Carl Friedrich Gauss

In this volume are included all of Gauss's number-theoretic works: his masterpiece, Disquisitiones Arithmeticae, published when Gauss was only 25 years old; several papers published during the ensuing 31 years; and papers taken from material found in Gauss's handwriting after his death. These papers include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. This reprint of the German translation from Latin of the second edition published in 1889 includes an extensive appendix and concludes with a commentary on the papers (with references, where appropriate, to the relevant pages of the Disquisitiones).

The first translation into English of the standard work on the theory of numbers by one of the greatest masters of modern mathematical analysis, this classic was first published in 1801 in Latin. It has continued to be important to mathematicians as the source of the ideas from which number theory was developed and to students of the history of the electrical, astronomical, and engineering sciences, which were furthered by Gauss’ application of his mathematical principles to these fields. Father Clarke has achieved a sympathetic and faithful translation of this monumental work. The book is complete and unabridged, and a bibliography of the references cited by Gauss has been added by the translator. "Whatever set of values is adopted, Gauss's Disquistiones Arithmeticae surely belongs among the greatest mathematical treatises of all fields and periods. . . . The appearance of an English version of this classic is most welcome."—Asger Aaboe.

In the 1820s Gauss published two memoirs on least squares, which contain his final, definitive treatment of the area along with a wealth of material on probability, statistics, numerical analysis, and geodesy. These memoirs, originally published in Latin with German Notices, have been inaccessible to the English-speaking community. Here for the first time they are collected in an English translation. For scholars interested in comparisons the book includes the original text and the English translation on facing pages. More generally the book will be of interest to statisticians, numerical analysts, and other scientists who are interested in what Gauss did and how he set about doing it. An Afterword by the translator, G. W. Stewart, places Gauss's contributions in historical perspective.