E U L 
Gg 
there is an appetite of union and evitation, of folution and 
continuity. Bacon. 
Tc EVI'TE, v. a. \_evito, Lat. ] To avoid : 
’Gainft open fit a me no text can well be cited, 
The blow once given cannot be evitcd. Drayton. 
EVITER'NAL, adj. [aviternus, Lat.] Eternal in a 
limited fenfe ; of duration not infinitely but indefinitely 
long. 
EVITER'NITY, f. [,aviternitas, low Lat.] Duration 
not infinitely but indefinitely long. 
EUK'SINEH, a town of Afiatic Turkey, in the pro¬ 
vince of Natolia : ten miles north-eaft of Eregri. 
EU'LE,/ [from tvXafy, Gr. to putrefy.] A worm 
bred in foul and putrid ulcers. 
EU'LE, a town of Bohemia, in the circle of Kaurzim: 
tyvelve miles fouth of Prague. 
EU'LENBERG, a town of Moravia, in the circle of 
Olnuitz : fourteen miles north of Olmutz. 
EU'LENBURG, a town of Germany, in the circle of 
Upper Saxony, and territory of Leipfic, on the Mulda; 
containing three churches: beer confiiiutes the principal 
and almoft only article of commerce. 
EU'LER (Leonard), a profound mathematical genius, 
born at Bafil, in 1707. The firft years of his life were 
fpent at the village of Richen, of which his father was 
protefiant minifter, whence at a proper age he was fent 
to the univerfity of Bafil. In that univerfity he regularly 
attended the different profeffors, and performed his aca¬ 
demical talks with uncommon rapidity. The mathematics 
became his favourite purfuit, in which he was encouraged 
by profeffor John Bernouilli, who was then one of the 
chief mathematicians in Europe, and whofe diftinguilhed 
attention and efteem he obtained by his early proficiency 
and unwearied application. In 1723, M. Euler was ad¬ 
mitted to the degree of matter of arts ; on which occalion 
he obtained very great applaufe by delivering a Latin 
difcourfe, in which he drew a comparifon between the 
philofophy of Newton and the Cartefian fyftem. After¬ 
wards, to comply with his father’s defire, who defigned 
him for the church, he applied himfelf to the thidy of 
theology, and of oriental literature, in which he made 
no inconfiderable progrefs ; but his predominant bias (till 
engaging him to devote his principal attention to the ma¬ 
thematics, his father very prudently fuffered him to fol¬ 
low the bent of his inclination. In the courfe of his 
Itudies under the inftruthions of Bernouilli, lie contracted 
an intimate friendthip with his two fons, Nicholas and 
Daniel, which afterwards proved the means of his intro¬ 
duction to the feene where his abilities (hone with diltin- 
guifhed lultre. Thofe two celebrated geometricians hav¬ 
ing been invited to Peterfburgh in 1725, when Catharine I. 
was carrying into execution the order of Peter the Great 
for the eftabliffiment of an academy of fciences, they 
promifed Euler that they would endeavour to procure 
for him a fituation in that city. In the mean time he 
compofed a differtation On the Nature and Propagation ot 
Sound ; and alfo an anfwer to a prize queftion Concerning 
the Mailing of Ships, to which the academy of fciences 
at Paris adjudged the accejjit., or fecor.d rank, in the year 
1727. He then fet out for Peterfburgh, and obtained the 
appointment of joint profeffor with his countrymen Her¬ 
mann and Daniel Bernouilli. To the academical col¬ 
lections of that univerfity, he contributed a great variety 
of memoirs, which excited a noble fpirit of emulation 
between him and the Bernouillis, unalloyed by the lead 
mixture of feffifh jealoufy, and fuch as produced no al¬ 
teration in their friendlhip. The integral calculus he 
carried to new degrees of perfection ; invented the calcu¬ 
lation of fines; Amplified analytical operations; and thus 
threw a new light on all the branches of mathematical 
fcience. In 1730, M. Euler was appointed profeffor of 
natural philofophy; and, in 1733, upon the removal Of 
his friend Daniel Bernouilli to Bafil, he fucceeded him 
E U L 
in the mathematical chair. In 1733, the academy pro-- 
pofed an intricate and important problem for folution, irp 
as fliort a time as polfible. Some eminent mathematicians 
demanded a fpace of fome months for that purpofe : M. 
Euler, however, completed it in three days, to the afio- 
nifhment of the academy. But his exertion on this occa- 
fion was fo violent, that it produced a fever, which en¬ 
dangered his life, and deprived him of the ufe of one of 
his eyes. In 173S, the academy of fciences at Paris ad¬ 
judged the prize to his memoir On the Nature and Pro¬ 
perties of Fire. In 1740, they propofed for folution the 
important fubjeCt of The Flux and Reflux of the Sea, 
which required the mod; arduous and extenfive calcula¬ 
tions, and comprehended the theory of the folar fyftem. 
To this fubjeCt M. Euler applied the force of bis genius, 
and produced a memoir which was allowed to be a maf- 
ter-piece of analyfis and geometry. But he had illuftrious 
competitors for the prize; and it was not a little honour¬ 
able for him, that though not permitted to gain it alone, 
be was allowed to fliare it with Colin Maclaurin and 
Daniel Bernouilli. Such a brilliant competition rarely, 
if ever, adorned the annals of the academy ; and few fub- 
jeCts propofed before that body were ever treated with 
fuch accuracy of inveftigation, and force of genius, as 
the powers of this extraordinary triumvirate difplayed on 
the prelent occalion. In 1741, M. Euler was invited by 
Frederic II. king of Pruftia, to Berlin, toaftiftin forming 
and giving a luftre to the academy that was about to be 
eftablifhed under the aufpices of that prince. Such was 
the ftate of things at that time in Ruffia, under the pre¬ 
carious government of a regency which does not appear 
to have been favourable to the interefts of fcience, that 
he judged it prudent to accept of his majefty’s invitation, 
and accordingly repaired to Berlin, where he enriched 
the laft volume of the Melanges de Berlin with five e flays, 
which are, perhaps, the belt memoirs in that collection. 
In this new feene M. Euler’s genius and induftry appeared 
to eminent advantage, and produced an aftonifhing num¬ 
ber of interefting and important refearches, which are 
fcattered through the Memoirs of the Pruflian Academy, 
of which a volume has been regularly publilhed every 
yearfince its eftablifhment in 1744. At the fame time he 
continued his contributions to the academy of Peterf¬ 
burgh, which W33 now encouraged by the patronage and 
munificence of the emprefs Elizabeth, who granted M. 
Euler a penfion in 1742. The memoirs of that academy 
afford ftriking evidence of the wonderful fecundity of his 
genius. In 1760, a ftrong proof was exhibited of the 
refpeCi in which his character and talents were held among 
the Ruffians ; for when, during an irruption of their 
troops into the Pruflian territories, a fmall farm of his in 
the neighbourhood of Charlottenburg had been plundered 
in common with the furrounding country, general Tct- 
telben amply recompenfed him for his Ioffes, and the em¬ 
prefs Elizabeth alfo fent him a confiderable pecuniary 
donation. After M. Euler had remained twenty-five 
years at Berlin, lie was defirous of returning to Peterf¬ 
burgh to fpend 1 fie remainder of his days in that city. 
It was with much difficulty that in 1766 he obtained the 
king’s permiffion to follow his inclination, when the mu¬ 
nificence of Catharine II. liberally rewarded him fer the 
preference which he (hewed towards his Ruffian connec¬ 
tions. Soon after his return he had the misfortune 'en¬ 
tirely to lofe his fight, in confequence of a cataract that 
formed in his only ufef.nl eye, Which had been before in¬ 
jured by a too clofe application to his Itudies. But even 
in thefe circumftances he continued to excite the ap¬ 
plaufe and altonifhment of the world by his wonderful 
productions. In this fituation lie dictated to his fervant, 
a tailor’s apprentice, who was entirely unacquainted with, 
mathematical knowledge, his Elements of Algebra : a 
work which, by the fttlnefs of information, and profound- 
nefs of refearch that diftinguilh it, is equally recommend¬ 
ed to the moft experienced adepts, as it is to the Jftudent 
