# Mathematics, Analysis, Algebra

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

Berlin: Georg Reimer, 1874. First edition, rare, of the doctoral thesis of “the greatest woman mathematician prior to the twentieth century” (DSB) and the first woman in Europe to obtain a doctorate in mathematics. The thesis contains what is now called the ‘Cauchy-Kowalevsky’ theorem on the existence of solutions of..... More

Item #4203

Paris: L’imprimerie Royale / Jean Boudot, 1696/1700. A fine sammelband comprising the first editions of the first books on the differential and integral calculus, respectively. “It was through his wide network of acquaintances in various European countries that Leibniz put into effect all his strategies for the spread of his..... More

Item #2848

First edition. Paris: Duprat, 1802. A fine copy of this influential text, which according to Babbage was "so perfect that any comment was unnecassary". "In discussing with a friend the formation of a section of the British and Foreign Bible Society, a society which had the distribution of Bibles as... More

Item #2252

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

LEFÈVRE D’ÉTAPLES, Jacques, BO[U]VELLES, Charles de, & CLICHTOVE, Josse.

Paris: H. Estienne & W. Hopyl, 27 June 1503. First edition of this very rare collection of works, in an attractive Roger Payne binding. The individual works are all first editions with the exception of Lefèvre’s Epitome of Boethius’ De arithmetica (first, 1496) and an unattributed Opusculum de p[r]axi numerorum..... More

Item #3866

Leipzig: Christopher Günther for J. Gross & J. F. Gleditsch, 1684. First edition of Leibniz’s invention of the differential calculus. “Leibniz was an almost universal genius whose place in the history of mathematics depends on his being an independent inventor of the infinitesimal calculus and on his contributions to combinatorial..... More

Item #4714

London: Printed by S[arah]. G[riffin]. and B[ennet]. G[riffin]. for Benjamin Tooke and Thomas Sawbridge, [1669]. First edition, first issue, extremely rare, of the first of Leybourn’s books on the subject. This issue has ‘dialling:’ in line 2 of the title and lacks imprint date; the more common (but still rare)..... More

Item #4610

Kazan: Universitetskai a tip. 1835. First edition, incredibly rare offprint, of this important book-length memoir on the foundations of calculus and real analysis by the first inventor of non-euclidean geometry. “As early as 1835, Lobachevsky showed in a memoir [the offered work] the necessity of distinguishing between continuity and differentiability”... More

Item #3652

Lyons: Jacob Marechal for Simon Vincent, 5 May 1517. Third edition, the first edited by the Lullist Bernard de Lavinheta (d. ca. 1530), of the Ars Magna, his greatest work, now recognised as perhaps the first work in computer science. “Lull invented an ‘art of finding truth’ which inspired Leibniz's... More

Item #4363

London: Printed for the author’s children and sold by A. Millar, et al. 1748. First edition, large-paper copy, of Maclaurin’s statement of Newtonian theory, one of the three “most outstanding popular introductions to Newtonian science of the eighteenth century” (I. B. Cohen, Franklin and Newton, 1956, p. 209). “Though a...... More

Item #3409

1743. Edinburgh: 5 February. Important autograph letter from the great Scottish mathematician Colin Maclaurin (1698-1746) discussing his most important work, Treatise of Fluxions (1742), “the earliest logical and systematic publication of the Newtonian methods. It stood as a model of rigor until the appearance of Cauchy’s Cours d’analyse in 1821”..... More

Item #3411

Edinburgh: Printed by T.W. and T. Ruddimans, 1742. First edition, a very fine large and thick paper copy, of “the earliest logical and systematic publication of the Newtonian methods. It stood as a model of rigor until the appearance of Cauchy’s Cours d’Analyse in 1821” (DSB). The Treatise was written..... More

Item #4222

Florence: Giuseppe Cocchini, 1666 (dedication dated 14 July, 1667). First edition, first issue, a magnificent copy bound in contemporary Italian red morocco gilt, probably for presentation, of the only publication of the Accademia del Cimento, the first organisation founded for the sole purpose of making scientific experiments (the more common... More

Item #4707

Venice: Franciscum Franciscium Senensem, 1575. First and only edition (see Rara Aritmetica) of the first clear statement of the principle of mathematical induction. “Francesco Maurolico is generally recognized to have been one of the foremost mathematicians of the sixteenth century” (Rosen); Cajori has called him ‘the greatest geometer of the..... More

Item #2613

Messina: Pietro Spira, 1558. First edition, ‘excessively rare’ (Sotheran, 1917), of Maurolico’s Latin translations of works on ‘sphaerics’ by four ancient Greek writers, Autolycus, Menelaus, Euclid and Theodosius, those of the first two authors constituting the first printed editions. Maurolico, one of the most original mathematicians of the 16th century..... More

Item #2881

Leipzig: F.W. Vogel, 1909. First edition of Minkowski’s famous lecture on his theory of four-dimensional space-time, the first published account of this theory to be illustrated with ‘spacetime diagrams’, which were widely used later by Stephen Hawking, Roger Penrose and others in the development of general relativity. “In ‘Space and..... More

Item #4418

Paris: J. Quilau, 1708. A fine copy, of the first separately published textbook of probability. “In 1708 [Montmort] published his work on Chances, where with the courage of Columbus he revealed a new world to mathematicians” (Todhunter, p. 78). “The Essay (1708) is the first published comprehensive text on probability... More

Item #3894

Edinburgh; Padua: Andrew Hart; Giacomo Cadorino, 1619; [1667]. First edition, extremely rare, of this complement to Napier’s epoch-making Mirifici logorithmorum canonis descriptio (1614) – while the Descriptio gave the first ever table of logarithms, it was in the Constructio that Napier explained the method of their construction. It is here... More

Item #4638

Princeton: Princeton University Press, 1956. First edition of Nash’s most famous work in pure mathematics, his solution of “a deep philosophical problem concerning geometry”, first posed by Bernhard Riemann, “one of the most important pieces of mathematical analysis in this century” which “has completely changed the perspective on partial differential..... More

Item #3536

Cambridge / London: Typis Academicus / Benjamin Tooke, 1707. First edition of Newton’s treatise on algebra, or ‘universal arithmetic,’ his “most often read and republished mathematical work” (Whiteside). “Included are ‘Newton’s identities’ providing expressions for the sums of the ith powers of the roots of any polynomial equation, for any..... More

Item #4064

Cambridge; London: Typis Academicus; Benjamin Tooke, 1707. First edition of Newton’s treatise on algebra, or ‘universal arithmetic,’ his “most often read and republished mathematical work” (Whiteside). “Included are ‘Newton’s identities’ providing expressions for the sums of the ith powers of the roots of any polynomial equation, for any integer i...... More

Item #4639

First edition. Antwerp: heirs of Arnold Birckman, 1567. Exceptionally fine copy, bound in citron morocco for Jacques-Auguste de Thou (1553-1617), of this rare and celebrated treatise on algebra. “Considered the greatest of Portuguese mathematicians, Nuñez reveals in his discoveries, theories, and publications that he was a first-rate geographer, physicist, cosmologist..... More

Item #3645

Paris: Guillaume Desprez, 1659. First edition, extremely rare (one of about 120 copies printed), of one of Pascal’s most brilliant works. “Édition originale, extrêmement rare, de la dernière œuvre de Pascal, l’une des plus éclatantes de son génie” (Lucien Scheler in Tchemerzine, V, pp. 54-55). “Pascal devoted himself during 1658..... More

Item #4403