Another task to which he set himself immediately after his return to St Petersburg was the preparation of his Lettres a une princesse d'Allemagne sur quelques sujets de physique et de philosophie (3 vols., 1768-1772). It was in these circumstances that he dictated to his servant, a tailor's apprentice, who was absolutely devoid of mathematical knowledge, his Anleitung zur Algebra (1770), a work which, though purely elementary, displays the mathematical genius of its author, and is still reckoned one of the best works of its class. Soon after his return to St Petersburg a cataract formed in his left eye, which ultimately deprived him almost entirely of sight. In 1766 Euler with difficulty obtained permission from the king of Prussia to return to St Petersburg, to which he had been originally invited by Catherine II. On its being ascertained that the farm belonged to Euler, the general immediately ordered compensation to be paid, and the empress Elizabeth sent an additional sum of four thousand crowns. The respect in which he was held by the Russians was strikingly shown in 1760, when a farm he occupied near Charlottenburg happened to be pillaged by the invading Russian army.
At the same time he continued his philosophical contributions to the Academy of St Petersburg, which granted him a pension in 1742. He enriched the last volume of the Mélanges or Miscellanies of Berlin with five memoirs, and these were followed, with an astonishing rapidity, by a great number of important researches, which are scattered throughout the annual memoirs of the Prussian Academy. In 1741 Euler accepted the invitation of Frederick the Great to Berlin, where he was made a member of the Academy of Sciences and professor of mathematics. The Academy of Sciences at Paris in 1738 adjudged the prize to his memoir on the nature and properties of fire, and in 1740 his treatise on the tides shared the prize with those of Colin Maclaurin and Daniel Bernoulli - a higher honour than if he had carried it away from inferior rivals. In 1735 a problem proposed by the academy, for the solution of which several eminent mathematicians had demanded the space of some months, was solvecdby Euler in three days,but the effort threw him into a fever which endangered his life and deprived him of the use of his right eye. It was at this time that he carried the integral calculus to a higher degree of perfection, invented the calculation of sines, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics. At the commencement of his new career he enriched the academical collection with many memoirs, which excited a noble emulation between him and the Bernoullis, though this did not in any way affect their friendship. In 1730 he became professor of physics, and in 1733 he succeeded Daniel Bernoulli in the chair of mathematics.
In 1727, on the invitation of Catherine I., Euler took up his residence in St Petersburg, and was made an associate of the Academy of Sciences. While he was engaged in physiological researches, he composed a dissertation on the nature and propagation of sound, and an answer to a prize question concerning the masting of ships, to which the French Academy of Sciences adjudged the second rank in the year 5727.
At the same time, by the advice of the younger Bernoullis, who had removed to St Petersburg in 1725, he applied himself to the study of physiology, to which he made a happy application of his mathematical knowledge and he also attended the medical lectures at Basel.
Having taken his degree as master of arts in 1723, Euler applied himself, at his father's desire, to the study of theology and the Oriental languages with the view of entering the church, but, with his father's consent, he soon returned to geometry as his principal pursuit. His mathematical genius gained for him a high place in the 'esteem of Jean Bernoulli, who was at that time one of the first mathematicians in Europe, as well as of his sons Daniel and Nicolas Bernoulli. After receiving preliminary instructions in mathematics from his father, he was sent to the university of Basel, where geometry soon became his favourite study. LEONHARD EULER (1707-1783), Swiss mathematician, was born at Basel on the 15th of April 5707, his father Paul Euler, who had considerable attainments as a mathematician, being Calvinistic pastor of the neighbouring village of Riechen.
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