Demonstratio Nova Theorematis Omnem Functionem Algebraicam Rationalem Integram unius Variabilis in Factores Reales Primi vel Secundi Gradus resolvi posse

1799. One engraved plate (somewhat browned). 39, [1] pp. 4to, cont. half-calf & marbled boards. Helmstadt: C.G. Fleckeisen, 1799.

First edition of Gauss’s first book for which he received his doctorate degree; in this rare work Gauss gave the first rigorous proof of the fundamental theorem of algebra. This theorem, which states that every algebraic equation in one unknown has a root, was expressed by Albert Girard, Descartes, Newton, and Maclaurin. Attempts at a proof were made by d’Alembert, Euler, and Lagrange, but Gauss was the first to furnish a rigorous demonstration.

This is Gauss’s first great work and marks the beginning (truncated) of an extraordinary ten years which saw the publication of his Disquisitiones Arithmeticae (1801) and his calculation of the orbit of the newly discovered planet Ceres.

“Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics.”–Printing & the Mind of Man, p. 155.

A very good copy. Library stamp on blank portion of title removed and another stamp on final text leaf with circular piece of paper pasted over. On page 26 there are two corrections, presumably in the Gauss’s hand.

Provenance: Absolutely reliable.

❧ Bell, Men of Mathematics, pp. 218-69. D.S.B., V, pp. 298-315. Smith, History of Mathematics, II, pp. 473-74. (Inventory #: 3524)