Eulenspiegel

“ At a very early age, he displayed a remarkable talent for setting the other children by the ears, and this was his favourite amusement during life. His mother, who was now a widow, contemplating the extraordinary cunning of her child, which, as she thought, must necessarily ensure his advancement in the world, resolved that he should no longer remain idle, and put him apprentice to a baker; but his wicked and restless disposition defeated all the good intentions of his parent, and Eulenspiegel was obliged to leave his master in consequence of his mal-practices. ”

“ Till Eulenspiegel’s “merry pranks” have been made the subject of a well-known orchestral symphony by Richard Strauss. In France, it may be noted, the name has given rise to the words espiègle and espièglerie. ”

“ His Don Juan is delightful, too, but his Til Eulenspiegel (1895) which tells of the mischievous pranks of Til, is one of the finest examples of humor in music and probably will outlive many works of this modern period, his own as well as others. He wrote it in the form of a classical Rondo, because he could picture Til’s ever recurring deviltry and exploits in this form. Poor Strauss was reviled for this daringly written music, too, yet this tone poem is an amazing piece of work and was given gloriously as a ballet in New York City a few years ago by Diaghilev’s Russian Ballet. ”

“ They travelled on, eating and drinking, playing the fife, the bagpipe, and rommel-pot, and picking up by the way the goodwives they thought comely. In this way they begot foundling children, and beyond all, Ulenspiegel, whose gossip later bore a son which she named Eulenspiegelken, which signifies, in high German, little mirror and owl, and that because she did not understand clearly the meaning of her casual man’s name, and also perhaps in memory of the hour when [157] the child was made. ”

“ Several stories of Eulenspiegel were translated into Jew-German, and printed at Frankfort-on-the-Main, in octavo, according to Wolf, “Bibliotheca Hebraica,” vol. iii., p. 86, 1727. Another Hebrew-German edition appears referred to in the same work, vol. ii., p. 1255, 1721.
82. Flögel mentions, in 1789, an old Polish version (p. 473) : “Sowizrzal Krotochwilny Smiezny Poczatek, zywot y dokonanie iego.” Without year or place, in octavo.
83. “La Vie | joyeuse et récréative de Thiel Ulespiègle ... qu’il a eues. A Douai. Chez Deregnaucourt. Imprimeur-Libraire, rue Jacques, no. 45.” ”

“ This equation is in general of the 2nth order, and the 2n arbitrary constants which are contained in the complete /primitive-must be adjusted to satisfy the conditions that y, y′, y′′, . . . y (n−1) have given values at the limits of integration. If the function y is required also to satisfy the condition that another integral of the same form as the above, but containing a function φ instead of F, may have a prescribed value, Euler achieved his purpose by replacing F in the differential equation by F+λφ, and adjusting the constant λ so that the condition may be satisfied. ”

“ Euler was probably the most versatile as well as the most prolific of mathematicians of all time. There is scarcely any branch of modern analysis to which he was not a large contributor, and his extraordinary powers of devising and applying methods of calculation were employed by him with great success in each of the existing branches of applied mathematics; problems of abstract dynamics, of optics, of the motion of fluids, and of astronomy were all in turn subjected to his analysis and solved. ”

“ 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 1730 he became professor of physics, and in 1733 he succeeded Daniel Bernoulli in the chair of 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. ”

“ It is indeed by no means easy to distinguish and apportion the respective merits of the competitors. 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 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. ”

“ Euler had been under the necessity of resolving an integral into a sum of elements, recording the magnitude of the change produced in each element by a slight change in the unknown function, and thence forming an expression for the total change in the sum under consideration. Lagrange proposed to free the theory from this necessity. Euler had allowed such changes in the position of the curve, along which the integral, to be made a maximum or minimum, is taken, as can be produced by displacement parallel to the axis of ordinates. ”

“ Thus even in physics, the material is ever degraded before the spiritual. The astronomer, the geometer, rely on their irrefragable analysis, and disdain the results of observation. The sublime remark of Euler on his law of arches, "This will be found contrary to all experience, yet is true;" had already transferred nature into the mind, and left matter like an outcast corpse. ”

“ Leibniz and John Bernoulli once argued the question whether a negative number has a logarithm. Bernoulli claimed that since , we have and , and finally . Euler proved that has really an infinite number of logarithms, all of which are imaginary when is negative, and all except one when is positive. He then explained how might equal , and yet not equal .
The subject of infinite series received new life from him. To his researches on series we owe the creation of the theory of definite integrals by the development of the so-called Eulerian integrals. ”

“ The natural philosophers of the eighteenth century for the most part, like Maupertuis, accepted the corpuscular hypothesis; but the wave-theory was not without defenders. Franklin [8] declared for it; and the celebrated mathematician Leonhard Euler (b, 1707, d. 1783) ranged himself on the saune side. In a work entitled Nova Theoria Laucis et Colorum, published [9] while he was living under the patronage of Frederic the Great at Berlin, he insisted strongly on the resemblance between light and sound; "light is in the aether the same thing as sound in air." ”

“ But when the word has become general, the specialist is not very wise if he refuse to follow the mass, and perfectly foolish if he insist on others following him. There have been a few who demanded that Euler should be pronounced in the German fashion: [611] Euler has long been the property of the world at large; what does it matter how his own countrymen pronounce the letters? Shall we insist on the French pronouncing Newton without that final tong which they never fail to give him? ”

“ Has not the public a right to be surprised upon reading this Academic declaration: "the question affords no handle to geometry!" In matter of inventions, to attempt to dive into the future, is to prepare for one's self striking mistakes. One of the competitors, the great Euler, took these words in their literal sense; the reveries with which his memoir abounds, are not compensated in this instance by any of those brilliant discoveries in analysis, I had almost said of those sublime inspirations, which were so familiar to him. ”

“ Euler brought about an emancipation of the analytical calculus from geometry and established it as an independent science. Lagrange and Laplace scrupulously adhered to this separation. Building on the broad foundation laid for higher analysis and mechanics by Newton and Leibniz, Euler, with matchless fertility of mind, erected an elaborate structure. ”

“ For an investigation of this also the Academy of Sciences offered their prize. This led Euler to write a valuable essay disclosing a new method of computing perturbations, called the instantaneous ellipse with variable elements. The method was much developed by Lagrange.
But again it was Laplace who solved the problem of the inequalities of Jupiter and Saturn by the theory of gravitation, reducing the errors of the tables from 20’ down to 12”, thus abolishing the use of empirical corrections to the planetary tables, and providing another glorious triumph for the law of gravitation. ”

“ Euler, although farther advanced than Newton in a knowledge of the planetary pertubations, refused also to admit that the solar system was constituted so as to endure for ever.
Never did a greater philosophical question offer itself to the inquiries of mankind. Laplace attacked it with boldness, perseverance, and success. The profound and long-continued researches of the illustrious geometer established with complete evidence that the planetary ellipses are perpetually variable; that the extremities of their major axes make the tour of the heavens ”

“ No law of nature has been better established than that of universal gravitation, and we believe with the utmost confidence that any body capable of affecting the senses will attract other bodies, and fall to the earth if not prevented. Euler remarks238 that, although he had never made trial of the stones which compose the church of Magdeburg, yet he had not the least doubt that all of them were heavy, and would fall if unsupported. ”

“ Students of elementary geometry are not prepared to appreciate it, but teachers will be interested in the remarkable formula discovered by Euler (1707-1783) , the great Swiss mathematician, namely, 1 + eiπ = 0. In this relation are included the five most interesting quantities in mathematics,—zero, the unit, the base of the so-called Napierian logarithms, i = √ (-1) , and π. It was by means of this relation that the transcendence of [Pg 281] e was proved by the French mathematician Hermite, and the transcendence of π by the German Lindemann. ”

“ Were the character which superstition assumes in different ages an indication of man’s advance or retrogression, assuredly the nineteenth century would have no reason to plume itself, in comparison with the sixth B.C. A more earnest attempt to account for the more perfect consonance of the smaller ratios was made by the celebrated mathematician, Euler, and his explanation, if such it could be called, long silenced, if it did not satisfy, inquirers. Euler analyzes the cause of pleasure. We take delight in order; it is pleasant to us to observe means “co-operant to an end.” ”

“ The resolution of the questions concerning the motion of fluids was effected by means of Euler’s partial differential coefficients. 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.
One of the most successful labourers in the science of hydrodynamics at this period was Pierre Louis Georges Dubuat (1734–1809) . ”

“ Euler, assisted by his eldest son Johann Albert, was a competitor for these prizes, and obtained both. In the second memoir he reserved for further consideration several inequalities of the moon’s motion, which he could not determine in his first theory on account of the complicated calculations in which the method he then employed had engaged him. He afterwards reviewed his whole theory with the assistance of his son and W. L. Krafft and A. J. Lexell, and pursued his researches until he had constructed the new tables, which appeared in his Theoria motuum lunae (1772) . ”

“ Euler’s very clear statement brings out the pragmatic and anti-metaphysical attitude towards reality which is characteristic of scientific thought. From a failure to understand the significance of scientific hypotheses, the philosophers of the idealistic school felt it their duty to do away with absolute space. Had their attacks been limited to Newton’s theological expressions of opinion, there would have been no reason to criticise their arguments, for all theological opinions can be either defended or attacked. ”

“ Ulenspiegel ever young, and never to die, will run throughout the world without ever tying himself to any place. And he will be churl, noble, painter, sculptor, all together and at once. And through the world will journey in this wise, praising all things good and lovely, and flouting without stint all manner of folly. Claes is thy courage, noble Flanders folk, Soetkin thy valiant mother, Ulenspiegel is thy spirit; a darling sweet girl, Ulenspiegel’s mate and like him immortal, will be thy heart, and a fat paunch, Lamme Goedzak, will be thy stomach. ”

“ It has been said that an edition of Euler's complete works would fill 16,000 quarto pages. His mode of working was, first to concentrate his powers upon a special problem, then to solve separately all problems growing out of the first. No one excelled him in dexterity of accommodating methods to special problems. It is easy to see that mathematicians could not long continue in Euler's habit of writing and publishing. The material would soon grow to such enormous proportions as to be unmanageable. We are not surprised to see almost the opposite in Lagrange, his great successor. ”