‎Mathématiques‎

‎"EISENSTEIN, G. [GOTTHOLD].‎

‎Théorèmes sur les Formes cubiques et Solution d'une Equation du quatrième Degré à quatre indéterminées (+) Über die Anzahl der quadratischen Formen, welche in der Theorie der complexen Zahlen zu einer reellen Determinante gehören (+) Allgemeine Auflös... - [""THERE HAVE BEEN ONLY THREE EPOCH-MAKING MATHEMATICIANS: ARCHIMEDES, NEWTON, AND EISENSTEIN""]‎

‎Berlin, G. Reimer, 1844. 4to. In contemporary half cloth. In ""Journal für die reine und angewandte Mathematik"", 27. band, Heft 1-4, 1844. Entire volume 27 offered. A small library stamp to lower part of p. 1 and a white label pasted on to upper part of spine. Light occassional brownspotting, otherwise fine and clean.‎

‎"ELFVING, GUSTAV.‎

‎Optimum allocation in linear regression theory. - [BEGINNING ""METHODS OF COMPUTING OPTIMUM REGRESSION DESIGN""]‎

‎U.S.A., The Annals of Mathematical Statistics, 1952. 8vo. No wrappers (as issued). Offprint from ""The Annals of Mathematical Statistics"", Vol. 23, No. 2, June 1952. Light miscolouring to extremities, otherwise a fine and clean copy. Pp. 255-262.‎

‎Scarce offprint of Elfving's seminal paper which marks the beginning of optimality theory of regression theory. The paper also introduced concepts from convex geometry, including ""Elfving sets.""Pioneering work was done by Elfving in several papers on the methods of computing optimum regression design. The ""Optimum allocation in linear regression theory"" is without doubt Elfving's single most influential paper, inaugurating that line of research."" (Johnson, Leading Personalities in Statistical Sciences: From the Seventeenth Century)While accompanying a surveying expedition to western Greenland, extended and intense rains left Elving with three days in his tent, during which time he consider the best locations of observations to estimate parameters on linear models. Elfving's ideas appeared in his paper on the optimal design of experiments for estimating linear models. This paper also introduced concepts from convex geometry, including ""Elfving sets"" and Elfving's theorem‎

Referentie van de boekhandelaar : 48790

‎"ELFVING, GUSTAV.‎

‎Convex Sets in Statistics.‎

‎Lund, Håkan Ohlssons,1953. 8vo. In the original grey printed wrappers. Offprint from ""Comptes Rendu du Douzième Congrès des Mathématiciens Scandinaves tenu à Lund 10-15 août 1953"". A very fine clean copy, near mint. Pp. (2), 35-39.‎

‎"ELFVING, GUSTAV.‎

‎Zur theorie der markoffschen ketten.‎

‎Helsingfors, 1937. Royal8vo. In the original printed wrappers. Offprint from ""Acta Societatis Scientiarum Fennicæ"", Nova Series A. Tom. II, N:o 8. Wrappers partly detached and has been bended vertically. Internally fine. 17 pp.‎

‎"ERDMANN, BENNO.‎

‎Die Axiome der Geometrie. Eine philosophische Untersuchung der Riemann-Helmholtz'schen Raumtheorie.‎

‎Leipzig, Leopold Voss, 1877. Contemp. hcalf. Spine gilt and gilt lettering. Very lightly rubbed. X,174 pp. Internally fine and clean.‎

‎Scarce first edition of Erdmann's !Habilitationsschrift"", which deals with the epistemological aspects and consequences of the new non-euclidean geometry as porpoundeb by Riemann and Helmholtz.‎

Referentie van de boekhandelaar : 38675

‎"ERICKSON, V. B. + J. F. PELLEGRIN.‎

‎Build - A Software Construction Tool. [In: AT&T Bell LaboratoriesTechnical Journal, July-August 1984, Vol. 63 No. 6 Part 2]. - [THE UNIX-BASED BUILD TOOL]‎

‎[N.Y., AT&T Bell Laboratories, 1984]. 8vo. In the original yellow wrappers. A nice and clean copy. Pp. 1049-1059 (Entire volume: 1 leaf + pp. 1007-1212).‎

‎"EULER, LEONHARD - DIOPTICAL THEORY.‎

‎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.‎

Referentie van de boekhandelaar : 50190

‎"EULER, LEONARD. - ON THE ISOCHRONE PROBLEM.‎

‎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.‎

Referentie van de boekhandelaar : 50850

‎"EULER, LEONHARD. - INTRODUCING ""THE EULER CONSTANT"" AND ""THE FUNCTION NOTATION""‎

‎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.‎

Referentie van de boekhandelaar : 50926

‎"EUCLID (EUKLID) OF ALEXANDRIA. - FIRST DANISH EDITION OF ""EUCLID"".‎

‎Euclidis Elementa Geometriæ, Det er, Første Grund Til Geometrien, I det Danske Sprog oversat af Ernst Gotlieb Ziegenbalg.‎

‎Kjøbenhavn, Ernst Henrik Berling, 1744. 4to. Samt. hldrbd. over træ. Ryg lidt slidt Overtrækspapiret på permer med mangler.(12),20,311 pp. samt 5 foldede kobberstukne plancher, i teksten talrige geometriske figurer. De første blade og de 5 plancher med en svag vandskjold. Svag skjold på de sidste ca 20 blade. En del blade med brunplet i øvre margin.4to. Contemporary half calf over wooden boards. Spine a bit worn and lacing some of the paper over boards. Faint damp stain to first leaves, to plates, and to the last ab. 20 leaves. Some leaves with a brown spot to upper margin. (12), 20, 311 pp + 5 folded engraved plates. Numerous geometrical figures in the text.‎

‎Første udgave på dansk af Euclids ""Elementer"", omfattende Bog 1-6 og 11-12. J.F. Ramus have allerede nogle år tidligere udgivet Euclid, men disse var mindre lærebøger i uddrag og på latin. Oversættelsen indeholder en lang introduktion af Ramus ""Betænkning om Euclidis Elementer og om deres Oversættelse i det Danske Sprog.""Ziegenbalg var teologisk kandidat, men havde studeret matematik i flere år, både i Jena og i England. Han blev udnævnt til professor i matematik ved Københavns Universitet efter Ramus, og havde i nogle år forinden fungeret som dennes assistent. Hans oversættelse er dedikeret Christian den VI, og i forordet introducerer han den således ""offereres (oversættelsen) Deres Kongelige Majestæt...disse udi det Danske Sprog oversatte Elementa Geometriæ, som ere Hoved=Kilden til alle Mathematiske Videnskaber og have nu i 2000 Aar været i saa stor Estime, at alle de største og erfarne Mathematici have grundet deres Skrifter paa dem og at de til almindelig Nytte og Brug ere bekientgiorte næsten udi alle Europæiske, men ey tilforn i dette Sprog.""First edition of the first Euclid-translation into Danish, comprising Book 1-6 and 11-12. Bound in cont. hcalf. Rebacked in old style. A good copy. - Riccardi, Bibl. Euclideana, Parte 4, p. 47. - Bibl. Danica IV:96.‎

Referentie van de boekhandelaar : 41890

‎"EULER, LEONHARD.‎

‎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.‎

Referentie van de boekhandelaar : 45702

‎"EULER, LEONHARD - THE PRINCIPLE OF LEAST ACTION‎

‎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.‎

Referentie van de boekhandelaar : 41693

‎"EULER, LEONHARD.‎

‎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.‎

Referentie van de boekhandelaar : 39052

‎"EULER, LEONHARD.‎

‎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).‎

Referentie van de boekhandelaar : 39047

‎"EULER, LEONHARD.‎

‎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.‎

Referentie van de boekhandelaar : 41244

‎"EULER, [LEONHARD].‎

‎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.‎

Referentie van de boekhandelaar : 44268

‎"EULER, LEONHARD. - THE OPTICAL THEORY OF COMPOUND LENSES FOR TELESCOPES AND MICROSCOPES.‎

‎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.‎

Referentie van de boekhandelaar : 45126

‎"EULER, LEONHARD.‎

‎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

Referentie van de boekhandelaar : 35698

‎"EULER, LEONHARD.‎

‎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).‎

Referentie van de boekhandelaar : 39051

‎"EULER, LEONHARD.‎

‎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.‎

Referentie van de boekhandelaar : 42897

‎"EUCLID (EUKLID) OF ALEXANDRIA. - FIRST DANISH EDITION OF ""EUCLID"".‎

‎Euclidis Elementa Geometriæ, Det er, Første Grund Til Geometrien, I det Danske Sprog oversat af Ernst Gotlieb Ziegenbalg.‎

‎Kjøbenhavn, Ernst Henrik Berling, 1744. 4to. Samt. hldrbd. over træ. Ryg lidt slidt Overtrækspapiret på permer med mangler.(12),20,311 pp. samt 5 foldede kobberstukne plancher, i teksten talrige geometriske figurer. De første blade og de 5 plancher med en svag vandskjold. Svag skjold på de sidste ca 20 blade. En del blade med brunplet i øvre margin.4to. Contemporary half calf over wooden boards. Spine a bit worn and lacing some of the paper over boards. Faint damp stain to first leaves, to plates, and to the last ab. 20 leaves. Some leaves with a brown spot to upper margin. (12), 20, 311 pp + 5 folded engraved plates. Numerous geometrical figures in the text.‎

‎"EUCLID OF ALEXANDRIA - GESTRINIUS, MARTIN ERIK.‎

‎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.‎

‎"EULER, [LEONHARD].‎

‎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.‎

‎"EULER, [LEONHARD].‎

‎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.‎

‎"EULER, LEONARD. - ON THE ISOCHRONE PROBLEM.‎

‎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.‎