# Euler, Leonard

, a very eminent mathematician, was born at Basil, on the 14th of April, 1707: he was the son of Paul Euler and of Margaret Brucker (of a family illustrious in literature), and spent the first year of his life at the village of Richen, of which place his father was protestant minister. Being intended for the church, his father, who had himself studied under James Bernoulli!, taught him mathematics, as a ground-work of his other studies, or at least a noble and useful secondary occupation. But Euler, assisted and perhaps secretly encouraged by John Bernoulli, who easily discovered that he would be the greatest scholar he should ever educate, soon declared his intention of devoting his life to that pursuit. This intention the wise father did not thwart, but the son did not so blindly adhere to it, as not to connect with it a more than common improvement in every other kind of useful learn-, ing, insomuch that in his latter days men often wondered how with such a superiority in one branch, he could have been so near to eminence in all the rest. Upon the foundation of the academy of sciences at St. Petersburgh, in, 1723, by Catherine I. the two younger Bernouillis, NichoJas and Daniel, had gone thither, promising, when they set out, to endeavour to procure Euler a place in it: they accordingly wrote to him soon after, to apply his mathetics to physiology, which he did, and studied under the best naturalists at Basil, but at the same time, i. e. in 1727, published a dissertation on the nature and propagation of sound; and an answer to the question on the masting of ships, which the academy of sciences at Paris judged worthy of the accessit. Soon after this, he was called to St. Petersburgh, and declared adjutant to the mathematical class in the academy, a class, in which, from the circumstances of the times (Newton, Leibnitz, and so many other | eminent scholars being just dead), no easy laurels were to be gathered. Nature, however, who had organized so many mathematical heads at one time, was not yet tired of her miracles and she added Euler to the number. He indeed was much wanted the science of the calculus integralis, hardly come out of the hands of its creators, was still too near the stage of its infancy not to want to be made more perfect. Mechanics, dynamics, and especially hydrodynamics, and the science of the motion of the heavenly bodies, felt the imperfection. The application of the differential calculus, to them, had been sufficiently successful; but there were difficulties whenever it was necessary to go from the fluxional quantity to the fluent. With regard to the nature and properties of numbers, the writings of Fermat (who had been so successful in them), and together with these all his profound researches, were lost. Engineering and navigation were reduced to vague principles, and were founded on a heap of often contradictory observations, rather than a regular theory. The irregularities in the motions of the celestial bodies, and especially the complication of forces whitfh influence that of the moon, were still the disgrace of geometers. Practical astronomy had jet to wrestle with the imperfection of telescopes, insomuch, that it could hardly be said that any rule for making them existed. Euler turned his eyes to all these objects he perfected the calculus integralis he was the inventor of a new kind of calculus, that of sines he simplified analytical operations and, aided by these powerful help-mates, and the astonishing facility with which he knew how to subdue expressions the most intractable, he threw a new light on all the branches of the mathematics. But at Catherine’s death the academy was threatened with extinction, by men who knew not the connection which arts and sciences have with the happiness of a people. Euler was offered and accepted a lieutenancy on board one of the empress’s ships, with the promise of speedy advancement. Luckily things changed, and the learned captain again found his own element, and was named Professor of Natural Philosophy in 1733, in the room of his friend John Bernouilli. The number of memoirs which Euler produced, prior to this period, is astonishing,*

On the theory of the more remarkable curves—the nature of num bers and series—the calculus integralis—the movement of the celestial bo-

|dies the attraction of spberoidicoelliptical bodies the famous solution of the isoperimetrical problem—and an infinity of other objects, the hundredth part of which would have made an ordinary man illustrious.

*genera*and the modes of music is here cleared up with all the clearness and precision which mark the works of Euler. Dr. Burney remarks, that upon the whole, Euler seems not to have invented much in this treatise; and to have done little more than arrange and methodize former discoveries in a scientific and geometric manner. He may, indeed, not | have known what antecedent writers had discovered before; and though not the first, yet to have imagined himself an inventor. In 1740, his genius was again called forth by the academy of Paris (who, in 1738, had adjudged the prize to his paper on the nature and properties of fire) to discuss the nature of the tides, an important question, which demanded a prodigious extent of calculations, aud an entire new system of the world. This prize Euler did not gain alone; but he divided it with Maclaurin and D. Bernouilli, forming with them a triumvirate of candidates, which the realms of science had not often beheld. The agreement of the several memoirs of Euler and Bernouilli, on this occasion, is very remarkable. Though the one philosopher had set out on the principle of admitting vortices, which the other rejected, they not only arrived at the same end of the journey, but met several times on the road; for instance, in the determination of the tides under the frozen zone. Philosophy, indeed, led these two great men by different paths; Bernouilli, who had more patience than his friend, sanctioned every physical hypothesis he was obliged to make, by painful and laborious experiment. These Euler’s impetuous genius scorned; and, though his natural sagacity did not always supply the loss, he made amends by his superiority in analysis, as often as there was any occasion to simplify expressions, to adapt them to practice, and to recognize, by final formulae, the nature of the result. In 1741, Euler received some very advantageous propositions from Frederic the Second (who had just ascended the Prussian throne), to go and assist him in forming an academy of sciences, out of the wrecks of the Royal Society founded by Leibnitz. With these offers the tottering state of the St. Petersburgh academy, under the regency, made it necessary for the philosopher to comply. He accordingly illumined the last volume of the “Melanges de Berlin,” with five essays, which are, perhaps, the best things in it, and contributed largely to the academical volumes, the first of which was published in 1744. No part of his multifarious labours is, perhaps, a more wonderful proof of the extensiveness and facility of his genius, than what he executed at Berlin, at a time when he contrived also that the Petersburgh acts should not suffer from the loss of him. In 1744, Euler published a complete treatise of isoperimetrical curves. The same year beheld the theory of the motions of tb.e planets and | comets; the well-known theory of magnetism, which gained the Paris prize; and the much-amended translation of Robins’ s “Treatise on Gunnery.” In 1746, his “Theory of Light and Colours” overturned Newton’s “System of Emanations;” as did another work, at that time triumphant, the “Monads of Wolfe and Leibnitz.” Navigation was now the only branch of useful knowledge, for which the labours of analysis and geometry had done nothing. The hydrographical part alone, and that which relates to the direction of the course of ships, had been treated by geometricians conjointly with nautical astronomy. Euler was the first who conceived and executed the project of making this a complete science. A memoir on the motion of floating bodies, communicated to the academy of St. Petersburgh, in 1735, by M. le Croix, first gave him this idea. His researches on the equilibrium of ships furnished him with the means of bringing the stability to a determined measure. His success encouraged him to go on, and produced the great work which the academy published in 1749, in which we find, in systematic order, the most sublime notions on the theory of the equilibrium and mo. tion of floating bodies, and on the resistance of fluids. This was followed by a second part, which left nothing to be desired on the subject, except the turning it into a language easy of access, and divesting it of the calculations which prevented its being of general use. Accordingly*

See our life of Dollond, (vol. XII.)

*l*. from the English parliament, for the theorems, by the assistance of which Meyer made his lunar tables .†

It was with great difficulty that this extraordinary man, in 1766, obtained permission from the king of Prussia to return to Petersburgh, where he wished to pass the remainder of his days. Soon after his return, which was graciously rewarded by the munificence of Catherine II. he was seized with a violent disorder, which ended in the total loss of his sight. A cata ract, formed in his left eye, which had been essentially damaged by the loss of the other eye, and a too close application to study, deprivcd him entirely of the use of that organ. It was in this distressing situation that he dictated to his servant, a taylor’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 unhappy circmnstances in which they were composed, have equally excited wonder and applause. This work, though purely elementary, plainly discovers the proofs of an inventive genius and it is per haps here alone that we meet with a complete theory of the analysis of Diophantus. Some time after this he underwent the operation of couching, which partly restored his sight, but by some neglect or misconduct after the operation, he again became blind.

This reminds us of the illustrious Boerhaave, who kept feeling his pulse the morning of his death, to see wheher it would beat till a book he was eager to see was published, read the book, and said, “Now the business of life is over.”

“Another proof of the strength of his memory and imagination deserves to be related. Being engaged in teaching his grandchildren geometry and algebra, and obliged, in consequence, to initiate them in the extraction of roots, he was obliged to give them numbers, which should be the powers of other numbers; these he used to make in his head; and one night, not being able to sleep, he calculated the six first powers of all the numbers above twenty, and to our great astonishment, repeated them to us several days after.”

“Euler was twice married, and had thirteen children, four of whom only have survived him. The eldest son was | for some time his father’s assistant and successor the second, physician to the empress and the third a lieutenantcolonel of artillery, and director of the armory at Sesterbeck. The daughter married major Bell. From these children he had thirty-eight grand-children, twenty-six of whom are still alive. Never have I been present at a more touching sight than that exhibited by this venerable old man, surrounded, like a patriarch, by his numerous offspring, all attentive to make his old age agreeable, and enliven the remainder of his days, by every species of kind solicitude and care.”

The catalogue of his works in the printed edition makes
50 pages, 14 of which contain the ms works. The
printed books consist of works published separately, and
others to be found in the several Petcrsburgh acts, in 38
volumes, (from 6 to 10 papers in each volume) in the
Paris acts in 26 volumes of the Berlin acts (about 5 papers to each volume) in the “Acta Eruditorum,” in
2 volumes; in the “Miscellanea Taurinensia” in vol.
IX. of the society of Ulyssingue in the “Ephemerides
de Berlin;” and in the “Memoires de la Societe” CEconomique for 1766.“His” Letters on Physics and Philoophy" were translated by the late Dr. Henry Hunter, and
published in 1802, 2 vols. 8vo. ^{1}

^{1}

Principally from his Eloge by Fuss, printed at Petersburg and Berlin, 1783, 4to.—Hutton’s Math. Dictionary.