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EUG immediately after his election, to leave the city. Floods of argument were poured forth on both sides of the question, as happens at this very day. But the pope wisely determined to

and enlisted the services of the men of Tivoli against the Romans. Too weak to resist the force brought against them, the people of Rome opened their gates to Eugenius, and, with their customary fickleness, greeted his entry with enthusiastic acclamations. Eugenius warmly promoted the second crusade. He died in the year 1153.

IV. , a Venetian, assumed the tiara on the death of Martin V. in 1431. That pontiff had shortly before, in pursuance of the decree of the council of Constance establishing periodical synods, summoned a general council to meet at Basle. Eugenius wished to transfer the place of meeting to Italy, and upon the council's resisting, issued a bull, declaring it dissolved. This bull, however, he afterwards was induced to revoke. In 1434 an insurrection broke out at Rome, which compelled Eugenius to escape from the city in the disguise of a monk. For four hundred and fourteen years subsequently, down to 1848, no pope had been driven from the Vatican by the violence of the Roman people. The city was reduced to submission before the end of the year. About this time the council of Basle began to make overtures to the Byzantine emperor, John Palæologus, for a reunion of the Greek and Latin churches. But the choice of the place of meeting presented difficulties. The emperor refused to pass the Alps, and yielded to the timely proposal of Eugenius, that a united council should be held at Ferrara. Early in 1438, the emperor, attended by the patriarch Joseph Bessarion, archbishop of Nice, and the most illustrious prelates of the Eastern church, landed at Venice, and proceeded by land to Ferrara, where he was met by Eugenius. But the breaking out of the plague at Ferrara compelled the transference of the council to Florence. There, in July, 1438, the terms of union between East and West were solemnly agreed upon; the phrase "Filioque," embodying the disputed doctrine of the double procession of the Holy Ghost, was added to the Nicene creed, and for the moment all was harmony. But the blind fanaticism of the Greeks undid the work of the council of Florence. Upon the return of the emperor and patriarch to Constantinople, the clergy and people everywhere disclaimed the act of their representatives; and the feelings which their suicidal bigotry excited in the Latin world may perhaps be traced, fifteen years later, in the unhindered, unavenged fall of the Byzantine empire. At the same time that the terms of union were being arranged at Florence, the council of Basle published a decree, depriving the pope of all spiritual and temporal power. In 1439, having been now deserted by all the more moderate bishops, the synod declared Eugenius a heretic, and deposed him from the papacy. In 1440 they nominated an antipope, Amadeus, the ex-duke of Savoy, who took the title of Felix V. In 1443 the pope, bent upon carrying out his pledges of amity and union given to Palæologus, organized a league of christian powers against the Turks. This was, however, annihilated by the disastrous battle of Varna in 1444, in which Amurath defeated Ladislaus, king of Poland, who fell in the action. Eugenius died in 1447. His life was irreproachable, and his habits austerely temperate.—T. A.  EUGENIUS,, a prelate of the Greek church, was born at Corfu in 1716, and died at St. Petersburg in 1806. He received his education in Greece, and afterwards acted as professor in his native island and other places. He was at one time at the head of the school of Mount Athos. Bulgaris made an attempt to introduce the arts and sciences into his native country; but, meeting with little success, he accepted an invitation from Catherine II. of Russia, and was afterwards raised to the archiepiscopal see of Slavonia and of Cherson. He was the author of a considerable number of works.—R. M., A.  EULER,, son of Leonhard, born at St. Petersburg in 1734, and died in 1800. He enjoyed the valuable instructions of his father, and became himself a distinguished mathematician. He was engaged in engineering at a very early age, and was admitted a member of the Berlin Academy when only twenty. His most original investigations are those on resisting media. Many of his papers are to be found in the Berlin, Munich, and Göttingen Transactions.—R. M., A.  EULER,, one of the greatest mathematicians of the eighteenth century, was the son of Paul Euler, Calvinistic pastor of Riessen. He was born at Basel on the 15th of April, 1707 (new style), and died at St. Petersburg on the 7th of September, 1783 (old style, corresponding to the 18th of September, new style). His father, who had been a pupil of James Bernoulli, instructed him in the rudiments of mathematics, which science he continued to study at the university of Basel, under John Bernoulli, with such success that he acquired the esteem and friendship of that famous professor, and of his sons, Daniel and Nicholas, and induced his father to permit him to abandon the ecclesiastical profession, for which he had at first been destined, for the cultivation of science. He soon acquired such celebrity as a mathematician, that the Empress Catharine I. of Russia was induced to invite him to St. Petersburg, where, on his arrival in 1727, he was created an associate of the Academy of Sciences in the department of the higher mathematics. In 1730 he became professor of physics, and in 1733, on the resignation of his friend, Daniel Bernoulli, he was appointed to the chair of the higher mathematics. In the course of the same year he married a lady of the name of Gsell, daughter of a Swiss artist who had emigrated to Russia during the reign of Peter the Great. In 1741 Euler was induced, by the disturbed state of Russia, and the invitation of Frederick the Great, to migrate to Berlin, where he became professor of mathematics and a member of the Academy of Sciences. In 1744 he was appointed director of the mathematical division of the Academy of Sciences. Soon after the death of his father in 1745, he brought his mother to reside with him in Berlin, where she remained until her death in 1761. During this period the connection of Euler with Russia did not wholly cease. He continued to receive part of his salary as an academician; and in 1760, when a party of Russian soldiers, in the course of the Seven Years' war, pillaged a farm belonging to him in Brandenburg, the Russian general Todleben caused full restitution to be made for the damage done, and the Empress Elizabeth added a gift of four thousand florins. In 1766, on the pressing invitation of Catharine II., he returned to St. Petersburg. Euler had lost the sight of one eye in 1735. Soon after his second removal to St. Petersburg he became nearly blind of the other, so as to be barely able to read large letters written with chalk. He continued, nevertheless, his scientific labours with as much activity as ever, employing his children and pupils as secretaries. In 1771 his house and library were destroyed by a conflagration, from which his manuscripts were saved by the care of Count Orloff, and himself by the courage and affection of a Bâlese fellow-countryman, Peter Grimmon. In 1776 he was married, for the second time, to the paternal half-sister of his first wife.

On the evening of the 18th of September, 1783, he died suddenly, and without pain, in the midst of his family, having preserved his faculties and continued his labours to the end of his life. Euler's personal character, as well as his philosophical writings, were marked by great devotion to the faith in which his youth had been trained. He was of simple habits, kind and cheerful in disposition, and had a turn for harmless pleasantry. He had several children, of whom the most remarkable were Johann Albert, already noticed; Charles, physician; and Christopher, major-general of artillery in the Russian service. The scientific treatises and papers of Euler are reckoned to be upwards of seven hundred and fifty in number: a mere catalogue of their titles would fill at least seven pages of this dictionary. It was estimated that an edition of his entire works, lately projected at St. Petersburg, would occupy from sixty to eighty quarto volumes. They treat of every branch of pure and applied mathematics. The part which has proved of most value in later times is certainly that which relates to the differential and integral calculus, to the calculus of variations, and to the properties of definite integrals, of which functions a numerous class are known by the name of "Eulerian Integrals" in honour of their discoverer. In the application of mathematics to physical questions, the utility of Euler's researches was to a certain extent impaired by the assumption of unsound data; but the extent to which this is the case has been exaggerated by his critics. An account of his life, with a list of his works, was written by Nicholas von Fuss, perpetual secretary of the Imperial Academy of St. Petersburg; and two volumes of his scientific correspondence were edited by Paul Henry von Fuss, son and successor of the foregoing. His éloge for the French Academy 