# Mathematics, Analysis, Algebra

Lyon: Jean de Tournes, 1554. First edition, very rare, of “the first printed book on algebra in French and the richest among vernacular books on algebra” (Cifoletti, ‘The algebraic art of discourse,’ in Chemla, p. 125). Peletier believed that French was the perfect instrument for the sciences and “wrote L’Algèbre... More

Item #4026

Paris: Gauthier-Villars et Fils, 1892. First edition of Poincaré’s first paper on topology, which gave birth to the subject in its modern sense. “One of the most unexpected developments in twentieth-century mathematics has been the meteoric rise of the subject known as topology. Topology is sometimes described as ‘rubber-sheet geometry’... More

Item #3776

First edition. Paris: Gauthier-Villars, 1879. A fine copy, with the original printed wrappers, of Poincaré's thesis for his doctorate in science from the University of Paris. “Poincaré's doctoral thesis [was] on differential equations (not on methods of solution, but on existence theorems), which led to one of his most celebrated... More

Item #2928

First edition. Paris: l'Imprimerie Royal, 1820. An important contribution to the foundation of complex function theory. In this paper Possion was the first to carry out integration along a path in the complex plane. "Poisson noted in 1815 and discussed in [this paper] the use of integrals of complex functions... More

Item #1993

Paris: Bachelier, 1835. First edition of this classic work on the mathematical theory of heat conduction. “Poisson scored a point in this work by demonstrating how the conductibility of heat in the interior of bodies, far from being contained in the notion of flux as Fourier had held, must be... More

Item #3999

[The Association for Symbolic Logic], 1936. First edition, very rare offprint, of Post’s formulation of the notions of computation and solvability by means of a theoretical machine very similar to the concept of a Turing machine proposed by Alan Turing in his famous paper ‘On computable numbers.’ Alonzo Church had... More

Item #4062

Basel: Heinrich Petri & Peter Perna, 1561. Rare augmented edition of “the first systematic treatise on plane and spheric trigonometry to be published in Europe. Although it drew heavily on Arabic sources, those earlier treatises had been either lost or forgotten by 1533 when Regiomontanuss work was first printed. Among... More

Item #2852

Rome: Giacomo Mazzochi, 1516. Extremely rare first edition of this influential and controversial work, an important step towards the arithmetization of the theory of proportion. In the Eudoxian theory of proportion, treated in Book V of Euclid’s Elements, proportion is a relation between magnitudes of the same kind, and is... More

Item #3078

Göttingen: Dieterich, 1867. First edition, the very rare offprint issue, of Riemann’s important paper on minimal surfaces (i.e. surfaces of least area for a given boundary). “What his work lacks in quantity is more than compensated for by its superb quality. One of the most profound and imaginative mathematicians of... More

Item #3861

Göttingen: E. A. Huth, 1851. First edition of Riemann’s Dissertation, “one of the most important achievements of 19th century mathematics” (Laugwitz), “which marked a new era in the development of the theory of analytic functions” (Kolmogorov & Yushkevich, p. 199), introducing geometric and topological methods, notably the idea of a ‘Riemann... More

Item #4286

Göttingen: E. A. Huth, 1851. Very rare first edition of Riemann’s Dissertation, “one of the most important achievements of 19th century mathematics” (Laugwitz), “which marked a new era in the development of the theory of analytic functions” (Kolmogorov & Yushkevich, p. 199), introducing geometric and topological methods, notably the idea... More

Item #4523

Berlin: G. Reimer, 1857. First edition of Riemann's paper on Abelian functions, “one of the most notable masterworks of mathematics” (DSB), which develops much further the methods of his dissertation (Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse, 1851), using them to give the general solution of the... More

Item #4285

First edition. Paris: Hermann & Cie, 1950-1951. A fine copy of his classic text on distribution theory. Distributions (or generalized functions) were first introduced by Sergei Sobolev in 1935, but it was Schwartz who systematically studied the subject and eventually developed it into a full theory with practical applications. In... More

Item #1906

First edition. Helsingfors: Finnischen Literatur-Gesellschaft, 1885. A fine copy of his path-breaking memoir in which he first derived the Cauchy-Schwarz inequality – “one of the most widely used and most important inequalities in all of mathematics.” (J.Michael Steele). “In his most important work, a Festschrift for Weierstrass’ seventieth birthday, Schwarz... More

Item #2629

Nuremberg: Simon Halbmayer, 1627. First complete edition and the first edition of the fourth part (the first part was published in 1616, the first three parts together in 1618). The first book is a treatise on general mathematics and the principles of geometry. The second deals entirely with techniques of... More

Item #2235

[Amsterdam: Jan Rieuwertsz], 1677. First edition, and a very fine copy, of Spinoza’s Opera Posthuma which “have served, then and since, with the Tractatus Theologico-Politicus, to immortalize his name” (PMM 153). The first work in the volume is “Spinoza’s one indisputable masterpiece, the Ethics” (Bennett, A Study of Spinoza’s Ethics... More

Item #4364

Leyden: Jan Paedts Jacobsz, 1608-05-05-08. Very rare first edition in French of this collection of works, which was published almost simultaneously in Dutch, French and Latin. They deal, among other topics, with geometry, trigonometry, perspective, and double-entry book-keeping – Stevin was one of the first authors to compose a treatise... More

Item #4588

London: [by Thomas Dawson] for John Harrison [the elder], 1588. First edition in English, very rare, of the first three books of Tartaglia’s 1546 Quesiti et Inventioni Diverse, dealing with ballistics and expanding and correcting the treatment in his 1537 Nova Scientia, the first systematic treatise on the subject. The... More

Item #4103

London: C. F. Hodgson and Son, 1939. First edition, journal issue in original printed wrappers, of Turing’s PhD thesis, “one of the key documents in the history of mathematics and computer science” (Appel), and perhaps Turing’s most formidable paper. ““Systems of logic based on ordinals” is a profound work of... More

Item #4425

London: C.F. Hodgson & Son, 1939. First edition, the incredibly rare offprint issue, and the copy of Robin Gandy, of Turing’s PhD thesis, “one of the key documents in the history of mathematics and computer science” (Appel), and perhaps Turing’s most formidable paper. “Systems of logic based on ordinals is... More

Item #4537

Princeton: Princeton University Press, 1950. First edition of Turing’s last paper in pure mathematics, a return to his great work ‘On computable numbers’ in which he had proved that the halting problem – the problem of deciding whether a given Turing machine ever reaches the halting state when provided with... More

Item #3490

Paris: J. Jacquin, 1629/1630. Very rare first edition of the first French translation and exposition of Viète’s In artem analyticum isagoge (Tours, 1591), the earliest work on symbolic algebra, here bound with a first edition of Vaulezard’s translation of Viète’s Zeteticorum libri quinque (Tours, 1593), which gives examples of the... More

Item #3128

Cambridge: at the University Press, 1910-12-13. First edition of all three volumes of this monumental work. Complete sets of the first edition which, like ours, are not ex-library, are very rare on the market – only two such copies have sold at auction in the past 25 years. Probably named... More

Item #3562