# Mathematics, Analysis, Algebra

Paris: David l'aîné, 1747. First edition of this important work on atmospheric tides: “Alembert’s treatise on winds contained the first general use of partial differential equations in mathematical physics, a technique later perfected by Euler.” (Norman 34). “In 1747 d’Alembert published two more important works, one of which, the Réflexions... More

Item #3480

Paris: Chez David l’aîné, 1743. First edition of this landmark in the history of mechanics. “This book, D’Alembert’s magnum opus, was one of the first to give a unified view of mechanics. It started out from a minimum of principles, one of which came to be named after him.” (Landmark... More

Item #3429

First edition. Venice: Bernardinus Bindonus, 1537. Very rare editio princeps of Apollonius’ Conics, the basic treatise on the subject, “which recognized and named the ellipse, parabola, and hyperbola” (Horblit 4, on the later edition of 1566). This is one of the three greatest mathematical treatises of antiquity, alongside those of... More

Item #3075

Cambidge: printed by J. Smith . . . and sold by Deighton & Sons [etc.], 1813. First edition, extremely rare, of the only volume of the Memoirs of the Analytical Society, written entirely by Babbage and Herschel while students at Cambridge University. The aim of the society was to promote... More

Item #3307

Strasbourg: Johann Reinhold Dulsseker, 1738. First edition of Bernoulli’s epochal work on fluid dynamics and the kinetic theory of gases, containing the famous ‘Bernoulli equation’ for fluid flow. “Besides introducing the first hydraulic theory of fluid flow, this book is the most remarkable general work in theoretical and applied mechanics... More

Item #3842

First edition. Lausanne & Geneva: Marci-Michaelis Bousquet, 1742. An exceptionally fine and complete copy with both the portraits which often lack, from the collection of Robert Honeyman. “Bernoulli published only one book, Théorie de la manoeuvre des vaisseaux (1714) and apart from this, his dissertation De motu musculorum (1694) and... More

Item #3597

First edition. Bologna: G.B. Ferroni, 1648. An outstanding copy of this rare compendious scholastic mathematical work by the Jesuit mathematician Mario Bettini (1582-1657), encompassing all the major fields of mathematics, but paying special attention to geometry. Bettini’s Aerarium covers a wealth of information not just in mathematics but also astronomical... More

Item #2435

London: Printed by N[icholas] O[kes] for Simon Waterson, 1609. First edition, very rare, of one of the earliest English books on dialing, the last of four books published by the famous English mathematician during his lifetime. It is unusual to find such early English scientific books in fine condition and... More

Item #3366

First edition. Marosvasarhely: Kali Simon, 1843. An exceptionally fine copy, in the original boards, of Bolyai’s work on the foundations of mathematics, and the last of the great works of Farkas Bolyai. It is in part based on the author’s Az arithmethica eleje published in 1830 and on the second... More

Item #3558

First edition. Vienna: In Officina Libraria Kaliwodiana, 1758. An exceptionally fine copy, in untouched contemporary blind tooled pigskin, of “Boscovich’s masterpiece” (Norman), a work “now recognized as a fundamental influence on modern mathematical physics” (Printing and the Mind of Man), and a notorious rarity. Only two copies of this rare... More

Item #4128

Paris: Chez de Bure Frères, 1829. First edition, very rare. Following his earlier textbooks, the Cours d’Analyse (1821) and R sum des Leçons (1823), which provided the first rigorous formulation of the calculus of functions of a real variable, Cauchy in this work for the first time treats complex functions... More

Item #3696

Paris: Chez de Bure Frères, 1825. First edition of this very rare memoir in which “Cauchy began to lay the foundations of the general theory of analytic functions of a complex variable and their integration by residues.” (Landmark Writtings in Western Mathematics, ch. 28). “This paper is considered by many... More

Item #3163

Bologna: Heirs of Evangelista Dozza, 1653. Second edition (first, 1635) of Cavalieri’s text containing the discovery of the ‘method of indivisibles’, one of the most important forerunners of the integral calculus. Book II of the work includes the statement of ‘Cavalieri's principle’ for the determination of areas and volumes, which... More

Item #4202

Bologna: Victor Benatis, 1643. First edition. “Cavalieri, a pupil of Galileo, introduced logarithms into Italy in his Trigonometria and several other works.” (Hook & Norman: Origins of Cyberspace, No. 3). “From the standpoint of mathematics alone the Italian writer who influenced the science most in the 17th century was probably... More

Item #3005

First edition. Leiden: Joost van Colster and Jacob Marcus, 1615. First edition of this rare work, containing the best approximation to the value of π achieved at that time. “Van Ceulen was an indefatigable computer and concentrated on the computation of π sometimes called Ludolph’s number … He became... More

Item #3273

First edition. Paris: Gauthier-Villars, 1865. A very good copy in contemporary half calf of his sequel to the ' Géométrie Superiéure'. "Chasles wrote two textbooks for his course at the Sorbonne. The first of these, the 'Traité de Géométrie Supérieure (1852), is based on the elementary theories of the cross... More

Item #2023

Venice: Aldus (Paolo Manuzio), 1558. First edition of Commandino's commentary. The Greek text of this writing by Ptolemy on stereographic projection is lost, a Latin version appeared in Basel in 1536, but this is the first separate and best edition, translated from the Arabic and edited by Commandino with his... More

Item #2236

Geneve: Freres Cramer & Cl. Philbert, 1750. First edition of this major treatise on analytic geometry, containing Cramer’s rule and paradox, “the most complete exposition of algebraic curves existing at that time” (Struik), and “a worthy successor to Newton’s Enumeratio.” (Boyer). According to Cantor, this together with Euler’s Introductio, forms... More

Item #2618

Amsterdam: Elzevir, 1659-1661. A fine copy of van Schooten’s important second edition of the Geometria, Descartes’s magnum opus (DSB), and one of the key texts in the history of mathematics. Descartes’ “application of modern algebraic arithmetic to ancient geometry created the analytical geometry which was the basis of the post-Euclidean... More

Item #3462

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

Lausanne & Geneve: Marcum-Michaelem Bosquet & Socios, 1744. First edition of “Euler’s most valuable contribution to mathematics in which he developed the concept of the calculus of variations.” (Norman). “This work displays an amount of mathematical genius seldom rivaled.” (Cajori). “The book brought him immediate fame and recognition as the... More

Item #4048