pace of fome months. The problem was folved by Euler in three days, to the great aftonishment of the Academy; but the violent and laborious efforts it cost him threw him into a fever, which endangered his life, and deprived him of the ufe of his right eye.

"The Academy of Sciences at Paris, which, in 1738, had ad. judged the prize to his Memoir concerning the Nature and Properties of Fire, propofed, for the year 1740, the important fubject of the fea-tides, a problem whofe folution required the moft arduous calculations, and comprehended the theory of the folar fyftem. Euler's difcourfe on this question was judged a mafter-piece of analyfis and geometry; and it was more honourable for him to fhare the academical prize with fuch illuftrious competitors as Colin Maclaurin and Daniel Bernoulli, than to have carried it away from rivals of lefs magnitude. Rarely, if ever, did fuch a brilliant competition adorn the annals of the Academy; and no fubject, perhaps, propofed by that learned body, was ever treated with fuch accuracy of investigation and force of genius, as that which here difplayed the philofophical powers of thefe three extraordinary men. We shall not follow the learned eulogit in his remarks on the particular merit of Euler's difcourfe. It has been long acceffible to the perufal of thofe, who have a taste and a capacity to relish and comprehend investigations of this kind: but we cannot omit a circumftance, which, befide the confirmation that experience has given to the refearches of Euler, is a very frong, prefumption in their favour; and that circum@ance is the remarkable conformity between his memoir and that of Fernoulli, though they fet

out from different principles. The one adopted the Cartefian vortices, which the other rejected; and yet they arrived at the fame conclufion: they even met together often in the courfe of their inveftigations; of which, one example, among others, is their determination of the tide in the frigid zone. Thus, obferves our panegyrift,. does truth feem, at times, to multiply itself, that it may fhed its light upon its genuine votaries, in whatever path they pursue it.

"In the year 1741, M. Euler was invited to Berlin, to augment the luftre of the academy, that was there rifing into fame, under the auspicious protection of the prefent. king of Pruffia; for whom the mufes and the fciences have prepared a wreath, which will bloom unfaded to the latest ages. He enriched the laft volume of the Mifcellanies (Melanges) of Berlin with five Memoirs, which make an eminent, perhaps the principal, figure in that collection. Thele were followed, with an aftonishing rapidity, by a great number of important refearches, which are fcattered through the Memoirs of the Pruffian Academy; of which a yolume has been regularly published every year, fince its establishment in 1744.

"The labours of Euler will appear more especially aftonishing, when it is confidered, that while he was enriching the Academy of Berlin with a prodigious number of memoirs, on the deepest parts of mathematical fcience, containing always fome new points of view, often fublime truths, aud fometimes difcoveries of great importance, he did not difcontinue his philofophi cal contributions to the Academy of Petersburgh, which granted him a penfion in 1742, and whofe me

moirs

moirs difplay the marvellous fecundity of Euler's genius.

"It was with much difficulty that this great man obtained, in 1766, permiffion from the king of Pruffia to return to Peterfburgh, where he defired to pafs the rest of his days, Soon after his return, which was graciously rewarded by the munificence of Catherine II. he was feized with a violent diforder, which terminated in the total lofs of his fight. A cataract, formed in his left eye, which had been effentially damaged by a too ardent application to ftudy, deprived him entirely of the ufe of that organ. It was in this diftreffing fituation, that he dictated to his fervant, who had been a tailor's apprentice, and was abfolutely devoid of mathematical knowledge, his Elements of Algebra; which, by their intrinfical merit, in point of perfpicuity and method, and the unhappy circumstances in which they were compofed, have equally excited applaufe and aftonifhment. This work, though purely elementary, difcovers the palpable characteristics of an inventive genius; and it is here alone that we meet with a complete theory of the analyfis of Diophantes.

"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; 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-queftions, propofed by the fame Academy, for 1770 and 1772, were defigned to obtain from the labours of astronomers a more perfect theory of the moon. M. Euler, af fifted by his eldest fon, was a competitor for thefe prizes, and obsained them both, In this last me

moir, he referved for farther confideration, feveral inequalities of the moon's motion, which he could not determine in his first theory, on acconnt of the complicated calcu lations in which the method he then employed had engaged him. He had the courage afterward to review his whole theory, with the affiftance of his fon, and Meff. Krafft and Lexell, and to purfue his refearches, until he had conftructed the new tables, which appeared, together with the great work, in 1772. Instead of confining himfelf, as before, to the fruitless integration of three differential equations of the fecond degree, which are furnished by mathematical principles, he reduced them to the three ordinates, which determine the place of the moon : he divided into claffes all the inequalities of that planet, as far as they depend either upon the mean elongation of the fun and moon, or upon the excentricity, or the pa rallax, or the inclination of the lunar orbit. All these means of invefligation, employed with fuch art and dexterity, as could only be expected from an analytical genius of the first order, were attended with the greatest fuccefs; and it is impoffible to obferve, without admiration, and a kind of aftonishment, fuch immenfe 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 become aftonishment, when we confider at what period, and in what circumstances, all this was effectuated by M. Euler. It was when he was totally blind, and confequently obliged to arrange all his computations by the fole powers of his memory and his genius. It was when he was em

ban

barraffed in his domeftic circumfances, by a dreadful fire, that had confumed a great part of his fubftance, and forced him to quit a ruined houfe, of which every corner was known to him by habit, which, in fome meafure, fupplied the place of fight. It was in thefe circumstances that Euler compofed a work, which, alone, was fufficient to render his name immortal. The heroic patience and tranquillity of mind which he difplayed here needs no defcription: and he derived them not only from the love of fcience, but from the power of religion. His philofophy was too genuine and fublime to flop its analyfis at mechanical caufes: it led him to that divine philofophy of religion, which ennobles human nature, and can alone form a habit of true magnanimity and patience in fuffering.

"Sometime after this, the famous Wentzel, by couching the cataract, reftored Mr. Euler's fight; but the fatisfaction and joy that this fuccefsful operation produced, were of fhort duration. Some inftances of negligence, on the part of his fargeons, and his own impatience to ufe an organ, whofe cure was not completely finished, deprived him of his fight a fecond time; and this relapfe was accompanied with tormenting pain. He, however, with the affiftance of his fons, and of Meffrs. Kraft and Lexell, continued his labours; neither the lofs of his fight, nor the infirmities of an advanced age, could damp the ardour of his genius. He had engaged to furnish the Academy of Petersburgh with as many memoirs as would be fufficient to complete its acts for twenty years after his death. In the space of feven years, he tranfmitted to the academy, by Mr. Golfwin, above feventy me

moirs, and above two hundred more, which were revised and completed by the author of this eulogy. Such of these memoirs as were of ancient date were feparated from the rest, and form a collection that was publifhed in the year 1783, under the title of Analy tical Works. There is not one of thefe pieces, obferves our eulogist, which does not contain fome new difcovery, or fome ingenious view, that may lead to the fuccefsful inveftigation of truths yet unknown. They contain the happiest integratiens, the most refined and fublime analytical proceffes, deep researches concerning the nature and properties of numbers, an ingenious demonftration of feveral theorems of Fermat; the folution of many difficult problems relative to the equilibrium and motion of folid, flexible, and elastic bodies, and explications of feveral feeming paradoxes. No part of the theory of the motion of the celestial bodies, of their mutual action, and their anomalies, however abftract and difficult, was overlooked, or left unimproved, by Mr. Euler. There is not one branch of mathematical science that has not been benefited by his labours: no geometrician ever before embraced fo many objects at the fame time: none, perhaps, ever equalled him, either in the number of his publications, or in the multitude and variety of his difcoveries. His name will live as long as the sciences fubfift: It will go down to the latest ages with the immortal names of Defcartes, Galilei, Newton, Leibnitz, and other illuftrious men, whofe genius and virtues have ennobled humanity it will fhine with an unfading lustre, when many names, which have been raifed to fame by the frivolous part of mankind, in our