# ALEMBERT, Jean Le Rond d'

ALEMBERT, JEAN LE ROND D'

(zhäN lərôN` däläNbĕr`), 1717–83, French mathematician and philosopher. The illegitimate son of the chevalier Destouches, he was named for the St. Jean le Rond church, on whose steps he was found. His father had him educated. Diderot made him coeditor of the Encyclopédie, for which he wrote the "preliminary discourse" (1751) and mathematical, philosophical, and literary articles. Discouraged, however, by attacks on his unorthodox views, he withdrew (1758) from the Encyclopédie. A member of the Academy of Sciences (1741) and of the French Academy (1754; appointed secretary, 1772), he was a leading representative of the Enlightenment. His writings include a treatise on dynamics (1743), in which he enunciated a principle of mechanics known as D'Alembert's principle; a work on the theoretical and practical elements of music (1759); and a valuable history of the members of the French Academy (1787).

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## Alembert, Jean le Rond d’

Born Nov. 16, 1717, in Paris, died there Oct. 29, 1783. French mathematician and philosopher. Member of the Paris Academy of Sciences (1754), the St. Petersburg Academy of Sciences (1764), and other academies.

Beginning in 1751 d’Alembert collaborated with D. Diderot on the Encyclopédie, heading the mathematics and physics sections. In 1757, unable to withstand the persecution to which he was subjected by reactionaries for his work on the Encyclopédie he withdrew from the publication and devoted himself entirely to scientific work. In the Traité de dynamique (1743) he for the first time formulated the general rules of constructing differential equations of the motion of any material system, reducing problems of dynamics to statics (d’Alembert’s principle). He applied this principle in the treatise Réflexions sur la cause générale des vents (1744), which laid the groundwork for hydrodynamics (he proved the existence of air tides in addition to oceanic tides). In astronomy d’Alembert substantiated the theory of the perturbation of planets and for the first time rigorously explained the theory of the precession of the equinoxes and nutation.

D’Alembert’s principal mathematical investigations were related to the theory of differential equations, where he provided a method for solving the second-order partial differential equation that expresses the transverse vibration of a string (wave equation) in the form of the sum of two arbitrary functions, and on the basis of the so-called boundary conditions was able to express one by means of the other. These works by d’Alembert and also the subsequent works of L. Euler and D. Bernoulli constitute the foundation of mathematical physics. In the solution of one elliptic partial differential equation encountered in hydrodynamics, d’Alembert was the first to use the functions of a complex variable. In d’Alembert’s work (and at the same time in Euler’s work) one encounters equations that relate the real and imaginary parts of an analytic function and that later came to be called Cauchy-Riemann equations. D’Alembert also achieved important results in the theory of ordinary differential equations with constant coefficients and in systems of such equations of the first and second orders. He attempted to substantiate the calculus of infinitesimals by means of the theory of limits, and in the theory of series his name has been given to a widely used sufficiency test for convergence. In algebra he provided the first (but not completely rigorous) proof of the fundamental theorem of the existence of a root in an algebraic equation. In the first volumes of the Encyclopédie d’Alembert wrote the important articles “Differentials,” “Equations,” “Dynamics,” and “Geometry.”

His most important philosophical works are the introductory article to the Encyclopédie, the Discours préliminaire (1751, Russian translation in the book Rodonachalniki pozitiviima [Forefathers of Positivism], 1910), which contains a classification of the sciences, and Éléments de philosophie (1759). In his theory of knowledge, d’Alembert adhered to J. Locke’s sensationalism. In solving the principal philosophical problems, d’Alembert was inclined to skepticism, considering it impossible to positively assert anything about god and his interaction with matter or about eternity and the creation of matter. While doubting the existence of god and engaging in anticlerical criticism, he nevertheless did not take an atheistic position. Unlike the French materialists, he considered that there are immutable principles that do not depend on the moral principles of the social environment. His views on questions of the theory of knowledge and religion were criticized by Diderot in his works Rêve de d’Alembert (d’Alembert’s Dream. 1769) and Entretien entre d’Alembert et Diderot (Conversation Between d’Alembert and Diderot, 1769), among others. D’Alembert also wrote works on musical theory and musical aesthetics, such as Traité sur la liberté de la musique (Treatise on the Freedom of Music), in which he summarized the so-called war of the buffoons (guerre des bouffons), the quarrel pertaining to the art of opera.

## WORKS

In Russian translation: Dinamika. Moscow-Leningrad, 1950. “Izvlechenie iz memuara ’O ravnovesii zhidkostei’ i ’O figure zemli.’” In A. Clairaut, Teoriia figury zemli, osnovannaia na nachalakh gidrostatiki. Moscow-Leningrad, 1947. (Translated from French.)

## REFERENCES

Engels, F. Dialektika prirody. Moscow, 1955. Pages 61–64, 70. Lenin. V. I. Materializm iempiriokrititsizm. In Poln. sobr. soch., 5th ed., vol. 18. Litvinova, E. F. Dalamber, ego zhizn’ i nauchnaia deiatel’nost’. St. Petersburg, 1891. Wieleitner. H. Istoriia Matematiki ot Dekarta do serediny XIXstoletiia, 2nd ed. Moscow, 1966. (Translated from German.) Istoriia filosofii, vol. 2. Moscow, 1941. Pages 353–55. Muller, M. Essai sur la philosophie de Jean d’Alembert. Paris, 1926.

SOURCE: The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

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