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**KARL FRIEDRICH GAUSS (1777-1855)**

*Disquisitiones Arithmeticae*. Leipzig: Gerhard Fleischer, junior, 1801. 8° (204 x 120mm). Leaves B7, G4, K3, Ff7 and Tt6 are cancels, 16pp. adverts. for the Parisian bookseller Courcier, November 1818, at end. (Spotted, marginal dampstain at corner at end.) 19th-century half dark green calf, vellum-tipped corners, flat spine gilt (lightly rubbed).

FIRST EDITION. A FUNDAMENTAL BOOK IN THE MODERN THEORY OF NUMBERS BY 'ONE OF THE GREATEST GENIUSES IN THE HISTORY OF MATHEMATICS' (PMM). In it 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 significance today' (DSB V, 299). Among his contributions are the law of quadratic reciprocity; the notation of binary quadratic forms; the introduction of the theory of congruences; and a new theory of the division of the circle. The complexity of the type-setting resulted in errors, which Gauss insisted be corrected by cancelling a number of leaves in addition to a 4-page errata. Dibner

*Heralds*, 114; Grolier

*Science*38; PMM 257; Norman 878.

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