D'AYALA Mariano. A Lagrangian Manuscript in the Royal Library of Turin

8/7/2019 D'AYALA Mariano. A Lagrangian Manuscript in the Royal Library of Turin

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Mariano D'Ayala

Un manoscritto sconosciutodiLagrange

nella biblioteca del duca di Genova

inRivista enciclopedica italiana, Torino, UTET,. 1856, pp. 534-536.


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Joseph Louis Lagrange

From Wikipedia, the free encyclopedia

Joseph-Louis (Giuseppe Lodovico), comte de Lagrange

Born 25 January 1736Turin,Piedmont

Died 10 April 1813 (aged 77) Paris, France

Residence PiedmontFrancePrussia

Nationality ItalianFrench

Fields MathematicsMathematical physicsInstitutions cole Polytechnique

Doctoral advisor Leonhard Euler

Doctoral students Joseph FourierGiovanni PlanaSimon Poisson

Known for Analytical mechanicsCelestial mechanicsMathematical analysisNumber theory

NotesNote he did not have a doctoral advisor butacademic genealogy authorities link his intellectual heritage toLeonhard Euler, who played the equivalent role.

Joseph-Louis Lagrange (25 January 1736 10 April 1813), born Giuseppe Lodovico (Luigi) Lagrangia, was amathematicianandastronomer, who was born in Turin, Piedmont, lived part of his life in Prussiaand part inFrance, making significant contributions to allfields ofanalysis, tonumber theory, and to classical andcelestial mechanics. On the recommendation ofEulerandd'Alembert, in 1766Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, where he stayed for overtwenty years, producing a large body of work and winning several prizes of the French Academy of Sciences. Lagrange's treatise onanalytical mechanics (Mcanique Analytique, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1888-89), written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for thedevelopment of mathematical physics in the nineteenth century. Lagrange's parents were Italians, although he also had French ancestorson his father's side. In 1787, at age 51, he moved from Berlin to France and became a member of the French Academy, and heremained in France until the end of his life. Therefore, Lagrange is alternatively considered a French and an Italianscientist. Lagrangesurvived the French Revolution and became the first professor of analysis at the cole Polytechnique upon its opening in 1794.Napoleonnamed Lagrange to theLegion of Honourand made him aCountof the Empire in 1808. He is buried in thePanthon.Scientific contributionLagrange was one of the creators of the calculus of variations, deriving the EulerLagrange equations for extrema of functionals. Healso extended the method to take into account possible constraints, arriving at the method of Lagrange multipliers. Lagrange inventedthe method of solving differential equations known as variation of parameters, applied differential calculusto the theory of probabilities

and attained notable work on the solution of equations. He proved that every natural number is a sum of four squares. His treatiseTheorie des fonctions analytiques laid some of the foundations ofgroup theory, anticipatingGalois. In calculus, Lagrange developed anovel approach to interpolationand Taylor series. He studied the three-body problem for the Earth, Sun, and Moon (1764) and themovement of Jupiters satellites (1766), and in 1772 found the special-case solutions to this problem that are now known asLagrangianpoints. But above all he impressed on mechanics, having transformed Newtonian mechanics into a branch of analysis, Lagrangianmechanics as it is now called, and exhibited the so-called mechanical "principles" as simple results of the variational calculus.
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BiographyEarly yearsLagrange was born, of French and Italian descent (a paternal great grandfather was a French army officer who then moved to Turin), [1]

as Giuseppe Lodovico Lagrangia inTurin. His father, who had charge of theKingdom of Sardinia's military chest, was of good socialposition and wealthy, but before his son grew up he had lost most of his property in speculations, and young Lagrange had to rely onhis own abilities for his position. He was educated at the college of Turin, but it was not until he was seventeen that he showed anytaste for mathematics his interest in the subject being first excited by a paper byEdmund Halley 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 accomplishedmathematician, and was made a lecturer in the artillery school.Variational calculusLagrange is one of the founders of the calculus of variations. Starting in 1754, he worked on the problem oftautochrone, discovering a

method of maximizing and minimizing functionals in a way similar to finding extrema of functions. Lagrange wrote several letters toLeonhard Eulerbetween 1754 and 1756 describing his results. He outlined his "-algorithm", leading to the EulerLagrange equationsof variational calculus and considerably simplifying Euler's earlier analysis.[2] Lagrange also applied his ideas to problems of classicalmechanics, generalizing the results of Euler andMaupertuis. 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 theyoung Italian might have time to complete his work, and claim the undisputed invention of the new calculus"; however, this chivalricview has been disputed.[3] Lagrange published his method in two memoirs of the Turin Society in 1762 and 1773.Miscellanea TaurinensiaIn 1758, with the aid of his pupils, Lagrange established a society, which was subsequently incorporated as the Turin Academy ofSciences, and most of his early writings are to be found in the five volumes of its transactions, usually known as the MiscellaneaTaurinensia. Many of these are elaborate papers. The first volume contains a paper on the theory of the propagation of sound; in this heindicates a mistake made byNewton, obtains the general differential equationfor the motion, and integrates it for motion in a straightline. 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,D'Alembert, and Euler, and arrives at the conclusion that the form ofthe curve at any time tis given by the equation . The article concludes with a masterly discussion ofechoes,beats, and compound sounds. Other articles in this volume are on recurringseries,probabilities, and the calculus of variations.The second volume contains a long paper embodying the results of several papers in the first volume on the theory and notation of thecalculus of variations; and he illustrates its use by deducing the principle of least action, and by solutions of various problems indynamics. The third volume includes the solution of several dynamical problems by means of the calculus of variations; some paperson theintegral calculus; a solution ofFermat's problem mentioned above: given an integer n which is not a perfect square, to find anumberx such that x2n + 1 is a perfect square; and the general differential equations of motion for three bodiesmoving under theirmutual attractions. The next work he produced was in 1764 on the librationof the Moon, and an explanation as to why the same facewas always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting ascontaining the germ of the idea of generalized equations of motion, equations which he first formally proved in 1780.Berlin Academy

Already in 1756 Euler, with support from Maupertuis, made an attempt to bring Lagrange to the Berlin Academy. Later, D'Alambertinterceded on Lagrange's behalf withFrederick of Prussia and wrote to Lagrange asking him to leave Turin for a considerably moreprestigious position in Berlin. Lagrange turned down both offers, responding in 1765 that

It seems to me that Berlin would not be at all suitable for me while M.Euler is there.In 1766 Euler left Berlin forSaint Petersburg, and Frederick wrote to Lagrange expressing the wish of "the greatest king in Europe" tohave "the greatest mathematician in Europe" resident at his court. Lagrange was finally persuaded and he spent the next twenty years inPrussia, where he produced not only the long series of papers published in the Berlin and Turin transactions, but his monumental work,the Mcanique analytique. His residence at Berlin commenced with an unfortunate mistake. Finding most of his colleagues married,and assured by their wives that it was the only way to be happy, he married; his wife soon died, but the union was not a happy one.Lagrange was a favourite of the king, who used frequently to discourse to him on the advantages of perfect regularity of life. The lessonwent home, and thenceforth Lagrange studied his mind and body as though they were machines, and found by experiment the exactamount of work which he was able to do without breaking down. Every night he set himself a definite task for the next day, and oncompleting 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 always thought out the subject of his papers before he began to compose them, and usually wrote themstraight off without a single erasure or correction.FranceIn 1786, Frederick died, and Lagrange, who had found the climate of Berlin trying, gladly accepted the offer ofLouis XVI to move toParis. He received similar invitations from SpainandNaples. In France he was received with every mark of distinction and specialapartments in the Louvre were prepared for his reception, and he became a member of the French Academy of Sciences, which laterbecame part of theNational Institute. At the beginning of his residence in Paris he was seized with an attack of melancholy, and eventhe printed copy of his Mcanique 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 first stirred him out of his lethargy, a curiosity which soon turned to alarm as therevolution developed. It was about the same time, 1792, that the unaccountable sadness of his life and his timidity moved thecompassion of a young girl who insisted on marrying him, and proved a devoted wife to whom he became warmly attached. Althoughthe decree of October 1793 that ordered all foreigners to leave France specifically exempted him by name, he was preparing to escapewhen he was offered the presidency of the commission for the reform of weights and measures. The choice of the units finally selected

was largely due to him, and it was mainly owing to his influence that the decimal subdivision was accepted by the commission of 1799.In 1795, Lagrange was one of the founding members of the Bureau des Longitudes. Though Lagrange had determined to escape fromFrance while there was yet time, he was never in any danger; and the different revolutionary governments (and at a later time,Napoleon) loaded him with honours and distinctions. A striking testimony to the respect in which he was held was shown in 1796 whenthe French commissary in Italy was ordered to attend in full state on Lagrange's father, and tender the congratulations of the republic on
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the achievements of his son, who "had done honour to all mankind by his genius, and whom it was the special glory of Piedmont tohave produced." It may be added that Napoleon, when he attained power, warmly encouraged scientific studies in France, and was aliberal benefactor of them.cole normaleIn 1795, Lagrange was appointed to a mathematical chair at the newly established cole normale, which enjoyed only a brief existenceof four months. His lectures here were quite elementary, and contain nothing of any special importance, but they were publishedbecause the professors had to "pledge themselves to the representatives of the people and to each other neither to read nor to repeatfrom memory," and the discourses were ordered to be taken down in shorthand in order to enable the deputies to see how the professorsacquitted themselves.cole PolytechniqueLagrange was appointed professor of thecole Polytechnique in 1794; and his lectures there are described by mathematicians who had

the good fortune to be able to attend them, as almost perfect both in form and matter.[citation needed]

Beginning with the merest elements, heled his hearers on until, almost unknown to themselves, they were themselves extending the bounds of the subject: above all heimpressed on his pupils the advantage of always using general methods expressed in a symmetrical notation. On the other hand,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 pronounced Italian accent and pronouncesthe s like z The students, of whom the majority are incapable of appreciating him, give him little welcome, but theprofessors make amends for it.

Late yearsIn 1810, Lagrange commenced a thorough revision of the Mcanique analytique, but he was able to complete only about two-thirds ofit before his death at Paris in 1813. He was buried that same year in the Panthon in Paris. The French inscription on his tomb therereads:JOSEPH LOUIS LAGRANGE. Senator. Count of the Empire. Grand Officer of the Legion of Honour. Grand Cross of the ImperialOrder of Runion. 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 BerlinLagrange was extremely active scientifically during twenty years he spent in Berlin. Not only did he produce his splendid Mcaniqueanalytique, but he contributed between one and two hundred papers to the Academy of Turin, the Berlin Academy, and the FrenchAcademy. Some of these are really treatises, and all without exception are of a high order of excellence. Except for a short time whenhe was ill he produced on average about one paper a month. Of these, note the following as amongst the most important. First, hiscontributions to the fourth and fifth volumes, 17661773, of the Miscellanea Taurinensia; of which the most important was the one in1771, in which he discussed how numerousastronomicalobservations should be combined so as to give the most probable result. Andlater, his contributions to the first two volumes, 17841785, of the transactions of the Turin Academy; to the first of which hecontributed a paper on the pressure exerted by fluids in motion, and to the second an article on integration by infinite series, and thekind of problems for which it is suitable. Most of the papers sent to Paris were on astronomical questions, and among these one oughtto particularly mention his paper on the Jovian system in 1766, his essay on the problem of three bodies in 1772, his work on thesecular equationof the Moon in 1773, and his treatise on cometary perturbations in 1778. These were all written on subjects proposed

by the Acadmie franaise, and in each case the prize was awarded to him.Lagrangian mechanicsBetween 1772 and 1788, Lagrange re-formulated Classical/Newtonian mechanics to simplify formulas and ease calculations. Thesemechanics are calledLagrangian mechanics.AlgebraThe greater number of his papers during this time were, however, contributed to the Prussian Academy of Sciences. Several of themdeal with questions inalgebra.

His discussion of representations of integers byquadratic forms(1769) and by more general algebraic forms (1770). His tract on theTheory 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 thealready known formulas for solving equations of second, third, and fourth degrees as manifestations of a single principle, andwas foundational in Galois theory. The complete solution of a binomial equation of any degree is also treated in these papers.

In 1773, Lagrange considered a functional determinantof order 3, a special case of a Jacobian. He also proved the expressionfor thevolumeof a tetrahedronwith one of the vertices at the origin as the one sixth of the absolute value of thedeterminantformed by the coordinates of the other three vertices.

Number TheorySeveral of his early papers also deal with questions of number theory.

Lagrange (17661769) was the first to prove thatPell's equationx2 ny2 = 1 has a nontrivial solution in the integers for anynon-square natural numbern.[4]

He proved the theorem, stated by Bachetwithout justification, thatevery positive integer is the sum of four squares, 1770. He proved Wilson's theorem that ifn is a prime, then (n 1)! + 1 is always a multiple ofn, 1771. His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved. His Recherches d'Arithmtique of 1775 developed a general theory of binary quadratic forms to handle the general problem of

when an integer is representable by the form ax2 + by2 + cxy.Other mathematical workThere are also numerous articles on various points ofanalytical geometry. In two of them, written rather later, in 1792 and 1793, hereduced theequations of the quadrics (or conicoids) to theircanonical forms. During the years from 1772 to 1785, he contributed a long
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series of papers which created the science ofpartial differential equations. A large part of these results were collected in the secondedition of Euler's integral calculus which was published in 1794. He made contributions to the theory ofcontinued fractions.AstronomyLastly, there are numerous papers on problems in astronomy. Of these the most important are the following:

Attempting to solve thethree-body problemresulting in the discovery ofLagrangian points, 1772 On the attraction of ellipsoids, 1773: this is founded onMaclaurin'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 thepoint. Lagrange showed that if the potential of a body at an external point were known, the attraction in any direction could beat 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'sorbit, 1774. On the stability of the planetary orbits, 1776. Two papers in which the method of determining the orbit of a cometfrom 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 ofmechanical 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 assignedfor these agree closely with those obtained later by Le Verrier, and Lagrange proceeded as far as the knowledge thenpossessed 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 inthe same stage as that in which Lagrange left it.

Mcanique analytiqueOver and above these various papers he composed his great treatise, the Mcanique analytique. In this he lays down the law of virtualwork, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole ofmechanics, 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 formulaefrom which any particular result can be obtained. The method of generalized co-ordinates by which he obtained this result is perhapsthe most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert andEuler had done, he showed that, if we determine its configuration by a sufficient number of variables whose number is the same as thatof the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms ofthose variables, and the differential equations of motion thence deduced by simple differentiation. For example, in dynamics of a rigidsystem he replaces the consideration of the particular problem by the general equation, which is now usually written in the form

where Trepresents the kinetic energy and Vrepresents the potential energy of the system. He then presented what we now know as themethod ofLagrange multipliersthough this is not the first time that method was publishedas a means to solve this equation.[5]

Amongst other minor theorems here given it may mention the proposition that the kinetic energy imparted by the given impulses to a

material system under given constraints is a maximum, and theprinciple of least action. All the analysis is so elegant that SirWilliamRowan Hamiltonsaid the work could only be described as a scientific poem. It may be interesting to note that Lagrange remarked thatmechanics was really a branch of pure mathematics analogous to a geometry of four dimensions, namely, the time and the threecoordinates 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 asingle diagram. At first no printer could be found who would publish the book; but Legendre at last persuaded a Paris firm to undertakeit, and it was issued under his supervision in 1788.Work in FranceDifferential calculus and calculus of variationsLagrange's lectures on thedifferential calculusat cole Polytechnique form the basis of his treatise Thorie 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, andits object is to substitute for the differential calculus a group of theorems based on the development of algebraic functions in series. Asomewhat similar method had been previously used byJohn Landenin theResidual Analysis, published in London in 1758. Lagrangebelieved 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 firsttreats of the general theory of functions, and gives an algebraic proof of Taylor's theorem, the validity of which is, however, open toquestion; the second deals with applications to geometry; and the third with applications to mechanics. Another treatise on the samelines was his Leons sur le calcul des fonctions, issued in 1804, with the second edition in 1806. It is in this book that Lagrangeformulated his celebrated method ofLagrange 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 ofCauchy, Jacobi, andWeierstrass.InfinitesimalsAt a later period Lagrange reverted to the use of infinitesimals in preference to founding the differential calculus on the study ofalgebraic forms; and in the preface to the second edition of the Mcanique Analytique, which was issued in 1811, he justifies theemployment 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 thegeometrical 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.Continued fractionsHisRsolution des quations numriques, published in 1798, was also the fruit of his lectures at cole Polytechnique. There he givesthe method of approximating to the real roots of an equation by means ofcontinued fractions, and enunciates several other theorems. Ina note at the end he shows how Fermat's little theorem that
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ap1 1 0 (modp)wherep is a prime and a is prime top, may be applied to give the complete algebraic solution of any binomial equation. He also hereexplains how the equation whose roots are the squares of the differences of the roots of the original equation may be used so as to giveconsiderable information as to the position and nature of those roots. The theory of theplanetary motions had formed the subject ofsome of the most remarkable of Lagrange's Berlin papers. In 1806 the subject was reopened by Poisson, who, in a paper read before theFrench Academy, showed that Lagrange's formulae led to certain limits for the stability of the orbits. Lagrange, who was present, nowdiscussed the whole subject afresh, and in a letter communicated to the Academy in 1808 explained how, by the variation of arbitraryconstants, the periodical and secular inequalities of any system of mutually interacting bodies could be determined.Prizes and distinctionsEuler 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 Edinburghin 1790, a Fellow of theRoyal Societyand a foreign member of the Royal Swedish Academy of Sciences

in 1806. In 1808,Napoleon made Lagrange a Grand Officer of the Legion of Honourand a Comteof the Empire. He was awarded theGrand Croix of the Ordre Imprial de la Runion in 1813, a week before his death in Paris. Lagrange was awarded the 1764 prize of theFrench Academy of Sciences for his memoir on the libration of the Moon. In 1766 the Academy proposed a problem of the motion ofthesatellites of Jupiter, and the prize again was awarded to Lagrange. He also won the prizes of 1772, 1774, and 1778. Lagrange is oneof the 72 prominent French scientists who were commemorated on plaques at the first stage of the Eiffel Towerwhen 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 isnamed via Lagrange. Thelunar craterLagrangealso bears his name.Apocrypha

He was of medium height and slightly formed, with pale blue eyes and a colorless complexion. He was nervous and timid, hedetested controversy, and, to avoid it, willingly allowed others to take credit for what he had done himself. [6]

Due to thorough preparation, he was usually able to write out his papers complete without a single crossing-out or correction.[6]

See also List of topics named after Joseph Louis Lagrange

Notes The initial version of this article was taken from the public domainresourceA Short Account of the History of Mathematics(4thedition, 1908) byW. W. Rouse Ball.

1. ^ Lagrange biography2. ^ Although some authors speak of general method of solving "isoperimetric problems", the eighteenth century meaning of this

expression amounts to "problems in variational calculus", reserving the adjective "relative" for problems with isoperimetric-type constraints. The celebrated method of Lagrange multipliers, which applies to optimization of functions of severalvariables subject to constraints, did not appear until much later, see Fraser, Craig (1992). "Isoperimetric Problems in theVariational Calculus of Euler and Lagrange".Historia Mathematica19: 423. doi:10.1016/0315-0860(92)90052-D.

3. ^ Galletto, D., The genesis of Mcanique analytique, La Mcanique analytique de Lagrange et son hritage, II (Turin, 1989).Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 126 (1992), suppl. 2, 277--370,MR1264671.

4. ^ Oeveres, t.1, 671732

5. ^ Marco Panza, "The Origins of Analytic Mechanics in the 18th Century", in Hans Niels Jahnke (editor), A History ofAnalysis, 2003, p. 1496. ^ abW. W. Rouse Ball, 1908, "Joseph Louis Lagrange (1736 - 1813),"A Short Account of the History of Mathematics, 4th ed.

pp. 401 - 412References

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. Chanson, Hubert, 2007, "Velocity Potential in Real Fluid Flows: Joseph-Louis Lagrange's Contribution,"La Houille Blanche

5: 127-31. Fraser, Craig G., 2005, "Thorie des fonctions analytiques" in Grattan-Guinness, I., ed.,Landmark Writings in Western

Mathematics. Elsevier: 258-76. Lagrange, Joseph-Louis. (1811). Mecanique Analytique. Courcier (reissued byCambridge University Press, 2009;ISBN

9781108001748) Lagrange, J.L. (1781) "Mmoire sur la Thorie 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, "Mchanique Analytique" in Grattan-Guinness, I., ed.,Landmark Writings in Western Mathematics.Elsevier: 208-24.

External links

Wikimedia Commons has media related to:Joseph-Louis Lagrange

O'Connor, John J.;Robertson, Edmund F.,"Joseph Louis Lagrange",MacTutor History of Mathematics archive,University ofSt Andrews,http://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.html.

Weisstein, Eric W.,Lagrange, Joseph (1736-1813)from ScienceWorld. Lagrange, Joseph Louis de: The Encyclopedia of Astrobiology, Astronomy and Space Flight Joseph Louis Lagrange at theMathematics Genealogy Project The Founders of Classical Mechanics: Joseph Louis Lagrange The Lagrange Points Lagrange's works (in French) Oeuvres de Lagrange, edited by Joseph Alfred Serret, Paris 1867, digitized by Gttinger

Digitalisierungszentrum(Mcanique analytique is in volumes 11 and 12.)
http://en.wikipedia.org/wiki/Planetary_motionhttp://en.wikipedia.org/wiki/Simeon_Poissonhttp://en.wikipedia.org/wiki/Simeon_Poissonhttp://en.wikipedia.org/wiki/Royal_Society_of_Edinburghhttp://en.wikipedia.org/wiki/Royal_Society_of_Edinburghhttp://en.wikipedia.org/wiki/Royal_Societyhttp://en.wikipedia.org/wiki/Royal_Societyhttp://en.wikipedia.org/wiki/Royal_Societyhttp://en.wikipedia.org/wiki/Royal_Swedish_Academy_of_Scienceshttp://en.wikipedia.org/wiki/Napoleonhttp://en.wikipedia.org/wiki/Legion_of_Honourhttp://en.wikipedia.org/wiki/Legion_of_Honourhttp://en.wikipedia.org/wiki/Comtehttp://en.wikipedia.org/wiki/Comtehttp://en.wikipedia.org/w/index.php?title=Ordre_Imp%C3%A9rial_de_la_R%C3%A9union&action=edit&redlink=1http://en.wikipedia.org/wiki/French_Academy_of_Scienceshttp://en.wikipedia.org/wiki/Librationhttp://en.wikipedia.org/wiki/Satellites_of_Jupiterhttp://en.wikipedia.org/wiki/Satellites_of_Jupiterhttp://en.wikipedia.org/wiki/Satellites_of_Jupiterhttp://en.wikipedia.org/wiki/Eiffel_Towerhttp://en.wikipedia.org/wiki/Lunar_craterhttp://en.wikipedia.org/wiki/Lunar_craterhttp://en.wikipedia.org/wiki/Lunar_craterhttp://en.wikipedia.org/wiki/Lagrange_(crater)http://en.wikipedia.org/wiki/Lagrange_(crater)http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_note-RouseBall-5http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_note-RouseBall-5http://en.wikipedia.org/wiki/List_of_topics_named_after_Joseph_Louis_Lagrangehttp://en.wikipedia.org/wiki/Public_domainhttp://en.wikipedia.org/wiki/Public_domainhttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-0http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Lagrange.htmlhttp://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-1http://en.wikipedia.org/wiki/Lagrange_multipliershttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1016%2F0315-0860(92)90052-Dhttp://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-2http://en.wikipedia.org/wiki/Mathematical_Reviewshttp://en.wikipedia.org/wiki/Mathematical_Reviewshttp://www.ams.org/mathscinet-getitem?mr=1264671http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-3http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=41029http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=41029http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=41029http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-4http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-RouseBall_5-0http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-RouseBall_5-1http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-RouseBall_5-1http://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.htmlhttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://www.encyclopedia.com/html/L/Lagrange.asphttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.htmlhttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://espace.library.uq.edu.au/eserv.php?pid=UQ:119883&dsID=hb07_5.pdfhttp://en.wikipedia.org/wiki/Ivor_Grattan-Guinnesshttp://en.wikipedia.org/wiki/Cambridge_University_Presshttp://en.wikipedia.org/wiki/Cambridge_University_Presshttp://en.wikipedia.org/wiki/Special:BookSources/9781108001748http://en.wikipedia.org/wiki/Special:BookSources/9781108001748http://en.wikipedia.org/wiki/Special:BookSources/9781108001748http://commons.wikimedia.org/wiki/Category:Joseph-Louis_Lagrangehttp://en.wikipedia.org/wiki/John_J._O'Connor_(mathematician)http://en.wikipedia.org/wiki/John_J._O'Connor_(mathematician)http://en.wikipedia.org/wiki/John_J._O'Connor_(mathematician)http://en.wikipedia.org/wiki/Edmund_F._Robertsonhttp://en.wikipedia.org/wiki/Edmund_F._Robertsonhttp://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.htmlhttp://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.htmlhttp://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_archivehttp://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_archivehttp://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_archivehttp://en.wikipedia.org/wiki/University_of_St_Andrewshttp://en.wikipedia.org/wiki/University_of_St_Andrewshttp://en.wikipedia.org/wiki/University_of_St_Andrewshttp://en.wikipedia.org/wiki/University_of_St_Andrewshttp://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.htmlhttp://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.htmlhttp://en.wikipedia.org/wiki/Eric_W._Weissteinhttp://en.wikipedia.org/wiki/Eric_W._Weissteinhttp://scienceworld.wolfram.com/biography/Lagrange.htmlhttp://scienceworld.wolfram.com/biography/Lagrange.htmlhttp://en.wikipedia.org/wiki/ScienceWorldhttp://en.wikipedia.org/wiki/ScienceWorldhttp://www.daviddarling.info/encyclopedia/L/Lagrange.htmlhttp://genealogy.math.ndsu.nodak.edu/id.php?id=17864http://en.wikipedia.org/wiki/Mathematics_Genealogy_Projecthttp://en.wikipedia.org/wiki/Mathematics_Genealogy_Projecthttp://about-physicists.org/lagrange.htmlhttp://map.gsfc.nasa.gov/m_mm/ob_techorbit1.htmlhttp://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN308899466http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN308899466http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN308899466http://en.wikipedia.org/wiki/Planetary_motionhttp://en.wikipedia.org/wiki/Simeon_Poissonhttp://en.wikipedia.org/wiki/Royal_Society_of_Edinburghhttp://en.wikipedia.org/wiki/Royal_Societyhttp://en.wikipedia.org/wiki/Royal_Swedish_Academy_of_Scienceshttp://en.wikipedia.org/wiki/Napoleonhttp://en.wikipedia.org/wiki/Legion_of_Honourhttp://en.wikipedia.org/wiki/Comtehttp://en.wikipedia.org/w/index.php?title=Ordre_Imp%C3%A9rial_de_la_R%C3%A9union&action=edit&redlink=1http://en.wikipedia.org/wiki/French_Academy_of_Scienceshttp://en.wikipedia.org/wiki/Librationhttp://en.wikipedia.org/wiki/Satellites_of_Jupiterhttp://en.wikipedia.org/wiki/Eiffel_Towerhttp://en.wikipedia.org/wiki/Lunar_craterhttp://en.wikipedia.org/wiki/Lagrange_(crater)http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_note-RouseBall-5http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_note-RouseBall-5http://en.wikipedia.org/wiki/List_of_topics_named_after_Joseph_Louis_Lagrangehttp://en.wikipedia.org/wiki/Public_domainhttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-0http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Lagrange.htmlhttp://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-1http://en.wikipedia.org/wiki/Lagrange_multipliershttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1016%2F0315-0860(92)90052-Dhttp://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-2http://en.wikipedia.org/wiki/Mathematical_Reviewshttp://www.ams.org/mathscinet-getitem?mr=1264671http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-3http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=41029http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-4http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-RouseBall_5-0http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange#cite_ref-RouseBall_5-1http://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.htmlhttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://www.encyclopedia.com/html/L/Lagrange.asphttp://en.wikipedia.org/wiki/W._W._Rouse_Ballhttp://www.maths.tcd.ie/pub/HistMath/People/Lagrange/RouseBall/RB_Lagrange.htmlhttp://en.wikipedia.org/wiki/Rouse_History_of_Mathematicshttp://espace.library.uq.edu.au/eserv.php?pid=UQ:119883&dsID=hb07_5.pdfhttp://en.wikipedia.org/wiki/Ivor_Grattan-Guinnesshttp://en.wikipedia.org/wiki/Cambridge_University_Presshttp://en.wikipedia.org/wiki/Special:BookSources/9781108001748http://en.wikipedia.org/wiki/Special:BookSources/9781108001748http://commons.wikimedia.org/wiki/Category:Joseph-Louis_Lagrangehttp://en.wikipedia.org/wiki/John_J._O'Connor_(mathematician)http://en.wikipedia.org/wiki/Edmund_F._Robertsonhttp://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.htmlhttp://en.wikipedia.org/wiki/MacTutor_History_of_Mathematics_archivehttp://en.wikipedia.org/wiki/University_of_St_Andrewshttp://en.wikipedia.org/wiki/University_of_St_Andrewshttp://www-history.mcs.st-andrews.ac.uk/Biographies/Lagrange.htmlhttp://en.wikipedia.org/wiki/Eric_W._Weissteinhttp://scienceworld.wolfram.com/biography/Lagrange.htmlhttp://en.wikipedia.org/wiki/ScienceWorldhttp://www.daviddarling.info/encyclopedia/L/Lagrange.htmlhttp://genealogy.math.ndsu.nodak.edu/id.php?id=17864http://en.wikipedia.org/wiki/Mathematics_Genealogy_Projecthttp://about-physicists.org/lagrange.htmlhttp://map.gsfc.nasa.gov/m_mm/ob_techorbit1.htmlhttp://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN308899466http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN308899466


10/11

Rue Lagrange, Paris

Joseph-Louis Lagrange

Da Wikipedia, l'enciclopedia libera.

Quando chiediamo un consiglio, stiamo di solito cercando un complice. Joseph-Louis Lagrange, nato Giuseppe Lodovico Lagrangia o ancora Giuseppe Luigi Lagrangia o Lagrange (Torino,25 gennaio1736 Parigi, 10 aprile 1813), stato un matematico e astronomo italiano per nascita e formazione e attivo nella sua maturitscientifica per ventuno anni a Berlino e per ventisei a Parigi. Lagrange viene unanimemente considerato uno tra i maggiori e pi

influenti matematici del XVIII secolo. La sua pi importante opera il testo Mcanique analytique, pubblicato nel 1788. In campomatematico Lagrange ricordato per le sue attivit in teoria dei numeri, per aver sviluppato il calcolo delle variazioni, per averdelineato i fondamenti della meccanica razionale, per i risultati nel campo delle equazioni differenziali e per essere stato uno deipionieri della teoria dei gruppi. Nel settore della astronomiacondusse ricerche sui calcoli della librazione lunare e almoto dei pianeti.Lagrange, la cui famiglia aveva origini francesi (il bisnonno paterno era stato ufficiale dell'esercito francese prima di trasferirsi aTorino), nacque a Torinoda una famiglia tutt'altro che agiata. Lagrange era il maggiore di 11 fratelli ma di questi solo lui e un altroriuscirono ad arrivare all'et adulta. Studi all'Universit di Torino. La sua materia preferita era il latino. Si appassion di matematicasolo dopo aver letto un testo di Edmund Halley. Venne nominato professore di "matematiche" alle Scuole teoriche di Artiglieria eFortificazione del capoluogo piemontese all'et di appena diciannove anni. Della sua attivit didattica presso la scuola resta unmanoscritto delle sue lezioni intitolatoPrincipi di analisi sublime; invece andato disperso un trattato di meccanica. Lo stesso anno, inuna corrispondenza con Eulero, espose le sue idee sulcalcolo delle variazioni. Eulero rimase impressionato dalle sue doti e nel1759lofece eleggere membro dell'Accademia di Berlino. A vent'anni inizi ad insegnare presso le Reali Scuole d'Artiglieria di Torino. Nel1758partecip alla fondazione della Societ Privata (la futura Accademia reale delle Scienze di Torino) nel1757. I nervi risentirono

forse del suo incessante lavoro e divenne ipocondriaco. Nel1766, su proposta di Eulero e diD'Alembert, venne chiamato da Federico IIdi Prussiaa succedere a Eulero stesso come presidente della classe di scienze dell'Accademia di Berlino. In questo anno si spos conVittoria Conti. Il matrimonio fu felice. Rimase aBerlinofino alla morte del sovrano. Nel 1783 Vittoria mor. Nel1786, su invito del reLuigi XVI di Francia, si trasfer aParigi per entrare a far parte dell'Acadmie des Sciences.Nel 1787, nonostante fosse all'apice della sua fama, venne colpito da un periodo di forte depressione. Lo stesso anno si trasfer a Parigisu invito diLuigi XVI. Durante la rivoluzione francesegli fu offerto di tornare a Berlinoma egli rifiut. In questo periodo si mossesempre con prudenza per evitare guai politici e non finire ghigliottinato. Nel 1792 si rispos con Adelaide Le Monnier. Divennepresidente della commissione cui era stato affidato il compito di fissare un nuovo sistema di pesi e misure, il sistema metrico decimaledal quale avr origine l'odierno Sistema Internazionale. Dal 1797 insegn all'cole polytechnique appena fondata. La fama rimasecomunque immutata sia durante la Rivoluzione che sottoNapoleone Bonaparte. Con il suo affermarsi al potere, infatti, la posizione diLagrange si consolid: ricevette la Legion d'Onore, venne eletto al Senato diFranciae nominato conte dell'impero. Si spense nel 1813 evenne sepolto nel Pantheon.Il cognome Ci sono diverse grafie delcognome di Lagrange: da giovane si firm "De la Grangia Tournier", "Tournier de la Grangia" eanche "Tournier". Successivamente si trova scritto come "De la Ganja", e "la Grange". Dopo essersi trasferito a Berlino e soprattutto aParigi(dove un'origine nobile non era vista di buon occhio) si firm sempre "Lagrange". Lo storico della matematica Gino Loriaalfondo della p. 747 della sua Storia delle matematiche (1950) scrive testualmente:

Nel registro dei nati questo designato cos: "Lagrangia Giuseppe Lodovico"; ci giustifica il modo di scriverne il cognomeadottato in parecchie occasioni, per documentare l'italianit del soggetto.

Opere Comp ricerche di fondamentale importanza sul calcolo delle variazioni, sulla teoria delle funzioni e sulla sistemazionematematica della meccanica. Svolse inoltre studi di astronomia, trattando soprattutto il problema della mutua attrazione gravitazionalefra tre corpi.

Miscellanea Taurinensia vol. 1 (1759), vol. 2 (1763), vol. 3 (1765) Mcanique analytique (1788) Thorie des fonctions analytiques (1797) Leons sur le calcul des fonctions (1806)

Bibliografia Questo testo proviene in parte o integralmente dalla relativa voce del progetto Mille anni di scienza in Italia, opera

dell'Istituto Museo di Storia della Scienza di Firenze(home page) rilasciata sottolicenza Creative CommonsCC-BY-3.0 Sfogliando la "Mchanique Analitique" Giornata di Studio su Joseph Louis Lagrange (Milano, 19 ottobre 2006). A cura di

Giannantonio Sacchi Landriani e Antonio Giorgilli, LED Edizioni Universitarie, Milano, 2008, ISBN 978-88-7916-404-7Voci correlate

Teorema di Lagrange Punti di Lagrange Funzione lagrangiana Notazione di Lagrange Metodo dei moltiplicatori di Lagrange

Altri progetti

Wikimedia Commonscontiene file multimediali su Joseph-Louis Lagrange

Wikiquotecontiene citazioni di o su Joseph-Louis LagrangeCollegamenti esterni (EN)Biografia su MacTutor
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dia.org/wiki/Franciahttp://it.wikipedia.org/wiki/Franciahttp://it.wikipedia.org/wiki/Franciahttp://it.wikipedia.org/wiki/1813http://it.wikipedia.org/wiki/Pantheon_(Parigi)http://it.wikipedia.org/wiki/Pantheon_(Parigi)http://it.wikipedia.org/wiki/Cognomehttp://it.wikipedia.org/wiki/Cognomehttp://it.wikipedia.org/wiki/Berlinohttp://it.wikipedia.org/wiki/Parigihttp://it.wikipedia.org/wiki/Parigihttp://it.wikipedia.org/wiki/Nobilehttp://it.wikipedia.org/wiki/Gino_Loriahttp://it.wikipedia.org/wiki/Gino_Loriahttp://it.wikipedia.org/wiki/Gino_Loriahttp://it.wikipedia.org/w/index.php?title=Miscellanea_Taurinensia&action=edit&redlink=1http://it.wikipedia.org/w/index.php?title=M%C3%A9canique_analytique&action=edit&redlink=1http://it.wikipedia.org/w/index.php?title=Th%C3%A9orie_des_fonctions_analytiques&action=edit&redlink=1http://it.wikipedia.org/w/index.php?title=Le%C3%A7ons_sur_le_calcul_des_fonctions&action=edit&redlink=1http://www.imss.fi.it/milleanni/cronologia/biografie/lagrange.htmlhttp://www.imss.fi.it/milleanni/cronologia/biografie/lagrange.htmlhttp://www.imss.fi.it/milleannihttp://www.imss.fi.it/milleannihttp://it.wikipedia.org/wiki/Museo_di_storia_della_scienzahttp://it.wikipedia.org/wiki/Museo_di_storia_della_scienzahttp://www.imss.fi.it/http://it.wikipedia.org/wiki/Licenze_Creative_Commonshttp://it.wikipedia.org/wiki/Licenze_Creative_Commonshttp://creativecommons.org/licenses/by/3.0/deed.ithttp://creativecommons.org/licenses/by/3.0/deed.ithttp://it.wikipedia.org/wiki/Speciale:RicercaISBN/9788879164047http://it.wikipedia.org/wiki/Teorema_di_Lagrangehttp://it.wikipedia.org/wiki/Punti_di_Lagrangehttp://it.wikipedia.org/wiki/Funzione_lagrangianahttp://it.wikipedia.org/wiki/Notazione_di_Lagrangehttp://it.wikipedia.org/wiki/Metodo_dei_moltiplicatori_di_Lagrangehttp://commons.wikimedia.org/wiki/Pagina_principalehttp://commons.wikimedia.org/wiki/Pagina_principalehttp://commons.wikimedia.org/wiki/Joseph-Louis_Lagrangehttp://it.wikiquote.org/wiki/Pagina_principalehttp://it.wikiquote.org/wiki/Pagina_principalehttp://it.wikiquote.org/wiki/Joseph-Louis_Lagrangehttp://it.wikipedia.org/wiki/Lingua_inglesehttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Lagrange.htmlhttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Lagrange.htmlhttp://it.wikipedia.org/wiki/MacTutorhttp://it.wikipedia.org/wiki/File:Wikiquote-logo.svghttp://it.wikipedia.org/wiki/File:Commons-logo.svghttp://maps.google.com/maps/ms?hl=en&ie=UTF8&msa=0&msid=103015796427039682952.00046ac5940f4335f749d&ll=48.851435,2.34785&spn=0.003615,0.007778&z=17http://it.wikipedia.org/wiki/Torinohttp://it.wikipedia.org/wiki/25_gennaiohttp://it.wikipedia.org/wiki/1736http://it.wikipedia.org/wiki/Parigihttp://it.wikipedia.org/wiki/10_aprilehttp://it.wikipedia.org/wiki/1813http://it.wikipedia.org/wiki/Matematicohttp://it.wikipedia.org/wiki/Astronomohttp://it.wikipedia.org/wiki/Italiahttp://it.wikipedia.org/wiki/Berlinohttp://it.wikipedia.org/wiki/Parigihttp://it.wikipedia.org/wiki/XVIII_secolohttp://it.wikipedia.org/wiki/1788http://it.wikipedia.org/wiki/Matematicahttp://it.wikipedia.org/wiki/Teoria_dei_numerihttp://it.wikipedia.org/wiki/Calcolo_delle_variazionihttp://it.wikipedia.org/wiki/Meccanica_razionalehttp://it.wikipedia.org/wiki/Equazioni_differenzialihttp://it.wikipedia.org/wiki/Teoria_dei_gruppihttp://it.wikipedia.org/wiki/Astronomiahttp://it.wikipedia.org/wiki/Librazionehttp://it.wikipedia.org/wiki/Moto_dei_pianetihttp://it.wikipedia.org/wiki/Franciahttp://it.wikipedia.org/wiki/Torinohttp://it.wikipedia.org/wiki/Universit%C3%A0_di_Torinohttp://it.wikipedia.org/wiki/Lingua_latinahttp://it.wikipedia.org/wiki/Edmund_Halleyhttp://it.wikipedia.org/wiki/Matematicahttp://it.wikipedia.org/wiki/Artiglieriahttp://it.wikipedia.org/wiki/Fortificazionehttp://it.wikipedia.org/wiki/Eulerohttp://it.wikipedia.org/wiki/Calcolo_delle_variazionihttp://it.wikipedia.org/wiki/1759http://it.wikipedia.org/wiki/Accademia_delle_scienze_prussianahttp://it.wikipedia.org/wiki/1758http://it.wikipedia.org/wiki/Accademia_delle_Scienze_di_Torinohttp://it.wikipedia.org/wiki/1757http://it.wikipedia.org/wiki/Ipocondriacohttp://it.wikipedia.org/wiki/1766http://it.wikipedia.org/wiki/Leonhard_Eulerhttp://it.wikipedia.org/wiki/Jean_Baptiste_Le_Rond_d'Alemberthttp://it.wikipedia.org/wiki/Federico_II_di_Prussiahttp://it.wikipedia.org/wiki/Federico_II_di_Prussiahttp://it.wikipedia.org/wiki/Eulerohttp://it.wikipedia.org/wiki/Berlinohttp://it.wikipedia.org/wiki/1783http://it.wikipedia.org/wiki/1786http://it.wikipedia.org/wiki/Luigi_XVI_di_Franciahttp://it.wikipedia.org/wiki/Parigihttp://it.wikipedia.org/wiki/Acad%C3%A9mie_des_Scienceshttp://it.wikipedia.org/wiki/1787http://it.wikipedia.org/wiki/Luigi_XVIhttp://it.wikipedia.org/wiki/Rivoluzione_francesehttp://it.wikipedia.org/wiki/Berlinohttp://it.wikipedia.org/wiki/1792http://it.wikipedia.org/wiki/Sistema_metrico_decimalehttp://it.wikipedia.org/wiki/Sistema_Internazionalehttp://it.wikipedia.org/wiki/1797http://it.wikipedia.org/wiki/%C3%89cole_polytechniquehttp://it.wikipedia.org/wiki/Napoleone_Bonapartehttp://it.wikipedia.org/wiki/Legion_d'Onorehttp://it.wikipedia.org/wiki/Franciahttp://it.wikipedia.org/wiki/1813http://it.wikipedia.org/wiki/Pantheon_(Parigi)http://it.wikipedia.org/wiki/Cognomehttp://it.wikipedia.org/wiki/Berlinohttp://it.wikipedia.org/wiki/Parigihttp://it.wikipedia.org/wiki/Nobilehttp://it.wikipedia.org/wiki/Gino_Loriahttp://it.wikipedia.org/w/index.php?title=Miscellanea_Taurinensia&action=edit&redlink=1http://it.wikipedia.org/w/index.php?title=M%C3%A9canique_analytique&action=edit&redlink=1http://it.wikipedia.org/w/index.php?title=Th%C3%A9orie_des_fonctions_analytiques&action=edit&redlink=1http://it.wikipedia.org/w/index.php?title=Le%C3%A7ons_sur_le_calcul_des_fonctions&action=edit&redlink=1http://www.imss.fi.it/milleanni/cronologia/biografie/lagrange.htmlhttp://www.imss.fi.it/milleannihttp://it.wikipedia.org/wiki/Museo_di_storia_della_scienzahttp://www.imss.fi.it/http://it.wikipedia.org/wiki/Licenze_Creative_Commonshttp://creativecommons.org/licenses/by/3.0/deed.ithttp://it.wikipedia.org/wiki/Speciale:RicercaISBN/9788879164047http://it.wikipedia.org/wiki/Teorema_di_Lagrangehttp://it.wikipedia.org/wiki/Punti_di_Lagrangehttp://it.wikipedia.org/wiki/Funzione_lagrangianahttp://it.wikipedia.org/wiki/Notazione_di_Lagrangehttp://it.wikipedia.org/wiki/Metodo_dei_moltiplicatori_di_Lagrangehttp://commons.wikimedia.org/wiki/Pagina_principalehttp://commons.wikimedia.org/wiki/Joseph-Louis_Lagrangehttp://it.wikiquote.org/wiki/Pagina_principalehttp://it.wikiquote.org/wiki/Joseph-Louis_Lagrangehttp://it.wikipedia.org/wiki/Lingua_inglesehttp://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Lagrange.htmlhttp://it.wikipedia.org/wiki/MacTutor


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Joseph-Louis Lagrange Statua che ricorda lo studioso aTorino, nell'omonima piazza Lagrange

La tomba di Lagrange al Panthon di Parigi.
http://it.wikipedia.org/wiki/Torinohttp://it.wikipedia.org/wiki/Torinohttp://it.wikipedia.org/wiki/Torinohttp://it.wikipedia.org/wiki/Panth%C3%A9onhttp://en.wikipedia.org/wiki/File:Lagrange%27s_tomb_at_the_Pantheon.jpghttp://it.wikipedia.org/wiki/File:Langrange_portrait.jpghttp://it.wikipedia.org/wiki/File:Torino-080408073-statua_Luigi_Lagrange.JPGhttp://it.wikipedia.org/wiki/File:Joseph_Louis_Lagrange.jpghttp://it.wikipedia.org/wiki/Torinohttp://it.wikipedia.org/wiki/Panth%C3%A9on

Documents

D'AYALA Mariano. A Lagrangian Manuscript in the Royal Library of Turin