# Euler Sentence Examples

**Euler**(1 777).- 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. - 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. **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. - In 1754
**Euler**communicated to the Berlin Academy a further memoir, in - which, starting from the hypothesis that light consists of vibrations excited in an elastic fluid by luminous bodies, and that the difference of colour of light is due to the greater or less frequency of these vibrations in a given time, he deduced his previous results. - Argand had been led to deny that such an expression as i 2 could be expressed in the form A+Bi, - although, as is well known,
**Euler**showed that one of its values is a real quantity, the exponential function of --7112. - Hamilton at once found that the Law of the Norms holds, - not being aware that
**Euler**had long before decomposed the product of two sums of four squares into this very set of four squares. - It was shown by
**Euler**(1776) that any displacement in which one point 0 of the body is fixed is equivalent to a pure, rotation about some axis through 0. - The question was first discussed by
**Euler**(1750); the geometrical representation to be given is due to Poinsot (1851). - These equations are due to
**Euler**, with whom the conception of moving axes, and the application to the problem of free rotation, originated. - It will be suftlcient to take the case of motion about a fixed point 0; the angular co-ordinates 0, ~, i,l of
**Euler**may then be used for the purpose. - James Gregory and Leonhard
**Euler**arrived at the correct view from a false conception of the achromatism of the eye; this was determined by Chester More Hall in 1728, Klingenstierna in 1754 and by Dollond in 1757, who constructed the celebrated achromatic telescopes. - Similarly the continued fraction given by
**Euler**as equivalent to 1(e - 1) (e being the base of Napierian logarithms), viz. - Nicol Saunderson (1682-1739),
**Euler**and Lambert helped in developing the theory, and much was done by Lagrange in his additions to the French edition of**Euler's**Algebra (1795). - Leonhard
**Euler**(Acta Petrop. 1784) showed that the same hypocycloid can be generated by circles having radii of; (a+b) rolling on a circle of radius a; and also that the hypocycloid formed when the radius of the rolling circle is greater than that of the fixed circle is the same as the epicycloid formed by the rolling of a circle whose radius is the difference of the original radii. - Competent judges have compared him to Leonhard
**Euler**for his range, analytical power and introduction of new and fertile theories. - The problem set was "to perfect in one important point the theory of the movement of a solid body round an immovable point," and her solution added a result of the highest interest to those transmitted to us by Leonhard
**Euler**and J. **Euler**and G.- 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. - 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. - 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. - 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. - In 1755
**Euler**had been elected a foreign member of the Academy of Sciences at Paris, and some time afterwards the academical prize was adjudged to three of his memoirs Concerning the Inequalities in the Motions of the Planets. **Euler**, assisted by his eldest son Johann Albert, was a competitor for these prizes, and obtained both.- 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. **Euler**(Ber., 97, 30, 1989) by distilling the addition compound of methyl iodide and 2 3 5-trimethylpyrollidine with caustic potash.- 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.