettres à une princesse d'Allemagne; also Fuss, Correspondance mathématique et physique (Saint Petersburg, 1843).