‎Mathematics‎

‎"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.‎

Bookseller reference : 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

Bookseller reference : 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).‎

Bookseller reference : 39051

‎"EULER, [LEONHARD].‎

‎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.‎

Bookseller reference : 44264

‎"EUCLID (EUKLID) OF ALEXANDRIA.‎

‎Euclidis Megarensis mathematici clarissimi Elementorum geometricorum libri XV. Cum expositione Theonis in priores XIII à Bartholomæo Zamberto Veneto (= Zamberti) latinitate donata, Campani in omnes, & Hypsiclis Alexandrini in duos postremos. His addie...‎

‎Basel, Johannem Hervagium & Bernhardum Brand, 1558. Folio. (30,5x21,5). Bound in 19th century brown hmorocco with 5 raised bands. Light wear to back and corners a bit bumped. (2),587 pp.Numerous wood-cut diagrams and initials throughout. First ab. 20 leaves with different degrees of yellowing and occasional with marginal faint dampstaining. 3 leaves with upper right corners repaired without loss of text. The ""privilege"" at verso of title partly unreadable as a piece of paper is pasted on, some of these letters are faint, just as some letters in ""Basiliae"" on title are weak. Last leaf with colophon and printers large woodcut-device on verso is mounted, but not hiding the wood-cut. The word ""Basiliae"" on last leaf recto, is weak or nearly gone. Overall a large good copy as usually without the foreword by Melanchton. A small rubber-stamp on title: ""Duplum Bibliothecæ V.E."" and in old hand: ""Bibliothecæ Conventij Romani S. Andrea de Fratrij (?)""‎

‎"EUCLID (EUKLID) OF ALEXANDRIA. - TARTAGLIA'S TRANSLATION.‎

‎Euclide Megarense Philosopho, solo Introduttore delle Scientie Mathematice. Diligentementee Rassettato, et alla integrità ridotto, per il degno professore di tal Scientie Nicolo Tartalea Brisciano (Nicolo Tartaglia). Secondo le due Tradottioni. Con un...‎

‎Venetia, Curtio Trojano, 1565. 4to. Bound in a very nice recent hcalf in old style. Raised bands and richly gilt back. 315,(1) leaves (=632 pp). Profusely illustrated with gemetrical diagramss in the text. Printers woodcut-device at end. Small part of lower right corner of title gone, no loss of text. Light browning to first and last leaf. 6 last leaves with a faint dampstain. Very light browning to outher margins. Otherwise a fine clean copy.‎

‎"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.‎

‎"EULER, [LEONHARD].‎

‎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.‎

‎"EULER, [LEONHARD].‎

‎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.‎

‎"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"".‎

‎"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.‎

‎"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.‎

‎"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.‎

‎"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 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.‎

‎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 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.‎

‎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. - HYDRAULIC TURBINES.‎

‎Application de la Machine Hydraulique de M. Segner à toutes sortes D'Ouvrages et de ses Avantages sur les autres Machines hydrauliques dont on se sert ordinairement. (The application of Mr. Segner's hydrological machine to all sorts of work and its ...‎

‎(Berlin: Haude & Spener, 1753). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome VII. Pp. 271-304 and 2 folded engraved plates.‎

‎"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.‎

‎"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.‎

Bookseller reference : 43002

‎"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.‎

Bookseller reference : 44834