E U L E U L 665 printed at Strasburg in 1519 and hitherto regarded as the editio princeps was the work of Thomas Murner the Franciscan monk. A Latin t auslation was made by Nemius ; and another by Periander appeared at Frankfort-on-Maine in 1507 as Noctuce Speculum, omnes res mcmorabilcs variasque et admirabiles Tyli Saxonici machinationes complectens. An English translation called lloide- glas his life, printed at London by Copeland, is preserved among the Garriek plays in the British Museum; extracts from it are given in W. F. Thoms s Lays and Legends of various countries: Germany. French translations appeared at Lyons in 1550, at Oi leans, 1571, at Antwerp, 1579, at Rouen, 1701. Delepierre published an edition at Bruges, 1835, and another at Brussels, 1840 ; and a complete trans lation into modern French from the 1519 edition was printed at Paris by P. Jannet, 1858. An English edition was published in 1860, under the direction of Kenneth R. H. Mackenzie, and with illustrations by Alfred Crowquill. In 1S65 appeared a photolitho graphic reprint of the Lower Saxon version, originally printed by JServais Krutfter (Servetius Cruftanus). There is no complete copy of the original, but portions in the Royal Library at Vienna and in the Royal Library at Berlin complete ea* h other. See Gcirres, Die deutsc hen Vo ksbikher, 1807; Lapp-jnberg, Eitleiispiegtl, 1854. EULER, LEONARD (1707-1783), one of the most dis tinguished mathematicians of the l^th century, was born at Basel on the 15th of April 1707, his father Paul Euler, vlu> had considerable attainments as a mathematician, being Calvinistic pastor of the neighbouring village of Riechen. After receiving preliminary instructions in mathematics from his father, lie was sent to the university of Basel, where geometry soon became his favourite study. Hu genius for analytical science gained for him a high place in the esteem of John Bernoulli, who was at that time one of the first mathematicians in Europe, as well as of his sons Daniel and Nicholas Bernoulli. Having taken his degree as master of arts in 1723, Euler afterwards applied himself, at his father s desire, to the study of theology and the Oriental languages with the view of entering the church, but, with his father s consent, he soon returned to geometry as his principal pursuit. At the same time, by the advice of the younger Bernoullis, who had removed to St Peters burg in 1725, he applied himself to the study of physi ology, to which he made a happy application of his mathe matical knowledge ; and he also attended the medical lec tures of the most eminent professors of Basel. While he was keenly engaged in physiological researches, he composed a dissertation on the nature and propagation of sound, and an answer to a prize-question concerning the masting of ships, to which the French Academy of Sciences adjudged the second rank in the year 1727. In 1727,on the invitation of Catherine I., Euler took up his residence in St Petersburg, and was made an associate of the Academy of Sciences. In 1730 he became professor of physics, and in 1733 he succeeded his friend Daniel Bernoulli in the chair of mathematics. At the commence ment of his new career he enriched the academical collec tion with many memoirs, which excited a noble emulation between him and the Bernoullis, though this did not in any way affect their friendship. It was at this time that lie carried the integral calculus to a higher degree of perfection, in vented the calculation of sines, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of abstract or pure mathematics. In 1735 a problem proposed by the academy, for the solution of which several eminent mathematicians had demanded the space of some months, was solved b/ Euler in three days, but the effort threw him into a fever which endangered his life and deprived him of the use of his right eye. The Academy of Sciences at Paris in 1738 adjudged the prize to his memoir on the nature and properties of fire, and in 1740 his treatise on the tides shared the prize with those of Colin Miiclaurin and Daniel Bernoulli, a higher honour than if lie had carried it away from inferior rivals. In 1741 Euler accepted the invitation of Frederick the Great to Berlin, where he was made a member of the Academy of Sciences and professor of mathematics. He enriched the last volume of the Melanges or Miscellanies of Berlin with five memoirs, and these were followed, with an astonishing rapidity, by a great number of important researches, which are scattered throughout the annual memoirs of the Prussian Academy. At the same time he continued his philosophical contributions to the Academy of St Petersburg, which granted him a pension in 1742. The respect in which he was held by the Russians was strikingly shown in 1760, when a farm he occupied near Charlotten- burg happened to be pillaged by the invading Russian army On its being ascertained that the farm belonged to Euler, the general immediately ordered compensation to be paid, and the empress Elizabeth sent an additional sum of four thousand crowns. In 1766 Euler with difficulty obtained permission from the king of Prussia to return to Petersburg, to which he had been originally invited by Catherine II. Soon after his return to St Petersburg a cataract formed in his left eye, which ultimately deprived him almost entirely of sight. It was in these circumstances that he dictated to his servant, a tailor s apprentice, who was absolutely devoid of mathematical knowledge, his Elements of Algebra, a work which, though purely elementary, displays the mathe matical genius of its author, and is still reckoned one of the best works of its class. Another task to which he set himself immediately after his return to St Petersburg was the preparation of his Lettres ct line Princesse d Allemagne sur quelques svjets de Physique (3 vols., 1768-72). They were written at the request of the princess of Anhalt-Dessau, and contain an admirably clear exposition of the principal facts of mechanics, optics, acoustics, and physical astronomy. Theory, however, is frequently unsoundly applied in it, and it is to be observed generally that Euler s strength lay rather in pure than in applied mathematics. In 1755 Euler had been elected a foreign member of the Academy of Sciences at Paris, and some time afterwards the academical prize was adjudged to three of his memoirs Concerning the Inequalities in the Motions of the Planets. The two prize-questions pro posed by the same academy for 1770 and 1772 were de signed to obtain a more perfect theory of the moon s motion. Euler, assisted by his eldest son Johann Albert, was a com petitor for these prizes, and obtained both. In the second memoir he reserved for further consideration several ine qualities of the moon s motion, which he could not determine in his first theory on account of the complicated calculations in which the method he then employed had engaged him. He afterward -5 reviewed his whole theory with the assistance of his son and Krafft and Lexcll, and pursued his researches until he had constructed the new tables, which appeared, together with the great work, in 1772. Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three ordinates which determine the place of the moon ; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the parallax, or the inclination of the lunar orbit. The inherent difficulties of this task were immensely enhanced by the fact that Euler was virtually blind, and had to carry all the elaborate computations it involved in his memory. A further difficulty arose from the burning of his house and the destruction of the greater part of his property in 1771. His manuscripts were fortunately preserved. His own life was only saved by the courage of a native of Basel, Peter Grimmon, who" carried him out of the burning house. Some time after this the celebrated Wenzell, by couching the cataract, restored Euler s sight ; but a too harsh use of the recovered faculty, along with some carelessness on the part of the surgeons, brought about a relapse. With the
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