Matriculating at the university of Gottingen in 1811, he began by devoting himself to astronomy under Carl Friedrich Gauss; but he enlisted in the Hanseatic Legion for the campaign of 1813 - 14, and became lieutenant of artillery in the Prussian service in 1815.
Gauss, P. G.
Gauss had shown how to reduce all the phenomena of statical electricity to mere attractions and repulsions exerted at a distance by particles of an imponderable on one another.
Gauss in his celebrated work Theoria Motus Corporum Coelestium.
Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.
A few Devonian forms have also been recorded from the Parry Archipelago, and Nathorst has shown the existence of Old Red Sandstone facies of Devonian in Traill Island, Geographical Society Island, Ymer Island and Gauss Peninsula.
As far back as 1 773 Joseph Louis Lagrange, and later Carl Friedrich Gauss, had met with simple cases of such functions, George Boole, in 1841 (Camb.
Gauss, which gives the value not only of M, but also that of H, the horizontal component of the earth's force.
The accuracy of this law was in 1832 confirmed by Gauss, 3 who employed an indirect but more perfect method than that of Coulomb, and also, as Maxwell remarks, 1 The quotations are from the translation published by the Gilbert Club, London, 1900.
This memoir excited the admiration of Gauss, and at once marked its author's rank as a mathematician.
In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor.
Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light from Clerk Maxwell's interpretation of harmonics with reference to poles on the sphere.
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.
Kuhn (1750-1751) and Jean Robert Argand (1806) were completed by Karl Friedrich Gauss, and the formulation of various systems of vector analysis by Sir William Rowan Hamilton, Hermann Grassmann and others, followed.
Brooke, a midshipman of the U.S.N., invented the principle on the " Valdivia " in 1898-1899, and to those of the " Belgica " already foreshadowed by Nicolaus Cusanus in the 15th century in 1897-1898, the " Gauss " in 1902-1903, and the " Scotia " and by Robert Hooke in the 17th, of using a heavy weight so in 1903-1904.
In the tropical and subtropical belts of the Atlantic and Indian Oceans south of the equator the salinity diminishes rapidly from the surface downwards, and at 500 fathoms reaches a minimum of 34.3 or 34.4 p e r mille; after that it increases again to 800 fathoms, where it is almost 34.7 or 34.8, and this salinity holds good to the bottom, even to the greatest depths, as was first shown by the " Gauss " and afterwards by the " Planet " between Durban and Ceylon.
This is a particular case of a general theorem, due to Gauss, that, if u is an algebraical function of x of degree 2p or 2p + I, the area can be expressed in terms of p -}- i ordinates taken in suitable positions.
Gauss, that the definite results attainable by the hypothesis of mutual atomic attractions really reposed on much wider and less special principles - those, namely, connected with the modern doctrine of energy.
Gauss in his memoir Disquisitiones generales circa series infcnitas (1816), but in a very different manner.
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 had, however, been applied by Gauss as early as 1795, and the method was fully explained, and the law of facility for the first time given by him in 1809.
The first table that was actually published is due to Gauss, and was printed in Zach's?llonatliche Correspondenz, xxvi.
Another Had Previously Been Given By Gauss, But Inaccurately, Inasmuch As The Correction Depending On A Was Omitted.
Tisri calcolo della Pasqua, e correzione di quello di Gauss, con critiche o;servazioni sit quanto ha scrittc del calendario it Delambri, di Lodovico Ciccolini (Rome, 1817); E.
They were invented by Gauss to facilitate the computation of elliptic integrals.
Gauss at GÃ¶ttingen, and returned to America in 1848.
This observation applies in particular to the general theory of the meteorology of the South Polar area, as expounded for the Gauss expedition by Prof. Meinardus and for Scott's last expedition by Dr. G.
Gauss introduced a system of absolute measurement of electric and magnetic phenomena.
It was established by the work of Weber and Gauss at GÃ¶ttingen in 1836, and that of C. A.
2 The quantitative study of electrical phenomena has been enormously assisted by the establishment of the absolute system of electrical measurement due originally to Gauss and Weber.
Gauss did for magnetic quantities, that it is both theoretically and practically possible to define them, not merely by reference to other arbitrary quantities of the same kind, but absolutely in terms in which the units of length, time, and mass are alone involved.
In 1801 Gauss published his Disquisitiones arithmeticae, which, although written in an obscure form, gave a new impetus to investigations on this and kindred subjects.
To Gauss is due the establishment of the important theorem, that the product of two determinants both of the second and third orders is a determinant.
Gauss and W.
KARL FRIEDRICH GAUSS (1777-1855), German mathematician, was born of humble parents at Brunswick on the 30th of April 1777, and was indebted for a liberal education to the notice which his talents procured him from the reigning duke.
The volumes of their publication, Resultate aus den Beobachtungen des magnetischen Vereins, extend from 1836 to 1839; and in those for 1838 and 1839 are contained the two important memoirs by Gauss, Allgemeine Theorie des Erdmagnetismus, and the Allgemeine Lehrscitze - on the theory of forces attracting according to the inverse square of the distance.
Gauss was well versed in general literature and the chief languages of modern Europe, and was a member of nearly all the leading scientific societies in Europe.
That for the conversion of a fraction into decimals (giving the complete period for all the prime numbers up to 997) is a specimen of the extraordinary love which Gauss had for long arithmetical calculations; and the amount of work gone through in the construction of the table of the number of the classes of binary quadratic forms must also have been tremendous.
The Nachlass contains further researches on this subject, and also researches (unfortunately very fragmentary) on the lemniscate-function, &c., showing that Gauss was, even before 1800, in possession of many of the discoveries which have made the names of N.
This explanation of the action of the solid is equivalent to that by which Gauss afterwards supplied the defect of the theory of Laplace, except that, not being expressed in terms of mathematical symbols, it does not indicate the mathematical relation between the attraction of individual particles and the final result.
Gauss thus supplied the principal defect in the great work of Laplace.