162 books for « euler »Edit

‎MAUPERTUISIANA-- EDITION ORIGINALE -- BEL EXEMPLAIRE –16 PARTIES reliées en un volume‎

‎Hambourg, 1753, un volume in 8 relié en plein veau marbré, dos orné de fers dorés, tranches rouges (reliure de l'époque), (un coin légèrement émoussé), 1 feuillet non chiffré blanc, 1 feuillet non chiffré (titre : MAUPERTUISIANA - verso blanc), 2 feuillets non chiffrés (avertissement - Pièces conenues dans ce recueil, pp. 7 à 48pp., 26pp., 192pp., (1), 65pp., 56pp., 40pp., (1), 41pp., 74pp., 32pp., 16pp., 8pp., 8pp., 8pp., (4), 88pp., 16pp., 19pp.. – Soit 16 parties reliées en un volume‎

‎---- EDITION ORIGINALE ---- BEL EXEMPLAIRE ---- TRES RARE RECUEIL PUBLIE PAR KOENIG dans lequel sont réunies les diverses publications qui ont paru à l'époque concernant la célèbre polémique relative au principe de moindre action qui opposa Maupertuis à Koenig. Euler et Voltaire prirent part au débat et publièrent à cette occasion : "Dissertation sur le principe de moindre action avec l'examen des objections de Mr. Le Professeur Koenig faites contre ce principe" (Euler), "Diatribe du Docteur Akakia, médecin du pape..." (Voltaire). Ces deux écrits sont au nombre de ceux réunis dans ces deux volumes ---- Pour plus de détails au sujet de cette célèbre querelle voir M. Gueroult : "Dynamique et métaphysique leibnitizienne" et plus particulièrement la note "Sur le principe de moindre action chez Maupertuis", pp. 215/235 ---- "Maupertuis clearly was successful in attracting to Berlin scientific luminaries who greatly enhanced the luster of the new Academy. Euler, one of the greatest mathematicians of the day, was already there. Matters were going well, when the celebrated "affaire Koenig" erupted : Samuel Koenig, a protégé of Maupertuis... submitted a dissertation attacking the validity of the principle of least action and then - most strangely for a devoted adherent of Leibnitz - ascribed the discredited law to the latter, citing a letter from Leibnitz to Hermann... The controversy touched off by this work, resulted in perhaps the ugliest of all the famous scientific disputes. Its principal figures were Koenig, Maupertuis, Euler and Voltaire. Maupertuis demanded that the letter be produced. Koenig produced a copy but stated that the original was in the hands of a certain swiss named Henzi... After exhautive search no trace of the letter was found in Henzi's belongings. Maupertuis then demanded that the Academy take action against Koenig... When it became clear that the original could not be found, Euler published, with the approval of the Academy "Exposé concernant l'examen de la lettre de M. De Leibnitz", where, among other things, he declared the letter a fake. The conflict grew critical when, later in the same year, Voltaire published his Diatribe du Docteur Akakia, defending Koenig and making laughingstocks of both Maupertuis and Euler...". (DSB IV, VII et XI) ---- COLLATION ET PIECES CONTENUES DANS CE RECUEIL :. - 1 feuillet blanc non chiffré, 1 feuillet non chiffré : titre (MAUPERTUISIANA - verso blanc), 2 feuillets non chiffrés : avertissement, Pièces contenues dans ce recueil (pp. 1-6 non chiffrées). 1. Lettre de Mr. T*** à Mr. *** S tirée du magasin français ; Seconde lettre de Monsieur T*** à Mr s*** ; Réponse d'un Académicien de Berlin à un Académicien de Paris ; Extrait d'une lettre de Berlin du 15 Août 1752 ; Lettre que Mr. EULER a fait mettre dans la Gazette de Berlin en date du 2 Septembre 1752 ; Lettre de Mr. De VOLTAIRE à Mr. ROQUES, Conseiller ecclésiastique du sérénissime Landgrave de Hesse Hombourg, mise à la tête du supplément au siècle de Louis XIV. (pp. 7-48). 2. Jugement de l'Académie Royale des Sciences et Belles Lettres ; (2 feuillets non chiffrés : titre et avertissements - pp. 5-26 : Exposé). 3. KOENIG. Appel au Public du jugement de l'Académie Royale de Berlin sur un fragment de lettre de Mr. Leibnitz, cité par Mr. Koenig (exposé de l'origine de la controverse entre MM. De Maupertuis et Koenig - Remarques littérales sur le fragment dont Mr. De Maupertuis conteste l'authenticité - Examen des droits de l'Académie et de la conduite de ses membres). Appendice contenant les lettres écrites par Mess. De Maupertuis et Formey d'une part et Mr. Koenig de l'autre - Lettres de Mr. De Leibnitz) - Leyde, de l'Imp. d'Elie LUZAC, 1753, 6 pp. non chiffrées, pp. 7-192. 4. KOENIG. Défense de l'appel au public ou réponse aux lettres concernant le jugement de l'Académie de Berlin addressée à Mr. De Maupertuis par Mr. Koenig ; 2 pp. non chiffrées, pp. 1-63. 5. Lettres concernant le jugement de l'Académie ; 2pp. non chiffrées, pp. 3-56 contenant : lettre de Mr. Euler à Mr. Merian - Lettre de Mr. De Maupertuis à Mr. Euler - Lettre de Mr. Merian à Mr. Euler) . 6. Lettre de Mr. Le Marquis de L*** N** à Mme La Marquise A** G** sur le procès intenté par Mr. Moreau Maupertuis contre Mr. Koenig devant l'Académie Royale de Berlin - 2pp. non chiffrées, pp.3-40. 7. Réponse de l'Académicien de Paris à l'Académicien de Berlin ; 2pp. non chiffrées, pp. 1-41. 8. Eloges de trois philosophes ; 2pp. non chiffrées, pp. 1-74 comprenant : l'éloge de Monsieur JOURDAN, l'éloge du Sieur LA METTRIE, Lettre d'un Académicien de Berlin à un Académicien de Paris - Réponse de l'Académicien de Paris à l'Académicien de Berlin. 9. (VOLTAIRE) - Diatribe du Docteur Akakia, médecin du pape - Decret de l'inquisition et rapport des professeurs de Rome au sujet d'un prétendu Président - 4 pp. non chiffrées ; pp.5-32. 10. Extrait d'une lettre de Berlin du 12 Novembre 1752 - Lettre d'un savant à Mr. Le Marquis L** N** - 2pp. non chiffrées, pp.3-16. 11. Extrait d'une lettre d'un Académicien de Berlin à un membre de la Société Royale de Londres - 2 pp. non chiffrées, pp.3-8. 12. (VOLTAIRE). Séance mémorable - 2pp. non chiffrées, pp. 3-8. 13. L'art de bien argumenter en philosophie réduit en pratique par un vieux capitaine de cavallerie travesti en philosophe (lettre de Mr. De Maupertuis à Mr. De Voltaire - Réponse de Mr. De Voltaire à Mr. De Maupertuis) - 2pp. non chiffrées, pp. 3-8. 14. EULER. Dissertation sur le principe de moindre action avec l'examen des objections de Mr. Le Professeur Koenig faites contre ce principe par M. Euler, Directeur de l'Académie Royale des Sciences et Belles Lettres de Berlin. Traduction. Leyde, de l'imp. d'Elie LUZAC, 1753 comprenant : Dissertation sur le principe de la moindre action - examen de la dissertation de Mr. Le Professeur Koenig insérée dans les actes de Leipzig et Addition - 8pp. non chiffrées, pp. 1-88. 15. La berlue remarquable des deux philosophes les plus clair voyans de ce siècle par un étudiant en philosophie de l'Université de Wittemberg. Wittemberg, 1753, 2pp. non chiffrées pp. 3-16. 16. Traité de paix conclu entre Mr. Le Président De Maupertuis et Mr. Le Professeur Koenig. Berlin, 1753 - 2pp. non chiffrées, pp. 3-19**8753/ARB5 ‎

‎De Linea celerrimi descensus in Medio qvocunqve resistente. (On the curve of fastest descent in whatever resistent medium). (+) De progressionibus harmonicis observationes. (On harmonic progressions). (+) De infinitis curvis iusdem generis seu methodu...‎

‎(Petropoli, St. Petersburg, Typis Academiae, 1740). 4to. No wrappers. In: ""Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tomus VII ad Annum 1735, &..... Euler's papers: pp. 135-149, 150-161, 174-183 a. 184-200 and 2 engraved plates. Clean and fine.‎

‎First printing of 4 importent early papers by Euler. Enestroem: E42, E43, E44 a. E45.E42: This is Euler's second paper on the ""Brachistochrone problem"".E43. Here Euler introduces THE EULER CONSTANT. ""The Euler-Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.""E44: ""This is an extensive paper that develops a method for finding a family of curves arising from the constant of integration of dz = Pdx, which is treated as the second variable"" the rudiments of partial differentiation are presented, and there is an extensive survey of homogeneous functions centred around what is now know as Euler's Theorem for such functions. The origins of this paper would seem to be Proposition 15 of Vol. 2 of the Mechanica, relating to families of tautochronous curves, where an integration relying on Euler's Theorem is required."" (Ian Bruce).E45: Here Euler introduces the FUNCTION NOTATION f(x). ""This is an equally extensive paper that continues the development of methods for finding a family of curves arising from the constant of integration of dz = Pdx, which is treated as the second variable. A method is developed for finding the modular equation for the first order equation that is extended to cover a number of cases"" this in turn is extended to second and higher orders. The method involves finding suitable functions to integrate, starting from a part of the modular equation that is integrable, so that the whole equation is of this form. This paper is noteworthy in addition as it seems to be the first in which the function notation, albeit in a slightly different form from the modern meaning, is introduce. I have not been able to check all the equations at this stage.""(Ian Bruce).This section also contains DANIEL BERNOULLI: Demonstrationes theorematum svorum de oscillationibus corporum filo flexili connexorum et catenae verticaliter suspensae. Pp. 162-173.‎

‎Ce diable d'homme d'Euler (Leonhard Euler) , Tome III (3) de la série Arithmétique pour amateurs‎

‎Aléas Editeur - IREM Malicorne sur Sarthe, 72, Pays de la Loire, France 1994 Book condition, Etat : Bon broché, sous couverture imprimée éditeur blanche In-8 1 vol. - 426 pages‎

‎Quelques figures dans le texte en noir 1ere édition, 1994 Contents, Chapitres : Le théorème d'Euler-Fermat - Euler et les sommes de carrés - Sommes diverses et variées - Programmes pour calculatrices de poche, tables numériques, index des sujets abordés, bibliographie - Leonhard Euler, né le 15 avril 1707 à Bâle (Suisse) et mort à 76 ans le 7 septembre 1783 (18 septembre 1783 dans le calendrier grégorien) à Saint-Pétersbourg, est un mathématicien et physicien suisse, qui passa la plus grande partie de sa vie dans l'Empire russe et en Allemagne. Il était notamment membre de l'Académie royale des sciences de Prusse à Berlin. Euler fit d'importantes découvertes dans des domaines aussi variés que le calcul infinitésimal et la théorie des graphes. Il introduisit également une grande partie de la terminologie et de la notation des mathématiques modernes, en particulier pour l'analyse mathématique, comme la notion de fonction mathématique. Il est aussi connu pour ses travaux en mécanique, en dynamique des fluides, en optique et en astronomie. Euler est considéré comme un éminent mathématicien du xviiie siècle et l'un des plus grands et des plus prolifiques de tous les temps. Une déclaration attribuée à Pierre-Simon de Laplace exprime l'influence d'Euler sur les mathématiques : « Lisez Euler, lisez Euler, c'est notre maître à tous ». Il était un fervent chrétien, croyant en l'inerrance biblique, et s'opposa avec force aux athées éminents de son temps. couverture à peine jaunie, sinon bel exemplaire, intérieur frais et propre‎

‎Theoria motuum planetarum et cometarum. Continens methodum facilem ex aliquot observationibus orbitas cum planetarum tum cometarum determinandi. Una cum calculo, quo cometae, qui annis 1680 et 1681. Itemque ejus, qui nuper est visus, motus verus inves... - [EULER'S FIRST WORK IN ASTRONOMY]‎

‎Berlin: Ambrosii Haude, 1744. 4to. (246x199mm). Uncut in original marbled paper wrappers. Spine strip nearly worn away, but sewing still strong. A fine copy in its original and untouched state. Large engraved frontispiece showing comets orbiting the sun and planets, 187 pp. and 4 copper engraved folding plates. A4 (pp.7-8) canceled - catchword continues. Complete.‎

‎First edition of this important work containing the first complete mathematical treatment of the two-body problem, consisting in a planet and the Sun. Great minds such as Newton, Bernoulli and Poincaré all made important contributions to solving the exceedingly important mathematical Two-Body Problem, but Euler here gave the first full exposition of it. ""In 1744, Euler developed the first completely analytical method for determining a parabolic orbit through successive approximations in his Theory of the Motion of Planets and Comets. This was built upon Newton's earlier work, which [...] tended to be very complex and messy and incomplete. Today, the method of successive approximation known to every student of calculus is known by this man's name, Euler's Method."" (Summy, Analysis of the Two-Body and Restricted Three-Body Problem, p. 4).In the present work Euler gives ""the solutions of the main problems of theoretical astronomy dealing with the structure, nature, motion and action of comets and planets. With regard to the theory of perturbed motion of celestial bodies, Euler formulated the perturbation theory in general terms so that it can be used to solve the mathematical problem of dynamic models and particular problems of theoretical astronomy [...] He gave an extensive mathematical treatment of the problem of improving approximations of orbits within the framework of the two-body problem and taking perturbations into account. In his Theoria motuum planetarum et cometarum published in 1744, Euler gave a complete mathematical treatment of the two-body problem consisting of a planet and the Sun."" (Debnath, The Legacy of Leonhard Euler, p. 364).In 1687, in the 'Principia', Newton had solved the problem geometrically" In 1710 Johann Bernoulli had proved that the motion of one particle with respect to the other is described by a conic section In 1734 Daniel Bernoulli won a French Academy prize for his analytical treatment of the Two Body problem - but it was Euler, with his present work, who gave the fully complete mathematical treatment of the problem. Enestroem E66, Houzeau & Lancaster 11948The Barchas Collection 649Honeyman 1063‎

‎Sur l'atmosphere de la Lune prouvée par la derniere eclipse annulaire du Soleil. (On the atmosphere of the moon as proved by the last ringed eclipse of the sun) + Sur le frottement des corps solides. (On the friction of solid bodies) + Sur la diminu...‎

‎(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IV, pp. 103-121 + pp. 122-132 + pp. 133-148 and 6 engraved plates (on 5).‎

‎Three first editions by Euler. Euler's goal in the first paper is to show that certain phenomena that resulted from the eclipse of July 25, 1748 are evidence that the moon has an atmosphere that is almost 200 times less dense than that of the earth. (The phenomena Euler observed are optical effects of light passing close to a sharp edge, and not the refraction of a lunar atmosphere).The other papers on the physics of rigid bodies are groundbreaking as Euler here set forth what is known as ""Euler's dynamical equations of the motion of the mass-center of any solid"", and thus STATING FOR THE FIRST TIME THE LAW OF DRY FRICTION, mathematically. Euler explains his experiments with the inclined plane and discovers the DIFFERENCE BETWEEN KINETIC AND STATIC FRICTION.""Leonhard Euler occupied himself with the mathematical point of view of friction as well as the experimental. He introduced the differentiation between static frictional forces and kinetic frictional forces, and solved the problem of rope friction, probably the first contact problem to be analytically solved in history. (1750, the papers offered). He was the first to lay the foundations of the mathematically way of dealing with the law of dry friction and in this way promoted further development. We have to thank for the symbol as the coefficient of friction. Euler worked with the idea that friction originates from the interlocation, between small triangular irregularities.This understanding survived, in different variations,for a hundred years and is also used today as the ""Tomlinson Model"" in connection with friction on atomic scale.""(L. Popov ""History of the Contact Mechanics and the Physics of Function"", p.3).Eneström: E142, E143, E144. ‎

‎De numeris amicabilibus. - [EULER ON AMICABLE NUMBERS.]‎

‎Leipzig, Grosse & Gleditsch, 1747. 4to. Contemp. full vellum. Faint handwritten title on spine. Two small stamps to title page and pasted library label to pasted down front free end-paper. In: ""Nova Actorum Eruditorum Anno MDCCXLVII"". (4), 720, (27) pp. + 6 engraved plates. The entire volume offered. [Euler's paper:] Pp. 267-9.‎

‎First edition of Euler's paper in which he describes the work that European mathematicians have done on amicable numbers and shows how to find pairs of amicable numbers. He gives the first 30 pairs of which some, but not all, were found with his method.When Euler began his studies only three pairs of amicable numbers were known. In the present and early Euler-paper he mentions the technique that Descartes and Fermat had used ""and listing 30 amicable pairs, including the three already known, and including one ""pair"" that was not actually amicable. Nevertheless, in one paper, Euler lengthened the list of known amicable pairs by a factor of almost ten. Euler gives us almost no clue about how he found these numbers"" (Sandifer, Charles Edward. How Euler did it, 2007, p. 50). ""At this time in which mathematical Analysis has opened the way to many profound observations, those problems which have to do with the nature and properties of numbers seem almost completely neglected by Geometers, and the contemplation of numbers has been judged by many to add nothing to Analysis. Yet truly the investigation of the properties of numbers on many occasions requires more acuity than the subtlest questions of geometry, and for this reason it seems improper to neglect arithmetic questions for those. And indeed the greatest thinkers who are recognized as having made the most important contributions to Analysis have judged the affection of numbers as not unworthy, and in pursuing them have expended much work and study."" (Translation of the introduction of the present paper by Jordan Bell of Carleton University).Enestroem E100.Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume. ‎

‎Principes de la Trigonometrie Spherique tirés de la Méthode des plus Grands et plus Petits (Principles of spherical Trigonometry deduced from the Method of Maxima and Minima). (And same author:) Élémens de la Trigonometrie spheroidique tirés de la Met... - [EULER'S SPHERICAL GEOMETRY]‎

‎(Berlin, Haude et Spener, 1755). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IX, pp. 223-257 and 1 folded engraved plate (a tear to plate, no loss), and pp. 258-293 and 1 folded engraved plate.‎

‎Both papers first edition. The modern form of trigonometry as well of all trigonometry are due to Euler. Whereas trigonometry before Euler was concerned with trigonomic Lines, Euler's trigonometry deals with trigonomic Function. - ""In the first paper Euler constructs spherical trigonometry as the intrinsic geometry of the surface of the sphere. He expresses the line element ds of the surface in terms of the longitude and latitude of a point, defines the great circles as curves that minimize the integral of the line element, and, in connection with with the determination of the minimum of a side of a spherical triangle, derives 10 equations of spherical geometry.. After the discovery that the shape of the earth is that of a spheroid, Euler, (in the second paper here offered) extended his methods to spheroids. He develops this subject in its entirety...and here deduced very many of the formulas of spherical geometry"" (Rosenfeld & Abramovich). - Enestrom: E:214 a. E: 215. - Another Paper by Euler is withbound: Examen d'une Controverse sur la Loi de Refraction de Rayon de differentes Couleurs par Rapport a la diversité des Milieux transparens par lesquels ils sont transmis."" pp. 294-320. (Enestrom: E 216.‎

‎Einleitung in die Analysis des Unendlichen. Aus dem Lateinischen übersetzt und mit Anmerkungen und Zusätzen begleitet von Johann Andreas Christian Michelsen. Erstes- (Drittes Buch). 3 Bde. (Bd. 3 auch mit eigenen Titel: Die Theorie der Gleichungen. Au... - [THE INTRODUCTION OF THE NOTATION F(x)]‎

‎Berlin, Carl Matzdorff, 1788-91. Bound in 3 nice uniform contemp. calf. Spinesgilt. Tome-and titlelabels withgiltlettering. A paperlabel pasted on top of spines. Stampson title-pages. XXIV,626,(3)VIII,578"(8),530 pp., 2 tables (one folded) and 9 double-page folded engraved plates (8+1). A bit of soiling and browning to title-page in volume 1. Volume 3 has a rather faint dampstain to the lower third of leaves, causing a bit of yellowing to some leaves in the middle of the volume. A few scattered brownspots,but clean.‎

‎Scarce first German edition of his ""Introductio in analysin infinitorum"" from 1748, a work by which Euler lays the foundation of modern mathematical analysis, by summarizing his numerous discoveries in infinite series, infinite products, and continued fractions, and it is here he introduces the CONCEPT OF FUNCTION by the notation F(x), and defines it as any analytical expression formed in any manner from a variable quantity and constants. He includes polynomials, power series, and logarithmic and trigonometric expressions. He also defines a function of several variables. - ""Euler's book is one of the few books on mathematics that is mentioned by John Carter and Percy H. Muir in their Printing and the Mind of Man. There Euler is compared with Euclid: what Euclid did with his ""Elements"" for geometry, Euler did with his ""Introductio"" for analysis. It was by means of this textbook that analysis became an independent discipline within mathematics."" (Karin Reich in ""Landmark Writings in Western Mathematics""). Enestrom (Euler Archive): E 101-02 (Introductio) - Volume 3 is not listed by Enestrom, and it comprises 7 memoirs on equations, 2 by Euler and 5 by Lagrange. All 7 are first German translations as the memoirs originally appeared in Latin and French in St. Petersbourg Akad. der Wissenschaften and in Königl. Akademie der Wissenschaften zu Berlin. (Euler: translation of Enestrom E 30 (1738) and E 282 (1764)).The 5 memoirs by Lagrange consist of his famous contributions to the theory of algebraic equations originally published in French in Königl. Akademie der Wissenschaften zu Berlin 1769-73, here in the first German translations, and among these his groundbreaking ""Von der Auflösung der numerischen Gleichungen"" (Sur la Résolution des Équations Numèriques 1769), where he provides methods, by examining the roots of algebraic equations, of separating the real and imaginary roots of approximating the real roots with continued fractions.Enestrom E 101-102 (1. ed., not listing vol. 3) - PMM: 196 (Introductio).‎

‎De Superficie Conorum Scalenorum, aliorumqve corporum conicorum. (On the surface of scalene cones and of other conic bodies). (+) Theoremata circa divisores numerorum. (Theorems on divisors of numbers). (2 papers by Euler).‎

‎(Petropoli (St. Petersbourg), 1750). 4to. Uncut, without wrappers. Extracted from ""Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tom. I. ad Annum 1747 et 1748. Pp. 3-19 a. 1 engraved plate., and pp. 20-48.‎

‎First printing of both papers. The second is important as it contains Euler'is second proof of the Euler-Fermat theorem, which Euler presents as a consequence of the theorem that (a+b)p = ap+bp (mod p). This paper also includes results about possible divisors of a2n + b2n, and Euler uses this to show again that F5 is not prime. - Enestroem No. 133 a. 134.‎

‎Recherches des Mouvemens d'un Globe sur un Plan horizontal. (1.-) Seond Mémoire. (2 Papers).‎

‎(Berlin, Haude et Spener, 1765 u. 1767). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"" 1758, tome XIV a. XVI, pp. 284-353 a. 2 folded engraved plates + pp. 261-284 a. 1 folded engraved plate.‎

‎First printing of Johann Albert Euler's importent paper in which he set forth the so-called ""Theorem of Johann-Albert Euler"", stating that the trajectory of a ball is a parabola followed by a straight line. The eldest son of Leonhard Euler was a prominent geometer in his own right. In 1758, Johann-Albert Euler (1734-1800) published a study of the motion of a sphere on an horizontal plane in the presence of Newtonian friction. His main result would be rediscovered independently by Gaspard Coriolis as part of his authoritative theoretical work on the topic: Théorie mathématique des effets du jeu de billard (1835). Johann Albrecht Euler, born in St. Petersburg 1732 was a Swiss-Russian astronomer and mathematician and he was the first child born to the great Swiss mathematician Leonhard Euler. ‎

‎Recherche sur une nouvelle maniere d'elever de l'eau proposee par M. de Mour. - [EULER ON HOW TO RAISE WATER]‎

‎(Berlin, Haude et Spener, 1753). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome VII, pp. 305-330 + two engraved plates.‎

‎First printing of Euler's paper on how to raise water, which was a study written on the background of his - unsuccessful - garden-project in Frederick the Great's large complex of summer palaces, Sanssouci where Euler was asked to design the pumps to the many fountains. ""I wanted to make a fountain in my Garden"", Frederic the Great wrote to Voltaire on 25 January 1778. But the water-art project ended in a fiasco. The fountain design was supposed to be executed according to the latest knowledge in hydraulics and should even surpass Versailles with its splendor. ""Euler calculated the effort of the wheels for raising the water to a basin, from where it should fall down through canals, in order to form a fountain jet at Sans-Souci. My mill was constructed mathematically, and it could not raise one drop of water to a distance of fifty feet from the basin.""Since then the fiasco at Sanssouci stands out as an example for the gulf between theory and practice. And Leonhard Euler, the mathematical genius from Basel, became a target of mockery and malicious joy"". (Michael Eckert: Euler and the Fountains of Sanssouci).See Enetröm E202.‎

‎Euler L., Lettres a une princesse de Allemagne sur divers sujets de physique et ‎

‎"In French. Short description: Euler, Leonhard. Lettres a une princesse d'Allemagne sur divers sujets de physique et de philosophie. [Letters To a Princess of Germany on Various Subjects of Physics and Philosophy]. Volume 2. St. Petersburg, Imperial Printing House, 1768. Letters to a German Princess on Various Physical and Philosophical Matters occupy a special place in the scientific heritage of Leonhard Euler. The essay is written in an epistolary form unusual for Euler and is a presentation of the foundations of natural science and philosophy of that time in its interpretation; it bears a bright imprint of the author's personality, his many years of searching and thinking about the nature of physical phenomena, his ideas about the structure of the Universe, about the philosophical and physical picture of the world. This very serious and complex scientific material is presented in the form of letters-conversations, in which scientific rigor is combined with clarity and accessibility of presentation, designed for an unprepared reader. The Letters were published anonymously, but Euler's authorship was no secret to anyone. For the first time Letters were published in St. Petersburg in French and in Russian translation. Please feel free to contact us for a detailed description of the copies available. SKUMS002189 kn_nat"‎

‎1. Opérations infinitésimales linéaires - Applications aux équations différentielles et fonctionnelles, par Volterra et Hostinsky - 2. Leçons sur les principes topologiques de la théorie des fonctions analytiques, par S. Stoilow - 3. Léonard Euler et ses amis, par L.-G. du Pasquier - 4. Théorie invariantive du calcul des variations, par Th. de Donder (envoi autographe) - 5. Sur les cavitations solitaires dans un liquide infini, par Basile Demtchenko‎

‎Gauthier-Villars - Hermann - Albert Blanchard Malicorne sur Sarthe, 72, Pays de la Loire, France 1938 Book condition, Etat : Bon relié, pleine toile bleu, pièce de titre en cuir bleu marine fort et grand In-8 1 vol. - 892 pages‎

‎ Contents, Chapitres : 1. Opérations infinitésimales linéaires - Applications aux équations différentielles et fonctionnelles, par Volterra et Hostinsky - Gauthier-Villars, 1938. Préface, vii, Texte, 238 pages - 2. Leçons sur les principes topologiques de la théorie des fonctions analytiques, par S. Stoilow - Gauthier-Villars, 1938. Préface, x, Texte, 148 pages - 3. Léonard Euler et ses amis, par L.-G. du Pasquier - J. Hermann, 1927. Préface, ix, Texte, 125 pages, complet du portrait d'Euler en frontispice - 4. Théorie invariantive du calcul des variations, par Th. de Donder (envoi autographe) - Gauthier-Villars, 1935. Préface, x, Texte, 230 pages, travaux de Th. De Donder, xi - 5. Sur les cavitations solitaires dans un liquide infini suivi de Sur l'influence des bords sur le mouvement d'un corps solide dans un liquide, par Basile Demtchenko - Blanchard, 1928. Tcxte, 125 pages - 1. VOLTERRA : Notions fondamentales sur les substitutions - Equation caractéristique et diviseurs élémentaires - Réduction d'une substitution à la forme normale - Substitutions permutables avec une substitution donnée - Dérivée et différentielle d'une substitution - Intégrale d'une substitution - Intégration des substitutions continues - Dérivées d'ordre supérieur, différentielles totales - Intégration des différentielles totales, variation d'une substitution - Intégrales doubles et intégrales curvilignes des substitutions, paramètres différentiels - Substitutions fonctions d'une variable réelle - Théorème des résidus relatifs aux substitutions, points singuliers - Substitutions algébriques et substitutions abéliennes - Substitutions abéliennes apparentes, constantes relatives aux coupures - Transformations fonctionnelles linéaires - Transformations de seconde classe, théorèmes d'addition - Transformations de première classe, théorème de Chapman - 2. STOILOW : Généralités et considérations topologiques préliminaires - Les surfaces de Riemann et les fonctions correspondantes - Les propriétés topologiques des surfaces de Riemann - Les types topologiques des surfaces de Riemann - Les transformations intérieures des variétés à deux dimensions et les fonctions analytiques d'une variable complexe - Etude topologique des fonctions analytiques et des recouvrements riemanniens - 3. L.-G. du PASQUIER sur EULER : A Bale, 1707-1727 - Premier séjour à Saint-Petersbourg, 1727-1741 - A Berlin, 1741-1766 - 2eme séjour à Saint-Petersbourg, 1766-1783 - Le caractère de Léonard Euler - Aperçu de l'oeuvre scientifique - 4. De DONDER : 1. Variations d'un intégrale n-uple à frontière variable : Variation première et dérivées variationnelles premières - Variations et dérivées variationnelles d'ordres supérieurs - Extension au cas où il y a plusieurs variables variationnelles - La forme paramétrique - La forme implicite - La forme intrinsèque - Variances - 2. Extrémales : Extrémales et invariant intégral relatif - Généralisation du théorème direct de Jacobi - Généralisation du théorème d'indépendance de David Hilbert - La formule d'excès de Weierstrass généralisée, application à la réduction de la variation seconde - Solutions aux variations - 3. Applications à la physique mathématique : Equations fondamentales de la physique mathématique - Identités fondamentales - Systèmes adjoints - Applications du théorème de Jacobi et du théorème de Hilbert généralisés - Applications aux espaces métriques et à la capillarité - 5. DEMTCHENKO : Sur les cavitations solitaires dans un liquide infini suivi de Sur l'influence des bords sur le mouvement d'un corps solide dans un liquide - Thèse de la Faculté des sciences de Paris 5 publications de mathématiques reliées entre elles dans un fort et gros volume, reliure ordinaire en toile en très bon état, belle pièce de titres au dos, légère trace d'étiquette au bas du dos, intérieur frais et propre, exemplaire ex-bibliothèque, quelques cachets en début d'ouvrage et un bel ex-libris sur la page de gardes, intérieur sinon particulièrement frais et propre, la publication de De Donder est agrémentée d'un envoi autographe signé de l'auteur à Edgar Girard Croker Poole, 1891-1940, un mathématicien anglais‎

‎De Summis serierum reciprocarum. (On the sums of series of reciprocals).‎

‎(Petropoli, St. Petersburg, Typis Academiae, 1740). 4to. No wrappers. In: ""Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tomus VII ad Annum 1735, &..... Euler's paper: pp. 123-134 a. 1 engraved plates. A small brownspot in margin of first leaf, otherwise clean.‎

‎First printing of a major mathematical paper in Number Theory in which Euler solves the Basel Problem. Euler finds an exact expression for the sum of the squares of the reciprocals of the positive integers, namely pi2/6. It was ""Euler’s first celebrated achievement ... his solution in 1735 of the ""Basel Problem""..."" (Ed Sandifer).""This is one of Euler's most celebrated papers, in which he demonstrates formulas such as Pi 2= sum of the inverse squares of the positive integers, and many more, on equating the sine expansion of a circular arc to the infinite product of the simple factors of the associated multiple arcs."" (Ian Bruce).Enestroem E41.‎

‎Euler L., Polnoe umozrenie stroeniya i vozhdeniya korablej, 1778. /Euler L., Com‎

‎In Russian. Short description: Euler L., Polnoe umozrenie stroeniya i vozhdeniya korablej. [Complete reasoning on the structure and driving of ships]. Composed for the benefit of students of navigation by Leonhard Euler, and translated from the French original by the Academy of Sciences associate Mikhail Golovin. St. Petersburg: At the Imperial Academy of Sciences, 1778. 13 sheets of drawings (full set) 19.5 ? 11.5 cm. In cardboard binding of the first half of the 19th century. Circulation 600 copies. With dedication of M. Golovin to S.G. Domashnev on 4 pages, with the typographical vignette on the title page. Rarity, especially in a complete set. Please feel free to contact us for a detailed description of the copies available. SKUMS002190 kn_nat‎

‎Introductio in analysin infinitorum auctore Leonhardo Eulero. ‎

‎Lausanne, Apud Marcum-Michaelem Bousquet & Socios (Marc-Michel Bousquet), 1748. 2 tomes reliés en un volume, complet. In-4 20,5 x 25,5 cm. Reliure de lépoque en demi-basane marbrée et petits coins en vélin, dos à 5 nerfs, pièce de titre en maroquin rouge, tranches rouges. 2f, XVI, 320pp, 1 tableau, 2f, 398pp, 1ff, 40pl. Edition originale. Exemplaire bien complet de ses 2 frontispices allégoriques, de son tableau dépliant ainsi que de ses 40 planches dépliantes reliées in fine. En revanche, le portrait de Jean-Jacques Dortous de Mairan est absent. Les lacunes dans limpression pages 374 et 375 de la seconde partie ont été comblées, à lépoque, de manière manuscrite, à lencre. Mathématicien et physicien suisse, Leonhard Paul Euler (1707-1783) a vécu essentiellement en Russie et en Allemagne. Elève de Johan Bernoulli, il a publié des travaux dans une grande variété de domaines scientifiques : la mécanique, la balistique, lacoustique, lastronomie, la théorie de la musique et la construction des bateaux. Quant aux mathématiques précisément, son apport est considérable, car il sest intéressé à quasiment tous les champs : le calcul différentiel et intégral, le calcul infinitésimal, lalgèbre, la géométrie, la trigonométrie et la théorie des nombres. LIntroductio in analysin infinitorum (Introduction à lanalyse des infiniment petits) est le premier de ses trois grands traités didactiques sur l'analyse infinitésimale, dans lesquels Euler expose sa conception nouvelle du calcul différentiel et intégral et de ses rapports avec la géométrie. Le premier tome de lIntroductio est consacré au calcul « algébrique » sur les fonctions tandis que le second applique les méthodes et les résultats du premier à des problèmes de géométrie (étude des courbes algébriques ou transcendantes, surfaces, changements daxes de coordonnées). Il sagit donc dun changement complet de perspective puisque jusqualors, pour les mathématiciens, cétait le calcul qui découlait de la géométrie. ‎

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‎Printed in Lausanne, by Apud Marcum-Michaelem Bousquet & Socios (Marc-Michel Bousquet), in 1748.2 Volumes bound together, complete.In-quarto 20,5 x 25,5 cm.Contemporary binding in marbled half-sheepskin and small vellum corners, spine with 5 raised bands, title label in red morocco, red edges.Number of pages : 2 leaves, XVI pages, 320 pages, 1 table, 2 leaves, 398 pages, 1 leaf, 40 plates.First edition.This copy is complete of its 2 allegorical frontispieces, its folding table as well as its 40 folding plates bound at the end of the book. However, the portrait of Jean-Jacques Dortous de Mairan is absent.The gaps in the printing on pages 374 and 375 of the second part were filled, at the time, handwritten in ink.Very important restorations of the binding (title piece restored), pale and healthy watering on the first 3 leaves, 3 handwritten notes in modern ink on pages 77 and 105, foxing and some browning, notably on the first 3 folding plates, paper missing on the corner of leaf 139/140, without any damage to the text, otherwise rare and beautiful copy.Swiss mathematician and physicist, Leonhard Paul Euler (1707-1783) lived mainly in Russia and Germany. He was a student of Johan Bernoulli and published works in a wide variety of scientific fields : mechanics, ballistics, acoustics, astronomy, music theory and boat construction.As for mathematics specifically, his contribution is major, because he was interested in almost all fields: differential and integral calculus, infinitesimal calculus, algebra, geometry, trigonometry and number theory.The Introductio in analysin infinitorum (Introduction to the analysis of infinitesimals) is the first of his three major didactic treatises on infinitesimal analysis, in which Euler sets out his new conception of differential and integral calculus in links with geometry.The first volume of the Introductio is devoted to algebraic calculation of functions while the second applies the methods and results of the first one to geometry problems (study of algebraic or transcendent curves, surfaces, changes of coordinate axes). This is therefore a complete change of perspective since until then, for mathematicians, it was calculation that resulted from geometry. Très importantes restaurations de la reliure (pièce de titre renouvelée), pâle et saine mouillure sur les 3 premiers feuillets, 3 notes manuscrites à lencre moderne pages 77 et 105, rousseurs et quelques brunissures, notamment sur les 3 premières planches dépliantes, un manque angulaire de papier au feuillet 139/140, sans aucune atteinte au texte, sinon rare et bel exemplaire. Clients Livre Rare Book : Les frais postaux indiqués sont ceux pour la France métropolitaine et la Corse, pour les autres destinations, merci de contacter la librairie pour connaître le montant des frais d'expédition, merci de votre compréhension. Livre Rare Book Customers : The shipping fees indicated are only for France, if you want international shipping please contact us before placing your order, thank you for your understanding. ‎

‎Sciences à l'époque de la Révolution française - Travaux de l'équipe REHSEIS édités par R. Rashed , (1. Algèbre et théorie des nombres : La résolution algébrique des équations - Lagrange, lecteur de Diophante - 2. Calcul intégral, Condorcet : Condorcet et le calcul intégral - 3. Trigonométrie sphérique, Euler, Lagrange : Préhistoires de la dualité : Explorations algébriques en trigonométrie sphérique - 4. Calcul des probabilités, d'Alember, Condorcet : D'Alembert et les probabilités - Condorcet, la théorie des probabilités et les calculs financiers - 5. Mécanique et physique, Euler, Lagrange, Cauchy : La formalisation de la dynamique par Lagrange - Etudes des méthodes et des styles de mathématisation, la science de l'élasticité - 6. Histoire des sciences naturelles, Condorcet : Condorcet et les naturalistes de son temps)‎

‎Librairie Scientifique et Technique Albert Blanchard Malicorne sur Sarthe, 72, Pays de la Loire, France 1988 Book condition, Etat : Bon broché, sous couverture imprimée éditeur blanche, illustrée d'un portrait de Condorcet sur le plat supérieur grand In-8 1 vol. - 474 pages‎

‎quelques figures dans le texte en noir 1ere édition, 1988 Contents, Chapitres : Présentation et préface de Roshdi Rashed - 1. Algèbre et théorie des nombres : C. Houzel : La résolution algébrique des équations - R. Rashed : Lagrange, lecteur de Diophante - 2. Calcul intégral, Condorcet : C. Gilain : Condorcet et le calcul intégral - 3. Trigonométrie sphérique, Euler, Lagrange : K. Chemla et S. Pahaut : Préhistoires de la dualité : Explorations algébriques en trigonométrie sphérique - 4. Calcul des probabilités, d'Alember, Condorcet : M. Paty : D'Alembert et les probabilités - P. Crépel : Condorcet, la théorie des probabilités et les calculs financiers - 5. Mécanique et physique, Euler, Lagrange, Cauchy : W. Barroso-Filho et C. Comte : La formalisation de la dynamique par Lagrange - A. Dahan-Dalmedico : Etudes des méthodes et des styles de mathématisation, la science de l'élasticité - 6. Histoire des sciences naturelles, Condorcet : M. Morange : Condorcet et les naturalistes de son temps - Index des noms, index des notions couverture à peine jaunie avec d'infimes traces de pliures aux coins des plats sans gravité, sinon bel exemplaire, intérieur frais et propre‎

‎Essai d'une Explication physique des Couleurs engendrees sur des Surfaces extrémement minces. (Essay concerning the physical explanation of colors which are issued from extremely thin surfaces). - [EULER'S WAVE-THEORY OF LIGHT]‎

‎(Berlin, Haude et Spener, 1754). 4to. Without wrappers as extracted from ""Mémoires de L'Academie Royale des Sciences et belles Lettres"", Tome VIII, pp. 262-282.‎

‎First printing of Eulers's importent paper in which he defended the wave-theory of light in opposition to the newtonian corpuscular hypothesis.Most of the scientists and philosophers of the 18th century defended the corpuscular theory of light, but Euler ""being impressed by the notion that the emission of particles would cause a diminuation in the mass of the radiating body, which was not observed, while the emission of waves involved no such consequence...he insisted strongly on the resamblance between light and sound" the whole of the space through which the heavenly bodies move is filled with a subtle matter, the aether, and light consists in vibrations of this aether 'light is the same thing as sound in air'....The chief novelty of Euler's writings on light is his explanation of the manner in which material bodies appear coloured when wieved with white light" and, in particular the way in which colours of thin plates are produced."" (Whittaker,A History of the Theories of Aether and Electricity: pp. 97-98.). - Euler's worg comes here together with a paper by L'Abbe Mazeas on ""Observations sur les Coleurs engendres par le Frottement des Surfaces plane et transparentes."". - Enestrom E:209.‎

‎Nouvelle Méthode de Déterminer les Dérangemens dans le Mouvement des Corps Célestes, Causés par leur Action mutuelle. (New Method to determine the pertubations during the motion of heavenly bodies caused by their mutual attraction) - Réflexions sur le...‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XIX,. (2 =halftitle Mémoires..),141-220. 1.memoir pp. 141-179 a. 1 enraved plate. - 2. pp. 180-193. - 3. pp. 194-220. - 4. pp. 221-234 a. 1 plate.‎

‎First printing of these 4 fundamental papers on the perturbations of the moon, as Euler was the first to use of the Calculus on the motion of the moon in relation to the attractive powers of the Moon, the Earth and the Sun. The theories laid down here is also called Euler's second theory and it is the most interesting. It was of the greatest importtence as a basis for later developments.""He applied his mathematics to astronomy, working out the nature of some perturbations, being in this respect the precursor of Lagrange and Laplace. He began to replace the geometric methods of proof used by Galileo and Newton with the algebraic, a tendency carried to its conclusion by Lagrange. In particular he worked on lunar theory, that is, on the analysis of the exact motion of the moon, the complications of which have been the despair of astronomers and mathematicians since the time of Kepler. - Eneström: 398, 399, 400 a. 401.‎

‎Théorie de L'Inclination de LÉguille magnetique confirmé par des Expériences. Traduit du Latin.‎

‎(Berlin, Haude et Spener, 1757). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XI, Année 1755, pp. 117-201 and 2 folded engraved plates.‎

‎First printing of Johann Euler's large memoir on earth magnetism.""Johann Albrecht Euler (27 November 1734 in St. Petersburg - 17 September 1800 in St. Petersburg) was an astronomer and mathematician. He was the first child of Leonhard Euler himself. In 1754 he became a member of the Berlin Academy. On Euler's return to St. Petersburg in 1765, he was appointed as the chair of physics at the St. Petersburg Academy. In St. Petersburg, he lived in his father's house"" Johann Albrecht's family occupied the ground floor. He won a total of 7 international academy prizes.""‎

‎Vollständige Anleitung zur Integralrechnung. Aus dem Lateinischen ind Deutsche übersetz von Joseph Salomon. 4 Bde. - [A LANDMARK TEXTBOOK ON THE INTEGRAL CALCULUS]‎

‎Wien, Carl Gerold, 1828-30. 8vo. Bound in 4 contemp. marbled boards, titlelabels with gilt lettering. A few scratches to hinges and spine ends. Very small loos to 2 titlelabels. Light wear to top of spine on volume 4. Corners a bit bumped. 2 small paperlabels pasted to lower part of spines. A small stamp to foot of titlepages. VIII,439IV,424VIII,439"VI,520 pp. and 3 folded engraved plates.‎

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‎First German edition (a translation from the Latin ""Institutiones Calculi Integralis"", 1768-70) of this landmark work on the integral calculus, being the most complete and accurate work on the subject at the time. It ""contained not only a full summary of everything then known on this subject, but also the Beta and Gamma functions and other original investigations"" (Cajori). The work exhibits Euler's numerous discoveries in the theory of both ordinary and partial differential equations, which were especially useful in mechanics.""(Euler) presents methods of definite and indefinite integration, having invented many of the methods himself, such as the use of an ""Euler substitution"" for rationalizing particular irrational differentials. His treatment is near exhaustive for integrals expressive as elementary functions. He also develops the theory of ordinart and partial differential equations and presents many properties of the beta and gamma function Eulerian integrals introduced by Euler earlier.""(Parkinson ""Breakthroughs"" 1768 M).Enestroem E 342, E 385, E 385 (The Latin edition). - Poggendorff I, 690.‎

‎Vollständige Anleitung zur Integralrechnung. Aus dem Lateinischen ind Deutsche übersetz von Joseph Salomon. 4 Bde. - [A LANDMARK TEXTBOOK ON THE INTEGRAL CALCULUS]‎

‎Wien, Carl Gerold, 1828-30. 8vo. Bound in 4 contemp. hcalf. Gilt spines with gilt lettering. Very light wear to top of spine on vol. 2. A stamp on title-pages and a previous owners name. A printed paperlabel on all 4 frontcovers. A few corners a bit bumped. VIII,439IV,424VIII,439"VI,520 pp. and 3 folded engraved plates. Internally clean and fine.‎

‎First German edition (a translation from the Latin ""Institutiones Calculi Integralis"", 1768-70) of this landmark work on the integral calculus, being the most complete and accurate work on the subject at the time. It ""contained not only a full summary of everything then known on this subject, but also the Beta and Gamma functions and other original investigations"" (Cajori). The work exhibits Euler's numerous discoveries in the theory of both ordinary and partial differential equations, which were especially useful in mechanics.""(Euler) presents methods of definite and indefinite integration, having invented many of the methods himself, such as the use of an ""Euler substitution"" for rationalizing particular irrational differentials. His treatment is near exhaustive for integrals expressive as elementary functions. He also develops the theory of ordinart and partial differential equations and presents many properties of the beta and gamma function Eulerian integrals introduced by Euler earlier.""(Parkinson ""Breakthroughs"" 1768 M).Enestroem E 342, E 385, E 385 (The Latin edition). - Poggendorff I, 690.‎

‎Lettres de L. Euler à une princesse d'Allemagne sur divers sujets de physique et de philosophie précédées de l'éloge d'Euler par Condorcet et annotées par M. A.A. Cournot -- 2 VOLUMES (COMPLETE SET) -- BON EXEMPLAIRE‎

‎P., Hachette, 1842; 2 volumes in 8 reliés en demi-basane verte, dos ornés de filets dorés (reliures de l'époque), (quelques rousseurs), T.1 : 51pp., 472pp., 2 planches dépliantes, T.2 : (2), 524pp., 4 planches dépliantes‎

‎---- BON EXEMPLAIRE ---- Ces lettres, écrites à la Princesse d'Anhalt-Dassau à qui Euler avait donné des cours de physique, influencèrent profondément la philosophie. Euler's Lettres à une Princesse d'Allemagne (mainly on cosmology and physics), in which he attacked Leibniz's monadology, had an immense success and profoundly influenced contemporary philosophy . (Printing & the Mind of Man N 196)**2004/L2-1999/ARB.PLAC-2006/CART5‎

‎Lettres de M. EULER à une Princesse d'Allemagne sur différentes questions de physique et de philosophie - Nouvelle édition avec des ADDITIONS par MM. Le Marquis de CONDORCET et DE LA CROIX -- BEL EXEMPLAIRE -- 3 VOLUMES (COMPLETE SET°‎

‎P., Royez, 1787/1789, 3 volumes in 8 reliés en demi-basane marron, dos ornés de fers dorés, (reliure postérieure XIXe), (petit accroc à deux coiffes, mouillures pâles aux planches du tome 1), T.1 : (1), 44pp., 318pp., (1), 4 planches dépliantes, T.2 : (2), 348pp., T.3 : (2), 400pp., 11 planches dépliantes‎

‎---- BEL EXEMPLAIRE ---- Troisième édition des lettres d'Euler publiées par CONDORCET et LACROIX AUXQUELLES CES DERNIERS ONT FAIT QUELQUES ADDITIONS CONCERNANT NOTAMMENT LE CALCUL DES PROBABILITES ---- Le quatrième volume annoncé n'a jamais été publié ---- Ces lettres, écrites à la Princesse d'Anhalt-Dassau à qui Euler avait donné des cours de physique, influencèrent profondément la philosophie ---- "Euler's Lettres à une Princesse d'Allemagne (mainly on cosmology and physics), in which he attacked Leibniz's monadology, had an immense success and profoundly influenced contemporary philosophy". (Printing & the Mind of Man N° 196)**2007/ARM2A‎

‎De la Propagation du Son (On the Propagation of Sound). (And same author:) Supplement aux Recherches sur la Propagation du Son (Supplement to the Research on the Propagation of Sound). (And same author:) Continuation des Recherches sur la Propagation ... - [THE WAVE EQUIATION FOR AERIAL ACOUSTICS DISCOVERED]‎

‎(Berlin, Haude et Spener, 1766). 4to. Without wrappers as issued in ""Mémoires de L'Academie Royale des Sciences et Belles-Lettres"", tome XV, pp. 185-209 a. 1 engraved plate, pp.210-240 a. 2 engraved plates, pp. 241-264 and 1 engraved plate.‎

‎First editions of Eulers three main papers on the theory of sounds in which he formulated the WAVE EQUATION for the propagation of sounds in the air. In the first paper Euler analyzes the forces that act on a slice of air that is in a disturbed state at y but was initially at x. The analysis is customary in the modern elementary works. In the second paper Euler gets a result that is equivalent to the general formula ofinversion for partial differentiations, noting in addition that cylindrical and spherical waves also follow it.""Euler, Lagrange, and others worked on the propagation of sound in air. Euler wrote on the subject of sound frequently from the time he was twenty years old (1727) and established this field as a branch of mathematical physics...Three fine and definitive papers were read to the Berlin Academy in 1759 (the papers offered here). (Morris Kline). - Eneroth: E 305, E 306, E 307.‎