‎Mathématiques‎

‎"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.‎

‎First printing of this important paper in which Koenig set forth his ""Law of least Action"". The law states that the kinetic energy of a system of mass points is equal to the sum of the kinetic energy of the motion of the system relative to the center of gravity and of the kinetic energy of the total mass of the system considered as a whole, which moves as the center of gravity of the system.""While still in Franeker, Koenig wrote the draft of his important essay on the principle of least action, which was directed against Maupertuis. The controversy touched off by this work, which was published in March 1751, resulted in perhaps the ugliest of all the famous scientific disputes. Its principal figures were Koenig, Maupertuis, Euler, Frederick II, and Voltaire" and, as is well known, it left an unseemly stain on Euler’s otherwise untarnished escutcheon. The quarrel occupied Koenig’s last years almost completely" moreover, he had been ill for several years before it started. Koenig emerged the moral victor from this affair, in which all the great scientists of Europe—except Maupertuis and Euler—were on his side. The later finding of Kabitz2 testifies to Koenig’s irreproachable character.""(DSB).‎

Referenz des Buchhändlers : 46906

‎"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.‎

Referenz des Buchhändlers : 47253

‎"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.‎

‎"KORKINE, A (+) G. ZOLOTAREFF.‎

‎Sur les formes quadratique positives. - [INTRODUCING THE PERFECT LATTICE]‎

‎Leipzig, B. G. Teubner, 1877. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 11., 1877. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Title page missing a small piece of paper to the right margin, not affecting text. Very fine and clean. Pp. 242-292. [Entire volume: IV, 574, (2) pp.].‎

‎"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.‎

Referenz des Buchhändlers : 48378

‎"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.‎

Referenz des Buchhändlers : 40425

‎"KRONECKER, LEOPOLD.‎

‎Über Schaaren von quadratischen und bilinearen Formen.‎

‎Berlin, Königl. Akad. der Wissenschaften, 1874. No wrappers. Offprint from ""Monatsbericht der Königl. Akademie der Wissenschaften zu Berlin"", Januar, Februar und März 1874. Titlepage (1-2),3-55 pp.‎

‎First printing in the offprint-form of Kroneckers main paper in the quarrell with Camille Jordan over the theory of bilinear forms‎

Referenz des Buchhändlers : 40424

‎"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.‎

‎Offprint of William Henry Kruskal first published paper. Kruskal, American mathematician and statistician, is famous for having formulated the Kruskal-Wallis one-way analysis of variance (together with W. Allen Wallis), a widely-used nonparametric statistical method.‎

Referenz des Buchhändlers : 48895

‎"KUMMER, E. E.‎

‎Bemerkungen über die cubische Gleichung, durch welche die Haupt- Axen der Flächen zweiten Grades bestimmt werden.‎

‎[Berlin, G. Reimer, 1843]. 4to. As extracted, without backstrip. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Band 26, 1843. Fine and clean. Pp. 268-272. [Entire offered: Pp. 217-76 + 2 plates].‎

‎First printing of Kummer's paper on cubical equations by which the main axes of a surface of the second degree can be determined.‎

Referenz des Buchhändlers : 47332

‎"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.‎

Referenz des Buchhändlers : 47283

‎"KUMMER, F. F.‎

‎Über eine besondere Art, aus complexen Einheiten gebildeter Ausdrücke. - [THE FOUNDATION OF HILBERT'S THEOREM 90]‎

‎Berlin, Georg Reimer, 1855. 4to. Bound in contemporary half calf with gilt lettering to spine. In ""Journal für die reine und angewandte Mathematik, 50 Band, 1-4. Heft, 1855"". Entire year offered. Book plate to pasted down front free end-paper, library stamp to Fine and clean.‎

‎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.‎

Referenz des Buchhändlers : 47196

‎"KUMMER, F. F.‎

‎Über eine besondere Art, aus complexen Einheiten gebildeter Ausdrücke. - [THE FOUNDATION OF HILBERT'S THEOREM 90]‎

‎Berlin, Georg Reimer, 1855. 4to. Bound in contemporary half calf with gilt lettering to spine. In ""Journal für die reine und angewandte Mathematik, 50 Band, 1-4. Heft, 1855"". Entire year offered. Book plate to pasted down front free end-paper, library stamp to Fine and clean.‎

‎"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.‎

‎Den første danske oversættelse af Abraham Gotthelf Kästners ""Anfangsgründe der Arithmetik Geometrie ebenen und sphärischen Trigonometrie, und Perspectiv.""Bibl. Dan. II: 8.‎

Referenz des Buchhändlers : 58800

‎"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).‎

Referenz des Buchhändlers : 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.‎

‎This edition of the first treatise on the differential calculus, first published 1696, is the first with the commentaries by the famous French astronomer Nicolas-Louis De Lacaille, taken from his noted ""Leçons élémentaires de mathématiques"".""The Analyse des infiniment petits was the first textbook of the differential calculus. The existence of several commentaries on it - one by Varignon (1725) - attests to its popularity. The question of its intellectual ownership has been much debated. Jean Bernoulli, who is known to have instructed L’Hospital in the calculus about 1691, complained after L’Hospital’s death that he (Bernoulli) had not been given enough credit for his contributions. L’Hospital himself, in the introduction to his books, freely acknowledges his indebtedness to Leibniz and to the Bernoulli brothers. On the other hand, he states that he regards the foundations provided by him as his own idea, although they also have been credited by some to Jean Bernoulli. However, these foundations can be found, less explicitly, also in Leibniz, although Leibniz made it clear that he did not accept L’Hospital’s Platonistic views on the reality of infinitely small and infinitely large quantities.""(DSB).‎

Referenz des Buchhändlers : 50313

‎"L'HÔSPITAL, (GUILLAUME FRANÇOIS ANTOINE) MARQUIS DE. - CARTESIAN GEOMETRY APPLIED TO THE CONIC SECTIONS.‎

‎Traité Analytique des Sections Coniques et de leur Usage pour la Resolution des Equations dans les Problêmes tant déterminez qu'indéterminez. Ouvrage Posthume.‎

‎Paris, Jean Boudot et Jean Boudet fils, 1707. 4to. Contemporary full calf. A bit of cracking to front hinges, so that cords are seen, but cover not loosening. Spine with 6 raised bands, richly gilt compartments. Wear to top of spine. Two small old paperlabels, one to upper compartment, one to frontcover. Covers slightly rubbed. (4),459,(5) pp. Large woodcut vignette on titlepage, 2 other vignettes, one engraved , one in woodcut. 32 folded engraved plates and one smaller folded plate (Fig. A). An old owners stamp on flyleaf. Internally clean and fine. A few tiny brownspots. Wide-margined and 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.‎

‎"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.‎

‎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.‎

‎"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.‎

‎"LACHLAN, R.‎

‎On Systems of Circles and Spheres. Communicated by A. Cayley. Received February 23, - Read March 11, 1886.‎

‎(London, Harrison and Sons, 1887). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1886 - Vol. 177 - Part II. Pp. 481-625. Clean and fine.‎

‎"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.‎

‎"LACROIX, S.-F.‎

‎Traité élémentaire de Calcul Différentiel et de Calcul intégral. Cinquieme Édition. Revue, corrigée et augmentée.‎

‎Paris, Bachelier, 1837. 8vo. Cont. hcalf. Richly gilt back. Back worn and loosening. Block and covers tight. XVI,734,(2) pp., 5 folded engraved plates. Some browning throughout.‎

‎"LAGRANGE, (LA GRANGE), JOSEPH LOUIS. - A FUNDAMENTAL MEMOIR IN THE THEORY OF NUMBERS‎

‎Sur La Solution des Problemes Indéterminés du Second Degré.‎

‎(Berlin, Haude et Spener, 1769). 4to. No wrappers as issued in ""Memoires de L'Academie Royale des Sciences et Belles Lettres"", tome XXIII, pp. 165-310. Clean and fine.‎

‎First edition of a fundamental paper in the Theory of Numbers in which Lagrange gives a solution in integers of indeterminate equations of the second degree - a remarkable turning point in Diophantine analysis. - Fermat had asserted that he could determine when the more general equation x2-Ay2=B was solvable in integers and that he could solve it when solvable, but Lagrange solved it in this paper and furthermore he gives the complete solution to the problem of giving all integral solutions of a general equation where the coefficients are integers. - Cajori calls Lagrange ""One of the greatest mathematicians of all times."" - Poggendorff I:1344.‎

Referenz des Buchhändlers : 49805

‎"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.‎

Referenz des Buchhändlers : 45924