of April, 1707. His natural turn for mathematics soon appeared, from the eagerness and facility with which he became master of the elements, under the instruction of his father, by whom he was sent to the University of Basil at an early age. There, his abilities and his application were so distinguished, that he attracted the particular notice of John Bernoulli. That excellent mathematician seemed to look forward to the youth's future achievements in science, while his own kind care strengthened the powers by which they were to be accomplished. In order to superintend his studies, which far outstripped the usual routine of the public lectures, he gave him a private lesson regularly once a week; when they conversed together on the acquisitions which the pupil had been making since the last interview, considered whatever difficulties might have occurred in his progress, and arranged the reading and exercises for the ensuing week. Under such eminent advantages, the capacity of Euler did not fail to make rapid improvements, and in his seventeenth year, the degree of Master of Arts was conferred on him. On this occasion, he received high applause for his probationary discourse, the subject of which was a comparison between the Cartesian and Newtonian sys

tems.

His father having all along intended him for his successor, enjoined him now to relinquish his mathematical studies, and to prepare himself, by those of theology and general erudition, for the ministerial functions. After some time, however, had been consumed, this plan was given up. His father, a man of

learning and liberality, abandoned his own views for those to which the inclination and talents of his son were so powerfully directed; persuaded that in thwarting the propensities of genius, there is a sort of impiety against nature, and that there would be real injustice to mankind, in smothering those abilities which were evidently destined to extend the boundaries of science. Leonard was permitted, therefore, to resume his favourite pursuits; and at the age of nineteen, having transmitted two Dissertations to the Academy of Sciences at Paris, one on the masting of ships, and the other on the velocity of sound, he commenced that splendid career, which continued for so long a period the admiration and glory of Europe.

About the same time he stood candidate for a vacant professorship in the University of Basil, but having lost the election, he resolved, in consequence of this disappointment, to leave his native country. In 1727, he set out for Petersburgh, where his friends the young Bernoullis had settled about two years before, and he flattered himself with prospects of literary preferment, under the patronage of Catharine the First. Those prospects, however, were not immediately realized; nor was it till after he had been frequently and long disappointed, that he obtained any settlement. His first appointment appears to have been the chair of natural philosophy; and when Daniel Bernoulli removed from Petersburgh, Euler succeeded him as professor of mathematics. In this situation he remained many years, engaged in the most laborious researches, enriching the academical collections of the Continent with papers of the highest value, and

producing almost daily improvements in the various branches of physical, and more particularly analytical, science. In 1741, he complied with a pressing invitation from Frederic the Great, and resided at Berlin till 1766. Throughout this period he continued the same literary labours, directed by the same wonderful sagacity and comprehension of intellect. As he advanced with his own discoveries and inventions, the field of knowledge seemed to widen before his view, and new subjects still multiplied on him for further speculation. The toils of intense study only seemed to invigorate his future exertions, nor did the energy of Euler's mind give way, even when his bodily strength was overpowered; for in the year 1765, having completed in three days certain astronomical calculations which the academy called for in haste, but which several mathematicians of eminence had declared could not be performed within a shorter period than some months, the intense application threw him into a fever, by which he lost the sight of one eye. Shortly after his return to Petersburgh, he became totally blind. It was in this situation that he dictated to his servant, a tailor's apprentice, (who was absolutely devoid of mathematical knowledge,) his Elements of Algebra; which by their intrinsic merit in point of perspicuity and method, and the unhappy circumstances under which they were composed, have equally excited applause and astonishment. This work, though purely elementary, discovers the palpable characteristics of an inventive genius, and it is here alone we meet with a complete theory of the Analysis of Diophantes. About this time Euler was

elected by the Academy of Sciences at Paris one of the foreign members of that learned body; and after this, the academical prize was adjudged to three of his memoirs, concerning the inequalities in the motions of the planets. The two prize questions proposed by the same Academy for 1770 and 1772, were designed to obtain from the labours of astronomers a more perfect theory of the moon. Euler, assisted by his eldest son, was a competitor for these prizes, and obtained them both. In this last memoir he reserved for farther consideration, several inequalities 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 had the courage afterwards to review his whole theory, with the assistance of his son, and Messrs. Krafft and Lexell; and to pursue his researches until he had constituted 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; 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, parallax, or inclination of the lunar orbit. All these means of investigation, employed with such art and dexterity as could only be expected from an analytical genius of the first order, were attended with the greatest success; and it is impossible to observe without admiration, such

immense calculations on the one hand, and on the other the ingenious methods employed by this great man to abridge them, and to facilitate their application to the real motion of the moon. But this admiration will be raised to astonishment, when we consider at what period, and under what circumstances, all this was effected by Euler. It was when he was totally blind, and consequently obliged to arrange all his computations by the sole powers of his memory and genius. It was when he was embarrassed in his domestic circumstances by a dreadful fire, that had consumed a great part of his substance, and forced him to quit a ruined house of which every corner was so well known to him by habit, as in some measure to supply the place of sight. It was in these circumstances that Euler composed a work which, alone, was sufficient to render his name immortal. The heroic patience and tranquillity of mind which he displayed need no description; and he derived them, not only from the love of science, but from the power of religion. His philosophy was too genuine and sublime to end its analysis in mechanical causes; it led him to that divine philosophy of religion which ennobles human nature, and can alone form a habit of true magnanimity, and patience in suffering.

Some time after this, the famous Wentzell, by couching the cataract, restored Euler's sight; but the satisfaction and joy that this successful operation produced, were of short duration. Some instances of negligence on the part of his surgeons, and his own impatience to use an organ whose cure was not completely finished, deprived him of his sight a second