CARNOT Lazare-Nicolas-Marguerite Réflexions sur la métaphysique du calcul infinitésimal.

DSB, III, 75-76.

First edition of Carnot’s classic explanation of the genious of the infinitesimal calculus; this was a very popular book which went through six editions in French in over 100 years and was translated into English, Italian, Russian, Portuguese, and German.

“His Réflexions sur la métaphysique du calcul infinitésimal, first published in 1797 while he was still in political office as director, … frankly acknowledged the difficulties that infinitesimal analysis raises for common sense and although it was reserved to the reforms initiated by Cauchy, Bolzano and Gauss to put the calculus on a rigorous footing, Carnot’s justification evidently answered for well over a century to the needs of a public that wished to understand its own use of the calculus. The genious of the infinitesimal calculus, in Carnot’s account, lay in its capacity to compensate in its own procedures for errors that it deliberately admitted into the process of computation for the purpose of facilitating a solution… The art of infinitesimal calculus, therefore, consisted in transforming insoluble or difficult complete equations into manageable incomplete equations and then managing the calculation so as to eliminate all non designated quantities from the result. Their absence proved its correctness” (DSB).

Fine copy.