# Mathematics, Analysis, Algebra

Braunschweig: Friedrich Vieweg, 1872. First edition, very rare in commerce, of Dedekind’s great work on the foundations of mathematics. “This short work [Stetigkeit und irrationale Zahlen] marks a significant epoch in the movement known as the arithmetization of analysis, that is, the replacement of intuitive geometric notions by concepts described... More

Item #4558

First edition. Paris: H. Drouart, 1621. Editio princeps of the first systematic treatise on algebra (Smith, Rara Arithmetica, p. 348), comprising the first printing of the Greek text, accompanied by Xylander’s Latin translation (1575) and Bachet’s commentary. “The Arithmetica is essentially a logistical work, but with the difference that Diophantus’... More

Item #2441

[N.p. N.p.], 1879-81. Provenance: The January 1879 printing is Dodgson’s own copy with his autograph emendations. The other two printings are the copies of Dodgson’s child friend Agnes Caroline Smith: the February 1879 printing is signed by her (evidently the hand of a child), and the 1881 printing is inscribed... More

Item #3951

Paris: Melchior Mondiere, 1625. Very rare editio princeps of this important text by Euclid, his only work in pure geometry, other than the Elements, to have survived in Greek. It is here accompanied by a commentary, or rather an introduction, by Marinus of Naples (5th century AD), the pupil and... More

Item #3427

St. Petersburg: Imperial Academy of Sciences, 1769-1771. First edition, and a very fine copy, of Euler’s rare work on optics, ‘widely known and important in the physics of the eighteenth century’ and which ‘laid the foundations of the calculation of optical systems’ (DSB). The first volume presents his general theory... More

Item #3300

St. Petersburg: Imperial Academy of Sciences, 1768-1772. First edition, in the original interim wrappers, of these letters to the Princess Friederike Charlotte Leopoldine Louise of Brandenburg-Schwedt, to whom Euler had given lessons during his stay in Berlin. The work “had an immense success and profoundly influenced contemporary philosophy” (PMM 196... More

Item #3992

St. Petersburg: Academia Imperialis Scientiarum, 1783-85. First edition of this collection of 28 previously unpublished papers by Euler (listed below), of which the most important is ‘Observationes circa divisionem quadratorum per numeros primos’, which gives the first clear statement of the ‘law of quadratic reciprocity,’ called the ‘golden theorem’ by... More

Item #3318

Berlin: Haude & Spener, 1746; 1750; 1751. First edition, an outstanding copy uncut in the original boards, of Euler’s three-volume Opuscula varii argumenti (although only the first volume bears this title), a collection of thirteen tracts, all except one published here for the first time. The most important is the... More

Item #4420

Toulouse: Bernard Bosc, 1670. First edition, a fine copy, of Fermat’s annotated edition of Diophantus’ Arithmetica. This is the first printing of Fermat’s contributions to the theory of numbers, of which he is the undisputed founder, including his famous statement of ‘Fermat’s last theorem.’ Since most of Fermat’s work in... More

Item #4489

Paris: Firmin Didot, 1822. First edition of the first mathematical study of heat diffusion, the first major mathematization of a branch of physics outside mechanics. “This work marks an epoch in the history of both pure and applied mathematics. It is the source of all modern methods in mathematical physics... More

Item #3841

Jena: Hermann Pohle, 1891. First edition, very rare, of this important essay, in which Frege carried out a revision of his famous Begriffsschrift (1879), which was necessary in order to carry out his programme of reducing arithmetic to formal logic. Function und Begriff contains Frege’s two main innovations since the... More

Item #3523

First edition. Leipzig: Weidmannschen Buchhandlung, 1840. First separate edition, Gauss’s own personal copy, of “the first systematic treatment of potential theory as a mathematical topic, [which] recognized the necessity of existence theorems in that field, and reached a standard of rigor that remained unsurpassed for more than a century” (DSB... More

Item #3023

Leipzig: Gerh. Fleischer, 1801. First edition, rare, of Gauss’ masterpiece, “a book that begins a new epoch in mathematics … Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics” (PMM). “Published when Gauss was just twenty-four, Disquisitiones arithmeticae revolutionized number theory... More

Item #4572

Göttingen: Dieterich, 1811, 1813, 1816, 1820, 1828. First editions, journal issues, of thirteen important papers by Gauss, including works on the fundamental theorem of algebra, number theory, hypergeometric functions, approximation theory, differential geometry, gravitation, and celestial mechanics. “Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses... More

Item #4298

First edition. Berlin: Königlichen Akademie der Wissenschaften, 1828. First printing of what is now called the Gauss-Newton interpolation formula; which enables one to predict the value of a quantity given a finite number of observations. Gauss had lectured on the interpolation formula at Göttingen in 1812; his then student Encke... More

Item #2983

Salem, Mass. Salem Press, 1886. First edition, very rare offprint issue. “One of Gibbs’ most famous papers was entitled ‘On Multiple Algebra.’ It was given as an ‘Address before the Section of Mathematics and Astronomy of the American Association for the Advancement of Science, by the Vice-President’ and was published... More

Item #4433

Leipzig: Akademische Verlagsgesellschaft, 1931; 1930. First edition, extremely rare author’s presentation offprint, of Gödel’s famous incompleteness theorem, “one of the major contributions to modern scientific thought” (Nagel & Newman). “Every system of arithmetic contains arithmetical propositions, by which is meant propositions concerned solely with relations between whole numbers, which can... More

Item #4559

Leipzig & Berlin: B.G. Teubner, 1931-33. First editions, and a fine set in the original printed wrappers, of these rare proceedings to which Gödel contributed thirteen important papers and remarks on the foundations of logic and mathematics (see below for a complete annotated listing). The most important are perhaps ‘Über... More

Item #3707

First edition. Warsaw: Dziewulski, 1930. A fine copy of his doctoral dissertation - a seminal work in mathematical logic (Van Heijenoort: From Frege to Gödel). “Herbrand gave early signs of his mathematical gifts, entering the École Normale Supérieure at the exceptional age of seventeen and ranking first in the entering... More

Item #2294

London: printed by W. Bulmer [for the Royal Society], 1814. Very rare separately-paginated offprint of Herschel’s account of the ‘calculus of operations,’ which formed a major part of the programme of reform promoted by the group of Cambridge mathematicians (which included Babbage and Herschel) who called themselves the ‘Analytical Society.’... More

Item #4283

First edition, offprint issue. Berlin: Springer, 1925/1926. Very rare separate printing (WorldCat locates just two copies) of the most detailed exposition of Hilbert’s proposal for the foundation of classical mathematics, which became known as Hilbert’s Program. This paper further contains his attempted proof of the continuum hypothesis which led to... More

Item #3181

Berlin: Julius Springer, 1923. First edition, the extremely rare author’s presentation offprint issue, of the second major paper in the development of the 'Hilbert programme.' Based upon a lecture given at Leipzig in September 1923, it is the sequel to Hilbert's Neubegründung der Mathematik (1922), in which Hilbert had put forward his proposal... More

Item #4475

Leipzig: Teubner, 1901. First complete publication, extremely rare offprint issue, of Hilbert’s famous and enormously influential address to the International Congress of Mathematicians at Paris in 1900 in which he set forth a list of twenty-three problems that he predicted would be of central importance to the advance of mathematics... More

Item #3656

Florence: In officina Iuntarum, Bernardi filiorum, 1567. First edition, very rare, of the only surviving work of Hipparchus (c. 190-127 BC). “Even the most casual discussion of ancient astronomy will not fail to call Hipparchus of Nicaea in Bithynia ‘the greatest astronomer of antiquity’ (Otto Neugebauer, ‘Notes on Hipparchus,’ Astronomy... More

Item #3643

[1890]. Important autograph manuscript by “the greatest woman mathematician prior to the twentieth century” (DSB) and the first woman in Europe to obtain a doctorate in mathematics. This paper complements and completes her most famous work, ‘Sur le problème de la rotation d’un corps solide autour d’un point fixe’ (Acta... More

Item #4276