GAUSS, Carl Friedrich (1777–1855). Disquisitiones arithmeticae. Leipzig: G. Fleischer, 1801.

“Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics" (PMM).

Fine, uncut copy of the first edition of Gauss’s masterpiece: "a book that begins a new epoch in mathematics” (PMM). This work revolutionized number theory and established the twenty-four year old Gauss as a mathematical genius. The son of a bricklayer, he discovered a proof of the law of quadratic reciprocity—a task at which both Euler and Legendre had failed—at no more than 18 years old. He also described a method of inscribing in a circle a regular polygon of seventeen sides and presented a universal criterion for determining which regular n-sided polygons can be constructed only with straight-edge and compass and which cannot. This was the first discovery of this kind in Euclidean geometry for over two thousand years. The new mathematics so confused the typesetters that, in addition to the lengthy 4-page errata, the worst mistakes in the book were corrected by cancel leaves. In this copy leaves B7, G4, K3, Ff7, and Tt6 are cancels and Uu4 is not present, as usual. Dibner Heralds of Science 114; Grolier/Horblit 38; Norman 878; Parkinson Breakthroughs p 238; PMM 257.

Octavo (218 x 132mm). Untrimmed and partially unopened. (Light spotting to title, a few gatherings with light spotting/toning, faint marginal dampstain to several leaves at end). Contemporary quarter sheep over blue paste-paper boards, red morocco lettering piece. Provenance: Eight contemporary folded manuscript inserts of detailed mathematical calculations in Latin and Spanish (for pages 44, 56, 58, 59, 60, 64, 65, and 78).