EULER, oiler, Leonard, Swiss mathe matician: b. Basel, 4 or 5 April 1707; d. Saint Petersburg, 7 Sept. 1783. He was educated by his father, a minister and mathematician, and then studied at the University of Basel under the famous mathematician, Jacob Bernoulli, where he received the degree of Master in 1723. In his 19th year he gained the accessit of the prize offered by the Paris Academy of Sciences for the best treatise on the masting of vessels. He went to Russia in 1727 to become a member of the faculty of the newly founded Academy of Sciences of Saint Petersburg and, in 1733, became its professor of mathematics, where he labored with astonishing industry. He com posed more than half of the treatises in this branch of science contained in the 46 quarto volumes published by the Saint Petersburg Academy 1727-83; and at his death left about 200 unpublished dissertations, subsequently printed by the society. In 1741 he accepted an invitation from Frederick the Great to become professor of mathematics in the Berlin Acad emy, but in 1766 returned to Saint Petersburg. Soon after his arrival he was attacked by a very serious illness from which he finally re covered, but only after he had lost his eye sight. This, however, did not prevent him from continuing his work, employing a secretary and overcoming the difficulties in connection with his elaborate computations chiefly by means of his remarkable memory. He finally submitted to an operation which, at first, was successful; but in some way he suffered a relapse and lost his newly recovered sight again. He first gave the example of those long processes in which the conditions of the problem are first ex pressed by algebraic symbols, and then pure calculation resolves all the difficulties. He ap plied the analytic method to mechanics, and enlarged the boundaries of this science. He greatly improved the integral and differential calculus, of which he afterward published a complete course, which surpassed everything then extant on this subject. An extensive optical treatise, 'Sur la Perfection des Verres object. des Lunettes,) in the Memoires de Ber lin (1747), was the result of his inquiries into the means of improving spectacles. The share
which he contributed by this work toward the discovery of achromatic telescopes is sufficient to distinguish his name in this department also. He also employed himself in metaphysical and philosophical speculations. He attempted to prove the immateriality of the soul, and to de fend revelation against freethinkers. In his well-known 'Lettres a une Princesse d'Alle magne, sur Divers Sujets de Physique et de Philosophic) (3 vols., Saint Petersburg 1768 72), he attacks the Leibnitzian system of mon ads and pre-established harmony. Among his numerous writings may be mentioned here his 'Theoria Motuum Planetarum et Cometarum> (Berlin 1744) ; 'Introductio in Analysin Infini torunP (2 vols., Lausanne 1748), which has always been regarded as his greatest produc tion; 'Institutions Calculi Differentialis> (Saint Petersburg 1755) ; 'Institutiones Calculi Integralis' (3 vols., Saint Petersburg 1768-70); to Algebra) (Saint Petersburg 1770) ; his (3 vols., Saint Peters burg 1767-71) ; 'Opuscula Analytic.%) (2 vols., Saint Petersburg 1783-85). His industry was as remarkable as his genius. During his life of 76 years, of which about 60 were devoted to scientific studies, he published a total of 32 separately printed books written in Latin, Ger man and French, and many running to more than one volume; 331 treatises in the publica tions of the Saint Petersburg Academy, all in Latin; 14 treatises for the Royal Academy at Paris, in French; 128 treatises for the Royal Academy at Berlin, all in French; and 196 mis cellaneous treatises in Latin. For a detailed bibliography of his works consult Hagen, J. G., 'Index Operum Leonardi Euleri' (Berlin 1896L For his life, etc., consult Fuss, N., (Elo M. Leon. Euler> (Saint Petersburg 1783, Basel 1786) ; Hoppe, E., 'Die Philosophic L. (Gotha 1904) ; Schulz-Euler, S., 'Leonard Euler> (Frankfurt a. M. 1907) ; Rudio, F., Baseler Mathematiker D. Bernoulli and L. Euler) (Basel 1884) ; id., 'L. Euler> (Basel 1884).