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of which several eminent mathematicians hail demanded somemonths. The problem was solved by Euler in three days, to thegreat astonishment of the academy ; but the violent and laboriousefforts it cost him threw him into a fever, which endangered hislife, and deprived him of the use of his right eve. The academyof sciences at Paris , which in 1738 had adjudged the prize to hisuvinoir Concerning the Mature and Properties of Fire, proposedfor the year 1740 the important subject of the tides; a problemwhose solution required the most arduous calculations. Euler’sdiscourse on this question was adjudged a master-piece of analysisand geometry ; and it was more honourable for him to share theacademical prize with such illustrious competitors as Cohn Mac-laurin and Daniel Bernouilli , titan to have carried it away fromrivals of less magnitude. Seldom if ever did such a brilliant com-petition adorn the annals of the academy ; and perhaps no sub-ject, proposed by that learned body, \va< ever treated with suchaccuracy of investigation and force of genius, as that which heredisplayed the philosophical powers of this extraordinary triumvi-rate.. In 1741 he went to Berlin , at the invitation of the king, tosssiit.in establishing the academy there. lie continued at Berlin twenty-live years, and then returned to Petersburg!!, where hesoon after entirely lost his sight. But still he continued his fa-vourite pursuits, and it was in this distressing situation he dictatedto iiis servant a tailor’s apprentice, who was absolutely devoid ofmathematical knowledge, his “ Elements of Algebra;” which,by their intrinsieal merit, in point of perspicuity and method, andthe unhappy circmnstanceKin which they were composed, haveequally excited applause and astonishment. This work, thoughpurely elementary, discovers proofs of a most inventive genius ;and it is here alone that we meet with a complete theory of theanalysis of Diophantus . About this time .\I. Euler was honouredby the Academ of Sciences at Paris with the place of one of itsforeign members; and, the academical prize was adjudged to threeof his memoirs, Concerning the Inequalities in the Motions of thePlanets. The two prize questions, proposed by the same academyfor 1770 and 177ft, were designed to obtain from the labours ofastronomers a more Perfect Theory of the Moon . M. Euler, as-sisted by his eldest son, was a competitor for these prizes, and ob-tained them both. lie afterwards reviewed his whole theory,with the assistance of his son and Messrs. KralTt and Lexell, andpursued his researches until he had constructed the new tables,which appeared, together with the great work, in 1772. Insteadof confining himself, as before, to the fruitless integration of threedifferential equations of the second degree, which are furnished bymathen^atical principles, lie reduced them to the three ordinates,which determine the place of the moon ; he divided into classesall the inequalities of that planet, as far as they depend either onthe elongation of the sun and moon, or upon the eccentricity, orthe parallax - , or the inclination of the lunar orbit. All "thesemeans of investigation, employed with such art and dexterity ascould only be expected Iroin an analytical genius of the iir.strank, were attended with the greatest success; and it is impossi-ble to observe, without admiration, such immense calculations onthe one hand, and on the other the ingenious methods employedby this great man to abridge them, and to facilitate their applica-tion to the real motion of the moon. But this admiration be-comes astonishment, when we consider at what period and inwhat circumstances all this was effectuated by M. Euler. Itwas when he was totally blind, and consequently obliged toarrange all his computations by the sole powers of his memoryand genius. It was wtvm he was embarrassed in his domesticcircumstances by a dreadful lire, that had consumed great partof his sitbstame, and forced him to quit a ruined house, ofwhich every corner was known to him by habit, which, insome measure, supplied the place of sight. It was in these cir-cumstances, that Euler composed a work which, alone, was suffi-cient to render his name immortal. Some lime alter this, the fa-mous oculist, Wentzell, by couching the cataract, restored hissight; but the joy that this operation produced was of short dura-tion. Some negligence on the part of his surgeons, and his ownimpatience to use an organ, whose cure was not completed, de-prived him of his sight a second time; and this relapse was ac-companied with tormenting pain. He, however, with the assist-ance of his sons, and of Messrs. Krafft and Lexell, continued hislabours; neither the loss of his sight, nor the infirmities of an ad-

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vancctl age, could depress the ardour of his genius. He had en-gaged to lurnish the academy of Peter-buvgh with as many me-moirs as would be sufficient to complete its acts for 20 years afterhis death. In 7 years he transmitted to the academy, by Mr. Go-lofkin above 70 memoirs, and above 230 more lelt behind him,were revised and completed by a friend. .Such of these memoirsas were of ancient date were separated from the rest, and form acollection that was published in 1783, under the title of AnalyticalWorks. Euler’s knowledge was more universal than could wellbe expected in one, who had pursued, with such unremitting ar-dour, mathematics and astronomy as his favourite studies, liehad made a very considerable progress in medical, botanical, andchemical science. What was still more extraordinary, he possess-ed what is generally called erudition in a very high degree. Hehad read the most eminent writers of ancient Rome ; the civil andliterary history of all ages and nations was familiar to him; andforeigners, w ho were only acquainted with his works, were asto-nished to find in the conversation of a man, w ho seemed solely oc-cupied in mathematical and physical researches and discoveries,such an extensive acquaintance with the most interesting branchesof literature. In this he was doubtless much indebted to a veryuncommon memory, w Inch seemed to retain every idea that wasconveyed to it, either by reading or meditation. Ilecould repeatthe (Eneid of Virgil , from (he beginning to the end, w ithout hesita-tion, and indicate lhe first and last line of every page of the editionhe used. Several attacks of a vertigo, in Sept. 1783, (which, how-ever, did not prevent his calculating the motions of the aerostaticglobes,) were the forerunners of his mild and happy passagetrom this scene to a better. While lie was amusing himself at teawith one of his grandchildren, he was struck with an apoplexy,which terminated his illustrious career at the age of 7(1. His con-stitution was uncommonly strong and vigorous; his health wasgood; and the evening of his life was calm and serene, sweetenedby the tame that follows genius, the public respect that is paid toexemplary virtue, and several domestic comforts which he was ca-pable of feeling, anil therefore deserved to enjoy. His works areso numerous that the printed catalogue alone extends to 50 pages;14 of which contain those in.M.S. The printed ones consist ofworks published separately, and works to be found in the memoirsof several academies, viz. in thirty-eight volumes of the Peters-burgh acts, (from six to ten papers in each volume); in several vo-lumes of the Paris acts; in twenty-six volumes of the Berlin acts,(about live papers to each volume) ; in the Acta Eruditomm, intwo volumes; in the Miscellanea Taurinensia; in vol. ix. of theSociety of UlysMiigue; in the Ephemerides of Berlin ; in the Me-mcires de la Societe Oeconomiqiie, for 170().

EULOGV , EUI.OGIA, [trom w, bene, and >iyui, dico, q. d.bencdlctum, blessed,] a bit of consecrated bread. When theGreeks cut a loaf of bread to consecrate it, they break the rest intolittle bits, and distribute them among those who have not yet com-municated, or who are absent; and these pieces of bread they calleulogies. The Latin church has had something like eulogies formany ages; and thence arose the use of their holy bread. Thename was likewise given to loaves or cakes brought to clmreh bythe superstitious to have them blessed. It passed hence to merepresents, without any benediction. See Greiser, de Benedict, andMaledict. lib. ii. cap. 22, &e.

LI'MARIDES, [of tvfjuimi;, easy,] among the ancients, a kindof shoes common to men and women. The eumarides were usedfor pomp and delicacy, being neat, and painted with various co-lours.

EUMENES , a Greek officer in the army of Alexander, son ofa charioteer. He was the mod worthy of all the officers of Alex-ander. He conquered Paphlagonia, and Cappadocia , of w hich heobtained the government, till the power and jealousy of Antigonus obliged him to retire, lie joined his force, to those of Perdieeas,defeated C'raterus and Neoptolemus , and killed the latter. WhenCraterus was afterwards killed, his remains received an honourablefuneral from Eumenes , who, after weeping over the ashes of a manwho once was his dearest friend, sent his remains to his relations inMacedonia. Eumenes fought against Antiputer and conqueredhim; but after the death of Perdieeas his ally, he was conqueredby Antigonus , chiefly through the treachery of his officers. Anti-gonus ordered Eumenes to be put to death in the prison, B. C.315. Eumenes raised himself to power by merit alone. Ilia skill