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’ problems are..... More
Item #2441

[Berlin: c. 1846]. A remarkable survival, this is the autograph working manuscript of a paper on the application of mathematical analysis to problems in physics by “one of the most important mathematicians of the 19th century … the man who, more than any other, brought rigour to mathematical analysis” (Gray..... More
Item #4921

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: Academia Imperialis Scientiarum, 1783-85. First edition of this collection of 28 previously unpublished papers by Euler (listed below), of which the most important is ‘Observationes circa divisionem quadratorum per numeros primos’, which gives the first clear statement of the ‘law of quadratic reciprocity,’ called the ‘golden theorem’ by..... More
Item #3318

St. Petersburg: Typis Academiae, 1741. First edition of “one of Euler's most famous papers—the Königsberg bridge problem. It is often cited as the earliest paper in both topology and graph theory” (Euler Archive, E53). The city of Königsberg is situated on the River Pregel, across which seven bridges had been..... More
Item #4791

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

Leipzig: Gerh. Fleischer, 1801. First edition, rare, of Gauss’ masterpiece, “a book that begins a new epoch in mathematics … Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics” (PMM). “Published when Gauss was just twenty-four, Disquisitiones arithmeticae revolutionized number theory..... More
Item #4572

Berlin: Königlichen Akademie der Wissenschaften, 1828. First printing of what is now called the Gauss-Newton interpolation formula; which enables one to predict the value of a quantity given a finite number of observations. Gauss had lectured on the interpolation formula at Göttingen in 1812; his then student Encke attended Gauss’s..... More
Item #2983

Leipzig & Berlin: B.G. Teubner, 1931-33. First editions, and a fine set in the original printed wrappers, of these rare proceedings to which Gödel contributed thirteen important papers and remarks on the foundations of logic and mathematics (see below for a complete annotated listing). The most important are perhaps ‘Über..... More
Item #3707

London: printed by W. Bulmer [for the Royal Society], 1814. Very rare separately-paginated offprint of Herschel’s account of the ‘calculus of operations,’ which formed a major part of the programme of reform promoted by the group of Cambridge mathematicians (which included Babbage and Herschel) who called themselves the ‘Analytical Society.’..... More
Item #4283

Berlin: Julius Springer, 1923. First edition, the extremely rare author’s presentation offprint issue, of the second major paper in the development of the 'Hilbert programme.' Based upon a lecture given at Leipzig in September 1923, it is the sequel to Hilbert's Neubegründung der Mathematik (1922), in which Hilbert had put forward his proposal..... More
Item #4475

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’ (Otto Neugebauer, ‘Notes on Hipparchus,’ Astronomy..... More
Item #3643