''Mécanique analytique'' (1788–89) is a two volume French treatise on
analytical mechanics, written by
Joseph-Louis Lagrange, and published 101 years following
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the grea ...
's
''
Philosophiæ Naturalis Principia Mathematica''. It consolidated into one unified and harmonious system, the scattered developments of contributors such as
Alexis Clairaut
Alexis Claude Clairaut (; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had ou ...
,
Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the '' Encyclopéd ...
,
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
,
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
, and
Johann
Johann, typically a male given name, is the German form of ''Iohannes'', which is the Latin form of the Greek name ''Iōánnēs'' (), itself derived from Hebrew name '' Yochanan'' () in turn from its extended form (), meaning "Yahweh is Gracious ...
and
Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Le ...
in the historical transition from geometrical methods, as presented in Newton's ''Principia'', to the methods of
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
. The treatise expounds a great labor-saving and thought-saving general analytical method by which every mechanical question may be stated in a single differential equation.
Lagrange wrote that this work was entirely new and that his intent was to reduce the theory and the art of solving mechanics problems to general formulae, providing all the equations necessary for the solution of each problem. He stated that...
No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain.
Ernst Mach describes the work as follows:
Analytic mechanics... was brought to the highest degree of perfection... Lagrange's aim is... to dispose, ''once and for all'', of the reasoning necessary to resolve mechanical problems, by embodying as much as possible of it in a single formula. This he did. Every case... can now be dealt with by a very simple... schema; and whatever reasoning is left is performed by purely mechanical methods. The mechanics of Lagrange is a stupendous contribution to the economy of thought.
Publication History
The work was first published in 1788 (volume 1) and 1789 (volume 2). Lagrange issued a substantially enlarged second edition of volume 1 in 1811, toward the end of his life. His revision of volume 2 was substantially complete at the time of his death in 1813, but was not published until 1815.
The second edition of 1811/15 has been translated into English, and is available online at
archive.org
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
.
References
External links
*
*
* English translation of the 1811 edition
Theoretical physics
Mathematical physics
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