Legendre there was a feeling of "more than coldness," owing to his appropriation, with scant acknowledgment, of the fruits of the other's labours; and Dr Thomas Young counted himself, rightly or wrongly, amongst the number of those similarly aggrieved by him.
C. Maclaurin, Legendre and d'Alembert had furnished partial solutions of the problem, confining their 1 Annales de chimie et de physique (1816), torn.
Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.
The device known as the method of least squares, for reducing numerous equations of condition to the number of unknown quantities to be determined, had been adopted as a practically convenient rule by Gauss and Legendre; but Laplace first treated it as a problem in probabilities, and proved by an intricate and difficult course of reasoning that it was also the most advantageous, the mean of the probabilities of error in the determination of the elements being thereby reduced to a minimum.
See also notices by Emile Darnaud (Paris, 1874), "Marcus" (Paris, 1879), P. Legendre in Hommes de la revolution (Paris, 1882), E.
The early death of this talented mathematician, of whom Legendre said "quelle tete celle du jeune Norvegien!", cut short a career of extraordinary brilliance and promise.
Legendre, Vie du cardinal d'Amboise (Rouen, 1726); E.
ADRIEN MARIE LEGENDRE (1752-1833), French mathematician, was born at Paris (or, according to some accounts, at Toulouse) in 1752.
Legendre a eu cela de commun avec la plupart des geometres qui l'ont precede, que ses travaux n'ont fini qu'avec sa vie.
The third volume (1816) contains the very elaborate and now well-known tables of the elliptic integrals which were calculated by Legendre himself, with an account of the mode of their construction.
Legendre had pursued the subject which would now be called elliptic integrals alone from 1786 to 1827, the results of his labours having been almost entirely neglected by his contemporaries, but his work had scarcely appeared in 1827 when the discoveries which were independently made by the two young and as yet unknown mathematicians Abel and Jacobi placed the subject on a new basis, and revolutionized it completely.
The readiness with which Legendre, who was then seventy-six years of age, welcomed these important researches, that quite overshadowed his own, and included them in successive supplements to his work, does the highest honour to him (see Function).
In 1788 Legendre published a memoir on double integrals, and in 1809 one on definite integrals.
To Legendre is due the theorem known as the law of quadratic reciprocity, the most important general result in the science of numbers which has been discovered since the time of P. de Fermat, and which was called by Gauss the " gem of arithmetic."
It was first given by Legendre in the Memoires of the Academy for 1785, but the demonstration that accompanied it was incomplete.
Legendre was the author of four important memoirs on this subject.
In the first of these, entitled " Recherches sur l'attraction des spheroides homogenes," published in the Memoires of the Academy for 1785, but communicated to it at an earlier period, Legendre introduces the celebrated expressions which, though frequently called Laplace's coefficients, are more correctly named after Legendre.
Legendre shows that Maclaurin's theorem with respect to confocal ellipsoids is true for any position of the external point when the ellipsoids are solids of revolution.
- Besides the work upon the geodetical operations connecting Paris and Greenwich, of which Legendre was one of the authors, he published in the Memoires de l'Academie for 1787 two papers on trigonometrical operations depending upon the figure of the earth, containing many theorems relating to this subject.
Legendre was also the author of a memoir upon triangles drawn upon a spheroid.
In the preface Legendre remarks: " La methode qui me paroit la plus simple et la plus generale consiste a rendre minimum la somme des quarres des erreurs, .
The method was proposed by Legendre only as a convenient process for treating observations, without reference to the theory of probability.
Laplace also justified the method by means of the principles of the theory of probability; and this led Legendre to republish the part of his Nouvelles Methodes which related to it in the Memoires de l'Academie for 1810.
Legendre published two supplements to his Nouvelles Methodes in 1806 and 1820.
In one of the notes Legendre gives a proof of the irrationality of 7r.
On account of the objections urged against the treatment of parallels in this work, Legendre was induced to publish in 1803 his Nouvelle Theorie des paralleles.
A good account of the principal works of Legendre is given in the Bibliotheque universelle de Geneve for 18 33, pp. 45-82.
See Elie de Beaumont, " Memoir de Legendre," translated by C. A.
On the French side the work was conducted by Count Cassini, Legendre, and Mechain; on the English side by General Roy.
Those engaged upon the work were divided into three sections: the first consisted of five or six mathematicians, including Legendre, who were engaged in the purely analytical work, or the calculation of the fundamental numbers; the second section consisted of seven or eight calculators possessing some mathematical knowledge; and the third comprised seventy or eighty ordinary computers.
N See Legendre, Elements de ge'ometrie (Paris, 1794), note iv.; Schlomilch, Handbuch d.
LOUIS LEGENDRE (1752-1797), French revolutionist, was.
When Danton was arrested, Legendre at first defended him, but was soon cowed and withdrew his defence.
After the fall of Robespierre, Legendre took part in the reactionary movement, undertook the closing of the Jacobin Club, was.
Legendre, who recommended that it should be published in the Recueil des savants strangers, an unparalleled honour for a youth of eighteen.
This writer stated that he had found the germ of his remarks among the papers of his deceased brother, and that they had come from Legendre, who had himself received them from some one unnamed.
This led to a letter from Argand, in which he stated his communications with Legendre, and gave a résumé of the contents of his pamphlet.
Legendre for values of ~ ranging from 0 to 90.
Two cases have been given by Legendre as follows: If a2, a 31 ..., a n, b 2, b3, .., b n are all positive integers, then I.