EULER. 
answer a question, which may by the answer 
render him liable to an action at the suit of 
another party. 
EULER (Leonard), in biography, one 
of the most extraordinary and even prodi- 
gious mathematical geniuses that the world 
ever produced. He was a native of Basil, 
and was born April 15, 1707. The years 
of his infancy were passed at Richen, where 
his father was minister. He was afterwards 
sent to the university of Basil ; and as his 
memory was prodigious, and his application 
regular, he performed his academical tasks 
with great rapidity ; and all the time that 
he saved by this, was consecrated to the 
study of mathematics, which soon became 
his favourite science. The early progress 
he made in this study, added fresh ardour 
to his application, by which, too, he obtained 
a distinguished place in the attention and 
esteem of Professor John Bernoulli, who 
was then one of the chief mathematicians 
in Europe. 
In 1723, M. Euler took his degree as 
master of arts, and delivered on that occa- 
sion a Latin discourse, in which he drew a 
comparison between the philosophy of 
Newton and the Cartesian system, which 
was received with the greatest applause. 
At his father’s desire he next applied him- 
self to the study of theology and the orien- 
tal languages; and though these studies 
were foreign to his predominant propensity, 
bis success was considerable even in this 
line. However, with his father’s consent, 
he afterwards returned to mathematics as 
his principal object. In continuing to avail 
himself of the councils and instructions of 
M. Bernoulli, he contracted an intimate 
friendship with his two sons, Nicholas and 
Daniel ; and it was chiefly in consequence of 
these connections that he afterwards be- 
came the principal ornament of the philo- 
sophical world. 
The project of erecting an academy at 
Petersburgh, which had been formed by 
Peter the Qreat, was executed by Catha- 
rine the First ; and the two young Ber- 
noulli being invited to Petersburgh in 
1725, promised Euler, who was desirous 
of following them, that they would use their 
endeavours to procure for him an advanta- 
geous settlement in that city. In the mean- 
time, by their advice, he made close appli- 
cation to the study of philosophy, to which 
he made happy applications of his mathe- 
matical knowledge, in a dissertation on the 
nature and propagation of sound, and an 
answer to a prize question concerning the 
masting of ships ; to which the Academy of 
Sciences adjudged the accessit, or second 
rank in the year 1727. From this latter 
discourse, and other circumstances, it ap- 
pears, that Euler had very early embarked 
in the curious and useful study of naval ar- 
chitecture, which he afterwards enriched 
with so many valuable discoveries. The 
study of mathematics and philosophy, how- 
ever, did not solely engage his attention, as 
he, in the mean time, attended the medical 
and botanical lectures of the professors at 
Basil. 
Euler’s merit would have given him an 
easy admission to honourable preferment, 
either in the magistracy or university of his 
native city, if both civil and academical 
honours had not been there distributed by 
lot. The lot being against him in a certain 
promotion, he left his country, set out for 
Petersburgh, and was made joint professor 
with his countrymen, Hermann and Daniel 
Bernoulli, in the university of that city. 
At his first setting out in his new career, 
he enriched the academical collection with 
many memoirs, which excited a noble emu- 
lation between him and the Bernoullis’ ; an 
emulation that always continued, without 
either degenerating into a selfish jealousy, 
or producing the least alteration in their 
friendship. It was at this time that he car- 
ried to new degrees of perfection the inte- 
gral calculus, invented the calculation by 
sines, reduced analytical operations to a 
greater simplicity, and thus was enabled to 
throw new light on all the parts of mathe- 
matical science. 
In 1730, M. Euler was promoted to the 
professorship of natural philosophy ; and in 
1733 he succeeded his friend D. Bernoulli 
in the mathematical chair. In 1735, a pro- 
blem was proposed by the Academy, which 
required expedition, and for the calculation 
of which some eminent mathematicians had 
demanded the space of some months. The 
problem was undertaken by Euler, who 
completed the calculation in three days, to 
the astonishment 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 use of his 
right eye, which afterwards brought on a 
total blindness. 
The Academy of Sciences at Paris, which 
jn 1738 had adjudged the prize to his me- 
moir concerning the Nature and Properties 
of Fire, proposed for the year 1740, the' 
important subject of the tides of the sea ; 
a problem whose solution comprehended 
