Leonard Euler^[7] was born at Basle, April 15, 1707. His father was the clergyman of Reichen, near Basle, and had himself been a pupil of James Bernouilli. He intended his son for his own profession, and after having been himself his first instructor in mathematics, sent him to the university of Basle. John Bernouilli was at this time Professor, and his sons, Nicolas and Daniel, two more of the eight Bernouillis known to the history of science, were under him. With the sons Euler contracted an intimate friendship; and obtained such a degree of favour even with their father, that the latter gave him a private lesson weekly, upon points more advanced than those treated in the public course. This was a strong mark of favour from John Bernouilli, who was of an unamiable disposition, jealous of his brother, of his son, and finally of almost every one who displayed a superior talent for mathematics. Euler at first turned his attention to theology, in accordance with the wishes of his father, but this was not of long continuance. At the age of nineteen, besides obtaining a degree from his University, he had merited the notice of the Academy of Sciences for a memoir on some points of naval architecture. In the same year, he was an unsuccessful candidate for a Professorship at Basle, an unlucky event, M. Condorcet observes, for his country, inasmuch as a few days afterwards he left it for Russia, and never returned. His friends the Bernouillis (Nicolas and Daniel) had, two years before, accepted invitations from the Empress Catherine; and he followed them in hopes of obtaining employment and subsistence at St. Petersburgh. But by the time he arrived, both Nicolas Bernouilli and the Empress were dead, the Academy of St. Petersburgh was left without a patron, and Euler, a nameless stranger, could not for a long time obtain any settled avocation. How he maintained himself we are not told; but he was upon the point of entering the Russian service as a sailor, when his prospects brightened, and he obtained the place of Professor of Natural Philosophy. In 1733 he succeeded Daniel Bernouilli, who returned to his own country, as Professor of Mathematics. In the same year he married a young lady named Gsell, the daughter of an artist of Basle, who had emigrated to Russia in the reign of Peter the Great.

The despotism of the Russian government could not please the republican born; but circumstances obliged him to endure it till 1741, when he quitted Petersburgh for Berlin on the invitation of Frederic the Great. To the necessity for continual reserve and government of the tongue which was necessary in the Russian capital has been attributed his love of silence and study, which exceeded all that is related of any of his contemporaries. The mother of Frederic, who was as much attached to the conversation of distinguished men as the King himself, could never obtain more than a few syllables from Euler at any one time. On her asking the reason why he would not speak, he is said to have replied, “Madam, I have lived in a country where men who speak are hanged.”

Euler remained at Berlin till 1766. In 1761 he lost his mother, who had resided with him for eleven years. During this time he was not considered as having abandoned his Russian engagements, and a part of his salary was regularly paid. When the Russians invaded Brandenburg in 1760, a farm belonging to him was destroyed, but he was immediately more than reimbursed, by the order of the Empress Elizabeth. On the invitation of that princess he consented to return to Petersburgh in 1766. He had for some years suffered from weakness in the eyes; and not long after his return to Russia he became so nearly blind, that he could distinguish nothing except very large letters marked with chalk on a slate. In this state he continued for the remainder of his life; and by constant exercise he acquired a power of recollection, whether of mathematical formulÆ or figures, which would be totally incredible, if it were not supported by strong evidence. He formed in his head, and retained in his memory, a table of the first six powers of all numbers up to 100, containing about 3000 figures. Two of his pupils had summed seventeen terms of a converging series, and differed by a unit in the fiftieth decimal of the result; Euler decided between them correctly by a mental calculation^[8]. His chief amusement during his deprivation was the formation of artificial magnets, and the instruction of one of his grandchildren in mathematics. His studies were in no degree relaxed by it. In 1771 Euler’s house was destroyed by fire, together with a considerable part of the city. He was himself saved by a fellow-countryman named Grimm, and his manuscripts were also rescued. In 1776 he married the aunt of his first wife. No other event worthy of special notice occurred before his death, which took place suddenly, September 7, 1783. He had been employed in calculating the laws of the ascent of balloons, which were then newly introduced; he afterwards dined with his family and M. Lexell, his pupil, conversed with them on the newly-discovered planet of Herschel, and was amusing himself with one of his grandchildren; suddenly the pipe which he held in his hand dropped on the ground, and it was found that^[9] “life and calculation were at an end.” He had thirteen children, of whom only three survived him; one of them, John Albert Euler, was known as a mathematician.

Of the scientific character of Euler it is impossible to speak in detail, since even the resumÉ of M. Condorcet, which is much longer than any account we can here insert, is meagre in the extreme; and we imagine that the reader would form no idea whatsoever of the man we are describing, from any brief enumeration of discoveries for which we should be able to allow room. In more than fifty years of incessant thought, Euler wrote thirty separate works and more than seven hundred memoirs: which could not altogether be contained in forty large quarto volumes. These writings embrace every existing branch of mathematics, and almost every conceivable application of them, to such an extent, that there is no one among mathematicians, past or present, who can be placed near to Euler in the enormous variety of the subjects which he treated. And the contents of these volumes are without exception the original fruit of his own brain; seeing that he left no subject as he found it. He is not a diffuse writer, except in giving a large number of examples, and this renders him in some respects the most instructive of all writers. His works are full of the most original thoughts developed in the most original manner; so that they have been a mine of information for his successors, which is even now far from being exhausted. Let a student be employed upon any subject connected with mathematics, however remotely, and he has discovered but little if he has not found out that Euler was there before him.

Of all mathematical writers, Euler is one of the most simple, and this in a manner which renders his writings not by any means a sound preparation for future investigations. Difficulties seem to have disappeared in the progress, or never to have been encountered; and the student is rather made to feel that Euler could take him anywhere, than furnished with the means of providing for himself, when his guide shall have left him. Hence the writings of others, in every way inferior to Euler in elegance and simplicity, are to be preferred, and have been preferred, for the formation of mathematical power.

Euler is to be measured by the assistance which he gave to his immediate successors, and here it is well known that he paved the way for the research of others in a more effectual manner than any of his contemporaries. The incessant repetition of his name in later authors is sufficient authority for this assertion. His writings are the first in which the modern analysis is uniformly the instrument of investigation. His predecessors, James and John Bernouilli, had perhaps the largest share in bringing the infinitesimal analysis of Newton and Leibnitz to the state of power required for extensive application. To Euler (besides important extensions) belongs the distinct merit of showing how to apply it to physical investigations, in conjunction with D’Alembert, who ran a splendid and contemporary career of a similar character in this respect. But though it would be perhaps admitted that there are individual results of the latter which exceed anything done by the former, in generality of application, there is no comparison whatsoever between the extent of the labours of the two.

Euler was a man of a simple, reserved, and benevolent mind; with a strong sense of devotion, and a decided religious habit, according to the Calvinism of the Established Church of his country. At the court of Frederic, he himself conducted the devotions of his family every evening; a practice which then and there implied much moral courage, and insensibility to ridicule. But he possessed humour, for when he was asked to calculate the horoscope of one of the Russian princes, he quietly suggested that it was the official duty of the astronomer, and imposed the duty upon a colleague, who doubtless did not feel very much flattered by the application.

There are few men whom the usual biographical formulÆ as to moral character and habits would better fit than Euler, according to every account which has appeared of him. But such praises are no distinction; and it will be more to the purpose to state that the only occasion in which he was betrayed into printing a word which his eulogists have regretted, was in the dispute between Maupertuis and himself against others on the principle known by the name of least action, one of the warmest and most angry discussions which ever took place.

Perhaps it is to the quiet abstraction of his life that he owed the perpetuity of his tenure of investigation. Many eminent mathematical discoverers have run the brilliant part of their career while comparatively young. Euler “ceased to calculate and to live” at once. But it may be that this was a part of his natural constitution, and a distinct feature of his mind. The nature of his writings rather confirms the latter supposition. There is the same difference between them and those of others, that there is between conversation and oratory. He seems to be moving in his natural element, where others are swimming for their lives.

The best works of Euler for a young mathematician to read, in order to get an idea of his style and methods, are the ‘Analysis Infinitorum,’ and the ‘Treatise on the Integral Calculus.’