''Mécanique analytique'' (1788–89) is a two volume French treatise on

analytical mechanics In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related formulations of classical mechanics. Analytical mechanics uses '' scalar'' properties of motion representing the sy ...

, written by

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaIsaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

's ''

Philosophiæ Naturalis Principia Mathematica (English: ''The Mathematical Principles of Natural Philosophy''), often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Lati ...

''.

Treatise

It consolidated into one unified and harmonious system, the scattered developments of contributors such as Alexis Clairaut,

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 ''Encyclopé ...

Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

, 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 Graciou ...

and

Jacob Bernoulli Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibniz ...

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 ( ...

. 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. File:Lagrange-1.jpg, Volumes I-II of "Mécanique Analytique," from 1811 and 1815, respectively File:Lagrange-3.jpg, Avertissement of volume I of "Mécanique Analytique" (1811) File:Lagrange-4.jpg, First page of volume I of "Mécanique Analytique" (1811)

References

External links

* * * English translation of the 1811 edition {{DEFAULTSORT:Mecanique analytique Mathematical physics Physics books Mathematics books