Disquisitiones Arithmeticae. GAUSS, Carl Friedrich

 

Disquisitiones Arithmeticae.

GAUSS, Carl Friedrich

 

Description :

An outstanding copy of Gauss’ masterpiece which created a new epoch in the history of mathematics; entirely untouched in the original interim wrappers and the copy of Polish mathematician and astronomer Jan Sniadecki who collaborated with Gauss on the observation of the planetoid Ceres which led Gauss to his discovery of the method of least squares (see below). "Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics" (Printing and the Mind of Man). PMM 257; Evans 11; Horblit 38; Dibner 114. "In the late eighteenth century [number theory] consisted of a large collection of isolated results. In his Disquisitiones Gauss summarized previous work in a systematic way, solved some of the most difficult outstanding questions, and formulated concepts and questions that set the pattern of research for a century and still have significant today. He introduced congruence of integers with respect to a modulus (a = b (mod c) if c divides a-b), the first significant algebraic example of the now ubiquitous concept of equivalence relation. He proved the law of quadratic reciprocity, developed the theory of composition of quadratic forms, and completely analyzed the cyclotomic equation. The Disquisitiones almost instantly won Gauss recognition by mathematicians as their prince" (DSB). "Published when Gauss was just twenty-four, Disquisitiones arithmeticae revolutionized number theory. In this book Gauss standardized the notation; he systemized the existing theory and extended it; and he classified the problems to be studied and the known methods of attack and introduced new methods The Disquisitiones not only began the modern theory of numbers but determined the direction of work in the subject up to the present time. The typesetters of this work were unable to understand Gauss’ new and difficult mathematics, creating numerous elaborate mistakes which Gauss was unable to correct in proof. After the book was printed Gauss insisted that, in addition to an unusually lengthy four-page errata, the worst mistakes be corrected by cancel leaves to be inserted in copies before sale [as in the offered copy]. Gauss’s highly technical work was printed in a small edition, and the difficulty of understanding it was hardly alleviated by the sloppy typesetting. The few mathematicians who were able to read the Disquisitiones immediately hailed Gauss as their prince, but the full understanding required for further development until the publication in 1863 of Dirichlet’s less austere exposition in his Vorelsungen über Zahlentheorie." (Norman). Provenance: Jan Sniadecki (1756-1830) was a Polish mathematician and astronomer, and the director of the astronomical observatories at Kraków and Vilnius. He was deeply involved in the celebrated discovery of the new planetoid Ceres in 1801 and, besides publishing several works himself on this subject, corresponded directly with Gauss on the orbit of Ceres. "In 1801 the creativity of the previous years was reflected in two extraordinary achievements, the Disquisitiones arithmeticae and the calculation of the orbit of the newly discovered planet Ceres In January 1801 G. Piazzi had briefly observed and lost a new planet. During the rest of that year the astronomers vainly tried to relocate it In September, as his Disquisitiones was coming off the press, Gauss decided to take up the challenge. To it he applied both a more accurate orbit theory (based on the ellipse rather than the usual circular approximation) and improved numerical methods (based on least squares). By December the task was done, and Ceres was soon found in the predicated position. This extraordinary feat of locating a tiny, distant heavenly body from seemingly insufficient information appeared to be almost superhuman, especially since Gauss did not reveal his methods. With the Disquisitiones it established his reputation as a mathematical and scientific genius of the first order. The decade that b. N° de réf. du libraire 2941

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