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Exposition de quelques paradoxes dans le Calcul Intégral. (Explanation of certain paradoxes in integral calculus).
(Berlin, Haude et Spener, 1758). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome 12 (1756), pp. 300-321 a. 1 folded engraved plate.
First edition. Euler looks at singular integrals of differential equations (derivation through differentiation"" proof that these integrals are not included in the general solution.) Enestroem: 236. - Also with Euler le Fils: ""Des Cerfs - Volans"", pp. 322-364 a. 1 plate.
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.
Recherches sur la Déclination de L'Aiguille aimantée. (And:) Corrections Nécessaires pour la Théorie de la Déclination. (And the same author:) Sur la Force de Colonnes.(Research concerning the declination of the magnetized needle - The necessary corre...
(Berlin, Haude et Spener, 1759-68). 4to. Without wrappers extracted from ""Mémoires de l'Academie Royale des Science et Belles-Lettres"", tome XIII, pp. 175-251 and 4 folded engraved plates, tome XXII, pp. 213-264 and 2 engraved plates., tome XIII, pp.and 1 folded engraved plate.
All 3 papers all in first edition. Euler's proposed theory of magnetic fields influenced both Faraday and Maxwell. Euler viewed the magnetic field as waves through the ether, jus like his theory of light was founded on the existence of the ether. - Enestrom E 237 + E 362 and E 238.
Recherches sur la veritable courbe que decrivent les corps jettes dans l'air ou dans un autre fluide quelconque.
(Berlin, Haude et Spener, 1755). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome IX, pp. 321-352.
First printing of this Euler-paper in which he examines curves of airborne bodies. Euler describes how the forces acting on a cannonball give different differential equations for the ascending branch than for descending branch. See Eneström E217.
Recherches sur le Mouvement de Rotation des Corps celestes (Studies on the rotational movement of celestial bodie). (And the same author:) Solution d'une Question curieuse qui ne paroit soumise a aucune Analyse. (Solutions of a curious question which ... - [RECREATIONAL MATHEMATICS]
(Berlin, aud et Spener, 1766). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XV, pp. 265-309 a. 2 engraved plates., pp. 310-337.
Both papers first edition. In the first paper Euler uses his method of pertubations on, or the ""variation of the elements or parameters"" on the movement of the planets. - The second pper is one of Euler's more famous papers and a good example of his work in an area called ""recreational mathematics"". It was the first mathematical paper on knight's tours (A knight's tour is a path that a knight chesspiece can follow to visit every square on the chessboard without revisiting any square). (Eneroth: E 308 a. E 309).
Recherches sur les plus Grand et plus Petits qui se trouvent dans les Actions des Forces.
(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IV, pp. 149-188 and 2 folded engraved plates..
First edition. Euler shows that any discrete system obeys the Maupertois principle" from this result, he derives the general equation for the balance of moments in a plane elastica, which includes the general catenary as a special case. He also proves that Daniel Bernoulli's principle for the elastica that is free of distributed loads is also a special case of this general equation. - Enestrom No. 145.
Recherches sur L'Origine des Forces.
(Berlin, Haude et Spener, 1752). 4to. Unbound, but stitched. In: ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome VI, pp. (419-)447 and 1 folded engraved plate.
First edition, in the periodical form. - Enestroem No. 181.
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.
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.
Solution d'une Question tres difficile dansl le Calcul des Probabilités.
(Berlin, Haude et Spener, 1771). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome XXV, pp. 285-302. Fine and clean.
First printing of one of Euler's papers in probabilistic analysis, dealing with an analysis of a lottery for which there are several classes and a guarateed payment.The Genoise lottery was the first number lottery. It and its variants were discussed by many mathematicians because such lotteries were perceived to be unfair and because they gave rise to many interesting problems. Usually it took the form of choosing 5 from 100 with various payoffs depending upon the wager made. - Enestroem E 412.
Sur la Probabilité des Séquences dans la Lotterie Génoise (On the Probability of Sequences in the genoise Lottery). - [THE GENOISE LOTTERY]
(Berlin, Haude et Spener, 1767). 4to. Without wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXI, pp. 191-230.
First edition of Euler first work on the probability in lottery. He examines the Genoise Lottery, which was the first number lottery. As the name implies he asks for the probability that various sequences of numbers to be drawn.""In the lottery here considered 90 tickets are numbered consecutevily from 1-90, and 5 tickets are drawn at random. The question may be asked, what is the chance that two or moree consecutive numbers should occur in drawing ? Such a result is called a sequence"" thus, for example, if the numbers drawn are 4,5,6,27,28, there is a sequence of three and also of two. Euler considers the question generally."" (Todhnuter).
Sur quelques Proprietés des Sections Coniques, qui conviennent à une infinité d'autres Lignes Courbes. Traduit du Latin.
(Berlin, Haude et Spener, 1746). 4to. No wrappers, as issued in ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome I, pp.71-98.
First edition. In this memoir Euler deals with properties shared by Conic Sections and other curves. - Ensestrom E 83
Sur une Contradiction apparente dans la Doctrine des Lignes courbes (On an apparent contradiction in the theory of curves) + (continuation:) Demonstration sur le Nombre des Points, ou deux Lignes des Ordres quelques peuvent se couper (A proof concerni...
(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in ""Mémoires de L'Academie Royale des Sciences et Belles-Lettres"", tome IV, pp. (219)-233 and (234)-248.
First edition of two early works by Euler on ""Higher Plane Curves"". He discusses the question of whether nine points determine a unique cubic curve, considers the same question for 14 points and quadratic curves, 20 points and so on. He solves the problem using a system of equations. In the following paper he concludes that there are at most mn points of intersection, with some of the points possibly imaginary. - Eneström, Euler Bibliography E 147 a. E 148.
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.
Variae Demonstrationes Geometriae. (Various geometric demonstrations).
(Petropoli (St. Petersbourg), 1750). 4to. Uncut, without wrappers. Extracted from ""Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tom. I. ad Annum 1747 et 1748. Pp. 49-66 a. 1 engraved plate. Clean and fine.
First printing of an importent paper in geometry in which ""Euler says that a proof of a theorem by Fermat can be done from a strictly Euclidean way. He also presents relations about triangles and quadrilaterals, relating products of side lengths, squares of side lengths, and areas."" - Enestroem No. 135.
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.
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.
Construction des Objectifs composés de deux différentes Sortes de verre qui ne produisent aucune Confusion, ni par leur Ouverture, ni par la Différente Réfrangibilité des Rayons, avec la Maniere la plus Avantageuse d'en faire des Lunettes. (+) Const...
(Berlin, Haude et Spener, 1768). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXII, Année 1766. Pp. 119-170 , pp. 171-201 and 2 folded engraved plates., pp. 202-212 and 1 folded engraved plate. With the section title-page to ""Classe Mathématique"".
First printing of three importent Euler-papers on the construction of composite lenses in order to avoid confusion. Euler presents the mathematical theory to explain the effects. The third paper describe how to analyze refraction phenomena in glasses by way of prisms. - Eneström E 359, E 360, E 361.
"EULER, LEONHARD. - INTRODUCING ""THE EULER CONSTANT"" AND ""THE FUNCTION NOTATION""
Reference : 50926
(1740)
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 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.
3 works by Euler: Nouvelle Méthode d'Éliminer les Quantités inconnues des Equations. - Recherches sur les Microscopes a´Trois Verres et les Moyens de les Perfectionner. - Sur L'Avantage du Banquier au Jeu du Pharaon.
(Berlin, Haude et Spener, 1766). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", tome XX, pp. 91-164 (91-116"117-143"144-164). 1 engraved plate ( belonging to ""Microscope..."")
3 first editions by Euler in algebra, in optics and in the theory of chance - in this last paper he discusses the so-called St. Petersburg paradox, the Game Pharon.
Examen de la dissertation de M. le Professeur Koenig, inseree dans les actes de Leipzig, pour le mois de mars 1751. (Examination of the dissertation of Professor Koenig inserted into the Acts of Leipzig for the month of March 1751) (+) Essay d'une D...
(Berlin, Haude et Spener, 1753). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome VII, Année 1751. Pp. 221-245 and pp. 246-254 a. 1 engraved plate.
First editions. The first paper concerns the Argument over the principle of least action, relating to the famous controversy - and one of the ugliest scientific controversies - between Koenig and Maupertuis. ""In 1751 a sensational new argument began when S. König published some critical remarks on Maupertuis’s principle of least action (1744) and cited a letter of Leibniz in which the principle was, in König’s opinion, formulated more precisely. Submitting to Maupertuis, the Berlin Academy rose to defend him and demanded that the original of Leibniz’ letter (a copy had been sent to König from Switzerland) be presented. 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"" (1752), 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, médecin du pape, defending König and making laughingstocks of both Maupertuis and Euler.""(DSB) - Enestrom No. 199.The second paper - Enestrom No. 200.
"EULER, LEONHARD. - THE OPTICAL THEORY OF COMPOUND LENSES FOR TELESCOPES AND MICROSCOPES.
Reference : 45126
(1759)
Régles générales pour la Construction des telescopes et de Microscopes, de quelque nombre de Verres qu'ils soient composés. (Rules for the construction of telescopes and microscopes).
(Berlin, Haude et Spener, 1759). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", Année 1757, tome XIII, pp. a. 1 engraved plate.
First printing of an importent paper in which Euler shows how to manufacture catoptrical telescopes and microscopes in accordance with general rules and founded on his own experiments. - The calculation concerning light ray aberrations, brought about due to the sphericty of the glass, is a masterpiece of analysis of the highest order and he also incorporates the mathematical theory of achromatic combination of lenses, which was first realized by Dollond in the same year, 1757.
Harmonie entre les Principes generaux de repos et de Mouvement de M. de Maupertuis.
(Berlin, Haude et Spener, 1753). 4to. No wrappers, as extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome VII, pp. (167-)198.and 2 folded engraved plates.
First printing of this memoir in which Euler tries to show that the ""harmony"" between Maupertuis' Law of rest, which he formulated for any system of bodies attracted by forces, is a generalization of his own Principle of least Action.
Élémens D'Algebre. Traduits de L'Allemand, Avec des Notes et des Additions. (Par J. Bernoulli). 2 vols. (1. De L'Analyse Determinée. 2. De L'Analyse Indéterminée.).
Lyon, Bruyset ainé & Compagnie, L'an IIIe (1795). 8vo. Bound undcut in 2 cont. boards with title-and tomelabels in leather on backs, gilt. Some scratches along edges and on backs. XVI,704"(4),668 pp. Some quires somewhat browned (variation in paperquality) and some scattered brownspots.
Scarce second French edition of Euler's large textbook, first published as ""Vollständige Anleitung zur Algebra"" 1774 and published in many languages. It is translated by his friend Bernoulli with his ""elaborate tractions"" and with Bernoulli's extensive ""Additions"". The work greatly influenced nineteenth-and twentieth-century texts on the subject, and it is one of the earliest attempts to put the fundamental processes on a sound basis.
