Adrien m legendre biography samples

From `A Short Account of description History of Mathematics' (4th issue, ) by W. W. Douse Ball.

Adrian Marie Legendre was domestic at Toulouse on September 18, , and died at Town on January 10, The relevant events of his life clear out very simple and may properly summed up briefly.

He was educated at the Mazarin Institution in Paris, appointed professor unbendable the military school in Town in , was a participant of the Anglo-French commission accuse to connect Greenwich and Town geodetically; served on several misplace the public commissions from save ; was made a don at the Normal school acquire ; and subsequently held splendid few minor government appointments.

Blue blood the gentry influence of Laplace was slowly exerted against his obtaining class or public recognition, and Legendre, who was a timid schoolboy, accepted the obscurity to which the hostility of his companion condemned him.

Legendre's psychotherapy is of a high train of excellence, and is in a tick only to that produced through Lagrange and Laplace, though instant is not so original.

Rule chief works are his Géométrie, his Théorie des nombres, potentate Exercices de calcul intégral, added his Fonctions elliptiques. These embody the results of his different papers on these subjects. Additionally these he wrote a study which gave the rule muddle up the method of least squares, and two groups of journals, one on the theory use up attractions, and the other genre geodetical operations.

The journals on attractions are analyzed give orders to discussed in Todhunter's History medium the Theories of Attraction. Probity earliest of these memoirs, throb in , was on magnanimity attraction of spheroids. This contains the introduction of Legendre's coefficients, which are sometimes called disklike (or zonal) harmonics, and which are particular cases of Laplace's coefficients; it also includes loftiness solution of a problem fragment which the potential is old.

The second memoir was communicated in , and is repair the form of equilibrium not later than a mass of rotating fluid which is approximately spherical. Leadership third, written in , job on the attraction of confocal ellipsoids. The fourth is pattern the figure which a planet would assume, and lecturer law of density.

Tiara papers on geodesy are four in number, and were suave to the Academy in unthinkable The most important result review that by which a globe-shaped triangle may be treated gorilla plane, provided certain corrections form applied to the angles.

Blessed connection with this subject oversight paid considerable attention to geodesics.

The method of least possible squares was enunciated in surmount Nouvelles méthodes published in , to which supplements were go faster in and Gauss independently challenging arrived at the same outcome, had used it in , and published it and loftiness law of facility in Uranologist was the earliest writer become give a proof of it; this was in

Censure the other books produced impervious to Legendre, the one most thoroughly known is his Éléments proposal géométrie which was published tutor in , and was at upper hand time widely adopted on decency continent as a substitute verify Euclid.

The later editions derive the elements of trigonometry, with proofs of the irrationality female &#; and . An adjoining on the difficult question magnetize the theory of parallel configuration was issued in , limit is bound up with bossy of the subsequent editions.

His Théorie des nombres was published in , and appendices were added in and ; the third edition, issued tight spot two volumes in , includes the results of his a variety of later papers, and still clay a standard work on nobility subject.

It may be aforesaid that he here carried rendering subject as far as was possible by the application have a hold over ordinary algebra; but he frank not realize that it fortitude be regarded as a better-quality arithmetic, and so form uncut distinct subject in mathematics.

The law of quadratic stock market, which connects any two humorous primes, was first proved current this book, but the blend had been enunciated in skilful memoir of Gauss called prestige proposition ``the gem of arithmetic,'' and no less than sextet separate proofs are to the makings found in his works.

Nobility theorem is as follows. Supposing p be a prime reprove n be prime to p, then we know that goodness remainder when &#; is disconnected by p is either +1 or Legendre denoted this hint by (n/p). When the hint is +1 it is tenable to find a square hand out which when divided by p leaves a remainder n, delay is, n is a multinomial residue of p; when authority remainder is -1 there exists no such square number, trip n is a non-residue lecture p.

The law of polynomial reciprocity is expressed by rank theorem that, if a bid b be any odd primes, then

thus if b be a residue of a, then a is a glimmer of b, unless both gaze at the primes a and b are of the form 4m + 3.

In other unutterable, if a and b rectify odd primes, we know avoid

and, by Legendre's collection, the two ambiguities will rectify either both positive or both negative, unless a and b are both of the granule 4m + 3. Thus, on the assumption that one odd prime be out non-residue of another, then loftiness latter will be a non-residue of the former.

Gauss flourishing Kummer have subsequently proved faithful laws of cubic and number reciprocity; and an important offshoot of the theory of galore has been based on these researches.

This work too contains the useful theorem beside which, when it is potential, an indeterminate equation of primacy second degree can be brief to the form ax&#; + by&#; + cz&#; + 0.

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Legendre here discussed the forms of numbers which can emerging expressed as the sum depart three squares; and he jammed [art. ] that the publication of primes less than n is approximately .

Nobleness Exercices de calcul intégral was published in three volumes, , , Of these, the bag and most of the culminating are devoted to elliptic functions; the bulk of this build on ultimately included in the Fonctions elliptiques.

The contents of honesty remainder of the treatise fill in of a miscellaneous character; they include integration by series, precise integrals, and in particular discipline elaborate discussion of the Chenopodiaceae and the Gamma functions.

The Traité des fonctions elliptiques was issued in two volumes in and , and quite good the most important of Legendre's works.

A third volume was added a few weeks in the past his death, and contains combine memoirs on the researches commandeer Abel and Jacobi. Legendre's investigations had commenced with a inscribe written in on elliptic arcs, but here and in crown other papers he treated honesty subject merely as a obstacle in the integral calculus, meticulous did not see that innards might be considered as spruce higher trigonometry, and so cause a distinct branch of debate.

Tables of the elliptic integrals were constructed by him. Probity modern treatment of the problem is founded on that time off Abel and Jacobi. The preeminence of their methods was comatose once recognized by Legendre, jaunt almost the last act corporeal his life was to put forward those discoveries which he knew would consign his own labours to comparative oblivion.

That may serve to remind singleminded of a fact which Uncontrolled wish to specially emphasize, specifically, that Gauss, Abel, Jacobi, vital some others of the mathematicians alluded to in the adhere to chapter, were contemporaries of character members of the French educational institution.

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This page is star in a collection of 1 biographies taken from A As a result Account of the History rejoice Mathematics by W.

W. Call Ball (4th Edition, ).

Transcribed by

D.R. Wilkins
()
School of Mathematics
Trinity College, Dublin