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: Imperial Academy of Sciences, 1770. First edition in German, its language of composition, and first obtainable edition, of Euler’s ‘Complete instruction in algebra’, which takes the reader step-by-step from the basics, including negative and imaginary numbers, through to the solution of quadratic, cubic and biquadratic equations, and concluding..... More
Item #5122

Toulouse: Bernard Bosc, 1670. First edition, the superb Macclesfield copy printed on large and thick paper and with the engraved frontispiece portrait of Fermat (intended only for the few large paper copies), of Fermat’s annotated edition of Diophantus’ Arithmetica. This is the first printing of Fermat’s contributions to the theory..... More
Item #5170

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

Göttingen: Dieterich, 1818. First edition, very rare separately-paginated offprint, preceding the journal appearance in Commentationes Societatis Regiae Scientiarum Gottingensis (vol. 4, pp. 21-48) by two years. “In his first years at Göttingen, Gauss experienced a second upsurge of ideas and publications in various fields of mathematics. Among the latter were several..... More
Item #5312

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

Warsaw: Dziewulski, 1930. First edition, rare, and a fine copy in the original printed wrappers, of Herbrand’s doctoral dissertation, written in 1929 as a contribution to Hilbert’s programme. Bernays described Herbrand’s theorem as “the central theorem of predicate logic”, and van Heijenoort wrote that “[Frege’s] Begriffsschrift (1879), Löwenheim’s paper [‘Über..... More
Item #5040

Hamburg: Verlag des mathematischen Seminars, 1922. First edition, journal issue in the original printed wrappers, and a copy with excellent provenance, of the first major paper in the development of the ‘Hilbert programme,’ in which Hilbert put forward his proposal for a foundation for all of mathematics based on axiomatics and logic..... More
Item #4823

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’” (Neugebauer, p. 320). Our knowledge of..... More
Item #3643

Paris: Gauthier-Villars, 1870. First edition, very rare, of “the book that established group theory as a subject in its own right in mathematics” (Gray, p. 149). “Jordan’s monumental work, Traité des Substitutions et des Équations algébriques, published in 1870, is a masterpiece of mathematical architecture. The beauty of the edifice..... More
Item #4912

Paris; Paris: Veuve Desaint; de l’Imprimerie de la République, 1788; An V [1797]. An exceptional volume, in a fine contemporary binding, containing the first edition of Lagrange’s masterpiece, the Méchanique, “one of the outstanding landmarks in the history of both mathematics and mechanics” (Sarton, p. 470) and “perhaps the most..... More
Item #4300

Paris: Firmin Didot, 1806. First edition, second issue, but the first to contain the Supplement, of the invention of the method of least squares, “the automobile of modern statistical analysis” and the origin of “the most famous priority dispute in the history of statistics” (Stigler). “In 1805 Legendre published the..... More
Item #5112