CARNOT, Lazare Nicolas Marguerite (1753-1823). De la Correlation des Figures de Geometrie.

CARNOT, Lazare Nicolas Marguerite (1753-1823).  De la Corrélation des Figures de Géométrie. Paris: Chez Duprat, 1801. 8vo (235 x 152mm). Half title, 4 folding engraved plates, 4-pages of publisher’s advertisements at the end (some light mainly marginal spotting, staining and browning, a few darker spots). Modern leatherette-backed marbled boards, spine lettered in gilt, uncut, new endpapers. Provenance: from the Collection of Peter and Margarethe Braune. FIRST EDITION. “Carnot's main geometric writings were motivated largely by the attempt to make reasonable the employment of unreasonable quantity in analysis, although with the focus on negative rather than infinitesimal quantity ... De la Corrélation des Figures de Géométrie of 1801 and its extension, the Géométrie de Position of 1803, constituted his most significant clarification of the procedures of mathematics. Carnot found absurd the notion that a quantity itself could be less than zero … He insisted in Corrélation des Figures on distinguishing between a quantity properly speaking and the algebraic value of a function. It was equally unacceptable to interpret the minus sign as meaning simply that a quantity was to be taken in a direction opposite to a positive one … By correlative systems Carnot meant all those that could be considered as different states of a single variable system undergoing gradual transformation. It was not necessary that all correlative systems should actually have been evolved out of the primitive system. It sufficed that they might be assimilated to it by changes involving no discontinuous mutations. The whole topic may be taken as the geometric operation of Carnot's favourite reasoning device - a comparison of systems between which the nexus of change is a continuum ..." (DSB). Honeyman II, 596; Poggendorf I, 381.