"EULER, LEONHARD. - SOLVING FOR THE FIRST TIME THE CONTACT PROBLEM OF FRICTION.
Reference : 45497
(1750)
(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.
(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.
Paris, chez Adrien Le Clere, 1805, 1 broché, sans couverture. in-8 de VIII-72 pages ;
Léonhard Euler, physicien et mathématicien suisse.
Phone number : 06 80 15 77 01
"EULER, LEONHARD. - INTRODUCING ""THE EULER CONSTANT"" AND ""THE FUNCTION NOTATION""
Reference : 50926
(1740)
(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.
(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.
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).
(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.
(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.
(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.
"EULER, LEONHARD. - EULER'S SECOND LUNAR THEORY AND THE PROBLEM OF THREE BODIES.
Reference : 41682
(1769)
(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.
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.
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.
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.
(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.
(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.
(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.
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.
Phone number : 41 (0)26 3223808
Leipzig, B.G. Teubner, 1948, gr. in-4to, XII + 1 Bl. + 327 S., Original-Pappband. Schönes Exemplar.
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Basel, Birkhäuser 1975, gr. in-4to, Frontispiz-Porträt in Farbe + XVIII + 1 Bl. + 666 S., Verlagseinband, Rückenschild, O.Umschlag (Eingerissen) / reliure blanc de l’éditeur (Imit. Leder?), pièce de titre orange au dos, jaquette (avcec déchirures)
Phone number : 41 (0)26 3223808
Basel, Birkhäuser 1980, gr. in-4to, Frontispiz-Porträt + VIII + 1 Bl. + 611 S., Verlagseinband, Rückenschild, O.Umschlag (eingerissen) / reliure blanche de l’éditeur, pièce de titre orange au dos, jaquette (avec déchirures).
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Basel, Birkhäuser 1986, gr. in-4to, Frontispiz-Porträt + XI (+1 leer) + 1 Bl. + 454 S., Verlagseinband, Rückenschild, O.Umschlag / reliure blanche de l’éditeur, pièce de titre orange au dos, jaquette.
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Zürich, Orell Füssli, 1957, gr. in-4to, XXXVII (+ 1 leer) + 302 S. Original-Pappband. Schönes Exemplar.
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Zürich, Orell Füssli, 1958, gr. in-4to, VIII + 326 S. + 1 Bl., Original-Pappband. Schönes Exemplar.
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Zürich, Orell Füssli, 1965, gr. in-4to, VIII + 417 S. + 1 Bl., Original-Pappband. Rücken etwas leimschattig.
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Zürich, Orell Füssli, 1968, gr. in-4to, XLII + 414 S. + 1 Bl., Original-Pappband. Schönes Exemplar.
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Basel, Birkhäuser 2004, gr. in-4to, CXCV (195 S.) (+ 1) + 414 S. + 1 Bl., Original-Pappband. Schönes Exemplar.
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