“Specimen novum analyseos pro scientia infiniti, circa summas & quadraturas.” In: Acta eruditorum anno MDCCII publicata.
Lipsiae [Leipzig]: Gross, Frisch and Groschuf, 1702. 4to. [ii], 566 pp. (entire volume). FIRST EDITION. With a total of 9 folding engraved plates. Leibnitz’ article covers pages 210-219 and includes 1 folding plate. Contemporary half-vellum and marbled boards, red speckled edges; very minor spotting, overall an excellent copy. Item #19260
First edition of Leibnitz’ New specimen of the analysis for the science of the infinite about sums and quadratures, his investigation of the fundamental theorem of algebra. The fundamental theorem of algebra is the assertion that every polynomial with real or complex coefficients has at least one complex root. An immediate extension of this result is that every polynomial of degree n with real or complex coefficients has exactly n complex roots, when counting individually any repeated roots. Leibnitz here provides examples of calculating with infinite numbers, although erroneously said that no polynomial of the type x4 + α4 (with α real and distinct from 0) can be written in such a way.
A first attempt at proving the theorem was made by d’Alembert in 1746, though his proof was incomplete. Other attempts were made by Euler (1749), de Foncenex (1759), Lagrange (1772), and Laplace (1795). It was finally proven in the nineteenth century by Argand, and more fully by Gauss.
Apart from Leibnitz’ work, the present volume also includes medical texts by Bartholin and Cowper, an essay (with illustration) by Halley on Hooke’s barometer, and articles by Lamy, Peletier and Locke among many others.
Price: $1,850.00