‎Mathematics‎

‎"TSCHIRNHAUS, EHRENFRIED W. V. [FIRST PUBLICATION OF THE ""TSCHIRNHAUS TRANSFORMATION"".]‎

‎Methodus datae figurae, rectis lineis & curva Geometrica terminate, aut Quadraturam, aut impossibilitatem ejusdem Quadraturae determinandi. (+) Nova Methodus determinandi Maxima & Minima (+) Aufrendi omnes terminos intermedios ex data aequatione. - [FORCED LEIBNIZ TO PUBLISH THE CALCULUS]‎

‎Leipzig, Grosse & Gleditsch, 1683. 4to. Contemporary full vellum. Handwritten title on spine. Library label to pasted down front free end-paper and a small stamps on titlepage. In: ""Acta Eruditorum Anno MDCLXXXIII"". As usual with various browning to leaves and plates. Tschirnhaus' paper: pp. 122-124" Pp. 204-207" Pp. 433-437. [Entire volume: (8), 561, (7) pp + 13 plates].‎

‎First appearance of Tschirnhaus's three exceedingly important papers which were to to initiate one of the most famous mathematical discoveries. In the papers he used infinitisimal methods which were very close to Leibniz's method and where he tried to lay down criteria for rational quadratures in the case of conic, cubic and quadratic curves, papers that led Leibniz to publish his first paper on the differential calculus, the ""Nova Methoda"" in the Acta for 1684 in order to secure his priority over Tschirnhaus concerning the calculus. Leibniz discovered, when he read Tschirnhaus' papers, that Tschirnhaus had here published results showing similarity with Leibniz's invention of the calculus as he had confided to Tschirnhaus earlier, during their Parisian stay, and this without references to Leibniz.The present volume of Acta also contain the first edition of Tschirnhaus' ""Tschirnhaus Tranformation"". Tschirnhaus work intensively on finding a general method for solving equations of higher of higher degree. ""His transformations constituted the most promising contribution to the solution of equations during the seventeenth century" but his elimination of the second and third coefficients by means of such transformation was far from adequate for the solution of the quintic.(Boyer. A History of Mathematics, 1968, 472 p.).Tschirnhaus (1651-1708) , a Saxon nobleman, had as wide interest as acquaintances: He studied in Leyden, served in the Dutch army, visited England and Paris several times. He set up a glassworks in Italy and is said to have introduced Porcelain to Europe. He wrote about philosophy and mathematics and was a close friend of Leibniz.‎

Bookseller reference : 46399

‎"TUKEY, JOHN W.‎

‎Some Notes on the Separation of Convex Sets.‎

‎Lisboa, R. Almirante Pessinha, 1942. 8vo. In the original grey printed wrappers. Offprint from: ""Portugaliae Mathematica"", Vol 3, 1942. Very fine and clean. Pp. 95-102‎

‎"TUKEY, JOHN. (+) ET AL‎

‎Compactness in General Spaces (+)Generalized ""Sandwich"" Theorems (+) Named and Faceless Values: An Initial Exploration in Memory of Prasanta C. Mahalanobis (+) Some Sèlected Quick and Easy Methods of Statistical Analysis (+) Correlation of Ranges of c... - [LARGE COLLECTION OF OFFPRINTS]‎

‎[Various places and printer] ,1945 - 1974. Collection of 24 offprint from various academic journals. All with wrappers (or as issued) and in fine condition. Contained in a black kassett.‎

‎"TURING, A(LAN) M(ATHISON).‎

‎On Computable Numbers with an Application to the Entscheidungsproblem. A Correction. - [TURING'S CORRECTION TO HIS ""ON COMPUTABLE NUMBERS""]‎

‎London, Hodgson & Son, 1937. Royal8vo. In a nice recent half cloth binding with gilt lettering to spine. In ""Proceedings of the London Mathematical Society. Second Series"", Volume 43. Two small stamps to title page. A very nice copy" " Binding tight and in excellent condition, Internally very clean and fresh. Pp. 544-46.‎

‎"TURING, A. M.‎

‎Computability and Lambda-Definability. (Extracted from The Journal of Sybolic Logic, Volume 2, 1937, pp.153-64.).‎

‎1937. 8vo. Bound in recent marbled boards. Title-page for volume 2 of Journal of Symbolic Logic withbound.‎

‎First edition of Turing's important paper, in which he links Kleene's recursive functions, Church's lambda-definable functions and his own computable functions and proves them to be identical. In the appendix of his milestone-paper ""On Computable Numbers"" from 1936, Turing gave a short outline of a method for proving that his notion of computability is equivalent with Alonzo Church's notion of lambda-definabilty. It was not until the present article, however, that it was proved that Steven Kleene's general recursive functions, Church's lambda-definable functions and Turing's computable functions were all identical. Kleene had already proved that every general recursive function is lambda-definable, so by showing that computability follows from lambda-definability and that general recursiveness follows from computability, Turing had ended the circle, which was a primary reason for its acceptance as a notion of ""effective calculable"" demanded by Hilbert's Entscheidungsproblem.""The purpose of the present paper is to show that the computable functions introduced by the author (in ""On computable numbers"") are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene."" Turing wrote this paper while at Princeton studying with Church.""(Hook and Norman No. 395)‎

Bookseller reference : 25248

‎"TURING, A. M.‎

‎Rounding-off Errors in Matrix Processes. - [TURING'S LU FACTORIZATION]‎

‎Oxford, Clarendon Press, 1948. 8vo. Bound in contemporary full calf with gilt lettering to spine. In ""The Quarterly Journal of Mechanics and Applied Mathematics"", Vol. 1, 1948. Previous owner's name written to front free-endpaper. Ver fine and clean. Pp. 287-380. [Entire volume: (4), 474 pp.].‎

‎First printing of this important paper in which Turing for the very first time introduced the concept of LU factorization or LU decomposition. ""Turing's paper was one of the earliest attempts to examine the error analysis of the various methods of solving linear equations and inverting matrices. His analysis was basically sound. The main importance of the paper was that it was published at the dawn of the modern computing era, and it gave indications of which methods were 'safe' when solving such problems on a computer"". (Burgoyne, Collected Works of A M Turing).""In 1945, [Turing] declined an offer of a Fellowship at King's [College, Cambridge] in favour of joining the newly formed Mathematical Division at the National Physical Laboratory (NPL). His early work on computability, combined with his wartime experience in electronics, had fired him with an enthusiasm for working on the design of an electronic computer. ethe machine he designed, which was called the Automatic Computing Engine (ACE) in recognition of Babbage's pioneering work, was characteristically original…""While in the Mathematics Division of NPL, Turing became keenly interested in numerical analysis. His paper, ""Rounding-off Errors in Matrix Processes"", showed that the acute anxiety about the effect of rounding errors in Gaussian elimination was largely unjustified. This paper has been overshadowed to some extent by the von Neumann and Goldstine paper on matrix inversion, but it is a brilliant piece of work and would have repaid closer study at the time"". (""Turing, Alan M."" by James H. Wilkinson, p. 1803, in Encyclopedia of Computer Science, A. Ralston et al (eds.), 4th edition, Nature Publishing Group, 2000).In linear algebra, LU decomposition factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix. LU decomposition is a key step in several fundamental numerical algorithms in linear algebra such as solving a system of linear equations, inverting a matrix, or computing the determinant of a matrix. Not in Origins of Cyberspace nor The Erwin Tomash Library.‎

Bookseller reference : 47095

‎"TURING, A.M.‎

‎A Method for the Calculation of the Zeta-Function. [Received 7 March, 1939. - Read 16 March, 1939]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 48]. - [TURING'S FIRST WORK ON THE ZETA-FUNCTION]‎

‎London, Hodgson & Son, 1945. Royal8vo. In a recent nice green full cloth binding with gilt lettering to spine. Entire volumes 48 of ""Proceedings of the London Mathematical Society. Second Series"". A very nice and clean copy without any institutional stamps. Pp. 180-197. [Entire volume: (4),477 pp.]‎

‎First printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous ""Zeta-function Machine"", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. ""Turing had ideas for the design of an ""analogue"" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides."" (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking ""A Method for the Calculation of the Zeta-Function"", which constitutes his first printed contribution to the subject.""After the publication of his paper ""On computable Numbers,"" Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers... Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]..."" (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).‎

Bookseller reference : 54013

‎"TURING, A.M.‎

‎Systems of Logic based on Ordinals. [Received 31 May, 1938. - Read 16 June, 1938.]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 45]. - [TURING'S PH.D.-THESIS]‎

‎London, Hodgson & Son, 1939. Royal8vo. In a recent nice red full cloth binding with gilt lettering to spine. Entire volume 45 of ""Proceedings of the London Mathematical Society. Second Series"". Small white square paper label pasted on to lower part of spine, covering year of publication stating: ""A Gift / From /Anna Wheeler"". A very nice and clean copy without any institutional stamps. Pp. 161-240. [Entire volume: (4), 475 pp.].‎

‎The rare first printing of Turing's Ph.D.-thesis, which ""opened new fields of investigation in mathematical logic"". This seminal work constitutes the first systematic attempt to deal with the Gödelian incompleteness theorem as well as the introduction to the notion of relative computing. After having studied at King's College at Cambridge from 1931 to 1934 and having been elected a fellow here in 1935, Turing, in 1936 wrote a work that was to change the future of mathematics, namely his seminal ""On Computable Numbers"", in which he answered the famous ""Entscheidungsproblem"", came up with his ""Universal Machine"" and inaugurated mechanical and electronic methods in computing. This most famous theoretical paper in the history of computing caught the attention of Church, who was teaching at Princeton, and in fact he gave to the famous ""Turing Machine"" its name. It was during Church's work with Turing's paper that the ""Church-Turing Thesis"" was born. After this breakthrough work, Newman, under whom Turing had studied at Cambridge, urged him to spend a year studying with Church, and in September 1936 he went to Princeton. It is here at Princeton, under the guidance of Church, that Turing in 1938 finishes his thesis [the present paper] and later the same year is granted the Ph.D. on the basis of it. The thesis was published in ""Proceedings of the London Mathematical Society"" in 1939, and after the publication of it, Turing did no more on the topic, leaving the actual breakthroughs to other generations. In his extraordinary Ph.D.-thesis Turing provides an ingenious method of proof, in which a union of systems prove their own consistency, disproving, albeit shifting the problem to even more complicated matters, Gödel's incompleteness theorem. It would be many years before the ingenious arguments and striking partial completeness result that Turing obtained in the present paper would be thoroughly investigated and his line of research continued. The present thesis also presents other highly important proofs and hypotheses that came to influence several branches of mathematics. Most noteworthy of these is the idea that was later to change the face of the general theory of computation, namely the attempt to produce an arithmetical problem that is not number-theoretical (in his sense). Turing's result is his seminal ""o-machines"""" he here introduces the notion of relative computing and augments the ""Turing Machines"" with so-called oracles (""o""), which allowed for the study of problems that could not be solved by the Turing machine. Turing, however, made no further use of his seminal o-machine, but it is that which Emil Post used as the basis for his theory of ""Degrees of Unsolvability"", crediting Turing with the result that for any set of natural numbers there is another of higher degree of unsolvability. This transformed the notion of computability from an absolute notion into a relative one, which led to entirely new developments and in turn to vastly generalized forms of recursion theory. ""In 1939 Turing published ""Systems of Logic Based on Ordinals,""... This paper had a far-reaching influence"" in 1942 E.L. Post drew upon it for one of his theories for classifying unsolvable problems, while in 1958 G. Kreisel suggested the use of ordinal logics in characterizing informal methods of proof. In the latter year S. Feferman also adapted Turing's ideas to use ordinal logics in predicative mathematics."" (D.S.B. XIII:498). A part from these groundbreaking points, which Turing never returned to himself, he here also considers intuition versus technical ingenuity in mathematical reasoning, does so in an interesting and provocative manner and comes to present himself as one of the most important thinkers of modern mathematical as well as philosophical logic.""Turing turned to the exploration of the uncomputable for his Princeton Ph.D. thesis (1938), which then appeared as ""Systems of Logic based on Ordinals"" (Turing 1939). It is generally the view, as expressed by Feferman (1988), that this work was a diversion from the main thrust of his work. But from another angle, as expressed in (Hodges 1997), one can see Turing's development as turning naturally from considering the mind when following a rule, to the action of the mind when not following a rule. In particular this 1938 work considered the mind when seeing the truth of one of Gödel's true but formally unprovable propositions, and hence going beyond rules based on the axioms of the system. As Turing expressed it (Turing 1939, p. 198), there are 'formulae, seen intuitively to be correct, but which the Gödel theorem shows are unprovable in the original system.' Turing's theory of 'ordinal logics' was an attempt to 'avoid as far as possible the effects of Gödel's theorem' by studying the effect of adding Gödel sentences as new axioms to create stronger and stronger logics. It did not reach a definitive conclusion.In his investigation, Turing introduced the idea of an 'oracle' capable of performing, as if by magic, an uncomputable operation. Turing's oracle cannot be considered as some 'black box' component of a new class of machines, to be put on a par with the primitive operations of reading single symbols, as has been suggested by (Copeland 1998). An oracle is infinitely more powerful than anything a modern computer can do, and nothing like an elementary component of a computer. Turing defined 'oracle-machines' as Turing machines with an additional configuration in which they 'call the oracle' so as to take an uncomputable step. But these oracle-machines are not purely mechanical. They are only partially mechanical, like Turing's choice-machines. Indeed the whole point of the oracle-machine is to explore the realm of what cannot be done by purely mechanical processes...Turing's oracle can be seen simply as a mathematical tool, useful for exploring the mathematics of the uncomputable. The idea of an oracle allows the formulation of questions of relative rather than absolute computability. Thus Turing opened new fields of investigation in mathematical logic. However, there is also a possible interpretation in terms of human cognitive capacity."" (SEP).Following an oral examination in May, in which his performance was noted as ""Excellent,"" Turing was granted his PhD in June 1938.‎

Bookseller reference : 54748

‎"TURING, M. (+) H. A. NEWMAN.‎

‎A Formal Theorem in Church's Theory of Types (+) Practical forms of type theory‎

‎(No place), The Association for Symbolic Logic, 1942, 1943 &1948. Lev8vo. Bound in two uniform red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 7, 8 [Bound together] & 13.. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. Minor scratches to extremities of volume 13. A fine set. Pp. 28-33" Pp. 80-94. [Entire volumes: IV, 164 pp. " IV, 236 pp.).‎

‎"URSIN, GEORG FREDERIK.‎

‎Logarithmer med 6 Decimaler for Tallene fra 1 til 100000 for Sinus og Tangens for hver 10"" tilligemed forskjellige constante Logarithmer og Tal, der ere af vigtighed i Mathematiken.‎

‎Kjøbenhavn, Schultz, 1827. Samtidigt hldrbd. Rygforgyldning. papirsetiket påsat øverst på ryg. Stempler på titelbladet. XXIV pp. + ca. 500 upaginerede sider. Indvendig ren og frisk, trykt på svært skrivepapir.‎

‎"URSIN, GEORG FREDERIK.‎

‎Øvelses=Exempler af Decimal=regning, Kjædebrøk, Bogstavregning, Ligninger, Logarithme=regning samt Opgaver af Plangeometrien.‎

‎Kjöbenhavn, Schultz, 1835. Lille 8vo. Samtidigt beskedent hldrbd. stempel på titelblad. 60 pp., tekstfigurer. Med dedikation på fribladet, underskrevet ""Forfatteren""‎

‎"URSIN, GEORG FREDRIK.‎

‎Logarithmer med 6 Decimaler for Tallene fra 1 til 100000 for Sinus og Tangens for hver 10"" tilligemed forskjellige Constante Logarithmer og Tal der ere af Vigtighed i Mathematiken. Kbhvn., 1827.‎

‎Orig. hollanderet papbd med shirtryg. Revne i false og rep. med tape. Stempel p. titel. Indvendig frisk, trykt på svært papir. XXIV,ca. 1000 pp.‎

‎"VOLTERRA, VITO.‎

‎Drei Vorlesungen über neuere Fortschritte der mathematischen Physik. Gehalten im September 1909 an der Clark-University.‎

‎Leibzig & Berlin, B.G. Tebner, 1914. Royal8vo. Original printed wrappers. Spine strip with wear, otherwise fine. Offprint from ""Archiv der Mathematik und Physik"" pp. (5),98-181 pp. and 1 photographic plate.‎

‎"VOLTERRA, VITO.‎

‎Lecons sur la Théorie mathematique de la Lutte pour la Vie. (Mathematical theory of the struggle for life) - [THE MATEMATIZATION OF BIOLOGY]‎

‎Paris, Gauthier-Villars, 1931. Royal 8vo. Uncut in orig. printed wrappers. Uppe and lower part of backstrip gone. VI,214 pp. + Publisher's cat. (7) pp.‎

‎First edition of this pioneering book on mathematical treatment of the dynamics of animal populations. ""The book mustbe considered as the most important contribution to the mathematization of biology made during the first half of the century, together with Lotka (1925). The origin of Volterra's direct intervention in the field of biomathematical research emerge clearly from his correspondance, manuscripts and direct testimony. In late 1925 D'Ancona showed him the results of a statistical survey of fish populations in the Upper Adriatic sea that pointed to a curious phenomenon. As a general rule, the percentage of predatory fish in the total fish catch in several ports in the Upper Adriatic remained constant, while it displayed an appreciable increase duringh the period 1915-18, that is, the years during which Italy was at war and the naval conflict in the Adriatic had led to an interruption of fishing activities. D'Ancona suggested that the lull in fishing activities was the cause of the increase in the number of predators, and he asked Volterra to provide a mathematical proof of this. Volterra threw himself into the question and came up with a description of the interaction between prey and predators beased on a simple mathematical model, which has since become famous and is known as the 'Lotka-Volterra equations'. (G. Israel in Landmarks Writings in Western Mathematics 1640-1940). - Vito Volterra (1860-1940) may be considered one of the greatest Italian mathematicians living between the 19th and the 20th centuries who also enjoied great international prestige. (G. Israel).‎

Bookseller reference : 39199

‎"VOLTERRA, VITO.‎

‎Sur la stratification d'une masse fluide en équilibre.‎

‎Berlin, Stockholm, Paris, Beijer, 1903. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 27, pp. 105-124.‎

‎First printing of Volterra's paper on the distribution of pressure around spheres in a viscous fluid. ""Volterra’s scientific work covers the period from 1881, when he published his first papers, to 1940 when his last paper was published in the Acta of the Pontifical Academy of Sciences. His most important contributions were in higher analysis, mathematical physics, celestial mechanics, the mathematical theory of elasticity, and mathematical biometrics. His major works in these fields included the foundation of the theory of functionals and the solution of the type of integral equations with variable limits that now bear his name, methods of integrating hyperbolic parctical differential equations, the study of hereditary phenomena, optics of birefringent media, the motion of the earth’s poles and elastic dislocations of multiconnected bodies, and, in his last years, placing the laws of biological fluctuations on mathematical bases and establishing principles of a demographic dynamics that preset analogies to the dynamics of material systems."" (DSB).‎

Bookseller reference : 45839

‎"VOLTERRA, VITO.‎

‎Sur les Vibrations des Corpes élastiques isotropes.‎

‎(Berlin, Stockholm, Paris, Alqvist & Wiksell, 1894). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", vol. 18, pp. 161-232.‎

‎First edition. ""Vito Volterra (1860-1940), who succeeded Beltrami as professor of mathematical physics at Rome, is the first of the founders of a general theory of integral equations. He wrote papers on the subject from 1884 on and principal ones in 1896 and 1897."" (Morris Kline).‎

Bookseller reference : 39161

‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎First printing of Volterra's paper on the vibrations of light in a birefringence media.‎

Bookseller reference : 49650

‎"VOLTERRA, VITO.‎

‎Sur les équations intégro-différentielles et leurs applications.‎

‎[Berlin, Stockholm, Paris, F. & G. Beijer, 1912]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 35. Fine and clean. Pp. 295-356.‎

‎First printing.‎

Bookseller reference : 45901

‎"VON NEUMANN, JOHN.‎

‎Die Einführung analytischer Parameter in topologischen Gruppen.‎

‎Princeton & Hamburg, 1933. Offprint from 'Annals of Mathematics' volume 34, pp. 170-190. Royal8vo. Original printed wrappers. Small tear to back wrapper. Corners a little bumped and frayed. Internally fine and clean. In all a good copy.‎

‎First edition offprint issue. ""One of the highlights of Von Neumann's career... solving Hilbert's fifth problem for compact groups."" (DSB).‎

Bookseller reference : 34733

‎"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

‎"WEIERSTRASS, KARL & LEOPOLD KRONECKER.‎

‎Über die Flächen, deren mittlere Krümmung überall gleich Null ist"" (And Kronecker:) Über bilineare Formen.‎

‎Berlin, Königl. Akad. d. Wissenschaften, 1866. Uncut in orig. printed wrappers in ""Monatsbericht der Königlichen Preussischen Akademie der Wissenschaften zu Berlin"", Sept., October 1866. Pp. 595-655. Weierstrass' paper: pp.612-625. Kronecker's paper: pp. 597-612‎

‎Both papers first edition. Weierstrass is considered the most importen nineteenth-century german mathematician after Gauss and Riemann.‎

Bookseller reference : 39156

‎"WEIERSTRASS, KARL.‎

‎Abhandlungen aus der Functionenlehre.‎

‎Berlin, Julius Springer, 1886. Lex8vo. Contemp. hcalf. Spine gilt and with gilt lettering. (8),262 pp. A faint dampstain to inner lower corners on some leaves. The last 5 leaves a bit soiled.‎

‎First edition in book form of Weierstarss' s main papers in Function Theory. In this collected form the papers were slightly revised by the author. - Parkinson: Breakthroughs (He rigorously develops the theory of functions in ""Abhandlungen aus Functionentheorie"").‎

Bookseller reference : 41357

‎"WEIERSTRASS, KARL.‎

‎Über eine besondere Gattung von Minimalflecken.‎

‎Berlin, Königl. Akad. d. Wissenschaften, 1867. Orig. printed wrappers, uncut. In ""Monatsbericht der Königlich Preussischen Akademie der Wissenschaften zu Berlin"", August 1867, pp. 511-598. Weierstrass' paper: pp. 511-518.‎

‎First edition. Weierstrass is considered the most important German mathematician in the nineteenth-century after Gauss and Riemann.‎

Bookseller reference : 39157

‎"WEIERSTRASS, KARL.‎

‎Über eine besondere Gattung von Minimalflächen.‎

‎Berlin, Harrwitz und Gossmann, 1867. 8vo. Uncut opened in the original printed wrappers. In ""Monatsbericht der Königlich Preussischen Akademie der Wissenschaften zu Berlin"", August 1867. Pp. 511-518. [Entire heft: Pp. 511-488].‎

‎First edition.‎

Bookseller reference : 58878