EULER. 
the theory of the solar system, and re- 
quired the most arduous calculations. Eu- 
ler’s solution of this question was adjudged 
a masterpiece of analysis and geometry ; 
and it was more honourable for him to share 
the academical prize with such illustrious 
competitors as Colin Maclaurin and Daniel 
Bernoulli, than to have carried it away 
from rivals of less magnitude. Seldom, if 
ever, did such a brilliant competition adorn 
the annals of the Academy ; and, perhaps, 
no subject proposed by that learned body 
was ever treated with such force of genius 
and accuracy of investigation, as that 
which here displayed the philosophical pow- 
ers of this extraordinary triumvirate. 
In the year 1741, M. Euler was invited 
to Berlin to direct and assist the Academy 
that was there rising into fame. On this 
occasion he enriched the last volume of the 
Miscellanies ( Melanges ) of Berlin with five 
memoirs, whicli form an eminent, perhaps 
the principal figure in that collection. These 
were followed, with amazing rapidity, by a 
great number of important researches, which 
are dispersed 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 astonish- 
ing, when it is considered, that while he 
was enriching the Academy of Berlin with 
a profusion of memoirs on the deepest parts 
of mathematical science, containing always 
some new points of view, often sublime 
truths, and sometimes discoveries of great 
importance; he still continued his philoso- 
phical contributions to the Petersburgh 
Academy, whose memoirs display the sur- 
prising fecundity of his genius, and which 
granted him a pension in 1742. 
It was with great difficulty that this ex- 
traordinary man, 1766, obtained permis- 
sion from the King of Prussia to return to 
Petersburgh, where he wished to pass the 
remainder of his days. Soon after his re- 
turn, which was graciously rewarded by the 
munificence of Catherine the Second, he 
was seized with a violent disorder, which 
ended in the total loss of his sight. A ca- 
taract 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 situ- 
ation that he dictated to his servant, a tailor’s 
apprentice, who was absolutely devoid of 
mathematical knowledge, his elements of 
algebra, which by their intrinsic merit in 
point of perspicuity and method, and the un- 
happy circumstances in which they were 
composed, 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 mem- 
bers of that learned body , after which the 
academical prize was adjudged to three of 
his memoirs, “ concerning the inequalities 
in the motions of the planets.” The two 
prize questions proposed by the same aca- 
demy for 1770 and 1772 were designed to 
obtain from the labours of astronomers a 
more perfect theory of the moon. M. 
Euler assisted by his eldest son, was a com- 
petitor for these prizes, and obtained 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 account of 
the complicated calculations in which the 
method he then employed had engaged him. 
He afterward revised his whole theory, 
with the assistance of his son and Messrs. 
Krafft and Lexell, and pursued his re- 
searches till he had constructed the new 
tables, which appeared together with the 
great work, 1772. Instead of confining 
himself, as before, to the fruitless integra- 
tion of three differential equations of the 
second degree, which are furnished by ma- 
thematical 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 excentricity, 
or the parallax, or the inclination of the 
lunar orbit. All these means of investiga- 
tion, 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 impossible 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 application to the real mo- 
tion of the moon. But this admiration will 
become astonishment, when we consider 
at what period, and in what circumstance# 
all this was effected. It was when our 
author was totally blind, and consequently- 
obliged to arrange all his computations by 
