‎Mathématiques‎

‎"KOLMOGOROV, ANDREI NIKOLAEVICH‎

‎Über die Summen durch den Zufall bestimmter unabhängiger Grössen.‎

‎Berlin, Springer, 1928. Royal8vo. Bound in recent blue/green full cloth with gilt lettering to spine. In ""Mathematische Annalen"", 99, 1928. A very nice and clean copy, near mint. Pp. 309-319. [Entire volume: IV, 751, (1) pp].‎

‎First printing Kolmogorav's famous paper in the convergence of sums of independent random variables.""Kolmogorov's publishing his celebrated three-series theorem (the present), which gives necessary and sufficient conditions for the convergence of sums of independent random variables, to his discovering necessary and sufficient conditions for the strong law of large numbers and to his proving the law of the iterated logarithm for sums of independent random variables. His 1931 paper, on continuous time Markov processes with continuous states, is widely regarded as having laid the foundations of modern diffusion theory. His 1949 work, Limit Distributions for Sums of Independent Random Variables, co-authored with B. V. Gnedenko, was for many years the standard source on the central limit theorem and surrounding topics."" (DSB)Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.‎

Référence libraire : 47253

‎"KOCH, HELGE VON.‎

‎Sur les déterminants infinis et les équations différentielles linéaires.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892-93]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16. Fine and clean. Pp. 217-295.‎

‎"KOENIG (KÖNIG), SAMUEL. - GIVING RISE TO ONE OF THE UGLIEST SCIENTIFIC CONTROVERSIES.‎

‎De universali Principio aequilibrii & motus, in Vi viva reperto, deque nexu inter Vim Vivam & Sctionem, utriusque Minimo, Dissertatio. (+) ...continuata & finita. (2 Parts).‎

‎Leipzig, Gleditsch & Lanckis, 1751. 4to. No wrappers. In: ""Nova Acta Eruditorum, Anno MDCCLI"", March- Issue, Pars I-II. Entire issue in 2 parts offered. With titlepage to the volume 1751. Pp. 97-192. Koenig's paper: pp. 125-135 a. pp. 162-176. With 2 engraved plates. Titlepage with 2 stamps and a bit soiled. Leaves as usual a bit browned.‎

‎"KOOPMAN, B. O. - GEORGE D. BIRKHOFF. - THE ERGODIC THEOREM DISCOVERED AND PROVED‎

‎Hamiltonian Systems and Transformation in Hilbert Space. (Koopman) (+) Proof of a Recurrence Theorem for strongly transitive Systems. (Birkhoff) (+) Proof of the Ergodic Theorem. (Birkhoff).‎

‎Easton, PA., Mack printing Compagny, 1931. Royal8vo. Contemp. full cloth. Spine gilt and with gilt lettering. In: ""Proceedings of the National Academy of Sciences of the United States of America"", Vol. 17. VII,710 pp. (Entire volume offered). The papers: pp. 315-318, 650-655 and 656-660.‎

‎"KRIPKE, SAUL A.‎

‎A Completeness Theorem in Modal Logic. - [KRIPKE MODELS FOR MODAL LOGIC]‎

‎(No place), The Association for Symbolic Logic, 1959. Lev8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 24. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. Pp. (1) - 14. [Entire volume: VI, 374 pp.).‎

‎The seminal first printing of Kripke's debut article, which provided the basis for his logic and for the model theory for modal logic in general. The work constitutes the very beginning of Kripke Semantics (often called possible world semantics). Kripke's works in general are rare in fist editions. Many of them remain unpublished and are only known in privately circulated manuscripts.The American philosopher Saul A. Kripke (born 1940) is an exceedingly important logician and philosopher of language and one of the most powerful and influential thinkers of analytic and Anglo-American philosophy. He is considered the greatest living philosopher and perhaps the greatest since Wittgenstein. In 2001 he was awarded the Schock Prize in Logic and Philosophy, which is considered the philosopical equivalent of the Nobel Prize.Kripke, who grew up in Omaha in a religious Jewish family, was somewhat of a prodigy child. During grammar school he got intimately acquainted with and mastered to perfection algebra, geometry and calculus, and very early on he took up philosophy, which later became his career. Still a teenager, in high school, he wrote a work that was to change the face of philosophical logic forever, namely the groundbreaking paper ""A Completeness Theorem for Modal Logic"", which was printed a few years later, in 1959, in the Journal of Symbolic Logic, while he was in his first year at Harvard University. This seminal debut work proposed what later came to be known as Kripke models for modal logic. The story goes that the paper earned a letter from the department of mathematics urging Kripke to apply for a job there, to which he is said to have written an answer explaining ""My mother said that I should finish high school and go to college first.""In 1962 he graduated from Harvard University, where he remained until 1968, first as a member of the Harvard Society of Fellows and then as a lecturer. During these years he developed the logical theories founded in the ""Completeness Theorem"" further and made seminal contributions to the field of logic and semantics. Kripke Semantics is a formal semantics for non-classical logic systems that Kripke began developing in his teenage years, first published something on in 1959 (the present work) and further developed in the 60'ies and. The development of Kripke Semantics was no less than a breakthrough in the making of non-classical logics, of which no model theory existed before Kripke's. With this work, Kripke laid the foundation for proving completeness theorems for modal logic, and for identifying the weakest normal modal logic, which is now named K after him.‎

Référence libraire : 48378

‎"KRAFT, JENS.‎

‎Methode at bevise, hvorledes man i alle Tilfælde kand bestemme den ene Ubekiendte ved en u-endelig Følge af Terminis, som gives ved den anden, i de Algebraiske Liigheder, som indeholde to Ubekiendte.‎

‎(Copenhagen, 1751). 4to. In recently blue paper covered card board binding with white paper-label title-label to front board. Previous owner's name to pasted down front end-paper. Without wrappers as issued in ""Videnskabernes Selskabs Skrifter"", a nice and clean copy. Pp. 323-354.‎

‎First edition of Kraft’s paper on algebra and infinite series, placing him among the most significant Danish mathematicians of his time. The work presents a method for determining an unknown variable in an algebraic equation using an infinite sequence of terms relating to series expansion techniques later formalized in Puiseux series, which play a role in modern algebraic geometry and analysis. This work is important in understanding Kraft’s ability as both a mathematician and a philosopher. It show his mathematical talent in algebra and infinite series while also aligning with his Newtonian physics and Leibnizian philosophy.‎

Référence libraire : 61841

‎"KRONECKER, LEOPOLD.‎

‎Über die verschiedenen Sturmschen Reihen und ihre gegenseitigen Beziehungen.‎

‎Berlin, Königl. Akad. der Wissenschaften, 1873. No wrappers. Offprint from ""Monatsberichte der Königl. Akademie der Wissenschaften zu Berlin"", Februar 1873. Titlepage. a. pp. (117-)154.‎

‎First printing in the offprint form.‎

Référence libraire : 40425

‎"KRONECKER, LEOPOLD.‎

‎Über die verschiedenen Sturmschen Reihen und ihre gegenseitigen Beziehungen.‎

‎Berlin, Königl. Akad. der Wissenschaften, 1873. No wrappers. Offprint from ""Monatsberichte der Königl. Akademie der Wissenschaften zu Berlin"", Februar 1873. Titlepage. a. pp. (117-)154.‎

‎"KRUSKAL, WILLIAM.‎

‎Helmert's Distribution.‎

‎[No place, no printer], 1946. 8vo. In the original printed wrappers. Offprint from: ""American Mathematical Monthly"", Vol. LIII, No. 8, 1946. A very fine and clean copy. Pp. 435-38.‎

‎"KUMMER, E. E.‎

‎Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen.‎

‎Berlin, G. Reimer, 1827. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 2. Band, 1827""., without backstrip. Fine and clean. [Gudermann:] Pp. 223-226. [Entire volue: Pp. 198-292 + two folded plates].‎

‎First printing of Kummer's paper on Transcendental Numbers.‎

Référence libraire : 47283

‎"KUMMER, F. F.‎

‎Über eine besondere Art, aus complexen Einheiten gebildeter Ausdrücke.‎

‎Berlin, Georg Reimer, 1855. 4to. Bound in contemporary half cloth with paper label to spine. In ""Journal für die reine und angewandte Mathematik"", 50. band, Heft 1-4, 1855. Extremities with wear. Number written to top right corner of title page. Small library stamp to lower part of p. 1. Internally fine and clean. Pp. 212-238. [Entire volume: IV, 392 pp. + 4 plates.‎

‎First printing of Kummer's paper which laid the foundation for Hilbert's Theorem 90 (or Satz 90). In abstract algebra Hilbert's Theorem 90 refers to an important result on cyclic extensions of fields that eventually leads to Kummer theory.‎

Référence libraire : 47530

‎"KUMMER, E. E.‎

‎Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen.‎

‎Berlin, G. Reimer, 1827. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 2. Band, 1827""., without backstrip. Fine and clean. [Gudermann:] Pp. 223-226. [Entire volue: Pp. 198-292 + two folded plates].‎

‎"KUMMER, F. F.‎

‎Über eine besondere Art, aus complexen Einheiten gebildeter Ausdrücke.‎

‎Berlin, Georg Reimer, 1855. 4to. Bound in contemporary half cloth with paper label to spine. In ""Journal für die reine und angewandte Mathematik"", 50. band, Heft 1-4, 1855. Extremities with wear. Number written to top right corner of title page. Small library stamp to lower part of p. 1. Internally fine and clean. Pp. 212-238. [Entire volume: IV, 392 pp. + 4 plates.‎

‎"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).‎

Référence libraire : 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)‎

Référence libraire : 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.‎

Référence libraire : 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).‎

Référence libraire : 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.‎

Référence libraire : 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.‎

Référence libraire : 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).‎

Référence libraire : 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).‎

Référence libraire : 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.‎

Référence libraire : 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.‎

Référence libraire : 45705