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In geormetriam Euclidis Demonstrationum Libri Sex. In quibus Geometria planorum traditur, & brevis Notis perspicue explicatur. Impensis & sumptibus Authoris. - [FIRST SWEDISH EUCLID-EDITION.]
Uppsala, Eschillus Matthiæ, 1637. Small 4to. Cont. full vellum over wood. Spine ends worn, tears to hinges, but not broken, lower edges of boards with old repairs. Some old ink annotations on boards. Inside frontcover and on title many old owner names, small wholes cut in titel without loss of letters. First ab. 20 leaves with a faint dampstain in upper margin, inkspots on last page. Internally clean. (24),350,(2) pp., numerous geometrical diagrams in the text.
Scarce first edition of the first Swedish edition of Euclid's Elements (Book I-VI) with Gestrinius' commentaries to the axioms and porpositions and with his attempt of a proof of the ""Parallel-axiom"" (The Fifth Postulate). In the preface he discusses the use of plane-geometry in the theories of Aristoteles, Eudoxus, Ptolemy and Kepler. - Gastrinius (1594-1648) became professor of mathematics in Uppsala in 1621 after studies in Greifswald.Collijn (1600-Talet) I:310. - Riccardi p. 436 (1637,2) - Poggendorff I:889. - Not in Max Steck.
Éléments de géométrie - deuxième édition revue et augmentée
Decq / Gauthier-Villars 1866 in8. 1866. Broché.
Mauvais état dos fortement fragilisé abîmé tranche fanée + rousseurs intérieur propre documents dépliant in-fine
Euklid's Elemente acht Bücher: die sechs, nebst dem eilften und zwölften, aus dem Griechischen übersetzt von Johann Friedrich Lorenz. (Auch mit dem Titel Euklid's Geometrie...).
Halle, Waisenhauses, 1825. Contemp. hcalf.Gilt spine, titlelabel with gilt lettering. Light wear to top of spine. With 2 titlepages. VI,204, many textfigs. Interleaved and with a large number of manuscripts diagrams, text and addenda in a contemporary hand.
Max Steck VI.14. - Riccardi p. 489.
Elémens d'algèbre traduits de l'allemande (par Daniel BERNOULLI) avec des notes et des additions (de J.L. LAGRANGE) -- BEL EXEMPLAIRE -- 2 VOLUMES (COMPLETE SET)
Lyon, Bruyset, An III (1795), 2 volumes in 8 reliés en plein Veau marbré, dos richement ornés de fers dorés, tranches rouges (reliure de l'époque, (pages de faux-titre et de titre du tome 1 uniformément jaunis ainsi que quelques feuillets de texte, mouillures angulaires à quelques feuillets au tome 2), T.1 : 16pp., 704pp., T.2 : (2), 668pp.
---- En dépit des défauts signalés BEL EXEMPLAIRE ---- Seconde traduction française et la première par D. BERNOULLI avec des notes et additions de J.L. LAGRANGE ---- Second edition in french of Euler's Vollständige Anleitung zur Algebra (1770). THE TRANSLATION was made by J. BERNOUILLI and CONTAINS NUMEROUS and VALUABLE ADDITIONS by LAGRANGE ---- "Euler's Vollständige Anleitung zur Algebra first appeared in Russian translation in 1768/1769 ; it went through numerous german, french, english, italian, dutch and russian editions" ---- "This book greatly influenced nineteenth and twentieth-century texts on the subject". (DSB IV p. 475) ---- "The first volume treats of determinate algebra. This contains one of the earliest attempts to place the fundamental processes on a scientific basis ; the same subject had attracted D'Alembert's attention. This work also includes the proof of the binomial theorem for an unrestricted real index... The second volume of the algebra treats of indeterminate or Diophantine algebra. This contains the solutions of some of the problems proposed by Fermat and which had hitherto remained unsolved". (Ball"A short history of the Hist. of math.", p. 397)**8014/ARB4
Introduction à l'analyse infinitésimale traduite du latin en français avec des notes et des éclaircissemens par J.B. Labey -- PREMIERE EDITION FRANCAISE -- BEL EXEMPLAIRE GRAND DE MARGES -- 2 TOMES RELIES EN UN VOLUME (COMPLETE SET)
P., Barrois, 1796/1797, 2 TOMES reliés en un volume in 4 (20cm x 26cm), pleine basane marbrée, dos orné de fers dorés, étiquette rouge (reliure de l'époque), T.1 : 14pp., (1-errata du tome premier), 364pp., 1 tableau dépliant (p. 252), T.2 : 6 feuillets non chiffrés (faux-titre, titre, dédicace, errata du tome 1, table des chapitres, errata du tome 2), 424pp., 16 planches dépliantes
---- PREMIERE EDITION de cette traduction française par J.B. LABEY, professeur de mathématiques à l'Ecole centrale, puis à l'Ecole polytechnique ---- BEL EXEMPLAIRE GRAND DE MARGES ---- "On paraissait désirer, il y a longtemps, une traduction complète de l'Introduction à l'analyse infinitésimale d'Euler, tant à cause de la difficulté de se procurer cet ouvrage devenu rare depuis plusieurs années que parce que beaucoup de jeunes gens qui se livrent à l'étude des mathématiques, n'entendent pas la langue dans laquelle il a été écrit...". (Préface) ---- "In the Introductio, Euler presented the first clear statement of the idea that mathematical analysis is a science of function ; and he also presented a more thorough investigation of the very concept of function...". (DSB IV p. 467) ---- "This work caused a revolution in analytical mathematics, a subject which had hitherto never been presented in so general and systematic manner". (Cajori p. 233)**8204/ARM3
De innumerabilibus Curuis tautochronis in in Vacuo. (On the innumerable tautochrone curves in a vacuum). (+) Curva Tautochrona in Fluido resistentiam faciente secundum Quadrata cerilitatum. (Tautochrone curves in a fluid making a second resistance pr...
(Petropoli, St. Petersburg, Typis Academiae, 1735). 4to. No wrappers. In: ""Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tomus IV ad Annum 1729. The whole section of ""Mathematica""offered. Pp 1-118 pp. and 10 engraved plates. Euler's papers: pp. 49-67 a. 2 engraved plates. Pp. 67-89 a. 1 engraved plate. Wide-margined, clean.
Both first editions and some of the earliest mathematical papers by Euler. The first paper is a masterful work, in which Euler first establishes a surprisingly simple geometric condition for tautochronic curves, and then shows how to generate such curves, both analytic and algebraic, starting from the familiar cycloid "" the next paper extends the analysis to a resistive medium where the resistance is in proportion to the square of the speed. - Enestroem E12 and E13.The section (Mathematica) also contains papers by Jacob Hermann, Christopher Maier, G.W. Krafft and Daniel Bernoulli ""Problema astronomicum inneniendi altitudinem poli,...."", pp. 89-94.
Auszug aus Herrn Leonhard Eulers vollständigen Anleitung zur Algebra mit einigen Weläuterungen und Vermehrungen herausgegeben von Johann Jacob Ebert. Erster- (Zweyter) Theil. 2 Bde.
Frankfurt am Mayn, Johann Georg Fleischer, 1789. Contemp. hcalf. Gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on top of spine. Spine slightly rubbed. Stamps on first title-page. VIII,246(6),282 pp. Scattered brownspots and occasional light browning.
Poggendorff I, 641.
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.
Exposition de quelques paradoxes dans le calcul integral.
(Berlin, Haude et Spener, 1758). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome XI, 1756 pp. 300-321 and 1 folded engraved plate.
First appearance of this paper in which Euler examines some peculiar differential equations that can be solved through the rather paradoxical method of integration by differentiation. He presents four such problems, which were found to all be members of the same family of differential equations, thus this presentation will focus on reworking several of these problems to make use of this generalization.Together with a paper by Eulers son (Euler le Fils - Johann Albrecht): Des Cerfs - Volans. Traduit du Latin. Pp. 322-364 and 3 folded engraved plates. - Johann here exposes his electrical theory in relation to kites, and indicates that kites were not only children's toys but had been used by the celebrated Romas in his electrical experiments.Enestroem E236.
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.
INTRODUCTION A L'ANALYSE INFINITESIMALE 2 VOL
JACQUES GABAY 2007 364+424+16 pages 19 2x6 4x25 4cm. 2007. broché. 364+424+16 pages.
Bon Etat Reproduction de l'impression de 1796 avec 16 planches en fin d'ouvrage
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 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.
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.
