St. Petersburg: Imperial Academy of Sciences, 1769-1770-1771. First edition, a beautiful copy in original wrappers, of Euler’s magnum opus on optics, “widely known and important in the physics of the eighteenth century,” which “laid the foundations of the calculation of optical systems” (DSB). “The Dioptricae presented a universal optics with..... More
Item #5225

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

Paris: Bernard, 1808. First printing, extremely rare, of the discovery of Fourier series, and their application to the mathematical theory of heat, appearing here 14 years before Fourier’s famous Théorie analytique de la chaleur. “This work marks an epoch in the history of both pure and applied mathematics. It is the..... More
Item #5302

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

Paris: Bachelier, 1846. First edition, a remarkable copy uncut in the original printed wrappers and very rare thus, of Galois' collected mathematical works, for the most part previously unpublished. Their posthumous publication was due to Joseph Liouville, editor of the leading French journal on pure and applied mathematics. “There have..... More
Item #5819

Göttingen: Dieterich, 1823-1828. First edition, extremely rare separately-paginated offprints, of Gauss’s definitive presentation of the theory of least squares which “was the dominant theme – the leitmotif – of nineteenth-century mathematical statistics” (Stigler, p. 11). “Surveying problems motivated Gauss to develop his ideas on least squares and more general problems..... More
Item #5422

New Haven: Tuttle, Morehouse & Taylor, 1881. First edition, first issue (see below), of this extremely rare pamphlet which “marks the beginning of modern vector analysis” (Crowe, p. 150). “Nearly all branches of classical physics and many areas of modern physics are now presented in the language of vectors, and..... More
Item #4853

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

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 #5482

Königsberg: Leupold, 1885. First edition, very rare, of Hilbert’s inaugural dissertation at the University of Königsberg, ‘On the invariant properties of special binary forms, in particular the spherical functions,’ in which he began his study of invariant theory. This subject was at the forefront of mathematics in the second half..... More
Item #4944

Leiden: Elzevir, 1657. First edition of Huygens' De ratiociniis in aleae ludo, the first printed treatise on probability. “Having heard in Paris about Pascal’s work in probability problems, Huygens (1629-95) himself took up their study in 1656. This resulted in the Tractatus de ratiociniis …, a treatise that remained the..... More
Item #5784

Linz: Hans Blanck, 1616. First edition, a considerably revised, rearranged and augmented version of Kepler’s Nova Stereometria published the year before, a work which is “generally regarded as one of the significant works in the prehistory of the calculus” (Gingerich in DSB). “Desiring to outfit his new household with the..... More
Item #5003

[Vols. I & II:] Brescia; [Vol. III:] Parma: Brescia: G. M. Riccardi; H. Rosati, 1684-86; 1692. First editions of two important works from the library of the distinguished Riccati family of mathematicians and physicists. The Prodromo, Lana’s most famous work, contains his design for an air-ship kept aloft by means..... More
Item #5640