# Gauss Sentence Examples

He was also the author of important papers in which he extended to complex quadratic forms many of

**Gauss**'s investigations relating to real quadratic forms. After 1864 he devoted himself chiefly to elliptic functions, and numerous papers on this subject were published by him in the Proc. Lond.It may be assumed that the planes I' and II' are drawn where the images of the planes I and II are formed by rays near the axis by the ordinary Gaussian rules; and by an extension of these rules, not, however, corresponding to reality, the

**Gauss**image point 0', with co-ordinates 'o, of the point 0 at some distance from the axis could be constructed.The three subjects to which Smith's writings relate are theory of numbers, elliptic functions and modern geometry; but in all that he wrote an "arithmetical" made of thought is apparent, his methods and processes being arithmetical as distinguished from algebraic. He had the most intense admiration of

**Gauss**.These two positions are sometimes called the first and second (or A and B) principal positions of

**Gauss**.The formula applied can then be either Simpson's rule or a rule based on

**Gauss**'s theorem for two ordinates (§ 56).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.They were invented by

**Gauss**to facilitate the computation of elliptic integrals.**Gauss**at GÃ¶ttingen, and returned to America in 1848.Advertisement**Gauss**introduced a system of absolute measurement of electric and magnetic phenomena.The images of the

**Gauss**theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero.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.In more recent times the method of

**Gauss**has been modified so as to take account of the variation of density near the surface, and its language has been translated in terms of the modern doctrine of the conservation of energy.'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.Advertisement**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.**Gauss**'s collected works were published by the Royal Society of GÃ¶ttingen, in 7 vols.The determination of the constants in

**Gauss**'s theory of terrestrial magnetism occupied him at intervals for over forty years.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.Advertisement**Gauss**'s system of absolute units to electromagnetism, Thomson took up the question, and, applying the principles of energy, calculated the absolute electromotive force of a Daniell cell, and determined the absolute measure of the resistance of a wire from the heat produced in it by a known current.**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.This includes the Neo which has a surface

**gauss**rating in excess of 1500**gauss**rating in excess of 1500**gauss**.This includes the Neo which has a surface

**gauss**rating in excess of 1500**gauss**.From the early 1800s

**Gauss**had an interest in the question of the possible existence of a non-Euclidean geometry.AdvertisementPlus a water wand containing a 2,300

**gauss**magnet.Use this &

**Gauss**' law of quadratic reciprocity, to show that 75 is a primitive root modulo 65537.He did not, however, confine himself to the consideration of forms involving only three indeterminates, but succeeded in establishing the principles on which the extension to the general case of n indeterminates depends, and obtained the general formulae, thus effecting what is probably the greatest advance made in the subject since the publication of

**Gauss**'s Disquisitiones arithmeticae.Faraday's discovery of the induced current produced by passing a magnet through a helix of wire forming part of a closed circuit was laid hold of in the telegraph of

**Gauss**and Weber, and this application was at the request of**Gauss**taken up by Steinheil, who brought it to considerable perfection.Steinheil of Munich, however, acting on a suggestion given by

**Gauss**, made in 1838 the important discovery that half of the circuit might be formed of the conducting earth, and so discovered the use of the earth return, since then an essential feature of nearly every telegraphic circuit.It must be noted, however, that since 1895 the soundings of Nansen in the north polar area, of the " Valdivia," " Belgica," "

**Gauss**" and " Scotia " in the Southern Ocean, and of various surveying ships in the North and South Pacific, have proved that the mean depth of the ocean is considerably greater than had been supposed, and mean-sphere level must therefore lie deeper than the calculations of 1895 show; possibly not far from the position deduced from the freer estimate of 1888.The valuable work of

**Gauss**on magnetic theory and measurements, especially in relation to terrestrial magnetism, was published in his Intensitas vis magneticae terrestris, 1833, and in memoirs communicated to the Resultate aus den Beobachtungen des magnetischen Vereins, 1838 and 1839, which, with others, are contained in vol.Of the customary three themes which he suggested for his trial lecture, that "On the Hypotheses which form the Foundation of Geometry" was chosen at the instance of

**Gauss**, who was curious to hear what so young a man had to say on this difficult subject, on which he himself had in private speculated so pro foundly (see Geometry, Non-Euclidian).Thus, although the method of least squares was first formally proposed by Legendre, the theory and algorithm and mathematical foundation of the process are due to

**Gauss**and Laplace.**Gauss**at GÃƒ¶ttingen, and returned to America in 1848.Mourey in France, independently of one another and of Argand, reinvented these modes of interpretation; and still later, in the writings of Cauchy,

**Gauss**and others, the properties of the expression a + b I were developed into the immense and most important subject now called the theory of complex numbers (see Number).**Gauss**(Dioptrische Untersuchungen, GÃƒ¶ttingen, 1841), named the focal lengths and focal planes, permits the determination of the image of any object for any system (see Lens).On these assumptions his results are certainly right, and are confirmed by the independent method of

**Gauss**, so that the objections raised against them by Poisson fall to the ground.**Gauss**'s collected works were published by the Royal Society of GÃƒ¶ttingen, in 7 vols.The " method of least squares," by which the most probable result can be educed from a body of observational data, was published by Adrien Marie Legendre in 1806, by Carl Friedrich

**Gauss**in his Theoria Motus (1809), which described also a mode of calculating the orbit of a planet from three complete observations, afterwards turned to important account for the recapture of Ceres, the first discovered asteroid (see Planets, Minor).**Gauss**'s dissertation was a discussion of the fundamental theorem of algebra.If you are in search of a magnetic bed for your pet, one of the main points you'll need to consider is the

**gauss**rating of the bed's magnets.The higher the

**gauss**rating is, the deeper the magnetic penetration will be.These beds are equipped with 100 mini ceramic biomagnets, and each magnet has a 3,950

**gauss**rating.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**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.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.**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.**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."**Gauss**thus supplied the principal defect in the great work of Laplace.