99 books for « euler leonhard »Edit

‎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. ‎

‎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. ‎

‎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.‎

‎DEFENSE DE LA REVELATION CONTRE LES OBJECTIONS DES ESPRITS-FORTS, par M. Euler, suivie des pensées de cet auteur sur la religion, supprimées dans la dernière édition de ses lettres à une princesse d'Allemagne.‎

‎ Paris, chez Adrien Le Clere, 1805, 1 broché, sans couverture. in-8 de VIII-72 pages ; ‎

‎Léonhard Euler, physicien et mathématicien suisse. ‎

‎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.‎

‎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.‎

‎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.‎

‎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.‎

‎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.‎

‎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.‎

‎Reflexions sur un probleme de geometrie traite par quelques geometres et qui es neanmoins impossible (+) Recherches physiques sur la diverse refrangibilite des rayons de lumiere. - [EULER ON LIGHT RAYS]‎

‎(Berlin, Haude et Spener, 1756). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome X, pp. 173-199" pp. 200-226. ‎

‎First printing of two Euler-papers in which he occupies himself with an unsolvable geometric problem and the physics of the different refrangibilities of light rays, a field Euler made important and original contributions to. Euler's wave theory of light, published in 1746, was based on an analogy between sound and light to a more and more mathematical elaboration on that notion. His wave theory degenerated, and it was not until Fresnel introduced transverse waves and an elaborate notion of interference that the wave theory again progressed. He was the second after Christian Huygens to proposed a wave theory of light, and thereby one of the earliest to argue against Newton's particle theory of light. His 1740s papers on optics helped ensure that the wave theory of light proposed by Christian Huygens would become the dominant mode of thought until the development of the quantum theory of light.See Eneström E220, E221.‎

‎Recherches sur les lunettes a trois verres qui representent les objets renverses. - [EULER ON GLASSES WITH THREE LENSES]‎

‎(Berlin, Haude et Spener, 1759). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome X, pp. 323-372.‎

‎First printing of this paper in which Euler made important research into the field of optics and how to construct glasses with three lenses. ""Euler composed his object-glasses of two bi-convex lenses of crown-glas, and a bi-concave of flint, to form a triple object-glass of six lines focal distance with a large aperture"" and it is because our microscope is achromatic that it is established on the principles of Euler."" (Brewster. The Edinburgh journal of science. P. 225).See Eneström E240. ‎

‎Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. 2 vols. ‎

‎Pavia, Typographeo Petri Galeatii, 1787. 4to (265x 200 mm). 2 volumes uniformly bound in contemporary black half calf over blue marbled boards with gilt lettering and ornamentation to spines. Missing upper outer corner of pp. 309/310. Internally very fine and clean. Overall a very nice and wide margined copy. (2), LXIV, 352 pp [2], 353-846 pp.‎

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‎The exceedingly rare second edition, preferable to the first of 1755 for being enlarged by Federico Speroni from manuscript notes by the author, of Euler’s landmark work on analysis" “the first textbook on the differential calculus which has any claim to be regarded as complete. And it may be said that many modern treatises on the subject are based on it” (Ball). Euler’s ‘Differential calculus’ constitutes the second part of his encyclopedic work on mathematical analysis. “He started to write this book already in Saint Petersburg and finished it around 1750 in Berlin, where it was published under the auspices of the Saint Petersburg Academy of Sciences. The existence of an early Latin manuscript, ‘Calculi differentialis’, conserved in the Archive of the Russian Academy of Sciences in Saint Petersburg shows that Euler worked over a very long period to present his modern view of the differential calculus. An account of his scientific manuscripts dated this one to the 1730s, while A. P. Yushkevich considered that it was written even earlier, around 1727.” (Landmark Writings in Western Mathematics, p. 191-2) ""Euler developed the calculus of finite differences in the first chapters of his Institutiones calculi differentialis, and then deduced the differential calculus from it. He established a theorem on homogeneous functions, known by his name, and contributed largely to the theory of differential equations, a subject which had received the attention of I. Newton, G.W. Leibniz, and the Bernoullis, but was still undeveloped”. (Cajori, A History of Mathematics, pp. 238-39) Graesse II, p. 518Landmark Writings in Western Mathematics, no. 14" (Norman 733, first edition)‎

‎Réfléxions sur quelques Loix génerales de la Nature qui s'observent dans les Effets des Forces quelconques. (Reflection on some general laws of nature which are observed in the effects of random forces).‎

‎(Berlin, Haude et Spener, 1750). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome IV, Année 1748. Pp. (189-) 218 and 1 engraved plate.‎

‎First appearance of this paper, in which Euler proves that given the static principle, he can derive the equilibrium conditions for a fluid, and from these, he obtains the integrability conditions for a ""Pfaffian"" form in three variables. He also looks at the equilibrium of a weight suspended from three elastic cords by looking, via analogy, to a special case of the problem for fluids.""In his 1748 paper, Euler in ""Reflexions sur quelques loix generales de la nature.."" starts by declaring his commitment to the least-action principle. His expression corresponds to what we would now call potential energy, so that his statement of least action (formulated by Maupertuis in 1746) in statics is equivalent to the principle that a system of bodies at rest will adopt a configuration that minimizes total potential energy. Euler called this quantity ""effort"".""Enestrom: E 146.‎

‎Lettre de M. Euler a M. Merian. (+) Expose concernant L'Examen de la Lettre de M. de Leibnitz, alleguée par M. Le Prof. Koenig, dans le Mois de Mars, 1751, des Actes de Leipzig a l'Occassion du Principe de la Moindre Action.‎

‎(Berlin, Haude et Spener, 1752). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", 1750, tome VI, Titlepage to the section. (3), pp. 520-532 (+) pp. 52-64 (Expose).‎

‎In 1751, Maupertuis' priority for the principle of least action was challenged in print (Nova Acta Eruditorum of Leipzig) by an old acquaintance, Johann Samuel Koenig, who quoted a 1707 letter purportedly from Leibniz that described results similar to those derived by Euler in 1744. However, Maupertuis and others demanded that Koenig produce the original of the letter to authenticate its having been written by Leibniz. Koenig only had a copy and no clue as to the whereabouts of the original. Consequently, the Berlin Academy under Euler's direction declared the letter to be a forgery and that its President Maupertuis could continue to claim priority for having invented the principle.Enestroem: 182.‎

‎De la Controverse entre Mrs. Leibnitz & Bernouilli sur les Logarithmes des Nombres Negatifs e Imaginaires. (Controversy between Mr Leibniz and Mr Bernouilli on the logarithms of negative and imaginary numbers).‎

‎(Berlin, Haude et Spener, 1751). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome V, pp. 139-179.‎

‎First edition of this importent paper on the logarithms of complex numbers, where Euler clarified such functions. He disagreed with Leibniz that a special function was only applicable for positive numbers, and showed that i was applicable for both negative and positive numbers, only with a difference of a constant. When Euler here (the offered item) came out with the correct form for the logarithm, it was not generally accepted. - Enestrom, Euler Bibliography E 168.‎

‎Theorie plus complette des machines qui sont mises en mouvement par la reaction de l'eau (+) De la variation de la latitude des etoiles fixes et de l'obliquite de l'ecliptique.‎

‎(Berlin, Haude et Spener, 1756). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome X, pp. 227-295"" pp. 296-336.‎

‎First printing of two influential and important Euler papers. In THEORIE PLUS COMPLETTE (i.e. A more complete theory of machines which are activated by their reaction to water), Euler's seminal and most in-depth paper on hydraulics regarding fluid driven turbines. Euler goes into the entire theory of his main idea of Recherches sur l'effet d'un machine hydraulique proposée par M. Segner, professeur à Goettingue (E179) in greater generality. He then proceeds to calculate the optimum proportions for his proposed turbine. His treament is so complete that an engineer today could use his calculations to design a turbine. He opens the paper with the statement that ""Having already explained in some reports the effect that the machine projected by Mr de Segner is capable of producing, I here propose to develop the same in greater detail"". In DE LA VARIATION DE LA LATITUDE he is concerned about the variation of latitude of fixed stars and the obliquity of the ecliptic).See Eneström E222, E223.‎

‎De Minimis oscillationibus Corporum tam rigidorum qvam flexibilium. Methodus nova et facilis. (On the smallest oscillations of rigid and flexible bodies. A new and easy method.)‎

‎(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. 99-122 a. 2 engraved plates. Wide-margined, clean.‎

‎First printing of Euler's first paper on vibrating bars. Euler here solves the partial differential equation for a forced harmonic oscillator and notices the resonnance phenomenon. - Enestroem E40.‎

‎Die Berliner und die Petersburger Akademie der Wissenschaften im Briefwechsel Leonhard Eulers. I und II. Teil. (2 Bände). Mitw. von P. Hoffmann, Quellen und Studien zur Geschichte Osteuropas, Band III , Teil 1 & 2.‎

‎Berlin : Akademie-Verlag, 1959, 1961. gr. in-8vo, (X) + 327 S. + 2 Tafeln / (XII) + 463 S., Original-Leinenband. OU.‎

‎1) Der Briefwechsel L. Eulers (Euler) mit G. F. Müller 1735 - 1767. / 2) der Briefwechsel mit Nartov, Razumovskij, Schumacher, Teplov und der Petersburger Akademie 1730-1763. ‎

‎Theoria motus corporum solidorum seu rigidorum exprimis nostrae cognitionis principiis stabilita et ad omnes motus qui in huiusmodi corpora cadere possunt accommodata. Volumen prius edidit Charles Blanc. ‘Leonardi Euleri Opera Omnia’ series secunda. Opera mechanica et astronomica. Volumen tertium (Gesamtausgabe der Werke von Leonhard EULER Band III). Auctoritate et impensis societatis scientiarum naturalium helveticae Bernae MCMXLVIII.‎

‎Leipzig, B.G. Teubner, 1948, gr. in-4to, XII + 1 Bl. + 327 S., Original-Pappband. Schönes Exemplar.‎