‎Mathématiques‎

‎"EULER, LEONHARD - LOGARITHMS OF NEGATIVE NUMBERS.‎

‎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.‎

Référence libraire : 36103

‎"EULER, LEONHARD - ON COMPOUND OBJECT-GLASSES.‎

‎Sur les Avantages des Verres Objectifs composés de deux Verres simples. (On the advantages of telescopic glasses built with two lenses)‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", Année 1762, tome XVIII, pp. 249-264 and 1 engraved plate.‎

‎First printing. In the paper Euler states the mathematical theory for compund object-glasses of different capabilities.Enestroem: E. 381.‎

Référence libraire : 45124

‎"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.‎

Référence libraire : 41693

‎"EULER, LEONHARD.‎

‎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.‎

Référence libraire : 50924

‎"EULER, LEONHARD.‎

‎De numeris amicabilibus. - [EULER ON AMICABLE NUMBERS.]‎

‎Leipzig, Grosse & Gleditsch, 1747. 4to. Contemp. full vellum. Faint handwritten title on spine. Two small stamps to title page and pasted library label to pasted down front free end-paper. In: ""Nova Actorum Eruditorum Anno MDCCXLVII"". (4), 720, (27) pp. + 6 engraved plates. The entire volume offered. [Euler's paper:] Pp. 267-9.‎

‎"EULER, LEONHARD.‎

‎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.‎

Référence libraire : 49129

‎"EULER, LEONHARD.‎

‎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.‎

‎"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.‎

‎"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.‎

‎"EULER, LEONHARD.‎

‎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.‎

‎"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.‎

‎"EULER, LEONHARD.‎

‎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..‎

‎"EULER, LEONHARD.‎

‎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.‎

‎"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.‎

‎"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.‎

‎"EULER, LEONHARD.‎

‎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.‎

‎"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.‎

‎"EULER, LEONHARD. - DEVELOPING THE TURBINE THEORY.‎

‎Recherches sur l'effet d'un machine hydraulique proposée par M. Segner, professeur à Goettingue. (Research concerning the effects of a hydraulic machine proposed by M. Segner, professor at Gottingen)‎

‎(Berlin, Haude et Spener, 1752). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome VI, Année 1750. Pp. 311-354 and 5 folded engraved plates.‎

‎"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.‎

Référence libraire : 50926

‎"EULER, LEONHARD. - SOLVING THE ""BASEL PROBLEM"".‎

‎De Summis serierum reciprocarum. (On the sums of series of reciprocals).‎

‎(Petropoli, St. Petersburg, Typis Academiae, 1740). 4to. No wrappers. In: ""Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tomus VII ad Annum 1735, &..... Euler's paper: pp. 123-134 a. 1 engraved plates. A small brownspot in margin of first leaf, otherwise clean.‎

‎"EULER, LEONHARD. - THE FUNDAMENTAL THEOREM OF ALGEBRA.‎

‎Sur le Point de Rebroussement de la seconde Espece de mr. le Marquis de l'Hopital. (On the nispidal points of the second kind of Mons. le Marquis de l'Hopital). (+) Recherches sur les Racines Imaginaires des Equations. (Research on imaginary roots o...‎

‎(Berlin, Haude et Spener, 1770). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome V, pp. 203-221, 1 plate and pp. 222-288, 1 engraved plate.‎

‎"EULER, LEONHARD. - THE KOENIG-MAUPERTUIS CONTROVERSY.‎

‎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.‎

Référence libraire : 49695

‎"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.‎

Référence libraire : 45126

‎"FABER, G.‎

‎Über stetige Funktionen. (In ""Mathematische Annalen. 66. Band. 1909""). - [FIRST PUBLICATION OF THE 'HIERARCHICAL BASIS' WITHIN MATHEMATICS]‎

‎Berlin, Julius Springer, 1909. 8vo. Bound with the original wrappers in black full cloth. A small white barcode pasted on to top left corner of front board. Library stamp pasted on the pasted down front free end-paper and stamp to verso of title page. A very nice and clean copy. [Faber:] Pp. 81-94. [Entire issue: IV, 575, (1) pp.].‎

‎First printing of Faber's important paper in which he introduces the 'hierarchical basis' and uses it for the representation of functions. Faber was building on the idea of Archimedes who computed approximately using a hierarchy of polygonal approximations of a circle. In the 1980s Faber's idea became an important ingredient for the efficient solution of partial differential equations.The issue contain the following papers of interest:Weyl, H. Singuläre Integralgleichungen. Pp. 273-324.Weyl, H & F. Jerosch. Über die Konvergenz von Reihen, die nach periodischen Funktionen fortschreiten. Pp. 67-80.And many other papers by contemporary mathematicians.‎

Référence libraire : 44834

‎"FARR, WILLIAM. - THE USE OF SCHEUTZ'S THIRD DIFFERENTIAL ENGINE.‎

‎On the Construction of Life-Tables, illustrated by a New Life-Table of the Healthy Districts of England. Received March 17, - Read April 7, 1859.‎

‎(London, Taylor and Francis, 1859). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1859 - Vol. 149 - Part II. With the titlepage to Part II. Pp. 837-878, 1 folded engraved plate, tables in the text. The plate slightly browned. It includes 1 typeset by the Scheutz calculator.Clean and fine.‎

‎First appearance of a pioneer paper in statistical calculations of life-expectations., containing THE VERY FIRST APPLICATION OF A DIFFERENCE ENGINE TO MEDICAL STATISTICS.""Farr's preliminary report (the paper offered), describing the use of the Scheutz Engine no. 3 to prepare life tables, was published 5 years before his ""English Life Table"". Farr, a pioneer in the quantitative study of morbidity and mortality, was chief statistician of the General Register Office, Englands central statistical office. Influenced by Babbage, he had long been interested in the use of a calculating machine, such as Babbage's Difference Engine to compute life tables"" see page 854 of the present report, in which Farr refers to his 1843 letter on the subject to the registrar-general. Farr had seen and tested the machine's predecessor, the Scheutz Engine No. 2, when it was on display in London. It was at Farr's recommandation that the British government authorized in 1857 the sum of Pound 1200 for the Scheutz Engine no. 3 to be constructed by the firm Bryan Donkin, a manufacturer of machines for the color printing of bank notes and stamps....Farr's printing report, received by the Royal Society on March 17 of that year, was written while Scheutz Engine no. 3 was still ""in the course of construction by Messr. Donkin"" (p. 854). The reports table B1, ""Life-Table of Healthy English Districts"", made from stereotype plates produced by the calculator, represents the very first application of a difference engine to medical studies.""(Hook and Norman, Origins of Cyperspace, No. 77.). - Garrison & Morton: 1700.1.‎

Référence libraire : 43002