‎Mathématiques‎

‎"KÄSTNER, ABRAHAM GOTTHELF.‎

‎Begyndelsesgrunde af Arithmetik, Geometrie og plane og sphæriske Trigonometrie. Oversat efter fjerde forøgede Oplag af Jacob Wolf. Mathem. Begyndelsesgr. 1 Deels 1ste Afdeling.‎

‎Kiøbenhavn, Gyldendals Forlag, 1788. 8vo. Indbundet i et samtidigt lidt slidt hellæderbind. Enkel stregforgyldning og fem ophøjede bind på ryggen. Forgyldt rygtitelfelt delvist slidt væk. Enkel blindtrykt ramme på permerne. Forgyldte initialer ""F. S. S."" på forpermen. Brugsspor ved kapitæler og false. Hjørner stødte. Enkelte spredte brunpletter og noter. (24),542,(1) pp.‎

‎"L'HOPITAL (L'HOSPITAL) LE MARQUIS DE.‎

‎Solution d'un Probléme Physico-Mathematique.‎

‎(Paris, Jean Boudot, 1703). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1700"". Pp. 9-21 and 1 folded engraved plate.‎

‎First appearance of a paper in mathematical physics in which L'Hospital - best known by his draft of the first treatise oof the differential calculus - in which he applies the new mathematical tool, the calculus to physics. ""L'Hospital was a major figure in the early development of the calculus on the continent of Europe. he advanced its cause not only by his scientific works but also by his many contacts, including correspondence with Leibniz, Jean Bernouilli, and with Huygens. Fontenelle tells us that it was he who introduced Huygens to the new calculus.""(DSB).‎

书商的参考编号 : 44386

‎"L'HÔPITAL (L'HOSPITAL), (GUILLAUME FRANÇOIS ANTOINE DE). - FIRST TREATISE ON THE DIFFERENTIAL CALCULUS.‎

‎Analyse des infinite Petits. Suivie d'un nouveau Commentaire pour l'intelligence des endroits les plus difficiles de cet Ouvrage. Par l'Autheur du Guide des jeunes Mathématiciens dans l'étude des Lecons de Mathematique de M. l'Abbé de la Caille.‎

‎Avignon, Veuve Girard & Francois Seguin, 1768. 8vo. Contemp. full mottled calf. Wear to top of spine. Richly gilt spine, titlelabel with gilt lettering. (2),XXXI,380 pp. and 8 folded engraved plates. On verso of title-page a stamped exlibris. On inside frontcover an engraved exlibris ""John Cookney"". Internally clean, printed on good paper.‎

‎"LA CHAPELLE, (ABBÉ JEAN-BAPTISTE).‎

‎Abandlung von den Kegelschnitten von den andern krummen Linien der Alten und der Cycloide nebst ihren Anwendungen auf verschiedene Künste. Uebersetzt und mit Anmerkungen versehen von Johann Lorenz Böckmann. Mit 11. Kupfertafeln.‎

‎Carlsruhe, Michael Mackler, 1771. Contemp. hcalf. Richly gilt spine. Titlelabel with gilt lettering. A paperlabel pasted on top of spine. Stamps on title-page. (32),520,(2) pp. (Inhalt pp. 1-24 bound at end) and 11 folded engraved plates. A few brownspots.‎

‎First German edition of la Chapelle's ""Traité des sections coniques et autre courbes ancienne..."", 1750. (Poggendorff I, 1338)‎

书商的参考编号 : 51159

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - LAGRANGE'S CONTINUED FRACTIONS.‎

‎Additions au Mémoire Sur la Résolution des Équations Numériques.‎

‎(Berlin, Haude et Spener, 1770). 4to. Clean and fine without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome XXIV, pp. 111-180. With titlepage to ""Classe de Mathematique"".‎

‎First appearance of Lagrange's importent paper in which he developed continous fraction solutions of equations.‎

书商的参考编号 : 45924

‎"LAMBERT, JOHANN HEINRICH.‎

‎Mémoire sur quelques Propriétés remarquable des Quantités transcendentes circulaires et logarithmiques. - [LAMBERT'S CONTINUED FRACTIONS AND IRRATIONALITY OF ""N""]‎

‎(Berlin, Haue et Spener, 1768). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XVII, pp. 265-322 and 1 folded engraved plate.‎

‎First edition, journal issue. ""One of Lambert's most famous results is the proof of the irrationality of ""N"" and e. It was based on the continued fractions, and two such fractions still bear his name.""(DSB).""Euler's work on continued fractions was used by Johann Heinrich Lambert.....to prove that if x is a rational number (not 0), then ex and tan x cannot be rational. He thereby proved not only that ex for positive integral x is irrational, but that all rational numbers have irrational natural (base e) logarithms.From the result of tan x, it follows tha, since tan (n/4)= 1, that neither n/4 nor n can be rational.Lambert actually proved the convergencee ofthe continued fraction expansion for tan x. (Morris Kline). - Struik, A Source Book, Chapter V, No 17).‎

书商的参考编号 : 38981

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Nouvelle Methode pour Résoudre les Équations littérales par les moyen des Séries.‎

‎(Berlin, Haude et Spener, 1770). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIV, pp. 251-326. Clean and fine.‎

‎First edition of an importent paper in algebraic analysis. The method used by Lagrange was probably suggested to him by Lambert, and both Euler, Lexell, d'Alembert and Condorcet all became highly intereste in this discovery as soon as they heard about it. ""Laplace later presented a better proof. Lagrange's formula occupied numerous other mathematicians, including Arbogast, Parceval, Servois, Hindenburg and Bürgman...."" and virtually every analyst of the nineteenth century considered the problem."" (Jean Itard in DSB). - Poggendorff I:1344.‎

书商的参考编号 : 34947

‎"LAMBERT, JOHANN HEINRICH.‎

‎Observations Analytiques.‎

‎(Berlin, C.F. Voss, 1772. 4to. Without wrappers as extracted from ""Nouveaux Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Annee 1770, pp. 225-244 and 1 engraved plate.‎

‎First edtion. In this paper Lambert starts from a simple problem for a function of 2 variables x and y, then proceeds to expand the method to more difficult differentiations.‎

书商的参考编号 : 39084

‎"LAPLACE, PIERRE-SIMON.‎

‎Philosophischer Versuch über Wahrscheinlichkeiten. Nach der dritten Pariser Auflage übersetzt von Friedrich Wilhelm Tönnies. Als wissenschaftliche Anleitung zur Berichtigung unsere Urtheile in Fällen der Ungewischheit für Philosophen, Aerzte, Richter,... - [THE LAPLACIAN DETERMINISM]‎

‎Heidelberg, Karl Groos, 1819. Contemp. marbled boards. Title-label with gilt lettering probably of more recent date. A stamp on titlepage. XIV,(2),207 pp. Very light browning to a few leaves and margins, otherwise fine.‎

‎Scarce first German edition of this ground-breaking work. It is the translation of Laplaces's work from 1814 with the title:""Essai philosophique sur la probabilités"" as a separate work of Laplaces introduction to the second edition of his ""Theorie analytique des probalités"". ""It contains the famous passage to the effect that the future of the world is completely determined by the past and that one possessed of the mathematical knowledge of the state of the world at any given instant could predict the future."" (Morris Kline).""The long introduction that Laplace added to the second edition (of Theorie analytique...) was also published separately in the same year, as ""Essai philosophique sur les probabilités""....This essay was extremely popular and influential, unlike the ""Theorie analytique..."" it required no guide and was widely read and quoted. The ""Essay"" was itself the product of years of thought by Laplace"" four different versions saw publication even before the first edition appeared !.....it presented the ideas of the ""Theorie analytique..."" to a broad popular audience while serving as a synopsis of the full treatise, in part mirroring it in organization. (S.M. Stigler in Landmark Writings in Western Mathematics...edited by Grattan-Guiness).‎

书商的参考编号 : 40130

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur L'Élimination des Inconnues dans les Équations.‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 303-318. Fine and clean.‎

‎First edition of this importent paper in algebraic analysis, read before the Academy October 29, 1767 and published as a Memoir 1771. He employed Cramer's method of symmetric functions but made it more rapid by use of the series development of log (1+u).‎

书商的参考编号 : 34680

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS.‎

‎Sur L'Integration des Equations à differences partielle du premier ordre. - [A MASTERPIECE OF ANALYSIS]‎

‎(Berlin, C.F. Voss, 1774). 4to. Uncut with wide margins, without wrappers as issued in ""Nouveaux Memoires de L'Academie Royales des Sciences et Belles- Lettres"", Année MDCCLXXII, pp. 353-372.‎

‎First edition of a work which is a breakthrough in the theory of ""First Order Partial Differential Equations"", generalizing the method of variation of parameters for solving differential equations. "" The oldest theory of integration of partial differential equations of the first order are due to Lagrange"" it is based on the fundamental fact that the most general solution of such differential equations can be calculated with the help of differentiations and eliminations if a complete integral of the differential equationn is known"" - ""This problem (of partial differential equations) had only been lightly touched on by Clairaut, Euler, d'Alembert, and Condorcet. Lagrange wrote: ""Finally I have just read a memoir that Mr de Laplace presented recently.....This reading aweakened old ideas that I had on the same subject and resulted in the following investigations...(which constitute) a new and complete theory."" Laplace wrote on 3 February 1778 that he considered Lagrange's essay ""a masterpiece of analysis, by the importence of the subject, by the beauty of method, and by the elegant manner in which it is represented."" (DSB). - Parkinson, Breakthroughs 1774 M.‎

书商的参考编号 : 39049

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur la Force des ressorts pliés. (+) Sur le Probleme de Kepler. (2 Memoirs).‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 167-203 a. pp. 204-233 a. 1 folded engraved plate. With titlepage to ""Classe de Mathematique.""‎

‎First appearance of these two importent memoirs, dealing with ""elastic stress"" and the Two-Body problem. In the first paper ""On the Force of bent springs"" Lagrange became the first to investigate mathematically ""elastic stress"" - the physical principles of elasticity - a problem suggested by the design of the spiral spring of a watch.""Although Lagrange's contributions to the strenght of materials are of more theoretical than practical interest, his method of generalized coordinates and generalized forces later found applications in the strenghts of materials and proved a great value in solving problems of practical importence.""(Timoshenko ""History of Strength of Materials""p. 40).The second paper offered deals with the Two-Body problem and here he comes up with the solution later called the lagrangian solution. In 1770 Lagrange read before the Academy his famous paper ""Nouvelle méthode pour résoudre les équations littérales par le moyen des séries."", the discovery of the Lagrange-Series. In the paper offered - read to the Academy on November 1, 1770 - Lagrange applies his Series to ""Kepler's Problem"".Together with 2 other papers, Jean Bernoulli ""Sur les Suites ou Sequences dans la Laotterie de Genes"", pp. 234-253 and D'Alembert ""Extrait d'une Lettre ...à M. de La Grange"", pp. 254-264.‎

书商的参考编号 : 45705

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Théorie des fonctions analytiques, contenant les principes du calcul différentiel, dégagés de toute considération d'infiniment petits ou d'évanouissans, de limites ou de fluxions et réduits à l'analyse algébrique des quantités finies. - [FOUNDATION OF ANALYSIS]‎

‎Paris, De L'Imprimerie de la République, An V (1797). 4to. Uncut and partially unopened. Contemporary manuscript-binding. Provenance: With the exlibris of Stillman Drake - one of the most renown Galileo scholars. Some light brown spotting through out. Otherwise a very good copy. (4),VIII,276 pp.‎

‎First edition, first printing. Several bibliographies mention that there are two issues of the first edition, with no priority established - one with 277 numbered pages and another with 276 numbered pages which compromises Vol. III of the ninth cahier of the 'Journal de l'Ecole Polytechnique' (see Norman 1258 for example). However, the second mentioned printing was first published in 1801 (See Prof. Craig G. Fraser's article in ""Landmark Writings in Western Mathematics 1640-1940"", pp. 258-276).Lagrange is the great formulizer of his time. In his masterpiece 'Méchanique Analytique' from 1788 he freed Newtonian mechanics from synthetic and geometrical reasoning by reducing the theory of mechanics and the art of solving problems in that field to the mere solution of general formulas. In this work, the 'Théorie des fonctions analytiques', Lagrange attempted to give calculus an algebraic foundation and avoid the employment of infinitely small quantities. In this work Lagrange developed a systematic foundation of the calculus. Throughout the eighteenth century a critical attitude had developed both within mathematics and within general scientific culture. Bishop George Berkeley had already in 1734 in his work 'The Analyst' called attention to what he perceived as logical weaknesses in the reasonings of the calculus arising from the employment of infinitely small quantities. And by the end of the century a growing interest in the foundations of analysis was reflected in the decisions of the academies of Berluin and Saint Petersburg to devote prize competitions to the metaphysics of the calculus and the nature of the infinite. In Original contributions: Lagrange's conception of theorem-proving in analysis" his derivation of what is today called the Lagrange remainder in the Taylor expansion of a function his formulation of the multipiler rule in the calculus of variations and his account of sufficiency questions in the calculus of variations.Barchas 1198. Riccardi I (2), 3. Norman 1258. Honeyman 1881, Stanitz ,‎

书商的参考编号 : 35989

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS.‎

‎Two Papers. 1. Sur une Nouvelle Espece de Calcul rélatifs à différentiation & à l'intégration des quantités variables. - 2. Sur la Forme des Racines Imaginaires des Equations. - [A NEW FOUNDATION OF THE CALCULUS]‎

‎(Berlin, Ch. Fr. Voss, 1774). 4to. Large uncut copy, broadmargins, without wrappers as issued in ""Nouvaux Memoires d l'Academie Royale des Sciences et Belles-Lettres. Année 1772."" pp. 185-221 and pp. 222-258.‎

‎First edition of these two important papers. In the first paper ""Sur une Nouvelle Espece de Calcul..."" he made the most ambitious attempt to rebuild the foundation of the calculus. The paper is in fact an outline of his ""Theorie des functions"", issued later in 1797.""This work greatly impressed Lacroix, Condorcet and Laplace. Based on the analogy between powers of biniminals and differentials, it is one of the sources of the symbolic calculuses of the nineteenth century. A typical example of Lagrange's thinking as an analyst in this sentence taken form the memoir: ""Although the principle of the analogy (between powers and diffrentials) is nor self-evident, nevertheless, since the conclusions drawn from it are not thereby less exact, I shall make use of it to discover various theorems...""""(Jean Itard in DSB). The second paper ""Sur la Forme...""When D'Alembert red the paper he gave the following respons:""Your demonstration on imaginary roots seem to me to leave nothing to be desired, and I am very much obliged to you for the justice you have rendered to mine, which, in fact, has the minor fault (pwerhaps more apparant than real) of not being direct, bu which is quite simple and easy. D'Alembert was alluding to his Cause de vents (1747).""(DSB).‎

书商的参考编号 : 38985

‎"LANDSBERG, GEORG.‎

‎Über die Krümmung in der Variationsrechnung.‎

‎Leipzig, B. G. Teubner, 1908. 4to. In ""Mathematische Annalen"", 65. Band, 3 Heft, 1865"". In the original printed wrappers, without backstrip. Front wrapper with small stamp to lower part, otherwise fine and clean. [Clebsch:] Pp. 313-349. [Entire issue: Pp. 331-432].‎

‎First printing of Polish mathematician Landsberg's paper on the curvature of calculus of variations" a topic originating in the brachistochrone curve problem raised by Johann Bernoulli (1696).‎

书商的参考编号 : 47284

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS.‎

‎Sur L'Integration des Equations à differences partielle du premier ordre. - [A MASTERPIECE OF ANALYSIS]‎

‎(Berlin, C.F. Voss, 1774). 4to. Uncut with wide margins, without wrappers as issued in ""Nouveaux Memoires de L'Academie Royales des Sciences et Belles- Lettres"", Année MDCCLXXII, pp. 353-372.‎

‎"LA GRANGE (LAGRANGE), JOSEPH LOUIS. - MAXIMA AND MINIMA.‎

‎Sur les Courbes Tautochrones. (and ) Nouvelles Réflexions sur les Tautochrones. - [THE CALCULUS OF VARIATIONS]‎

‎(Berlin, Haude et Spener, 1767 and Berlin, Ch. Fr. Voss, 1774). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"" Tome XXI, pp. 364-380 and "" Nouveau Mémoires..."", pp. 97-122.‎

‎"LACROIX, (SYLVESTRE FRANCOIS).‎

‎Weitere Ausführung zu Lacroix's Geometrie oder versuch einer Geometrie über die ebnen und krummen Oberflächen, nebst Anfangsgründen der Perspektive zum besonern Gebrauch für Archotekten, und für die ausübenden Messkünstler überhaupt. Aus dem Französis...‎

‎Berlin, Heinrich Frölich, 1806. Contemp. hcalf, spine gilt. Stamp on titlepage. XXXVI,166,(2) pp. and 10 folded engraved plates. Titlepage brownspotted. Some scattered brownspots. Plates clean.‎

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - A BREAKTHROUGH IN ""THE THEORY OF EQUATIONS"".‎

‎Sur la Résolution des Équations Numériques. (On the Solution of numerical Equations).‎

‎(Berlin, Haude et Spener, 1769). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Année 1767, Tome XXXIII, pp. 311-352.‎

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - LAGRANGE'S CONTINUED FRACTIONS.‎

‎Additions au Mémoire Sur la Résolution des Équations Numériques.‎

‎(Berlin, Haude et Spener, 1770). 4to. Clean and fine without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome XXIV, pp. 111-180. With titlepage to ""Classe de Mathematique"".‎

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Nouvelle Méthode pour Résoudre les Problemes indéterminés en Nombre entiers.‎

‎(Berlin, Haude & Spener, 1770). 4to. No wrappers, as issued in ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIV, pp. 181-250. Clean and fine.‎

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Sur la Force des ressorts pliés. (+) Sur le Probleme de Kepler. (2 Memoirs).‎

‎(Berlin, Haude et Spener, 1771). 4to. No wrappers, as issued in ""Mémoires des l'Academie Royale des Sciences et Belles-Lettres"", tome XXV, pp. 167-203 a. pp. 204-233 a. 1 folded engraved plate. With titlepage to ""Classe de Mathematique.""‎

‎"LAMBERT, JOHANN HEINRICH [NON-EUCLIDEAN GEOMETRY].‎

‎Observations Trigonometriques. - [FORESHADOWING NON-EUCLIDEAN GEOMETRY]‎

‎(Berlin, Haude & Spener, 1770). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", tome XXIV, pp. 327-354 and 1 engraved plates.‎

‎"LAMBERT, JOHANN HEINRICH.‎

‎Mémoire sur quelques Propriétés remarquable des Quantités transcendentes circulaires et logarithmiques. - [LAMBERT'S CONTINUED FRACTIONS AND IRRATIONALITY OF ""N""]‎

‎(Berlin, Haue et Spener, 1768). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XVII, pp. 265-322 and 1 folded engraved plate.‎

‎"LAMBERT, JOHANN HEINRICH.‎

‎Solution générale et absolue du problème de Trois Corps, moyennant des suite infinies. - [THE THREE BODY PROBLEM]‎

‎(Berlin, Haude et Spener, 1769). 4to. Without wrappers as extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIII. Pp. 353-364.‎