‎Mathematics‎

‎"GUDERMANN, CHRISTOPH.‎

‎Beweis des im zweiten Bande dieses Journals Seite 190. von Herrn Steiner aufgestellten Lehrsatzes No. 27. und Ableitung anderer ebenso einfacher Relationen.‎

‎(Berlin, G. Reimer, 1832) 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 8. Band, 1832"", without backstrip. Fine and clean. pp. 160-68.‎

‎First printing.‎

Bookseller reference : 49083

‎"WEIL, ANDRÉ. - ON COMPACT GROUPS.‎

‎Sur les fonctions elliptiques p-adiques. Presentée par Élie Cartan.‎

‎(Paris, Gauthier-Villars), 1936. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 203, No 1. Pp. (5-) 136 (entire issue offered). Weil's paper: pp. 22-24. Disbound and paper a bit fragile.‎

‎First printing of an importent paper on compact groups.""J. von Neumann an A. Weil, by different methods, obtained simultaneously the uniqueness in the case of of locally compact groups, A. Weil indicating at the same time how the procedure of Haar could be extended to general locally compact groups. It is also A. Weil (in the paper offered) who obtained the condition for the existence of a relatively invariant measure on a homogenous space, and showed finally that the existence of a ""measure"" (endowed with reasonable properties) on a separated topological group, implies ipse facto that the group is locally precompact.""(Bourbaki ""Elements of the istory of Mathematics"", p. 233).‎

Bookseller reference : 49093

‎"HERMITE, CHARLES. - THE THEORY OF TRANSFORMATIONS.‎

‎Sur la théorie de la transformation des fonctions abéliennes. ( I,II,III a. IV,V,VI). 2 papers.‎

‎(Paris: Gauthier-Villars), 1855. 4to. No wrappers. In: ""Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences"", Vol 40, No 5 + 6. Pp. (205-) 260 a. pp. (261-) 324. (2 entire issue offered). Hermite's paper's: pp. 249-256 a. 304-309.‎

‎First printing of Hermite's importent paper in which he created the theory of transformations.""Another topic on which Hermite worked and made important contributions was the theory of quadratic forms. This led him to study invariant theory and he found a reciprocity law relating to binary forms. With his understanding of quadratic forms and invariant theory he created a theory of transformations in 1855. His results on this topic provided connections between number theory, theta functions, and the transformations of abelian functions.""""Hermite’s 1855 results became basic for the transformation theory of Abelian functions as well as for Camille Jordan’s theory of ""Abelian"" groups. They also led to Herrnite’s own theory of the fifth-degree equation and of the modular equations of elliptic functions.""(DSB).‎

Bookseller reference : 49133

‎"VOSSIUS, GERHARD (GERARDUS) JOHANN. - ""ARTES LIBERALES"" AND THE HISTORY OF MATHEMATICS.‎

‎Ars Historica. Sive de Historiae, & Historicis naturâ, Historiaeque scribendae praeceptis, Commentario. Ad Illustrissimum Virum, Joannem Berckium. (+) De Qvattuor Artibus popularibus, de Philologia, et Scientiis Mathematicis, Cui Operi sunjungitur, Ch...‎

‎Leiden, Joannis Maire, 1653 - Amsterdam, Ioannes Blaeu, 1650. 4to. One contemp. full vellum. Contemp. handwritten titles (weak) to spine. First title in red/black with large engraved titlevignette. (8),154,(1) pp. (Ars Historica 1653) - (16),94,(14) pp. (Grammatistice etc. 1650) - (8),83,(15) pp. (De Philologia, 1650) - (16),467,(33) pp. (De Universae Mathesios..., 1650). Fine and clean.‎

‎First edition of ""De Qvattuor Artibus..."" (which includes ""De Universae Mathesios"" with separate titlepage) and second edition of ""Ars Historica""The mathematical work: Poggendorff II, 1235. ""de Mathesios."": ""According to prof. Cantor, (it) is the first history of mathematics in its widest sense"". Honeyman Coll., 3081.‎

Bookseller reference : 49198

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum. Supplementa. Tomus VII. 1754.‎

‎Leipzig, Gleditschii & Lanckii, 1754. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. Occassional brownspots throughout, otherwise fine. (4), 550, (40) pp.‎

‎First edition, containing many reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 49309

‎[ACTA ERUDITORUM]‎

‎Indices generales autorum et rerum sexti Actorum Eruditorum.‎

‎Leipzig, Grossii, Gleditschii & Fritschium, 1723. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. Occassional brownspots throughout, otherwise fine.‎

‎First printing of this index volume of Acta Eruditorum 1723.‎

Bookseller reference : 49312

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum. Supplementa. Tomus III. 1739.‎

‎Leipzig, Weidemannum, Lanckisii & Fritschium, 1739. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. Occassional brownspots throughout, otherwise fine. (4), 552, (29) pp.‎

‎First edition containing many reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 49314

‎"CLEBSCH, A.‎

‎Zur Theorie der algebraischen Flächen (+) Ueber eine Transformation der homogenen Funktionen dritter Ordnung mit vier Veränderlichen.‎

‎Berlin, Georg Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 58. Band, 1861"". Without backstrip. Fine and clean. Pp. 93-126.‎

‎First printing of these two important papers on Quaternary cubics (a degree 3 homogeneous polynomial in four variables).‎

Bookseller reference : 49316

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum MDCCLXIII [1763].‎

‎Leipzig, Gleditschii & Lanckisii, 1763. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. Occassional brownspots throughout, otherwise fine. (4), 600, (18) pp.‎

‎First edition of Acta Eruditorum 1763 containing many reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 49342

‎"GÖDEL, KURT.‎

‎Über Vollständigkeit und Widerspruchsfreiheit (+) Eine Eigenschaft der Realisierungen des Aussagenkalküls.‎

‎Leipzig & Berlin, B.G. Teubner, 1932. 8vo. In the original wrappers. In ""Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Menger, Heft 3"". A near mint copy, Pp. 12-13"" Pp. 20-21. [Entire volume: 26 pp].‎

‎First printing of these two important papers both closely related to Gödel landmark paper Über formal unentscheidbare Sätze"". Here Gödel applies the extensions of the incompleteness theorems to a wider class of formal systems : ""is already the more modern first-order Peano arithmetic, the system in which Godel in his abstract described his incompleteness results. The passage [in the present paper] envisages the introduction of higher-type variables, which would have the effect of re-establishing the system P, but as one proceeds to higher and higher types, that ""all the [unprovable] propositions constructed are expressible in Z (hence are number-theoretic propositions)"" is an important point about incompleteness. The last sentence of the [1932] passage is Godel's first remark on set theory of substance, and significantly, his example of an ""axiom of cardinality"" to take the place of type extensions is essentially the one that both Abraham Fraenkel [1922] and Thoralf Skolem [1923] had pointed out as unprovable in Ernst Zermelo's [1908] axiomatization of set theory and used by them to motivate the axiom of Replacement. "" (Kanamori, Gödel and Set Theory). ""By invitation, in October 1929 Gödel began at tending Menger's mathematics colloquium, which was modeled on the Vienna Circle. There in May 1930 he presented his dissertation results, which he had discussed with Alfred Tarski three months ear lier, during the latter's visit to Vienna. From 1932 to 1936 he published numerous short articles in the proceedings of that colloquium (including his only collaborative work) and was coeditor of seven of its volumes. Gödel attended the colloquium quite regularly and participated actively in many discus sions, confining his comments to brief remarks that were always stated with the greatest precision."" (DSB)‎

Bookseller reference : 49345

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum. Supplementa. Tomus I. 1735.‎

‎Leipzig, Grossiim, Gleditschii & Weidemannum, 1735. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. Occassional brownspots throughout, otherwise fine. (8), 627, (29) pp.‎

‎First edition containing many reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 49348

‎[NOVA ACTA ERUDITORUM].‎

‎Nova Acta Eruditorum MDCCLXXXVI [1736].‎

‎Leipzig, Grossii, Gleditschii & Weidemannum, 1736. 4to. The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. Occassional brownspots throughout, otherwise fine. (4), 562, (34) + 5 folded plates.‎

‎First edition containing many papers and reviews by influential contemporary mathematicians, philosophers and historians.‎

Bookseller reference : 49350

‎"STÄCKEL, PAUL und FRIEDRICH ENGEL.‎

‎Gauss, die beiden Bolyai und die nichteuklidischen Geometrie.‎

‎(Leipzig, Teubner, 1897). Lex8vo. No wrappers. Extracted from ""Mathematische Annalen"" Bd. IL, pp. 149-206.‎

‎First edition.‎

Bookseller reference : 36196

‎NIELSEN, NIELS.‎

‎Recherches sur les Nombres de Bernoulli.‎

‎K., 1913. 4to. 89 pp.‎

‎(Videnskabernes Selskabs Skrifter)‎

Bookseller reference : 3628

‎"HINTIKKA, JAAKKO.‎

‎Knowledge and Belief. An Introduction to the Logic of the two Notions. - [FOUNDING CONTEMPORARY EPISTEMIC LOGIC]‎

‎Ithaca, New York, Cornell University Press, (1962). 8vo. Orig. full blue cloth w. blue lettering to spine and front board. Very minor bumping to capitals and minor bleaching to small part of lower spine. Original blue dust-jacket w. red lettering. Spine faded and some minor brownspotting. Stamp to title-page ( Weston College Library Weston, Mass.) and stamped library-number and date to verso of title-page. An excellent, internally near mint, copy in an unusually fine dust-jacket. Not price-clipped. X, 179 pp.‎

‎The uncommon first edition, first issue of Hintikka's seminal main work, which also constitutes the main work of contemporary epistemic logic.The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, IN PARTICULAR THE CONCEPTS OF KNOWLEDGE AND BELIEF "". The first edition of this seminal work, which has founded contemporary epistemic logic, is very difficult to find. The work was reprinted three times between 1962 and 1969, but after that the work was only printed again in 2005.""In 1962 Jaakko Hintikka published ""Knowledge and Belief: An Introduction to the Logic of the Two Notions"" with Cornell University Press. Almost every paper or a book on epistemic and doxastic logic that has appeared since then has referred to this seminal work. Although many philosophers working in logic, epistemology, game-theory, economics, computer science and linguistics mention the book, it is very likely that most have never literally had their hands on it, much less owned a copy. After a fourth printing in 1969, Knowledge and Belief went out of print and as many of us have found to our dismay, it has become increasingly difficult to find used copies at our local shops or online. It is our pleasure to provide the interdisciplinary community with this reprint edition of Knowledge and Belief."" (Abstract of the re-issue edition, Prepared by Vincent F. Hendricks & John Symons, King's College Publications, 2005).In this breakthrough work, Hintikka sets out to understand and explain the logical behavior of the two fundamental epistemological notions, Knowledge and belief. ""The word ""logic"" which occurs in the subtitle of this work is to be taken seriously. My first aim is to formulate and to defend explicit criteria of consistency for certain sets of statements - criteria which, it is hoped, will be comparable with the criteria of consistency studied in the established branches of logic. What the statements in question are like is also indicated in the title [...]"" (Chapter One, Prolegomena, p.3).""Knowledge and Belief"" has been extremely influential from the time of its appearance and continues to be so to this day, also due to the fact that epistemic logic has greatly influenced the fields of game theory, artificial intelligence and distributed computing.‎

Bookseller reference : 36630

‎"HINTIKKA, JAAKKO.‎

‎Knowledge and Belief. An Introduction to the Logic of the two Notions.‎

‎Ithaca, New York, Cornell University Press, (1964). 8vo. Orig. full blue cloth w. blue lettering to spine and front board. Original blue dust-jacket w. red lettering. An excellent, near mint copy in an astonishingly fine dust-jacket, not price-clipped. Old owner's name to front free end-paper. Internally very nice and clean. A very good copy. X, 179 pp.‎

‎First edition, second printing of Hintikka's seminal main work, which also constitutes the main work of contemporary epistemic logic.The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, IN PARTICULAR THE CONCEPTS OF KNOWLEDGE AND BELIEF "". The first edition of this seminal work, which has founded contemporary epistemic logic, appeared in 1962 and is very difficult to find. The work was reprinted three times between 1962 and 1969, but after that the work was only printed again in 2005. The second issue appeared in 1964 and the third in 1967.""In 1962 Jaakko Hintikka published ""Knowledge and Belief: An Introduction to the Logic of the Two Notions"" with Cornell University Press. Almost every paper or a book on epistemic and doxastic logic that has appeared since then has referred to this seminal work. Although many philosophers working in logic, epistemology, game-theory, economics, computer science and linguistics mention the book, it is very likely that most have never literally had their hands on it, much less owned a copy. After a fourth printing in 1969, Knowledge and Belief went out of print and as many of us have found to our dismay, it has become increasingly difficult to find used copies at our local shops or online. It is our pleasure to provide the interdisciplinary community with this reprint edition of Knowledge and Belief."" (Abstract of the re-issue edition, Prepared by Vincent F. Hendricks & John Symons, King's College Publications, 2005).In this breakthrough work, Hintikka sets out to understand and explain the logical behavior of the two fundamental epistemological notions, Knowledge and belief. ""The word ""logic"" which occurs in the subtitle of this work is to be taken seriously. My first aim is to formulate and to defend explicit criteria of consistency for certain sets of statements - criteria which, it is hoped, will be comparable with the criteria of consistency studied in the established branches of logic. What the statements in question are like is also indicated in the title [...]"" (Chapter One, Prolegomena, p.3).""Knowledge and Belief"" has been extremely influential from the time of its appearance and continues to be so to this day, also due to the fact that epistemic logic has greatly influenced the fields of game theory, artificial intelligence and distributed computing.‎

Bookseller reference : 36632

‎HINTIKKA, JAAKKO.‎

‎Identity, Variables, and Impredicative Definitions + Vicious Circle Principles and the Paradoxes. (In Journal of Symbolic Logic, Volume 21, Number 3, 1956 + Volume 22, Number 3, 1957). - [HINTIKKA'S TRANSFORMATION RULES]‎

‎(No place), The Association for Symbolic Logic, Inc., 1956 + 1957. 8vo. Both entire issues present, both in original printed wrappers. Volume 21, 3 w. a small loss to lower corner of front wrapper, minor loss to lower capital and a tear to lower front hinge, no loss. Upper corner of least few leaves and back wrappers creased (w. tear to wrapper). Volume 22, 3. w. minor loss to capitals. Both issues internally near mint. Vol. 21, 3: pp. 225-248 (entire issue: pp. 225-336)" Vol. 22, 3: pp. 245-249 (entire issue: pp. 225-336).‎

‎First printing of these two important, but for long overlooked, articles, which together constitute Hintikka's attempt to cope with Wittgenstein's elimination of identity as proposed in the ""Tractatus"". With the translation rules that Hintikka here put forward, he is the first to try to carry out Wittgenstein's suggestions systematically. The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, in particular the concepts of knowledge and belief "". In the 1950'ies Hintikka took it upon himself to follow Wittgentein's suggestion of elimination of identity suggested in the ""tractatus"", and in the two offered articles, he succeeds in constructing a logic without identity. The main point of the two connected articles is to show that variables can be used in two ways. One way does not exclude coincidences of the values of different variables (inclusive interpretation of variables), the other does (exclusive interpretation of variables) and can be either weakly or strongly exclusive. He now claims that in the ""Tractatus"" Wittgenstein adopts the weakly exclusive interpretation of variable and then proves that the weakly exclusive quantifiers are able to express everything that the inclusive quantifiers plus identity can express, and without a sign for identity, - for the first time systematically supporting Wittgenstein's claim that identity is not an essential constituent of logical notation. ""There are a number of references to the exclusive interpretations of variables in current logical literature. An exclusive reading of variables was, in effect, suggested by Ludwig Wittgenstein in ""Tractatus logico-philosophicus. As far as I know, however, no one has previously tried to carry out his suggestions systematically. Several misconceptions seem to be current concerning the outcome of an attempts of this kind. Carnap expects radical changes in the rules of substitution. If I am not mistaken, however, at least one form of the exclusive interpretation may be formalized by making but slight alterations in the axioms and/or in the transformation rules of the predicate calculus. Also I hope to say that it is not correct to say (as Russell has done) that Wittgenstein tried to dispense with the notion of identity. What a systematic use of an exclusive reading of variables amounts to is a new way of coping with the notion of identity in a formalized system of logic. Under the most natural formalization of the new interpretations, the resulting system is equivalent to the old predicate calculus (with identity): every formula of the latter admits of a translation into the former, and vice versa."" (Vol. 21, Nr. 3, p. 228).""A deviation from standard English. Recent discussion serves to bring out, amply and convincingly, the utility of observing the ordinary correct use of words and phrases for the purpose of clearing up philosophical problems. In this paper, I shall endeavour to show, by means of an example, that the reverse method may have its interest, too. "" (Vol. 21, Nr. 3, p. 225). ""This note is a sequel to the previous paper of mine which was entitled ""Identity, variables, and impredicative definitions"" and published in this JOURNAL, vol. 21 (1956, pp. 225-245. That early paper served to call attention to the dependency of the set-theoretic paradoxes on the interpretation of the variables that may occur in the critical ""abstraction principle"". (Vol. 22, Nr. 3, p. 245).Besides these two articles, the two issues also include other important articles within logic, e.g. Quine, ""Unification of Universes in Set Theory"" and Symonds and Chisholm ""Inference by Complementary Elimination"".‎

Bookseller reference : 36635

‎LABOUREUR, MAURICE.‎

‎Cours de Calcul Mathematique. Algebrique, Differentiel, & Integral. Avec 357 Figures dans le texte.‎

‎Paris & Liege, Béranger, 1921. Royal8vo. Orig. full cloth. VIII,563 pp.‎

Bookseller reference : 36683

‎LAURENT, H.‎

‎Theorie & Pratique des Assurances sur la Vie.‎

‎Paris, n.d.ca. 1900. Small8vo. Contemp. hcalf. Gilt back. 176 pp.‎

Bookseller reference : 36784

‎"WIENER, NORBERT.‎

‎Extrapolation, Interpolation, and Smoothing of Stationary Time Series. With Engineering Applications.‎

‎Published jointly by The Technology Press of the Massachusetts Institute of Technology and John Wiley & Sons, New York - Chapman & Hall, London, 1949. 8vo. Publishers full cloth. Provenance: Handwritten signature to front free end paper of statistician Anders Hald (author of ""A History of Mathematical Statistics""). A fine and clean copy. IX,(1),163,(1) pp.‎

‎First edition of this classic in modern communication theory. The work was circulated as a classified memorandum in 1942, as it was connected with sensitive war-time efforts to improve radar communication. Combining ideas from statistics and time-series analysis, Wiener used Gauss's method of shaping the characteristic of a detector to allow for the maximal recognition of signals in the presence of noise. This method came to be known as the ""Wiener filter.""‎

Bookseller reference : 36948

‎BOUTROUX, PIERRE.‎

‎Lecons sur les Fonctions définies par Les Équations differentielles du Premier Ordre. Avec une Note de Paul Painlevé.‎

‎Paris, Gauthier-Villars, 1908. Solid private hcloth. (6),190 pp.‎

Bookseller reference : 37097

‎[BOLYAI - GAUSS] SCHMIDT, FRANZ. & PAUL STÄCKEL (EDS.).‎

‎Briefwechsel zwischen Carl Friedrich Gauss und Wolfgang Bolyai.‎

‎Leipzig, T.B. Teubner, 1899. 4to. Original half calf with gilt spine lettering. XII,(4),208 pp. and numerous facsimiles.‎

Bookseller reference : 37118

‎GARABEDIAN, H.L.‎

‎Approximation of Functions. Proceedings of the Symposium on Approximation of Functions, General Motors Research Laboratories, Warrwn, Michigan, 1964.‎

‎Amsterdam, London, New York: Elsevier, 1965. 8vo. Publishers full cloth with dust jacket. VIII, 220 pp.‎

Bookseller reference : 37440

‎HAYES, J.G. (ED.).‎

‎Numerical Approximation to Functions and Data. Based on a conference organized by the Institute of Mathematics and Its Applications, Canterbury, England, 1967.‎

‎London: Athlone, 1970. 8vo. Publishers full cloth with dust jacket. VIII,177,(1) pp.‎

Bookseller reference : 37443

‎BACHMANN, K.-H.‎

‎Programmierung fuer Digitalrechner.‎

‎Berlin: Deutscher Verlag der Wissenschaften, 1962. 8vo. Publishers full cloth. VIII,162,(2) pp.‎

Bookseller reference : 37445