These papers are chiefly geometrical, many of them being developments and applications of the methods laid down in his great work, Der barycentrische Calcul (Leipzig, 1827), which, as the name implies, is based upon the properties of the mean point or centre of mass (see Algebra: Universal).
In 1741 he received his first public distinction in being admitted a member of the Academy of Sciences, to which he had previously presented several papers, including a Memoire sur le calcul integral (1739).
In 1746 and 1748 he published in the Memoirs of the Academy of Berlin "Recherches sur le calcul integral," a branch of mathematical science which is greatly indebted to him.
Besides the separate works already named are Resolution des equations numeriques (1798, 2nd ed., 1808, 3rd ed., 1826), and Lecons sur le calcul des fonctions (1805, 2nd ed., 1806), designed as a commentary and supplement to the first part of the Theorie des fonctions.
The analytical tournament closed with the communication to the Academy by Laplace, 1 "Recherches sur le calcul integral," Mélanges de la Soc. Roy.
Although relegated to a note (vii.), and propounded "Avec la defiance que doit inspirer tout ce qui n'est point un resultat de l'observation ou du calcul," it is plain, from the complacency with which he recurred to it 3 at a later date, that he regarded the speculation with considerable interest.
Lacroix's Traite elementaire du calcul des probabilites and De Morgan's Essay, published in Lardner's Cabinet Cyclopaedia.
Mobius, Der barycentrische Calcul (Leipzig, 1827) (reprinted in his collected works, vol.
Continued fractions, one of the earliest examples of which is Lord Brouncker's expression for the ratio of the circumference to the diameter of a circle (see Circle), were elaborately discussed by John Wallis and Leonhard Euler; the convergency of series treated by Newton, Euler and the Bernoullis; the binomial theorem, due originally to Newton and subsequently expanded by Euler and others, was used by Joseph Louis Lagrange as the basis of his Calcul des Fonctions.
Other works of Cournot's were Traite elementaire de la theorie des fonctions et du calcul infinitesimal (1841); Exposition de la theorie des chances et des probabilLites (1843); De l'origine et des limites de la correspondance entre l'algebre et la geometrie (1847); Traite de l'enchainement des idees fondamentales dans les sciences et dans l'histoire (1861); and Revue somma.ire des doctrines economiques (1877).
Lagrange realized its powers and termed it " le principal fondement du calcul erentiel."
The idea may be compared with that of Joseph Louis Lagrange's Calcul des Fonctions.
Besides papers in scientific periodicals he published Indagaciones sobre el estanada de cobre, la vajilla de estano y el vidriado (1803); Memoire sur le sucre de raisins (1808); Recueil des memoires relatifs d la poudre a canon (1815); and Essai sur une des causes qui peuvent amener la formation du calcul (1824).
The contents of these memoirs are included in the first volume of his Exercices de calcul integral (1811).
The Exercices de calcul integral consist of three volumes, a great portion of the first and the whole of the third being devoted to elliptic functions.
Prony was charged with the direction of the work, and was expressly required " non seulement a composer des tables qui ne laissassent rien a desirer quant a l'exactitude, mais a en faire le monument de calcul le plus vaste et le plus imposant qui eut jamais ete execute ou meme congu."
Combebiac, Calcul des triquaternions (Paris, 1902); Don Francisco Perez de Munoz, Introduction al estudio del cdlculo de Cuaterniones y otras Algebras especiales (Madrid, 1905); A.
3 Lecons de calcul des variations (Paris, 1861).