Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaJoseph-Louis Lagrange, comte de l’Empire

''Encyclopædia Britannica'' or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian

St. Andrew University He was raised as a Roman Catholic (but later on became an

''Encyclopædia Britannica'' or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian

mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...

and astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

, later naturalized French
French (french: français(e), link=no) may refer to:
* Something of, from, or related to France
** French language, which originated in France, and its various dialects and accents
** French people, a nation and ethnic group identified with Franc ...

. He made significant contributions to the fields of analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

, number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

, and both classical and celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, ...

.
In 1766, on the recommendation of Swiss 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 ...

and French d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, Prussia
Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an e ...

, where he stayed for over twenty years, producing volumes of work and winning several prizes of the French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...

. Lagrange's treatise on analytical mechanics
In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the ...

('' Mécanique analytique'', 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1788–89), written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...

in the nineteenth century.
In 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy of Sciences. He remained in France until the end of his life. He was instrumental in the decimalisation
Decimalisation or decimalization (see spelling differences) is the conversion of a system of currency or of weights and measures to units related by powers of 10.
Most countries have decimalised their currencies, converting them from non-decimal ...

in Revolutionary France, became the first professor of analysis at the École Polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...

upon its opening in 1794, was a founding member of the Bureau des Longitudes
Bureau ( ) may refer to:
Agencies and organizations
* Government agency
*Public administration
* News bureau, an office for gathering or distributing news, generally for a given geographical location
* Bureau (European Parliament), the administ ...

, and became Senator
A senate is a deliberative assembly, often the upper house or chamber of a bicameral legislature. The name comes from the ancient Roman Senate (Latin: ''Senatus''), so-called as an assembly of the senior (Latin: ''senex'' meaning "the el ...

in 1799.
Scientific contribution

Lagrange was one of the creators of thecalculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

, deriving the Euler–Lagrange equations for extrema of functionals. He extended the method to include possible constraints, arriving at the method of Lagrange multipliers.
Lagrange invented the method of solving differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...

s known as variation of parameters, applied differential calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve ...

to the theory of probabilities and worked on solutions for algebraic equations. He proved that every natural number is a sum of four squares. His treatise ''Theorie des fonctions analytiques'' laid some of the foundations of group theory
In abstract algebra, group theory studies the algebraic structures known as groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen ...

, anticipating Galois. In calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

, Lagrange developed a novel approach to interpolation
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points.
In engineering and science, one often has ...

and Taylor's theorem. He studied the three-body problem for the Earth, Sun and Moon (1764) and the movement of Jupiter's satellites (1766), and in 1772 found the special-case solutions to this problem that yield what are now known as Lagrangian point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of t ...

s. Lagrange is best known for transforming Newtonian mechanics into a branch of analysis, Lagrangian mechanics. He presented the mechanical "principles" as simple results of the variational calculus.
Biography

Early years

Firstborn of eleven children as ''Giuseppe Lodovico Lagrangia'', Lagrange was of Italian and French descent. His paternal great-grandfather was aFrench
French (french: français(e), link=no) may refer to:
* Something of, from, or related to France
** French language, which originated in France, and its various dialects and accents
** French people, a nation and ethnic group identified with Franc ...

captain of cavalry, whose family originated from the French region of Tours
Tours ( , ) is one of the largest cities in the region of Centre-Val de Loire, France. It is the prefecture of the department of Indre-et-Loire. The commune of Tours had 136,463 inhabitants as of 2018 while the population of the whole metro ...

. After serving under Louis XIV
Louis XIV (Louis Dieudonné; 5 September 16381 September 1715), also known as Louis the Great () or the Sun King (), was List of French monarchs, King of France from 14 May 1643 until his death in 1715. His reign of 72 years and 110 days is the Li ...

, he had entered the service of Charles Emmanuel II, Duke of Savoy
The titles of count, then of duke of Savoy are titles of nobility attached to the historical territory of Savoy. Since its creation, in the 11th century, the county was held by the House of Savoy. The County of Savoy was elevated to a duchy at ...

, and married a Conti
Conti is an Italian surname.
Geographical distribution
As of 2014, 63.5% of all known bearers of the surname ''Conti'' were residents of Italy (frequency 1:756), 11.8% of the United States (1:24,071), 9.2% of Brazil (1:17,439), 6.3% of Argenti ...

from the noble Roman family. Lagrange's father, Giuseppe Francesco Lodovico, was doctor in Law at the University of Torino
The University of Turin (Italian language, Italian: ''Università degli Studi di Torino'', UNITO) is a public university, public research university in the city of Turin, in the Piedmont (Italy), Piedmont region of Italy. It is one of the List ...

, while his mother was the only child of a rich doctor of Cambiano, in the countryside of Turin
Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital ...

.LagrangeSt. Andrew University He was raised as a Roman Catholic (but later on became an

agnostic
Agnosticism is the view or belief that the existence of God, of the divine or the supernatural is unknown or unknowable. (page 56 in 1967 edition) Another definition provided is the view that "human reason is incapable of providing sufficien ...

).
His father, who had charge of the king's military chest and was Treasurer of the Office of Public Works and Fortifications in Turin, should have maintained a good social position and wealth, but before his son grew up he had lost most of his property in speculations. A career as a lawyer was planned out for Lagrange by his father, and certainly Lagrange seems to have accepted this willingly. He studied at the University of Turin
The University of Turin (Italian language, Italian: ''Università degli Studi di Torino'', UNITO) is a public university, public research university in the city of Turin, in the Piedmont (Italy), Piedmont region of Italy. It is one of the List ...

and his favourite subject was classical Latin. At first he had no great enthusiasm for mathematics, finding Greek geometry rather dull.
It was not until he was seventeen that he showed any taste for mathematics – his interest in the subject being first excited by a paper by Edmond Halley from 1693
which he came across by accident. Alone and unaided he threw himself into mathematical studies; at the end of a year's incessant toil he was already an accomplished mathematician. Charles Emmanuel III appointed Lagrange to serve as the "Sostituto del Maestro di Matematica" (mathematics assistant professor) at the Royal Military Academy of the Theory and Practice of Artillery in 1755, where he taught courses in calculus and mechanics to support the Piedmontese army's early adoption of the ballistics theories of Benjamin Robins
Benjamin Robins (170729 July 1751) was a pioneering British scientist, Newtonian mathematician, and military engineer.
He wrote an influential treatise on gunnery, for the first time introducing Newtonian science to military men, was an early en ...

and 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 that capacity, Lagrange was the first to teach calculus in an engineering school. According to Alessandro Papacino D'Antoni, the academy's military commander and famous artillery theorist, Lagrange unfortunately proved to be a problematic professor with his oblivious teaching style, abstract reasoning, and impatience with artillery and fortification-engineering applications. In this academy one of his students was François Daviet.
Variational calculus

Lagrange is one of the founders of thecalculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

. Starting in 1754, he worked on the problem of the tautochrone, discovering a method of maximizing and minimizing functionals in a way similar to finding extrema of functions. Lagrange wrote several letters to 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 ...

between 1754 and 1756 describing his results. He outlined his "δ-algorithm", leading to the Euler–Lagrange equations of variational calculus and considerably simplifying Euler's earlier analysis. Lagrange also applied his ideas to problems of classical mechanics, generalising the results of Euler and Maupertuis
Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the ...

.
Euler was very impressed with Lagrange's results. It has been stated that "with characteristic courtesy he withheld a paper he had previously written, which covered some of the same ground, in order that the young Italian might have time to complete his work, and claim the undisputed invention of the new calculus"; however, this chivalric view has been disputed. Lagrange published his method in two memoirs of the Turin Society in 1762 and 1773.
''Miscellanea Taurinensia''

In 1758, with the aid of his pupils (mainly with Daviet), Lagrange established a society, which was subsequently incorporated as the Turin Academy of Sciences, and most of his early writings are to be found in the five volumes of its transactions, usually known as the ''Miscellanea Taurinensia''. Many of these are elaborate papers. The first volume contains a paper on the theory of the propagation of sound; in this he indicates a mistake made by Newton, obtains the generaldifferential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...

for the motion, and integrates it for motion in a straight line. This volume also contains the complete solution of the problem of a string vibrating transversely; in this paper he points out a lack of generality in the solutions previously given by Brook Taylor
Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating Taylor's theorem and the Taylor series, which are important for their use in mathematical analysis.
Life and work
Brook Taylor ...

, D'Alembert, and Euler, and arrives at the conclusion that the form of the curve at any time ''t'' is given by the equation $y\; =\; a\; \backslash sin\; (mx)\; \backslash sin\; (nt)\backslash ,$. The article concludes with a masterly discussion of echoes, beats, and compound sounds. Other articles in this volume are on recurring
Recurring means occurring repeatedly and can refer to several different things:
Mathematics and finance
*Recurring expense, an ongoing (continual) expenditure
*Repeating decimal, or recurring decimal, a real number in the decimal numeral syste ...

series, probabilities
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

, and the calculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

.
The second volume contains a long paper embodying the results of several papers in the first volume on the theory and notation of the calculus of variations; and he illustrates its use by deducing the principle of least action, and by solutions of various problems in dynamics.
The third volume includes the solution of several dynamical problems by means of the calculus of variations; some papers on the integral calculus; a solution of a Fermat's problem: given an integer which is not a perfect square, to find a number such that is a perfect square; and the general differential equations of motion for three bodies moving under their mutual attractions.
The next work he produced was in 1764 on the libration
In lunar astronomy, libration is the wagging or wavering of the Moon perceived by Earth-bound observers and caused by changes in their perspective. It permits an observer to see slightly different hemispheres of the surface at different tim ...

of the Moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting as containing the germ of the idea of generalised equations of motion, equations which he first formally proved in 1780.
Berlin

Already by 1756,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 ...

and Maupertuis
Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the ...

, seeing Lagrange's mathematical talent, tried to persuade Lagrange to come to Berlin, but he shyly refused the offer. In 1765, d'Alembert interceded on Lagrange's behalf with Frederick of Prussia and by letter, asked him to leave Turin for a considerably more prestigious position in Berlin. He again turned down the offer, responding that
: ''It seems to me that Berlin would not be at all suitable for me while M.Euler is there''.
In 1766, after Euler left Berlin for Saint Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

, Frederick himself wrote to Lagrange expressing the wish of "the greatest king in Europe" to have "the greatest mathematician in Europe" resident at his court. Lagrange was finally persuaded. He spent the next twenty years in Prussia
Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an e ...

, where he produced a long series of papers published in the Berlin and Turin transactions, and composed his monumental work, the ''Mécanique analytique''. In 1767, he married his cousin Vittoria Conti.
Lagrange was a favourite of the king, who frequently lectured him on the advantages of perfect regularity of life. The lesson was accepted, and Lagrange studied his mind and body as though they were machines, and experimented to find the exact amount of work which he could do before exhaustion. Every night he set himself a definite task for the next day, and on completing any branch of a subject he wrote a short analysis to see what points in the demonstrations or in the subject-matter were capable of improvement. He carefully planned his papers before writing them, usually without a single erasure or correction.
Nonetheless, during his years in Berlin, Lagrange's health was rather poor, and that of his wife Vittoria was even worse. She died in 1783 after years of illness and Lagrange was very depressed. In 1786, Frederick II died, and the climate of Berlin became difficult for Lagrange.
Paris

In 1786, following Frederick's death, Lagrange received similar invitations from states including Spain andNaples
Naples (; it, Napoli ; nap, Napule ), from grc, Νεάπολις, Neápolis, lit=new city. is the regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 909,048 within the city's adm ...

, and he accepted the offer of Louis XVI
Louis XVI (''Louis-Auguste''; ; 23 August 175421 January 1793) was the last King of France before the fall of the monarchy during the French Revolution. He was referred to as ''Citizen Louis Capet'' during the four months just before he was ...

to move to Paris. In France he was received with every mark of distinction and special apartments in the Louvre were prepared for his reception, and he became a member of the French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...

, which later became part of the Institut de France
The (; ) is a French learned society, grouping five , including the Académie Française. It was established in 1795 at the direction of the National Convention. Located on the Quai de Conti in the 6th arrondissement of Paris, the institut ...

(1795). At the beginning of his residence in Paris he was seized with an attack of melancholy, and even the printed copy of his ''Mécanique'' on which he had worked for a quarter of a century lay for more than two years unopened on his desk. Curiosity as to the results of the French revolution
The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799. Many of its ideas are conside ...

first stirred him out of his lethargy, a curiosity which soon turned to alarm as the revolution developed.
It was about the same time, 1792, that the unaccountable sadness of his life and his timidity moved the compassion of 24-year-old Renée-Françoise-Adélaïde Le Monnier, daughter of his friend, the astronomer Pierre Charles Le Monnier. She insisted on marrying him, and proved a devoted wife to whom he became warmly attached.
In September 1793, the Reign of Terror
The Reign of Terror (french: link=no, la Terreur) was a period of the French Revolution when, following the creation of the First French Republic, First Republic, a series of massacres and numerous public Capital punishment, executions took pl ...

began. Under intervention of Antoine Lavoisier
Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),

CNRS ( tax farmers were arrested and sentenced to death and guillotined on the afternoon after the trial. Lagrange said on the death of Lavoisier: : ''It took only a moment to cause this head to fall and a hundred years will not suffice to produce its like.'' Though Lagrange had been preparing to escape from France while there was yet time, he was never in any danger; different revolutionary governments (and at a later time,

File:Lagrange-6.jpg, 1813 copy of "Theorie des fonctions analytiques"
File:Lagrange-7.jpg, Title page to "Theorie des fonctions analytiques"
File:Lagrange-9.jpg, Introduction to "Theorie des fonctions analytiques"
File:Lagrange-10.jpg, First page of "Theorie des fonctions analytiques"

CNRS ( tax farmers were arrested and sentenced to death and guillotined on the afternoon after the trial. Lagrange said on the death of Lavoisier: : ''It took only a moment to cause this head to fall and a hundred years will not suffice to produce its like.'' Though Lagrange had been preparing to escape from France while there was yet time, he was never in any danger; different revolutionary governments (and at a later time,

Napoleon
Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader wh ...

) gave him honours and distinctions. This luckiness or safety may to some extent be due to his life attitude he expressed many years before: "''I believe that, in general, one of the first principles of every wise man is to conform strictly to the laws of the country in which he is living, even when they are unreasonable''". A striking testimony to the respect in which he was held was shown in 1796 when the French commissary in Italy was ordered to attend in full state on Lagrange's father, and tender the congratulations of the republic on the achievements of his son, who "had done honor to all mankind by his genius, and whom it was the special glory of Piedmont
it, Piemontese
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to have produced." It may be added that Napoleon, when he attained power, warmly encouraged scientific studies in France, and was a liberal benefactor of them. Appointed senator
A senate is a deliberative assembly, often the upper house or chamber of a bicameral legislature. The name comes from the ancient Roman Senate (Latin: ''Senatus''), so-called as an assembly of the senior (Latin: ''senex'' meaning "the el ...

in 1799, he was the first signer of the Sénatus-consulte which in 1802 annexed his fatherland Piedmont to France. He acquired French citizenship in consequence. The French claimed he was a French mathematician, but the Italians continued to claim him as Italian.''
Units of measurement

Lagrange was involved in the development of themetric system
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Intern ...

of measurement in the 1790s. He was offered the presidency of the Commission for the reform of weights and measures ('' la Commission des Poids et Mesures'') when he was preparing to escape. After Lavoisier's death in 1794, it was largely Lagrange who influenced the choice of the metre
The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pre ...

and kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...

units with decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

subdivision, by the commission of 1799. Lagrange was also one of the founding members of the Bureau des Longitudes
Bureau ( ) may refer to:
Agencies and organizations
* Government agency
*Public administration
* News bureau, an office for gathering or distributing news, generally for a given geographical location
* Bureau (European Parliament), the administ ...

in 1795.
École Normale

In 1795, Lagrange was appointed to a mathematical chair at the newly established École Normale, which enjoyed only a short existence of four months. His lectures there were elementary; they contain nothing of any mathematical importance, though they do provide a brief historical insight into his reason for proposing undecimal or Base 11 as the base number for the reformed system of weights and measures. The lectures were published because the professors had to "pledge themselves to the representatives of the people and to each other neither to read nor to repeat from memory" .html" ;"title="Les professeurs aux Écoles Normales ont pris, avec les Représentans du Peuple, et entr'eux l'engagement de ne point lire ou débiter de mémoire des discours écrits"">Les professeurs aux Écoles Normales ont pris, avec les Représentans du Peuple, et entr'eux l'engagement de ne point lire ou débiter de mémoire des discours écrits" The discourses were ordered taken down in shorthand to enable the deputies to see how the professors acquitted themselves. It was also thought the published lectures would interest a significant portion of the citizenry .html" ;"title="Quoique des feuilles sténographiques soient essentiellement destinées aux élèves de l'École Normale, on doit prévoir quיelles seront lues par une grande partie de la Nation"">Quoique des feuilles sténographiques soient essentiellement destinées aux élèves de l'École Normale, on doit prévoir quיelles seront lues par une grande partie de la Nation"École Polytechnique

In 1794, Lagrange was appointed professor of theÉcole Polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...

; and his lectures there, described by mathematicians who had the good fortune to be able to attend them, were almost perfect both in form and matter. Beginning with the merest elements, he led his hearers on until, almost unknown to themselves, they were themselves extending the bounds of the subject: above all he impressed on his pupils the advantage of always using general methods expressed in a symmetrical notation.
But Lagrange does not seem to have been a successful teacher. Fourier, who attended his lectures in 1795, wrote:
:his voice is very feeble, at least in that he does not become heated; he has a very marked Italian accent and pronounces the ''s'' like ''z'' ..The students, of whom the majority are incapable of appreciating him, give him little welcome, but the ''professeurs'' make amends for it.
Late years

In 1810, Lagrange started a thorough revision of the ''Mécanique analytique'', but he was able to complete only about two-thirds of it before his death at Paris in 1813, in 128 rue du Faubourg Saint-Honoré. Napoleon honoured him with the Grand Croix of the Ordre Impérial de la Réunion just two days before he died. He was buried that same year in the Panthéon in Paris. The inscription on his tomb reads in translation:JOSEPH LOUIS LAGRANGE. Senator. Count of the Empire. Grand Officer of the Legion of Honour. Grand Cross of the ImperialOrder of the Reunion The Order of the Reunion (french: link=no, Ordre de la Réunion) was an order of merit of the First French Empire, set up to be awarded to Frenchmen and foreigners to reward services in the civil service, magistracy and army, particularly those fro .... Member of the Institute and the Bureau of Longitude. Born in Turin on 25 January 1736. Died in Paris on 10 April 1813.

Work in Berlin

Lagrange was extremely active scientifically during twenty years he spent in Berlin. Not only did he produce his ''Mécanique analytique'', but he contributed between one and two hundred papers to the Academy of Turin, the Berlin Academy, and the French Academy. Some of these are really treatises, and all without exception are of a high order of excellence. Except for a short time when he was ill he produced on average about one paper a month. Of these, note the following as amongst the most important. First, his contributions to the fourth and fifth volumes, 1766–1773, of the ''Miscellanea Taurinensia''; of which the most important was the one in 1771, in which he discussed how numerous astronomical observations should be combined so as to give the most probable result. And later, his contributions to the first two volumes, 1784–1785, of the transactions of the Turin Academy; to the first of which he contributed a paper on the pressure exerted by fluids in motion, and to the second an article on integration by infinite series, and the kind of problems for which it is suitable. Most of the papers sent to Paris were on astronomical questions, and among these including his paper on the Jovian system in 1766, his essay on the problem of three bodies in 1772, his work on the secular equation of the Moon in 1773, and his treatise on cometary perturbations in 1778. These were all written on subjects proposed by theAcadémie française
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosop ...

, and in each case the prize was awarded to him.
Lagrangian mechanics

Between 1772 and 1788, Lagrange re-formulated Classical/Newtonian mechanics to simplify formulas and ease calculations. These mechanics are called Lagrangian mechanics.Algebra

The greater number of his papers during this time were, however, contributed to the Prussian Academy of Sciences. Several of them deal with questions inalgebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...

.
*His discussion of representations of integers by quadratic form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
:4x^2 + 2xy - 3y^2
is a quadratic form in the variables and . The coefficients usually belong to ...

s (1769) and by more general algebraic forms (1770).
*His tract on the Theory of Elimination, 1770.
* Lagrange's theorem that the order of a subgroup H of a group G must divide the order of G.
*His papers of 1770 and 1771 on the general process for solving an algebraic equation of any degree via the '' Lagrange resolvents''. This method fails to give a general formula for solutions of an equation of degree five and higher, because the auxiliary equation involved has higher degree than the original one. The significance of this method is that it exhibits the already known formulas for solving equations of second, third, and fourth degrees as manifestations of a single principle, and was foundational in Galois theory. The complete solution of a binomial equation (namely an equation of the form $ax^n$ ± $b=0$) is also treated in these papers.
*In 1773, Lagrange considered a functional determinant of order 3, a special case of a Jacobian
In mathematics, a Jacobian, named for Carl Gustav Jacob Jacobi, may refer to:
* Jacobian matrix and determinant
* Jacobian elliptic functions
* Jacobian variety
*Intermediate Jacobian
In mathematics, the intermediate Jacobian of a compact Kähle ...

. He also proved the expression for the volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

of a tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all ...

with one of the vertices at the origin as the one sixth of the absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...

of the determinant
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if a ...

formed by the coordinates of the other three vertices.
Number theory

Several of his early papers also deal with questions of number theory. *Lagrange (1766–1769) was the first European to prove that Pell's equation has a nontrivial solution in the integers for any non-square natural number . *He proved the theorem, stated by Bachet without justification, that every positive integer is the sum of four squares, 1770. *He provedWilson's theorem
In algebra and number theory, Wilson's theorem states that a natural number ''n'' > 1 is a prime number if and only if the product of all the positive integers less than ''n'' is one less than a multiple of ''n''. That is (using the notations of m ...

that (for any integer ): is a prime if and only if is a multiple of , 1771.
*His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved.
*His Recherches d'Arithmétique of 1775 developed a general theory of binary quadratic forms to handle the general problem of when an integer is representable by the form .
*He made contributions to the theory of continued fractions.
Other mathematical work

There are also numerous articles on various points ofanalytical geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engine ...

. In two of them, written rather later, in 1792 and 1793, he reduced the equations of the quadrics (or conicoids) to their canonical forms.
During the years from 1772 to 1785, he contributed a long series of papers which created the science of partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to h ...

s. A large part of these results was collected in the second edition of Euler's integral calculus which was published in 1794.
Astronomy

Lastly, there are numerous papers on problems inastronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

. Of these the most important are the following:
*Attempting to solve the general three-body problem, with the consequent discovery of the two constant-pattern solutions, collinear and equilateral, 1772. Those solutions were later seen to explain what are now known as the Lagrangian point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of t ...

s.
*On the attraction of ellipsoids, 1773: this is founded on Maclaurin
Maclaurin or MacLaurin is a surname. Notable people with the surname include:
* Colin Maclaurin (1698–1746), Scottish mathematician
* Normand MacLaurin (1835–1914), Australian politician and university administrator
* Henry Normand MacLaurin ...

's work.
*On the secular equation of the Moon, 1773; also noticeable for the earliest introduction of the idea of the potential. The potential of a body at any point is the sum of the mass of every element of the body when divided by its distance from the point. Lagrange showed that if the potential of a body at an external point were known, the attraction in any direction could be at once found. The theory of the potential was elaborated in a paper sent to Berlin in 1777.
*On the motion of the nodes of a planet's orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...

, 1774.
*On the stability of the planetary orbits, 1776.
*Two papers in which the method of determining the orbit of a comet
A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...

from three observations is completely worked out, 1778 and 1783: this has not indeed proved practically available, but his system of calculating the perturbations by means of mechanical quadratures has formed the basis of most subsequent researches on the subject.
*His determination of the secular and periodic variations of the elements of the planets, 1781–1784: the upper limits assigned for these agree closely with those obtained later by Le Verrier, and Lagrange proceeded as far as the knowledge then possessed of the masses of the planets permitted.
*Three papers on the method of interpolation, 1783, 1792 and 1793: the part of finite differences dealing therewith is now in the same stage as that in which Lagrange left it.
Fundamental treatise

Over and above these various papers he composed his fundamental treatise, the ''Mécanique analytique''. In this book, he lays down the law of virtual work, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole ofmechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...

, both of solids and fluids.
The object of the book is to show that the subject is implicitly included in a single principle, and to give general formulae from which any particular result can be obtained. The method of generalised co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he showed that, if we determine its configuration by a sufficient number of variables ''x'', called generalized coordinates, whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation. For example, in dynamics of a rigid system he replaces the consideration of the particular problem by the general equation, which is now usually written in the form
:$\backslash frac\; \backslash frac\; -\; \backslash frac\; +\; \backslash frac\; =\; 0,$
where ''T'' represents the kinetic energy and ''V'' represents the potential energy of the system.
He then presented what we now know as the method of Lagrange multipliers—though this is not the first time that method was published—as a means to solve this equation.Marco Panza, "The Origins of Analytic Mechanics in the 18th Century", in Hans Niels Jahnke (editor), ''A History of Analysis'', 2003, p. 149
Amongst other minor theorems here given it may suffice to mention the proposition that the kinetic energy imparted by the given impulses to a material system under given constraints is a maximum, and the principle of least action. All the analysis is so elegant that Sir William Rowan Hamilton
Sir William Rowan Hamilton Doctor of Law, LL.D, Doctor of Civil Law, DCL, Royal Irish Academy, MRIA, Royal Astronomical Society#Fellow, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the ...

said the work could be described only as a scientific poem. Lagrange remarked that mechanics was really a branch of pure mathematics
Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, ...

analogous to a geometry of four dimensions, namely, the time and the three coordinates of the point in space; and it is said that he prided himself that from the beginning to the end of the work there was not a single diagram. At first no printer could be found who would publish the book; but Legendre at last persuaded a Paris firm to undertake it, and it was issued under the supervision of Laplace, Cousin, Legendre (editor) and Condorcet in 1788.
Work in France

Differential calculus and calculus of variations

Lagrange's lectures on thedifferential calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve ...

at École Polytechnique form the basis of his treatise ''Théorie des fonctions analytiques'', which was published in 1797. This work is the extension of an idea contained in a paper he had sent to the Berlin papers in 1772, and its object is to substitute for the differential calculus a group of theorems based on the development of algebraic functions in series, relying in particular on the principle of the generality of algebra.
A somewhat similar method had been previously used by John Landen
John Landen (23 January 1719 – 15 January 1790) was an English mathematician.
Life
He was born at Peakirk, near Peterborough in Northamptonshire, on 28 January 1719. He was brought up to the business of a surveyor, and acted as land agent to ...

in the ''Residual Analysis'', published in London in 1758. Lagrange believed that he could thus get rid of those difficulties, connected with the use of infinitely large and infinitely small quantities, to which philosophers objected in the usual treatment of the differential calculus. The book is divided into three parts: of these, the first treats of the general theory of functions, and gives an algebraic proof of Taylor's theorem, the validity of which is, however, open to question; the second deals with applications to geometry; and the third with applications to mechanics.
Another treatise on the same lines was his ''Leçons sur le calcul des fonctions'', issued in 1804, with the second edition in 1806. It is in this book that Lagrange formulated his celebrated method of Lagrange multipliers, in the context of problems of variational calculus with integral constraints. These works devoted to differential calculus and calculus of variations may be considered as the starting point for the researches of Cauchy, Jacobi Jacobi may refer to:
* People with the surname Jacobi
Mathematics:
* Jacobi sum, a type of character sum
* Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations
* Jacobi eigenvalue algorithm, ...

, and Weierstrass.Infinitesimals

At a later period Lagrange fully embraced the use ofinfinitesimal
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally re ...

s in preference to founding the differential calculus on the study of algebraic forms; and in the preface to the second edition of the ''Mécanique Analytique'', which was issued in 1811, he justifies the employment of infinitesimals, and concludes by saying that:
: ''When we have grasped the spirit of the infinitesimal method, and have verified the exactness of its results either by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, we may employ infinitely small quantities as a sure and valuable means of shortening and simplifying our proofs.''
Number theory

His ''Résolution des équations numériques'', published in 1798, was also the fruit of his lectures at École Polytechnique. There he gives the method of approximating to the real roots of an equation by means of continued fractions, and enunciates several other theorems. In a note at the end he shows howFermat's little theorem
Fermat's little theorem states that if ''p'' is a prime number, then for any integer ''a'', the number a^p - a is an integer multiple of ''p''. In the notation of modular arithmetic, this is expressed as
: a^p \equiv a \pmod p.
For example, if = ...

, that is
: $a^-1\; \backslash equiv\; 0\backslash pmod\; p$
where ''p'' is a prime and ''a'' is prime to ''p'', may be applied to give the complete algebraic solution of any binomial equation. He also here explains how the equation whose roots are the squares of the differences of the roots of the original equation may be used so as to give considerable information as to the position and nature of those roots.
Celestial mechanics

The theory of theplanetary motion
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a ...

s had formed the subject of some of the most remarkable of Lagrange's Berlin papers. In 1806 the subject was reopened by Poisson, who, in a paper read before the French Academy, showed that Lagrange's formulae led to certain limits for the stability of the orbits. Lagrange, who was present, now discussed the whole subject afresh, and in a letter communicated to the academy in 1808 explained how, by the variation of arbitrary constants, the periodical and secular inequalities of any system of mutually interacting bodies could be determined.
Prizes and distinctions

Euler proposed Lagrange for election to the Berlin Academy and he was elected on 2 September 1756. He was elected a Fellow of theRoyal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

in 1790, a Fellow of the Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

and a foreign member of the Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...

in 1806. In 1808, Napoleon
Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader wh ...

made Lagrange a Grand Officer of the Legion of Honour
The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleo ...

and a Count of the Empire
As Emperor of the French, Napoleon I created titles of nobility to institute a stable elite in the First French Empire, after the instability resulting from the French Revolution.
Like many others, both before and since, Napoleon found that th ...

. He was awarded the Grand Croix of the Ordre Impérial de la Réunion in 1813, a week before his death in Paris, and was buried in the Panthéon, a mausoleum
A mausoleum is an external free-standing building constructed as a monument enclosing the interment space or burial chamber of a deceased person or people. A mausoleum without the person's remains is called a cenotaph. A mausoleum may be cons ...

dedicated to the most honoured French people.
Lagrange was awarded the 1764 prize of the French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...

for his memoir on the libration
In lunar astronomy, libration is the wagging or wavering of the Moon perceived by Earth-bound observers and caused by changes in their perspective. It permits an observer to see slightly different hemispheres of the surface at different tim ...

of the Moon. In 1766 the academy proposed a problem of the motion of the satellites of Jupiter
There are 82 known moons of Jupiter, not counting a number of moonlets likely shed from the inner moons. All together, they form a satellite system which is called the Jovian system. The most massive of the moons are the four Galilean moons: ...

, and the prize again was awarded to Lagrange. He also shared or won the prizes of 1772, 1774, and 1778.
Lagrange is one of the 72 prominent French scientists who were commemorated on plaques at the first stage of the Eiffel Tower
The Eiffel Tower ( ; french: links=yes, tour Eiffel ) is a wrought-iron lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower.
Locally nicknamed ...

when it first opened. ''Rue Lagrange'' in the 5th Arrondissement in Paris is named after him. In Turin, the street where the house of his birth still stands is named ''via Lagrange''. The lunar crater
Lunar craters are impact craters on Earth's Moon. The Moon's surface has many craters, all of which were formed by impacts. The International Astronomical Union currently recognizes 9,137 craters, of which 1,675 have been dated.
History
The w ...

Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia1006 Lagrangea also bear his name.

Lagrange, Joseph Louis.

* W. W. Rouse Ball, 1908,

Joseph Louis Lagrange (1736–1813)

''A Short Account of the History of Mathematics'', 4th ed

also on Gutenberg

* Chanson, Hubert, 2007,

Velocity Potential in Real Fluid Flows: Joseph-Louis Lagrange's Contribution

" ''La Houille Blanche'' 5: 127–31. * Fraser, Craig G., 2005, "Théorie des fonctions analytiques" in Grattan-Guinness, I., ed., ''Landmark Writings in Western Mathematics''. Elsevier: 258–76. * Lagrange, Joseph-Louis. (1811). ''Mécanique Analytique''. Courcier (reissued by

Lagrange, Joseph Louis de: The Encyclopedia of Astrobiology, Astronomy and Space Flight

*

Derivation of Lagrange's result (not Lagrange's method)

* Lagrange's works (in French

Oeuvres de Lagrange, edited by Joseph Alfred Serret, Paris 1867, digitized by Göttinger Digitalisierungszentrum

(Mécanique analytique is in volumes 11 and 12.)

Joseph Louis de Lagrange – Œuvres complètes

Gallica-Math

Inventaire chronologique de l'œuvre de Lagrange

Persee * *

''Mécanique analytique'' (Paris, 1811-15)

{{DEFAULTSORT:Lagrange, Joseph-Louis Lagrangian mechanics 1736 births 1813 deaths Scientists from Turin 18th-century Italian mathematicians 19th-century Italian mathematicians Burials at the Panthéon, Paris Counts of the First French Empire Italian people of French descent French agnostics 18th-century French astronomers 18th-century Italian astronomers Mathematical analysts Members of the French Academy of Sciences Members of the Prussian Academy of Sciences Members of the Royal Swedish Academy of Sciences Honorary members of the Saint Petersburg Academy of Sciences Number theorists French geometers People from the Kingdom of Sardinia Grand Officiers of the Légion d'honneur Fellows of the Royal Society 18th-century French mathematicians 19th-century French mathematicians

See also

*List of things named after Joseph-Louis Lagrange
Several concepts from mathematics and physics are named after the mathematician and astronomer Joseph-Louis Lagrange, as are a impact crater, crater on the moon and :fr:Rue Lagrange, a street in Paris.
Lagrangian
*Lagrangian analysis
*Lagrangian c ...

* Four-dimensional space
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...

* Gauss's law
In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it st ...

* History of the metre
The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of ''De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and s ...

* Lagrange's role in measurement reform
* Seconds pendulum
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz.
Pendulum
A pendulum is a weight suspended from a pivot so that ...

Notes

References

Citations

Sources

The initial version of this article was taken from thepublic domain
The public domain (PD) consists of all the creative work to which no exclusive intellectual property rights apply. Those rights may have expired, been forfeited, expressly waived, or may be inapplicable. Because those rights have expired ...

resource '' A Short Account of the History of Mathematics'' (4th edition, 1908) by W. W. Rouse Ball.
*
* ''Columbia Encyclopedia'', 6th ed., 2005,Lagrange, Joseph Louis.

* W. W. Rouse Ball, 1908,

Joseph Louis Lagrange (1736–1813)

''A Short Account of the History of Mathematics'', 4th ed

also on Gutenberg

* Chanson, Hubert, 2007,

Velocity Potential in Real Fluid Flows: Joseph-Louis Lagrange's Contribution

" ''La Houille Blanche'' 5: 127–31. * Fraser, Craig G., 2005, "Théorie des fonctions analytiques" in Grattan-Guinness, I., ed., ''Landmark Writings in Western Mathematics''. Elsevier: 258–76. * Lagrange, Joseph-Louis. (1811). ''Mécanique Analytique''. Courcier (reissued by

Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer.
Cambridge University Pr ...

, 2009; )
* Lagrange, J.L. (1781) "Mémoire sur la Théorie du Mouvement des Fluides"(Memoir on the Theory of Fluid Motion) in Serret, J.A., ed., 1867. ''Oeuvres de Lagrange, Vol. 4''. Paris" Gauthier-Villars: 695–748.
* Pulte, Helmut, 2005, "Méchanique Analytique" in Grattan-Guinness, I., ed., ''Landmark Writings in Western Mathematics''. Elsevier: 208–24.
*
External links

* *Lagrange, Joseph Louis de: The Encyclopedia of Astrobiology, Astronomy and Space Flight

*

Derivation of Lagrange's result (not Lagrange's method)

* Lagrange's works (in French

Oeuvres de Lagrange, edited by Joseph Alfred Serret, Paris 1867, digitized by Göttinger Digitalisierungszentrum

(Mécanique analytique is in volumes 11 and 12.)

Joseph Louis de Lagrange – Œuvres complètes

Gallica-Math

Inventaire chronologique de l'œuvre de Lagrange

Persee * *

''Mécanique analytique'' (Paris, 1811-15)

{{DEFAULTSORT:Lagrange, Joseph-Louis Lagrangian mechanics 1736 births 1813 deaths Scientists from Turin 18th-century Italian mathematicians 19th-century Italian mathematicians Burials at the Panthéon, Paris Counts of the First French Empire Italian people of French descent French agnostics 18th-century French astronomers 18th-century Italian astronomers Mathematical analysts Members of the French Academy of Sciences Members of the Prussian Academy of Sciences Members of the Royal Swedish Academy of Sciences Honorary members of the Saint Petersburg Academy of Sciences Number theorists French geometers People from the Kingdom of Sardinia Grand Officiers of the Légion d'honneur Fellows of the Royal Society 18th-century French mathematicians 19th-century French mathematicians