The Academy of Sciences at Paris, which in 1738 had adjudged the prize to his memoir concerning the Nature and Properties of Fire, proposed for the year 1740, the important subject of the tides of the sea ; a problem whose solution comprehended the theory of the solar system, and required the most arduous calculations. Eider's solution of this question was adjudged a masterpiece of analysis and geometry ; and it was more honourable for him to share the academi cal prize with such illustrious competitors as Colin Maclaurin and Daniel Bernoulli, than to have carried it away from ri vals of less magnitude. Seldom, if ever, did such a brilliant competition adorn the annals of the Academy ; and per haps no subject, proposed by that learn ed body, was ever treated with such force of genius and accuracy of investigation, as that which here displayed the philoso phical powers of that extraordinary tri umvirate.
In the year 1741, M. Euler was invited to Berlin, to direct and assist the Acade my that was there rising into fame. On this occasion he enriched the last volume of the Miscellanies (Melanges) of Berlin with five memoirs, which form an emi nent, perhaps the principal figure in that collection. These were followed, with amazing rapidity, by a great number of important researches, which are dispers ed through the memoirs of the Prussian Academy : a volume of which has been regularly published every year since its establishment in 1744. The labours of Euler will appear more especially asto nishing, when it is considered, that, while he was enriching the Academy of Berlin with a profusion of memoirs on the deep est parts of mathematical science, con taining always some new points of view, often sublime truths, and sometimes dis coveries of great importance, he still continued his philosophical contributions to the Petersburgh Academy, whose me moirs display the surprising fecundity of his genius, and which granted him a pen sion in 1742.
It was with great difficulty that this extraordinary man, 1766, obtained per mission from the King of Prussia to re turn to Petersburgh, where he wished to pass the remainder of his days. Soon after his return, which was graciously re warded by the munificence of Catharine the Second, he was seized with a violent disorder, which ended in the total loss of his sight. A cataract formed in his left eye, which had been essentially damaged by the loss of the other eye, and a too close application to study, deprived him entirely of the use of that organ. It was in this distressing situation that he dictat ed to his servant, a tailor's apprentice, who was absolutely devoid of mathemati cal knowledge, his elements of algebra, which, by their intrinsic merit in point of perspicuity and method, and the unhappy circumstances in which they were com posed, have equally excited wonder and applause. This work, though purely ele
mentary, plainly discovers the proofs of an inventive genius; and it is perhaps here alone that we meet with a complete theory of the analysis of Diophantus.
About this time M. Euler was honoured by the Academy of Sciences at Paris with the place of one of the foreign members of that learned body ; after which the academical prize was adjudged to three of his memoirs, "concerning the inequa lities in the motions of the planets." The two prize questions proposed by the same academy, for 1770 and 1772, were de signed to obtain from the labours of astro nomers amore perfect theory of the moon. M. Euler, assisted by his eldest son, was a competitor for these prizes, and obtain ed them both. In this last memoir, he reserved for farther consideration several inequalities of the moon's motion, which he would not determine in his first theory, on acccount of the complicated calcula tions in which the method he then em ployed had engaged him. He afterward revised his whole theory, with the assist ance of his son, and Messrs. Krafft and Lexell, and pursued his researches till he had constructed the new tables, which appeared, together with the great work, 1772. Instead of confining himself, as be fore, to the fruitless integration of three differential equations of the second de gree, which are furnished by mathema tical 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 eccen tricity, or the parallax, or the inclination of the lunar orbit. All these means of in vestigation, employed with such art and dexterity as would only be expected from a genius of the first order, were attended with the greatest success ; and it is im possible 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 ap plication to the real motion of the moon. But this admiration will become astonish ment, when we consider at what period, and in what circumstances, all this was effected. It was when our author was totally blind, and consequently obliged to arrange all his computations by the sole powers of his memory, and of his genius : it was when he was embarrassed in his domestic affairs by a dreadful fire, that had consumed great part of his pro perty, and forced him to quit a ruined house, every corner of which was known to him by habit, which in some measure supplied the want of sight. It was in these circumstances that Euler composed a work, which alone was sufficient to ren der his name immortal.