The young Ampere, however, soon resumed his Latin lessons, to enable him to master the works of Euler and Bernouilli.
Bonnet, Euler, Haller, Schmid and others " suppose miracles to be already implanted in nature.
In 1740 Maclaurin divided with Leonhard Euler and Daniel Bernoulli the prize offered by the French Academy of Sciences for an essay on tides.
Euler (1 777).
The number of partitions of a biweight pq into exactly i biparts is given (after Euler) by the coefficient of a, z xPy Q in the expansion of the generating function 1 - ax.
At the age of nineteen he communicated to Leonhard Euler his idea of a general method of dealing with "isoperimetrical" problems, known later as the Calculus of Variations.
He is thus justly regarded as the inventor of the "method of variations" - a name supplied by Euler in 1766.
The post of director of the mathematical department of the Berlin Academy (of which he had been a member since 1759) becoming vacant by the removal of Euler to St Petersburg, the latter and d'Alembert united to recommend Lagrange as his successor.
This is especially the case between Lagrange and Euler on the one side, and between Lagrange and Laplace on the other.
The calculus of variations lay undeveloped in Euler's mode of treating isoperimetrical problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the analytical investigation of the planetary movements.
His development of the equation x m +- px = q in an infinite series was extended by Leonhard Euler, and particularly by Joseph Louis Lagrange.
Euler and J.
In this they were completely successful, for they obtained general solutions for the equations ax by = c, xy = ax+by+c (since rediscovered by Leonhard Euler) and cy 2 = ax e + b.
Diophantine problems were revived by Gaspar Bachet, Pierre Fermat and Euler; the modern theory of numbers was founded by Fermat and developed by Euler, Lagrange and others; and the theory of probability was attacked by Blaise Pascal and Fermat, their work being subsequently expanded by James Bernoulli, Abraham de Moivre, Pierre Simon Laplace and others.
This calculus was first applied to the motion of water by d'Alembert, and enabled both him and Euler to represent the theory of fluids in formulae restricted by no particular hypothesis.
He was as keen in his resentments as he was ardent in his friendships; fondly attached to his family, he yet disliked a deserving son; he gave full praise to Leibnitz and Leonhard Euler, yet was blind to the excellence of Sir Isaac Newton.
With a success equalled only by Leonhard Euler, Daniel Bernoulli gained or shared no less than ten prizes of the Academy of Sciences of Paris.
The first, for a memoir on the construction of a clepsydra for measuring time exactly at sea, he gained at the age of twenty-four; the second, for one on the physical cause of the inclination of the planetary orbits, he divided with his father; and the third, for a communication on the tides, he shared with Euler, Colin Maclaurin and another competitor.
He was tragically drowned while bathing in the Neva in July 1789, a few months after his marriage with a daughter of Albert Euler, son of Leonhard Euler.
His memoir (1775) on the rotatory motion of a body contains (as the author was aware) conclusions at variance with those arrived at by Jean le Rond, d'Alembert and Leonhard Euler in their researches on the same subject.
Their generalization is given by the Euler-Maclaurin formula = I, = 0, = 0, = 0 .
The Euler-Maclaurin formula (§ 75) assumes that the bounding values of u', u"',..
Tartaglia, Nova Scientia (1537) Galileo (1638); Robins, New Principles of Gunnery (1743); Euler (trans.
In 1764 Leonhard Euler employed the functions of both zero and integral orders in an analysis into the vibrations of a stretched membrane; an investigation which has been considerably developed by Lord Rayleigh, who has also shown (1878) that Bessel's functions are particular cases of Laplace's functions.
As far as the circlesquaring functions are concerned, it would seem that Gregory was the first (in 1670) to make known the series for the arc in terms of the tangent, the series for the tangent in terms of the arc, and the secant in terms of the arc; and in 1669 Newton showed to Isaac Barrow a little treatise in manuscript containing the series for the arc in terms of the sine, for the sine in terms of the arc, and for the cosine in terms of the arc. These discoveries 1 See Euler, ” Annotationes in locum quendam Cartesii," in Nov.
Leonhard Euler took up the subject several times during his life, effecting mainly improvements in the theory of the various series.
Gregory's series and the identities 7 r /4 =5 tan1 + + 2 tan-',A (Euler, 1779), 7r/4 = tani ++2 tan-' s (Hutton, 1776), neither of which was nearly so advantageous as several found by Charles Hutton, calculated 7r correct to 136 places."
Euler, who added to it a critical commentary of his own.
Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him.
Leonhard Euler in 1747 had suggested that achromatism might be obtained by the combination of glass and water lenses.
John Dollond, to whom the Copley medal of the Royal Society had been the first inventor of the achromatic telescope; but it was ruled by Lord Mansfield that" it was not the person who locked his invention in his scrutoire that ought to profit for such invention, but he who brought it forth for the benefit of mankind."3 In 1747 Leonhard Euler communicated to the Berlin Academy of Sciences a memoir in which he endeavoured to prove the possibility of correcting both the chromatic and.
They were accordingly taken up anew by a band of continental inquirers, primarily by three men of untiring energy and vivid genius, Leonhard Euler, Alexis Clairault, and Jean le Rond d'Alembert.
Euler devised in 1753 a new method, that of the " variation of parameters," for their investigation, and applied it to unravel some of the earth's irregularities in a memoir crowned by the French Academy in 1756; while in 1757, Clairault estimated the masses of the moon and Venus by their respective disturbing effects upon terrestrial movements.
Euler (Ber., 97, 30, 1989) by distilling the addition compound of methyl iodide and 2 3 5-trimethylpyrollidine with caustic potash.
The inherent difficulties of this task were immensely enhanced by the fact that Euler was virtually blind, and had to carry all the elaborate computations it involved in his memory.
The works which Euler published separately are: Dissertatio physica de sono (Basel, 1727, in 4to); Mechanica, sive motus scientia analytice exposita (St Petersburg, 1736, in 2 vols.
See Rudio, Leonhard Euler (Basel, 1884); M.
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.
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.
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.
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.
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.