1857:
4059:
3898:
1068:
2565:
514:
4131:
2554:
2542:
2530:
2518:
1870:
3773:
2289:, 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
4095:
1035:; 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.
4047:
2708:, 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.
4119:
4071:
4107:
2484:, 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
1968:. This method fails to give a general formula for solutions of an equation of degree five and higher because the auxiliary equation involved has a 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
4083:
55:
1111:, 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.
4035:
958:". 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 the full state on Lagrange's father and tender the congratulations of the republic on the achievements of his son, who "had done honour to all mankind by his genius, and whom it was the special glory of
2469:, 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
881:
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 the subject-matter were capable of improvement. He carefully planned his papers before writing them, usually without a single erasure or correction.
2692:, 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.
2280:
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.
1122:
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
1022:
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" . The discourses were ordered and taken down in
880:
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
641:
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
2224:
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
2423:—though this is not the first time that method was published—as a means to solve this equation. 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
2454:
577:
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
2590:
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
606:, 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
2435:
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
593:
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
2406:
884:
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.
499:
In appearance he was of medium height, and slightly formed, with pale blue eyes and a colourless complexion. In character he was nervous and timid, he detested controversy, and to avoid it willingly allowed others to take the credit for what he had himself done.
2242:
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
936:, who himself was by then already thrown out of the academy along with many other scholars, Lagrange was specifically exempted by name in the decree of October 1793 that ordered all foreigners to leave France. On 4 May 1794, Lavoisier and 27 other
869:, 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
1018:, 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
3442:
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
2499:, 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
3380:
2295:
920:
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
970:
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.
773:
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
1211:
2281:
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
3412:
no final do Seculo XVIII e a origem da Análise dimensional". In
Roberto de Andrade Martins; Lilian Al-Chueyr Pereira Martins; Cibelle Celestino Silva; Juliana Mesquita Hidalgo Ferreira (eds.).
589:
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.
4236:
370:, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1788–89), which was written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since
2675:
634:
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
381:
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
1023:
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 .
745:
956:
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
477:
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
1235:
901:
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
2257:
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.
2210:, 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
2134:
962:
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
950:
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,
653:
2225:
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.
4231:
3345:
2605:, published in 1798, was also the fruit of his lectures at École Polytechnique. There he gives the method of approximating the real roots of an equation by means of
2000:
3109:
2026:
830:. 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.
503:
He always thought out the subject of his papers before he began to compose them, and usually wrote them straight off without a single erasure or correction.
2273:
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 of
4226:
3485:, La Mécanique analytique de Lagrange et son héritage, II (Turin, 1989). Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 126 (1992), suppl. 2, 277–370,
660:. 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
4221:
2488:, the validity of which is, however, open to question; the second deals with applications to geometry; and the third with applications to mechanics.
2440:
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.
626:, discovering a method of maximizing and minimizing functionals in a way similar to finding extrema of functions. Lagrange wrote several letters to
4251:
2806:
1914:
Between 1772 and 1788, Lagrange re-formulated Classical/Newtonian mechanics to simplify formulas and ease calculations. These mechanics are called
1086:. 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
642:
new calculus"; however, this chivalric view has been disputed. Lagrange published his method in two memoirs of the Turin Society in 1762 and 1773.
147:
4256:
3982:
3937:
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3294:
854:
and by letter, asked him to leave Turin for a considerably more prestigious position in Berlin. He again turned down the offer, responding that
954:) gave him honours and distinctions. This luckiness or safety may to some extent be due to his life attitude he expressed many years before: "
3341:"IV. An Instance of the Excellence of the Modern ALGEBRA, in the Resolution of the Problem of finding the Foci of Optick Glasses universally"
2401:{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {x}}}}-{\frac {\partial T}{\partial x}}+{\frac {\partial V}{\partial x}}=0,}
1901:
4176:
4171:
585:
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
3733:
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.
3057:
4271:
4266:
1490:
603:
582:
and his favourite subject was classical Latin. At first, he had no great enthusiasm for mathematics, finding Greek geometry rather dull.
3838:
4186:
3877:
1609:
986:
913:
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
4181:
4211:
4191:
2581:
in preference to founding the differential calculus on the study of algebraic forms; and in the preface to the second edition of the
668:
for the motion, and integrates it for motion in a straight line. This volume also contains the complete solution of the problem of a
652:
In 1758, with the aid of his pupils (mainly with Daviet), Lagrange established a society, which was subsequently incorporated as the
3576:
Séances des Écoles normales, recueillies par des sténographes, et revues par les professeurs. Nouvelle édition. Leçons. Tome premier
4206:
3597:
3447:, which applies to the optimization of functions of several variables subject to constraints, did not appear until much later. See
2771:
2541:
1582:
3550:
Séances des écoles normales, recueillies par des sténographes, et revues par les professeurs. Seconde partie. Débats. Tome premier
2716:
Euler proposed Lagrange for election to the Berlin Academy and he was elected on 2 September 1756. He was elected a Fellow of the
2553:
1098:. Member of the Institute and the Bureau of Longitude. Born in Turin on 25 January 1736. Died in Paris on 10 April 1813.
873:, where he produced a long series of papers published in the Berlin and Turin transactions, and composed his monumental work, the
4196:
3792:
2529:
909:(1795). At the beginning of his residence in Paris, he was seized with an attack of melancholy, and even the printed copy of his
826:
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
2517:
940:
were arrested and sentenced to death and guillotined on the afternoon after the trial. Lagrange said on the death of Lavoisier:
846:, seeing Lagrange's mathematical talent, tried to persuade Lagrange to come to Berlin, but he shyly refused the offer. In 1765,
784:
The third volume includes the solution of several dynamical problems by means of the calculus of variations; some papers on the
3987:
2782:
in the 5th Arrondissement in Paris is named after him. In Turin, the street where the house of his birth still stands is named
1167:
2190:. A large part of these results was collected in the second edition of Euler's integral calculus which was published in 1794.
4261:
3757:
3727:
3513:
3423:
3320:
1046:
his voice is very feeble, at least in that he does not become heated; he has a very marked Italian accent and pronounces the
990:) when he was preparing to escape. After Lavoisier's death in 1794, it was largely Lagrange who influenced the choice of the
1138:
of the Moon in 1773, and his treatise on cometary perturbations in 1778. These were all written on subjects proposed by the
3972:
1952:
3883:
2130:
His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved.
3930:
1564:
2495:, issued in 1804, with the second edition in 1806. It is in this book that Lagrange formulated his celebrated method of
1094:
JOSEPH LOUIS LAGRANGE. Senator. Count of the Empire. Grand Officer of the Legion of Honour. Grand Cross of the Imperial
3855:
2704:
had formed the subject of some of the most remarkable of Lagrange's Berlin papers. In 1806 the subject was reopened by
3967:
3392:
2725:
2094:
1894:
1107:
Lagrange was extremely active scientifically during the twenty years he spent in Berlin. Not only did he produce his
984:
of measurement in the 1790s. He was offered the presidency of the Commission for the reform of weights and measures (
446:
430:
2431:
said the work could be described only as a scientific poem. Lagrange remarked that mechanics was really a branch of
574:
3679:
3260:
2619:
1856:
3535:
Mémoires de la classe des Sciences mathématiques et physiques de l'Institut de France, Année 1812, Seconde Partie
2036:
1230:
1083:
4216:
4166:
3923:
3872:
Oeuvres de Lagrange, edited by Joseph Alfred Serret, Paris 1867, digitized by Göttinger Digitalisierungszentrum
1485:
1225:
656:, and most of his early writings are to be found in the five volumes of its transactions, usually known as the
3693:
3159:
607:
4151:
3850:
2826:
2187:
1130:
Most of the papers sent to Paris were on astronomical questions, and among these, including his paper on the
1019:
1015:
531:
893:
In 1786, following Frederick's death, Lagrange received similar invitations from states including Spain and
3644:
3265:
1927:
1887:
1874:
1635:
1558:
1480:
1323:
917:
first stirred him out of his lethargy, a curiosity which soon turned to alarm as the revolution developed.
687:
382:
349:
2250:
of the planets, 1781–1784: the upper limits assigned for these agree closely with those obtained later by
945:
It took only a moment to cause this head to fall and a hundred years will not suffice to produce its like.
356:, where he stayed for over twenty years, producing many volumes of work and winning several prizes of the
2767:, and the prize again was awarded to Lagrange. He also shared or won the prizes of 1772, 1774, and 1778.
2585:, which was issued in 1811, he justifies the employment of infinitesimals, and concludes by saying that:
1554:
1355:
631:
414:
2186:
During the years from 1772 to 1785, he contributed a long series of papers which created the science of
1333:
554:
from the noble Roman family. Lagrange's father, Giuseppe Francesco Lodovico, was a doctor in Law at the
4025:
3871:
3719:
2756:
2717:
2610:
2254:, and Lagrange proceeded as far as the knowledge then possessed of the masses of the planets permitted.
1774:
1663:
1589:
1449:
1382:
1054:
The students, of whom the majority are incapable of appreciating him, give him little welcome, but the
902:
847:
677:
357:
345:
253:
3832:
3607:
3596:
Ivor Grattan-Guinness. Convolutions in French Mathematics, 1800–1840. Birkhäuser 1990. Vol. I, p.108.
602:. In that capacity, Lagrange was the first to teach calculus in an engineering school. According to
4246:
4241:
4201:
3621:
Marco Panza, "The Origins of Analytic Mechanics in the 18th Century", in Hans Niels Jahnke (editor),
3291:
2424:
1528:
922:
774:
35:
31:
1082:, but he was able to complete only about two-thirds of it before his death in Paris in 1813, in 128
3797:
2504:
2419:
represents the potential energy of the system. He then presented what we now know as the method of
1804:
1648:
418:
17:
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3068:
2286:
1754:
1518:
1139:
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279:
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2428:
2032:
1799:
1616:
767:
619:
466:
410:
159:
3243:
1032:
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231:
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2500:
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subdivision, by the commission of 1799. Lagrange was also one of the founding members of the
665:
434:
426:
394:
386:
322:
169:
54:
3821:
3530:
1975:
963:
925:. She insisted on marrying him and proved a devoted wife to whom he became warmly attached.
630:
between 1754 and 1756 describing his results. He outlined his "δ-algorithm", leading to the
398:
4161:
4156:
3997:
3865:
3489:
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3104:
2821:
2741:
2496:
2420:
1915:
1829:
1789:
1697:
1693:
1685:
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1465:
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1214:
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951:
778:
759:
590:
555:
486:
422:
375:
361:
154:
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3072:
1824:
489:. He presented the mechanical "principles" as simple results of the variational calculus.
8:
4123:
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3783:
2737:
2485:
2172:
2101:
2005:
1964:
1604:
1545:
1523:
1268:
1263:
1258:
1158:
898:
851:
756:
672:; in this paper, he points out a lack of generality in the solutions previously given by
579:
543:
482:
470:
442:
334:
330:
179:
164:
134:
121:
116:
102:
83:
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4002:
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Lagrange, Joseph Louis de: The Encyclopedia of Astrobiology, Astronomy and Space Flight
3362:
2606:
2207:
2159:
2069:
1959:
1946:
1734:
1475:
1350:
1318:
1278:
474:
438:
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1118:; of which the most important was the one in 1771, in which he discussed how numerous
1072:
458:
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3827:
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3553:
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3419:
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It seems to me that Berlin would not be at all suitable for me while M.Euler is there
785:
748:
3385:
The Heirs of Archimedes: Science and the Art of War through the Age of Enlightenment
2705:
1926:
The greater number of his papers during this time were, however, contributed to the
1067:
421:. He extended the method to include possible constraints, arriving at the method of
4075:
4039:
3902:
3860:
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3256:
3018:
3001:
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1839:
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1705:
1680:
1535:
1393:
1338:
1313:
1135:
906:
866:
789:
752:
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530:, Lagrange was of Italian and French descent. His paternal great-grandfather was a
478:
3669:
3085:
1134:
system in 1766, his essay on the problem of three bodies in 1772, his work on the
680:, and Euler, and arrives at the conclusion that the form of the curve at any time
226:
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3137:
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2138:
1834:
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In 1795, Lagrange was appointed to a mathematical chair at the newly established
929:
595:
506:
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4012:
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1972:. The complete solution of a binomial equation (namely an equation of the form
1939:
1861:
1769:
1670:
1387:
1039:
816:
627:
599:
551:
547:
341:
321:, later naturalized French. He made significant contributions to the fields of
274:
269:
247:
2266:
Over and above these various papers he composed his fundamental treatise, the
2141:
to handle the general problem of when an integer is representable by the form
4145:
3831:
3639:
3583:
3557:
3439:
2721:
2578:
1969:
1749:
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174:
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3694:
Velocity Potential in Real Fluid Flows: Joseph-Louis Lagrange's Contribution
2609:, and enunciates several other theorems. In a note at the end, he shows how
2082:
has a nontrivial solution in the integers for any non-square natural number
1114:
First, his contributions to the fourth and fifth volumes, 1766–1773, of the
578:
certainly Lagrange seems to have accepted this willingly. He studied at the
4087:
4051:
3813:
3740:
Pulte, Helmut, 2005, "Méchanique Analytique" in Grattan-Guinness, I., ed.,
3531:"Notice sur la vie et les ouvrages de M. Malus, et de M. le Comte Lagrange"
3358:
2787:
2775:
1814:
1739:
1428:
1308:
827:
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371:
3451:"Isoperimetric Problems in the Variational Calculus of Euler and Lagrange"
3340:
2763:
of the Moon. In 1766 the academy proposed a problem of the motion of the
2477:
2175:. In two of them, written rather later, in 1792 and 1793, he reduced the
2052:
2044:
937:
763:
623:
513:
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2745:
1087:
3548:
Lagrange, Joseph-Louis; Laplace, Pierre-Simon (1795). "Mathématiques".
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2064:
Several of his early papers also deal with questions of number theory.
1955:
that the order of a subgroup H of a group G must divide the order of G.
1599:
1273:
843:
318:
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534:
captain of cavalry, whose family originated from the French region of
3907:
3747:
2760:
2749:
2274:
2199:
1621:
1119:
933:
823:
539:
314:
210:
205:
2453:
3327:
Lagrange and Laplace, though of Catholic parentage, were agnostics.
2729:
2448:
1540:
1423:
1398:
1038:
However, Lagrange does not seem to have been a successful teacher.
995:
959:
567:
559:
462:
2568:
Title page of volume I of Lagrange's "Mécanique Analytique" (1811)
1958:
His papers of 1770 and 1771 on the general process for solving an
2744:
in 1813, a week before his death in Paris, and was buried in the
2176:
1931:
1513:
1366:
1283:
1131:
999:
870:
353:
348:, Lagrange succeeded Euler as the director of mathematics at the
2246:
His determination of the secular and periodic variations of the
3703:
Fraser, Craig G., 2005, "Théorie des fonctions analytiques" in
3269:, 4th ed. pp. 401–412. Complete article online, p.338 and 333:
3183:(in Italian). Accademia delle Scienze di Torino. pp. 86–95
3062:
2090:
2047:
with one of the vertices at the origin as the one-sixth of the
2040:
1572:
1418:
1328:
894:
815:
is a perfect square; and the general differential equations of
3656:
2971:
2879:
3772:
2941:
2564:
2239:
2238:
Two papers in which the method of determining the orbit of a
2229:
1408:
1403:
1345:
991:
839:
563:
535:
79:
4237:
Honorary members of the Saint Petersburg Academy of Sciences
3438:
Although some authors speak of a general method of solving "
755:, and compound sounds. Other articles in this volume are on
566:. He was raised as a Roman Catholic (but later on became an
2956:
2929:
2914:
2902:
2774:
who were commemorated on plaques at the first stage of the
1413:
1376:
1090:
in Paris. The inscription on his tomb reads in translation:
4082:
3856:
The Founders of Classical Mechanics: Joseph Louis Lagrange
3748:
A. Conte; C. Mancinelli; E. Borgi.; L. Pepe, eds. (2013),
3181:
Il primo secolo della R. Accademia delle Scienze di Torino
2947:
2920:
2217:
On the attraction of ellipsoids, 1773: this is founded on
2068:
Lagrange (1766–1769) was the first European to prove that
558:, while his mother was the only child of a rich doctor of
3346:
Philosophical Transactions of the Royal Society of London
2962:
2935:
2908:
2870:
2864:
1206:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
3408:
de Andrade Martins, Roberto (2008). "A busca da Ciência
3110:
The American Heritage Dictionary of the English Language
3866:
Derivation of Lagrange's result (not Lagrange's method)
3638:
The initial version of this article was taken from the
3415:
Filosofia E Historia Da Ciência No Cone Sul. 3 Encontro
393:
upon its opening in 1794, was a founding member of the
27:
Italian-French mathematician and astronomer (1736–1813)
3383:(2005). "13". In Brett Steele; Tamera Dorland (eds.).
2476:
A somewhat similar method had been previously used by
2465:
at École Polytechnique form the basis of his treatise
2171:
There are also numerous articles on various points of
2055:
formed by the coordinates of the other three vertices.
747:. The article concludes with a masterly discussion of
4023:
2944:
2917:
2622:
2577:
At a later period Lagrange fully embraced the use of
2298:
2008:
1978:
1170:
1127:, and the kind of problems for which it is suitable.
1078:
In 1810, Lagrange started a thorough revision of the
690:
305:; 25 January 1736 – 10 April 1813), also reported as
2965:
2953:
2938:
2926:
2911:
2899:
2873:
2861:
622:. Starting in 1754, he worked on the problem of the
2959:
2932:
2905:
2867:
2547:
Introduction to "Theorie des fonctions analytiques"
3407:
2669:
2400:
2020:
1994:
1942:(1769) and by more general algebraic forms (1770).
1205:
1142:, and in each case, the prize was awarded to him.
739:
3781:
3578:. Paris: Cercle-Social. 1795. pp. iii–viii.
3501:
2559:First page of "Theorie des fonctions analytiques"
2535:Title page to "Theorie des fonctions analytiques"
2202:. Of these the most important are the following:
2198:Lastly, there are numerous papers on problems in
2095:every positive integer is the sum of four squares
1938:His discussion of representations of integers by
1031:In 1794, Lagrange was appointed professor of the
877:. In 1767, he married his cousin Vittoria Conti.
4232:Members of the Royal Swedish Academy of Sciences
4143:
2807:List of things named after Joseph-Louis Lagrange
2523:1813 copy of "Theorie des fonctions analytiques"
2449:Differential calculus and calculus of variations
980:Lagrange was involved in the development of the
517:Portrait of Joseph-Louis Lagrange (18th-century)
389:, became the first professor of analysis at the
30:"Lagrange" redirects here. For the soldier, see
3884:Inventaire chronologique de l'œuvre de Lagrange
3874:(Mécanique analytique is in volumes 11 and 12.)
3842:. Vol. 16 (11th ed.). pp. 75–78.
3659:Lagrange, appunti per una biografia scientifica
3547:
3174:
2235:On the stability of the planetary orbits, 1776.
3019:[dʒuˈzɛppeludoˈviːkodelaˈɡranʒturˈnje]
2752:dedicated to the most honoured French people.
3931:
3684:A Short Account of the History of Mathematics
3645:A Short Account of the History of Mathematics
3266:A Short Account of the History of Mathematics
2137:of 1775 developed a general theory of binary
1895:
822:The next work he produced was in 1764 on the
447:every natural number is a sum of four squares
3983:Lagrange's identity (boundary value problem)
3522:
3310:
3287:
3285:
3283:
3281:
3279:
3277:
3091:Random House Webster's Unabridged Dictionary
2670:{\displaystyle a^{p-1}-1\equiv 0{\pmod {p}}}
1042:, who attended his lectures in 1795, wrote:
4227:Members of the Prussian Academy of Sciences
3878:Joseph Louis de Lagrange – Œuvres complètes
3537:. Paris: Firmin Didot. pp. xxvii–lxxx.
3387:. Cambridge: MIT Press. pp. 368, 375.
3103:
2755:Lagrange was awarded the 1764 prize of the
2491:Another treatise on the same lines was his
3938:
3924:
3495:
3338:
2711:
2427:. All the analysis is so elegant that Sir
2166:
1902:
1888:
777:, and by solutions of various problems in
645:
481:. Lagrange is best known for transforming
425:. Lagrange invented the method of solving
404:
374:and formed a basis for the development of
53:
4222:Members of the French Academy of Sciences
3945:
3657:Maria Teresa Borgato; Luigi Pepe (1990),
3466:
3274:
3250:
3153:
2228:On the motion of the nodes of a planet's
1930:. Several of them deal with questions in
932:began. Under the intervention of Antoine
736:
465:, Lagrange developed a novel approach to
3771:
3742:Landmark Writings in Western Mathematics
3709:Landmark Writings in Western Mathematics
3569:
3567:
3528:
3315:. Oxford University Press. p. 214.
3313:Mathematics and the Search for Knowledge
3160:Joseph-Louis Lagrange, comte de l’Empire
2740:. He was awarded the Grand Croix of the
2563:
2452:
2039:. He also proved the expression for the
1066:
966:in 1799, he was the first signer of the
512:
409:Lagrange was one of the creators of the
4252:Scientists from the Kingdom of Sardinia
3899:Works by or about Joseph-Louis Lagrange
3793:MacTutor History of Mathematics Archive
3776:"Œuvres De Lagrange," volume III (1869)
3529:Delambre, Jean Baptiste Joseph (1816).
3212:
3210:
3208:
3206:
3204:
3202:
3200:
3198:
2261:
2158:He made contributions to the theory of
1145:
975:
819:moving under their mutual attractions.
618:Lagrange is one of the founders of the
613:
303:Giuseppe Ludovico De la Grange Tournier
14:
4257:Grand Officers of the Legion of Honour
4144:
3826:
3448:
3379:
3216:
2695:
2591:shortening and simplifying our proofs.
1026:
3919:
3803:
3752:(in Italian), Torino: Hapax Editore,
3564:
3418:(in Portuguese). AFHIC. p. 406.
3168:
3026:
3017:
3002:[dʒuˈzɛppeluˈiːdʒilaˈɡrandʒa]
3000:
2983:
2827:Lagrange's role in measurement reform
2732:made Lagrange a Grand Officer of the
1584:Newton's law of universal gravitation
865:In 1766, after Euler left Berlin for
850:interceded on Lagrange's behalf with
740:{\displaystyle y=a\sin(mx)\sin(nt)\,}
3552:. Paris: L. Reynier. pp. 3–23.
3246:Encyclopedia of Space and Astronomy.
3223:Dizionario Biografico degli Italiani
3195:
1071:Lagrange's tomb in the crypt of the
4177:19th-century Italian mathematicians
4172:18th-century Italian mathematicians
3988:Lagrange's trigonometric identities
3737:. Paris" Gauthier-Villars: 695–748.
3483:The genesis of Mécanique analytique
3225:(in Italian). Enciclopedia Italiana
2659:
2603:Résolution des équations numériques
1565:Mechanics of planar particle motion
1173:
24:
4272:19th-century French mathematicians
4267:18th-century French mathematicians
2596:
2493:Leçons sur le calcul des fonctions
2415:represents the kinetic energy and
2380:
2372:
2357:
2349:
2325:
2317:
2028:) is also treated in these papers.
987:la Commission des Poids et Mesures
573:His father, who had charge of the
340:In 1766, on the recommendation of
25:
4283:
4187:Counts of the First French Empire
3973:Lagrange's theorem (group theory)
3767:
3680:Joseph Louis Lagrange (1736–1813)
3261:Joseph Louis Lagrange (1736–1813)
2726:Royal Swedish Academy of Sciences
2572:
2467:Théorie des fonctions analytiques
2443:
2089:He proved the theorem, stated by
1102:
905:, which later became part of the
451:Theorie des fonctions analytiques
4212:18th-century Italian astronomers
4192:Italian people of French descent
4129:
4117:
4105:
4093:
4081:
4069:
4057:
4045:
4033:
3714:Lagrange, Joseph-Louis. (1811).
2895:
2857:
2552:
2540:
2528:
2516:
2059:
2035:of order 3, a special case of a
1869:
1868:
1855:
1188:
1009:
542:, he had entered the service of
526:Firstborn of eleven children as
453:laid some of the foundations of
313:, was an Italian mathematician,
4207:18th-century French astronomers
3615:
3601:
3590:
3541:
3475:
3432:
3401:
3373:
3332:
3304:
3237:
2652:
2031:In 1773, Lagrange considered a
897:, and he accepted the offer of
4197:Naturalized citizens of France
4182:Burials at the Panthéon, Paris
3968:Lagrange's four-square theorem
3890:Works by Joseph-Louis Lagrange
3833:"Lagrange, Joseph Louis"
3809:"Lagrange, Joseph (1736–1813)"
3138:Merriam-Webster.com Dictionary
3125:
3097:
3079:
3050:
3008:
2991:
2844:
2772:72 prominent French scientists
2663:
2653:
2188:partial differential equations
733:
724:
715:
706:
521:
13:
1:
4003:Lagrange's mean value theorem
3870:Lagrange's works (in French)
3851:Mathematics Genealogy Project
3750:Lagrange. Un europeo a Torino
3661:(in Italian), Torino: La Rosa
3113:(5th ed.). HarperCollins
3038:
2277:, both of solids and fluids.
1491:Koopman–von Neumann mechanics
1062:
792:'s problem: given an integer
670:string vibrating transversely
4262:Fellows of the Royal Society
3468:10.1016/0315-0860(92)90052-D
3043:
2742:Ordre Impérial de la Réunion
2724:and a foreign member of the
2193:
2093:without justification, that
1928:Prussian Academy of Sciences
1559:Non-inertial reference frame
1084:rue du Faubourg Saint-Honoré
604:Alessandro Papacino D'Antoni
492:
441:and worked on solutions for
350:Prussian Academy of Sciences
7:
3735:Oeuvres de Lagrange, Vol. 4
2800:
2461:Lagrange's lectures on the
1486:Appell's equation of motion
1356:Inertial frame of reference
528:Giuseppe Lodovico Lagrangia
485:into a branch of analysis,
378:in the nineteenth century.
66:Giuseppe Lodovico Lagrangia
10:
4288:
3720:Cambridge University Press
3632:
3502:Richard B. Vinter (2000).
2757:French Academy of Sciences
2718:Royal Society of Edinburgh
2208:general three-body problem
2115:is a prime if and only if
1921:
903:French Academy of Sciences
358:French Academy of Sciences
254:Giovanni Battista Beccaria
250:(epistolary correspondent)
29:
3953:
3219:"Giuseppe Luigi Lagrange"
3028:[dəlaɡʁɑ̃ʒtuʁnje]
2985:[ʒozɛflwilaɡʁɑ̃ʒ]
2720:in 1790, a Fellow of the
2425:principle of least action
2177:equations of the quadrics
2135:Recherches d'Arithmétique
923:Pierre Charles Le Monnier
833:
775:principle of least action
684:is given by the equation
654:Turin Academy of Sciences
360:. Lagrange's treatise on
288:
262:
240:
219:
195:
188:
140:
130:
109:
90:
61:
52:
45:
36:Lagrange (disambiguation)
32:Joseph Lagrange (soldier)
3805:Weisstein, Eric Wolfgang
3798:University of St Andrews
3718:. Courcier (reissued by
3692:Chanson, Hubert, 2007, "
3175:Angelo Genocchi (1883).
3058:"Lagrange, Joseph Louis"
2837:
2206:Attempting to solve the
2179:(or conicoids) to their
1649:Rotating reference frame
1481:Hamilton–Jacobi equation
888:
632:Euler–Lagrange equations
562:, in the countryside of
415:Euler–Lagrange equations
299:Giuseppe Luigi Lagrangia
3839:Encyclopædia Britannica
3788:"Joseph-Louis Lagrange"
3670:Lagrange, Joseph Louis.
3648:(4th edition, 1908) by
3164:Encyclopædia Britannica
3069:Oxford University Press
2770:Lagrange is one of the
2712:Prizes and distinctions
2611:Fermat's little theorem
2287:generalized coordinates
2167:Other mathematical work
1590:Newton's laws of motion
1450:Newton's laws of motion
1116:Miscellanea Taurinensia
928:In September 1793, the
817:motion for three bodies
658:Miscellanea Taurinensia
647:Miscellanea Taurinensia
594:ballistics theories of
439:theory of probabilities
431:variation of parameters
405:Scientific contribution
307:Giuseppe Luigi Lagrange
3777:
3449:Fraser, Craig (1992).
3359:10.1098/rstl.1693.0074
2812:Four-dimensional space
2778:when it first opened.
2759:for his memoir on the
2671:
2569:
2458:
2429:William Rowan Hamilton
2402:
2104:that (for any integer
2033:functional determinant
2022:
1996:
1995:{\displaystyle ax^{n}}
1962:of any degree via the
1617:Simple harmonic motion
1530:Euler's laws of motion
1324:D'Alembert's principle
1207:
1100:
1075:
768:calculus of variations
741:
664:, obtains the general
620:calculus of variations
538:. After serving under
518:
510:
427:differential equations
411:calculus of variations
160:Calculus of variations
34:. For other uses, see
4217:Mathematical analysts
4167:Scientists from Turin
3947:Joseph-Louis Lagrange
3847:Joseph-Louis Lagrange
3775:
3666:Columbia Encyclopedia
3623:A History of Analysis
3311:Morris Kline (1986).
3301:St. Andrew University
3297:25 March 2007 at the
3065:UK English Dictionary
2765:satellites of Jupiter
2672:
2567:
2471:generality of algebra
2463:differential calculus
2457:Joseph-Louis Lagrange
2456:
2403:
2023:
1997:
1947:Theory of Elimination
1471:Hamiltonian mechanics
1289:Statistical mechanics
1208:
1092:
1070:
1004:Bureau des Longitudes
742:
666:differential equation
516:
497:
435:differential calculus
395:Bureau des Longitudes
295:Joseph-Louis Lagrange
170:Mathematical analysis
47:Joseph-Louis Lagrange
4152:Lagrangian mechanics
3998:Lagrangian mechanics
3909:Mécanique analytique
3784:Robertson, Edmund F.
3716:Mécanique Analytique
3705:Grattan-Guinness, I.
3455:Historia Mathematica
3445:Lagrange multipliers
2822:History of the metre
2797:also bear his name.
2620:
2583:Mécanique Analytique
2497:Lagrange multipliers
2421:Lagrange multipliers
2296:
2268:Mécanique analytique
2262:Fundamental treatise
2006:
1976:
1916:Lagrangian mechanics
1694:Angular acceleration
1686:Rotational frequency
1466:Lagrangian mechanics
1459:Analytical mechanics
1215:Second law of motion
1168:
1146:Lagrangian mechanics
1109:Mécanique analytique
1096:Order of the Reunion
1080:Mécanique analytique
976:Units of measurement
875:Mécanique analytique
852:Frederick of Prussia
688:
614:Variational calculus
591:Charles Emmanuel III
556:University of Torino
487:Lagrangian mechanics
423:Lagrange multipliers
387:Revolutionary France
376:mathematical physics
367:Mécanique analytique
362:analytical mechanics
155:Analytical mechanics
3993:Lagrange multiplier
3978:Lagrange's identity
3963:Lagrange polynomial
3958:Lagrange multiplier
3861:The Lagrange Points
3782:O'Connor, John J.;
3744:. Elsevier: 208–24.
3711:. Elsevier: 258–76.
3339:Halley, E. (1693).
2738:Count of the Empire
2696:Celestial mechanics
2607:continued fractions
2173:analytical geometry
2160:continued fractions
2021:{\displaystyle b=0}
1965:Lagrange resolvents
1546:Harmonic oscillator
1524:Equations of motion
1159:Classical mechanics
1153:Part of a series on
1058:make amends for it.
1033:École Polytechnique
1027:École Polytechnique
802:, to find a number
580:University of Turin
544:Charles Emmanuel II
483:Newtonian mechanics
443:algebraic equations
391:École Polytechnique
335:celestial mechanics
232:École Polytechnique
180:Theory of equations
165:Celestial mechanics
135:University of Turin
103:First French Empire
84:Kingdom of Sardinia
4008:Lagrange stability
3828:Clerke, Agnes Mary
3778:
3698:La Houille Blanche
3668:, 6th ed., 2005, "
2728:in 1806. In 1808,
2667:
2570:
2459:
2398:
2018:
1992:
1960:algebraic equation
1953:Lagrange's theorem
1862:Physics portal
1476:Routhian mechanics
1351:Frame of reference
1203:
1140:Académie française
1076:
907:Institut de France
788:; a solution of a
737:
519:
475:three-body problem
4021:
4020:
3894:Project Gutenberg
3759:978-88-88000-57-2
3728:978-1-108-00174-8
3688:also on Gutenberg
3574:"Avertissement".
3515:978-0-8176-4075-0
3425:978-1-4357-1633-9
3322:978-0-19-504230-6
3141:. Merriam-Webster
3075:on 23 April 2021.
2793:and the asteroid
2702:planetary motions
2482:Residual Analysis
2387:
2364:
2341:
2337:
2312:
2212:Lagrangian points
2123:is a multiple of
1945:His tract on the
1912:
1911:
1659:Centrifugal force
1654:Centripetal force
1610:Euler's equations
1595:Relative velocity
1371:Moment of inertia
1201:
1175:
915:French Revolution
838:Already by 1756,
786:integral calculus
479:Lagrangian points
473:. He studied the
445:. He proved that
292:
291:
241:Academic advisors
190:Scientific career
16:(Redirected from
4279:
4247:French geometers
4242:Number theorists
4202:French agnostics
4134:
4133:
4122:
4121:
4120:
4110:
4109:
4108:
4098:
4097:
4096:
4086:
4085:
4074:
4073:
4072:
4062:
4061:
4050:
4049:
4048:
4038:
4037:
4036:
4029:
3940:
3933:
3926:
3917:
3916:
3911:(Paris, 1811-15)
3903:Internet Archive
3843:
3835:
3818:
3800:
3762:
3676:W. W. Rouse Ball
3662:
3650:W. W. Rouse Ball
3626:
3619:
3613:
3605:
3599:
3594:
3588:
3587:
3571:
3562:
3561:
3545:
3539:
3538:
3526:
3520:
3519:
3499:
3493:
3479:
3473:
3472:
3470:
3436:
3430:
3429:
3405:
3399:
3398:
3377:
3371:
3370:
3353:(205): 960–969.
3336:
3330:
3329:
3308:
3302:
3289:
3272:
3257:W. W. Rouse Ball
3254:
3248:
3241:
3235:
3234:
3232:
3230:
3214:
3193:
3192:
3190:
3188:
3177:"Luigi Lagrange"
3172:
3166:
3157:
3151:
3150:
3148:
3146:
3129:
3123:
3122:
3120:
3118:
3101:
3095:
3083:
3077:
3076:
3071:. Archived from
3054:
3032:
3030:
3025:
3021:
3016:
3012:
3006:
3004:
2999:
2995:
2989:
2987:
2982:
2978:
2977:
2974:
2973:
2970:
2967:
2964:
2961:
2958:
2955:
2950:
2949:
2946:
2943:
2940:
2937:
2934:
2931:
2928:
2923:
2922:
2919:
2916:
2913:
2910:
2907:
2904:
2901:
2894:
2886:
2885:
2882:
2881:
2878:
2875:
2872:
2869:
2866:
2863:
2856:
2848:
2832:Seconds pendulum
2734:Legion of Honour
2700:A theory of the
2676:
2674:
2673:
2668:
2666:
2638:
2637:
2556:
2544:
2532:
2520:
2486:Taylor's theorem
2433:pure mathematics
2407:
2405:
2404:
2399:
2388:
2386:
2378:
2370:
2365:
2363:
2355:
2347:
2342:
2340:
2339:
2338:
2330:
2323:
2315:
2313:
2311:
2300:
2154:
2126:
2122:
2114:
2110:
2102:Wilson's theorem
2085:
2081:
2027:
2025:
2024:
2019:
2001:
1999:
1998:
1993:
1991:
1990:
1904:
1897:
1890:
1877:
1872:
1871:
1864:
1860:
1859:
1765:Johann Bernoulli
1760:Daniel Bernoulli
1681:Tangential speed
1585:
1561:
1536:Fictitious force
1531:
1383:Mechanical power
1373:
1314:Angular momentum
1212:
1210:
1209:
1204:
1202:
1200:
1192:
1191:
1182:
1177:
1176:
1150:
1149:
1136:secular equation
968:Sénatus-consulte
867:Saint Petersburg
814:
807:
797:
746:
744:
743:
738:
550:, and married a
471:Taylor's theorem
263:Notable students
97:
75:
73:
57:
43:
42:
21:
4287:
4286:
4282:
4281:
4280:
4278:
4277:
4276:
4142:
4141:
4140:
4128:
4118:
4116:
4106:
4104:
4094:
4092:
4080:
4070:
4068:
4056:
4046:
4044:
4034:
4032:
4024:
4022:
4017:
3949:
3944:
3770:
3765:
3760:
3635:
3630:
3629:
3620:
3616:
3606:
3602:
3595:
3591:
3573:
3572:
3565:
3546:
3542:
3527:
3523:
3516:
3505:Optimal Control
3500:
3496:
3480:
3476:
3437:
3433:
3426:
3406:
3402:
3395:
3378:
3374:
3337:
3333:
3323:
3309:
3305:
3299:Wayback Machine
3290:
3275:
3255:
3251:
3242:
3238:
3228:
3226:
3215:
3196:
3186:
3184:
3173:
3169:
3158:
3154:
3144:
3142:
3131:
3130:
3126:
3116:
3114:
3102:
3098:
3084:
3080:
3056:
3055:
3051:
3046:
3041:
3036:
3035:
3023:
3014:
3013:
3009:
2997:
2996:
2992:
2980:
2952:
2925:
2898:
2889:
2888:
2860:
2851:
2850:
2849:
2845:
2840:
2803:
2714:
2698:
2684:is a prime and
2651:
2627:
2623:
2621:
2618:
2617:
2599:
2575:
2560:
2557:
2548:
2545:
2536:
2533:
2524:
2521:
2451:
2446:
2379:
2371:
2369:
2356:
2348:
2346:
2329:
2328:
2324:
2316:
2314:
2304:
2299:
2297:
2294:
2293:
2264:
2196:
2181:canonical forms
2169:
2142:
2139:quadratic forms
2124:
2116:
2112:
2105:
2083:
2072:
2070:Pell's equation
2062:
2007:
2004:
2003:
1986:
1982:
1977:
1974:
1973:
1940:quadratic forms
1924:
1908:
1867:
1854:
1853:
1846:
1845:
1844:
1719:
1711:
1710:
1690:
1644:Circular motion
1638:
1628:
1627:
1626:
1583:
1553:
1550:
1529:
1508:
1500:
1499:
1496:
1495:
1453:
1443:
1435:
1434:
1433:
1392:
1388:Mechanical work
1381:
1365:
1303:
1295:
1294:
1293:
1248:
1240:
1217:
1193:
1187:
1183:
1181:
1172:
1171:
1169:
1166:
1165:
1148:
1125:infinite series
1123:integration by
1105:
1065:
1029:
1012:
978:
930:Reign of Terror
891:
836:
809:
803:
798:which is not a
793:
689:
686:
685:
650:
616:
608:François Daviet
596:Benjamin Robins
524:
511:
507:W.W. Rouse Ball
495:
457:, anticipating
449:. His treatise
417:for extrema of
413:, deriving the
407:
284:
258:
236:
215:
184:
131:Alma mater
126:
105:
99:
95:
86:
77:
76:25 January 1736
71:
69:
68:
67:
48:
39:
28:
23:
22:
15:
12:
11:
5:
4285:
4275:
4274:
4269:
4264:
4259:
4254:
4249:
4244:
4239:
4234:
4229:
4224:
4219:
4214:
4209:
4204:
4199:
4194:
4189:
4184:
4179:
4174:
4169:
4164:
4159:
4154:
4139:
4138:
4126:
4114:
4102:
4090:
4078:
4066:
4054:
4042:
4019:
4018:
4016:
4015:
4013:Lagrange point
4010:
4005:
4000:
3995:
3990:
3985:
3980:
3975:
3970:
3965:
3960:
3954:
3951:
3950:
3943:
3942:
3935:
3928:
3920:
3914:
3913:
3905:
3896:
3887:
3881:
3875:
3868:
3863:
3858:
3853:
3844:
3824:
3819:
3801:
3769:
3768:External links
3766:
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3763:
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3745:
3738:
3731:
3712:
3701:
3690:
3673:
3663:
3636:
3634:
3631:
3628:
3627:
3625:, 2003, p. 149
3614:
3611:, t.1, 671–732
3600:
3589:
3563:
3540:
3521:
3514:
3494:
3481:Galletto, D.,
3474:
3431:
3424:
3400:
3393:
3372:
3331:
3321:
3303:
3273:
3249:
3236:
3194:
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2802:
2799:
2795:1006 Lagrangea
2713:
2710:
2697:
2694:
2678:
2677:
2665:
2662:
2658:
2655:
2650:
2647:
2644:
2641:
2636:
2633:
2630:
2626:
2598:
2595:
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2593:
2579:infinitesimals
2574:
2573:Infinitesimals
2571:
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2561:
2558:
2551:
2549:
2546:
2539:
2537:
2534:
2527:
2525:
2522:
2515:
2450:
2447:
2445:
2444:Work in France
2442:
2409:
2408:
2397:
2394:
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2382:
2377:
2374:
2368:
2362:
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2327:
2322:
2319:
2310:
2307:
2303:
2263:
2260:
2259:
2258:
2255:
2244:
2236:
2233:
2226:
2222:
2215:
2195:
2192:
2168:
2165:
2164:
2163:
2156:
2131:
2128:
2098:
2087:
2061:
2058:
2057:
2056:
2049:absolute value
2029:
2017:
2014:
2011:
1989:
1985:
1981:
1956:
1950:
1943:
1923:
1920:
1910:
1909:
1907:
1906:
1899:
1892:
1884:
1881:
1880:
1879:
1878:
1865:
1848:
1847:
1843:
1842:
1837:
1832:
1827:
1822:
1817:
1812:
1807:
1802:
1797:
1792:
1787:
1782:
1777:
1772:
1767:
1762:
1757:
1752:
1747:
1742:
1737:
1732:
1727:
1721:
1720:
1717:
1716:
1713:
1712:
1709:
1708:
1689:
1688:
1683:
1678:
1673:
1671:Coriolis force
1668:
1667:
1666:
1656:
1651:
1646:
1640:
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1510:
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1501:
1498:
1497:
1494:
1493:
1488:
1483:
1478:
1473:
1468:
1462:
1456:
1454:
1447:
1444:
1441:
1440:
1437:
1436:
1432:
1431:
1426:
1421:
1416:
1411:
1406:
1401:
1396:
1390:
1385:
1379:
1374:
1363:
1358:
1353:
1348:
1343:
1342:
1341:
1336:
1326:
1321:
1316:
1311:
1305:
1304:
1301:
1300:
1297:
1296:
1292:
1291:
1286:
1281:
1276:
1271:
1266:
1261:
1256:
1250:
1249:
1246:
1245:
1242:
1241:
1239:
1238:
1233:
1228:
1222:
1219:
1218:
1213:
1199:
1196:
1190:
1186:
1180:
1162:
1161:
1155:
1154:
1147:
1144:
1104:
1103:Work in Berlin
1101:
1064:
1061:
1060:
1059:
1028:
1025:
1011:
1008:
977:
974:
948:
947:
890:
887:
863:
862:
835:
832:
800:perfect square
735:
732:
729:
726:
723:
720:
717:
714:
711:
708:
705:
702:
699:
696:
693:
649:
644:
628:Leonhard Euler
615:
612:
600:Leonhard Euler
523:
520:
496:
494:
491:
406:
403:
383:decimalisation
342:Leonhard Euler
290:
289:
286:
285:
283:
282:
280:Siméon Poisson
277:
275:Giovanni Plana
272:
270:Joseph Fourier
266:
264:
260:
259:
257:
256:
251:
248:Leonhard Euler
244:
242:
238:
237:
235:
234:
229:
223:
221:
217:
216:
214:
213:
208:
203:
199:
197:
193:
192:
186:
185:
183:
182:
177:
172:
167:
162:
157:
152:
144:
142:
141:Known for
138:
137:
132:
128:
127:
125:
124:
119:
113:
111:
107:
106:
100:
98:(aged 77)
92:
88:
87:
78:
65:
63:
59:
58:
50:
49:
46:
26:
9:
6:
4:
3:
2:
4284:
4273:
4270:
4268:
4265:
4263:
4260:
4258:
4255:
4253:
4250:
4248:
4245:
4243:
4240:
4238:
4235:
4233:
4230:
4228:
4225:
4223:
4220:
4218:
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4210:
4208:
4205:
4203:
4200:
4198:
4195:
4193:
4190:
4188:
4185:
4183:
4180:
4178:
4175:
4173:
4170:
4168:
4165:
4163:
4160:
4158:
4155:
4153:
4150:
4149:
4147:
4137:
4132:
4127:
4125:
4115:
4113:
4103:
4101:
4091:
4089:
4084:
4079:
4077:
4067:
4065:
4060:
4055:
4053:
4043:
4041:
4031:
4030:
4027:
4014:
4011:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3989:
3986:
3984:
3981:
3979:
3976:
3974:
3971:
3969:
3966:
3964:
3961:
3959:
3956:
3955:
3952:
3948:
3941:
3936:
3934:
3929:
3927:
3922:
3921:
3918:
3912:
3910:
3906:
3904:
3900:
3897:
3895:
3891:
3888:
3885:
3882:
3879:
3876:
3873:
3869:
3867:
3864:
3862:
3859:
3857:
3854:
3852:
3848:
3845:
3841:
3840:
3834:
3829:
3825:
3823:
3820:
3816:
3815:
3810:
3806:
3802:
3799:
3795:
3794:
3789:
3785:
3780:
3779:
3774:
3761:
3755:
3751:
3746:
3743:
3739:
3736:
3732:
3729:
3725:
3721:
3717:
3713:
3710:
3706:
3702:
3699:
3695:
3691:
3689:
3685:
3681:
3677:
3674:
3671:
3667:
3664:
3660:
3655:
3654:
3653:
3651:
3647:
3646:
3641:
3640:public domain
3624:
3618:
3612:
3610:
3604:
3598:
3593:
3585:
3581:
3577:
3570:
3568:
3559:
3555:
3551:
3544:
3536:
3532:
3525:
3517:
3511:
3507:
3506:
3498:
3491:
3488:
3484:
3478:
3469:
3464:
3460:
3456:
3452:
3446:
3441:
3440:isoperimetric
3435:
3427:
3421:
3417:
3416:
3411:
3404:
3396:
3394:0-262-19516-X
3390:
3386:
3382:
3381:Steele, Brett
3376:
3368:
3364:
3360:
3356:
3352:
3348:
3347:
3342:
3335:
3328:
3324:
3318:
3314:
3307:
3300:
3296:
3293:
3288:
3286:
3284:
3282:
3280:
3278:
3271:
3268:
3267:
3262:
3258:
3253:
3247:
3244:
3240:
3224:
3220:
3213:
3211:
3209:
3207:
3205:
3203:
3201:
3199:
3182:
3178:
3171:
3165:
3161:
3156:
3140:
3139:
3134:
3128:
3112:
3111:
3106:
3100:
3093:
3092:
3087:
3082:
3074:
3070:
3066:
3064:
3059:
3053:
3049:
3029:
3020:
3011:
3003:
2994:
2986:
2976:
2892:
2884:
2854:
2847:
2843:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2810:
2808:
2805:
2804:
2798:
2796:
2792:
2789:
2785:
2781:
2777:
2773:
2768:
2766:
2762:
2758:
2753:
2751:
2747:
2743:
2739:
2735:
2731:
2727:
2723:
2722:Royal Society
2719:
2709:
2707:
2703:
2693:
2691:
2687:
2683:
2660:
2656:
2648:
2645:
2642:
2639:
2634:
2631:
2628:
2624:
2616:
2615:
2614:
2612:
2608:
2604:
2597:Number theory
2592:
2588:
2587:
2586:
2584:
2580:
2566:
2555:
2550:
2543:
2538:
2531:
2526:
2519:
2514:
2513:
2512:
2510:
2506:
2502:
2498:
2494:
2489:
2487:
2483:
2479:
2474:
2472:
2468:
2464:
2455:
2441:
2439:
2434:
2430:
2426:
2422:
2418:
2414:
2395:
2392:
2389:
2383:
2375:
2366:
2360:
2352:
2343:
2334:
2331:
2320:
2308:
2305:
2301:
2292:
2291:
2290:
2288:
2284:
2278:
2276:
2271:
2269:
2256:
2253:
2249:
2245:
2241:
2237:
2234:
2231:
2227:
2223:
2220:
2216:
2213:
2209:
2205:
2204:
2203:
2201:
2191:
2189:
2184:
2182:
2178:
2174:
2161:
2157:
2153:
2149:
2145:
2140:
2136:
2132:
2129:
2120:
2108:
2103:
2099:
2096:
2092:
2088:
2079:
2075:
2071:
2067:
2066:
2065:
2060:Number theory
2054:
2050:
2046:
2042:
2038:
2034:
2030:
2015:
2012:
2009:
1987:
1983:
1979:
1971:
1970:Galois theory
1967:
1966:
1961:
1957:
1954:
1951:
1948:
1944:
1941:
1937:
1936:
1935:
1933:
1929:
1919:
1917:
1905:
1900:
1898:
1893:
1891:
1886:
1885:
1883:
1882:
1876:
1866:
1863:
1858:
1852:
1851:
1850:
1849:
1841:
1838:
1836:
1833:
1831:
1828:
1826:
1823:
1821:
1818:
1816:
1813:
1811:
1808:
1806:
1803:
1801:
1798:
1796:
1793:
1791:
1788:
1786:
1783:
1781:
1778:
1776:
1773:
1771:
1768:
1766:
1763:
1761:
1758:
1756:
1753:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1722:
1715:
1714:
1707:
1703:
1699:
1695:
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1691:
1687:
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1637:
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1623:
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1608:
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1603:
1602:
1601:
1598:
1596:
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1591:
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1578:
1574:
1571:
1570:
1566:
1563:
1560:
1556:
1552:
1551:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1511:
1504:
1503:
1492:
1489:
1487:
1484:
1482:
1479:
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1474:
1472:
1469:
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1464:
1463:
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1455:
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1439:
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1427:
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1422:
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1417:
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1407:
1405:
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1397:
1395:
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1389:
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1384:
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1327:
1325:
1322:
1320:
1317:
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1307:
1306:
1299:
1298:
1290:
1287:
1285:
1282:
1280:
1277:
1275:
1272:
1270:
1267:
1265:
1262:
1260:
1257:
1255:
1252:
1251:
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3081:
3073:the original
3061:
3052:
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2846:
2788:lunar crater
2784:via Lagrange
2783:
2780:Rue Lagrange
2779:
2776:Eiffel Tower
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1309:Acceleration
1302:Fundamentals
1129:
1120:astronomical
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220:Institutions
189:
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4162:1813 deaths
4157:1736 births
4112:Outer space
4100:Spaceflight
4064:Mathematics
2817:Gauss's law
2509:Weierstrass
2478:John Landen
2053:determinant
2045:tetrahedron
1840:von Neumann
1507:Core topics
1056:professeurs
998:units with
938:tax farmers
624:tautochrone
522:Early years
419:functionals
385:process in
352:in Berlin,
329:, and both
202:Mathematics
110:Citizenship
4146:Categories
3700:5: 127–31.
3686:, 4th ed.
3133:"Lagrange"
3105:"Lagrange"
3086:"Lagrange"
3039:References
2613:, that is
2252:Le Verrier
2100:He proved
1775:d'Alembert
1755:Maupertuis
1718:Scientists
1600:Rigid body
1274:Kinematics
1063:Late years
848:d'Alembert
844:Maupertuis
808:such that
766:, and the
678:D'Alembert
636:Maupertuis
433:, applied
346:d'Alembert
319:astronomer
149:(See list)
72:1736-01-25
4076:Astronomy
4040:Biography
3678:, 1908, "
3642:resource
3584:490193660
3558:780161317
3367:186212029
3187:2 January
3044:Citations
2761:libration
2750:mausoleum
2646:≡
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2318:∂
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2275:mechanics
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2200:astronomy
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1702:frequency
1622:Vibration
1339:potential
1264:Continuum
1259:Celestial
1236:Textbooks
1020:undecimal
1006:in 1795.
934:Lavoisier
911:Mécanique
899:Louis XVI
824:libration
757:recurring
722:
704:
540:Louis XIV
493:Biography
429:known as
401:in 1799.
331:classical
315:physicist
311:Lagrangia
211:Mechanics
206:Astronomy
3830:(1911).
3722:, 2009;
3461:: 4–23.
3410:a priori
3295:Archived
3292:Lagrange
3259:, 1908,
3145:6 August
3117:6 August
3015:Italian:
2998:Italian:
2801:See also
2791:Lagrange
2746:Panthéon
2730:Napoleon
2438:Legendre
2248:elements
2243:subject.
2221:'s work.
2037:Jacobian
1875:Category
1800:Hamilton
1785:Lagrange
1780:Clairaut
1745:Horrocks
1706:velocity
1676:Pendulum
1664:reactive
1636:Rotation
1605:dynamics
1555:Inertial
1541:Friction
1424:Velocity
1399:Momentum
1279:Kinetics
1269:Dynamics
1247:Branches
1231:Timeline
1088:Panthéon
1073:Panthéon
996:kilogram
960:Piedmont
952:Napoleon
779:dynamics
568:agnostic
560:Cambiano
463:calculus
323:analysis
117:Sardinia
18:Lagrange
4136:Science
4026:Portals
3901:at the
3849:at the
3807:(ed.).
3707:, ed.,
3633:Sources
3490:1264671
3024:French:
2981:French:
2706:Poisson
2480:in the
2232:, 1774.
2127:, 1771.
2097:, 1770.
2051:of the
1949:, 1770.
1932:algebra
1922:Algebra
1835:Koopman
1795:Poisson
1790:Laplace
1735:Huygens
1730:Galileo
1575: (
1514:Damping
1367:Inertia
1361:Impulse
1334:kinetic
1284:Statics
1254:Applied
1226:History
1040:Fourier
1000:decimal
964:senator
871:Prussia
437:to the
399:Senator
354:Prussia
101:Paris,
3886:Persee
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3063:Lexico
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2501:Cauchy
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2109:> 1
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1825:Appell
1810:Cauchy
1805:Jacobi
1750:Halley
1740:Newton
1725:Kepler
1577:linear
1573:Motion
1419:Torque
1394:Moment
1329:Energy
1319:Couple
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895:Naples
834:Berlin
790:Fermat
760:series
749:echoes
662:Newton
575:king's
532:French
459:Galois
372:Newton
297:(born
196:Fields
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1815:Routh
1770:Euler
1409:Speed
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1346:Force
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889:Paris
840:Euler
753:beats
564:Turin
552:Conti
536:Tours
461:. In
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3754:ISBN
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