KARL See also:

• FRIEDRICH, JOHANN (1836— )

FRIEDRICH See also:

• KARL FRIEDRICH GAUSS (1777-1855)

GAUSS (1777-1855)  , See also:

• GERMAN
• GERMAN, DUTCH AND SCANDINAVIAN

German mathematician, was See also:

• BORN, IGNAZ, EDLER VON (1742–1791)

born of humble parents at See also:

• BRUNSWICK
• BRUNSWICK (Ger. Braunschweig)
• BRUNSWICK, KARL WILHELM FERDINAND, DUKE OF (1735-18o6)

Brunswick on the 3oth of See also:

• APRIL

April 1777, and was indebted for a liberal See also:

• EDUCATION

education to the See also:

• NOTICE

notice which his talents procured him from the reigning See also:

• DUKE (corresponding to Fr. duc, Ital. duca, Ger. Herzog)

duke . His name became widely known by the publication, in his twenty-fifth See also:

• YEAR

year (18ot), of the Disquisitiones arithmelicae . In 1807 he was appointed director of the See also:

• GOTTINGEN

Gottingen See also:

• OBSERVATORY

observatory, an See also:

• OFFICE (from Lat. officium, " duty," " service," a shortened form of opifacium, from facere, " to do," and either the stem of opes, " wealth," " aid," or opus, " work ")

office which he retained to his See also:

• DEATH

death: it is said that he never slept away from under the roof of his observatory, except on one occasion, when he accepted an invitation from See also:

• BARON
• BARON (1835-1895)
• BARON, MICHEL (1653—1729)

Baron von See also:

• HUMBOLDT, FRIEDRICH HEINRICH ALEXANDER, BARON
• HUMBOLDT, KARL WILHELM VON (1767-1835)

Humboldt.to attend a See also:

• MEETING (from " to meet," to come together, assemble, 0. Eng. metals ; cf. Du. moeten, Swed. mota, Goth. gamotjan, &c., derivatives of the Teut. word for a meeting, seen in O. Eng. Wit, moot, an assembly of the people; cf. witanagemot)

meeting of natural philosophers at See also:

• BERLIN
• BERLIN, CONGRESS AND TREATY OF
• BERLIN, ISAIAH (1725–1799)

Berlin . In ',Soo he published at See also:

• HAMBURG

Hamburg his Theoria motus corporum coelestium, a See also:

• WORK

work which gave a powerful impulse to the true methods of astronomical observation; and his astronomical workings, observations, calculations of orbits of See also:

• PLANETS, MINOR

planets and comets, &c., are very numerous and valuable . He continued his labours in the theory of See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

numbers and other See also:

• ANALYTICAL

analytical subjects, and communicated a See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long See also:

• SERIES (a Latin word from serere, to join)

series of See also:

• MEMOIRS

memoirs to the Royal Society of Sciences (Konigliche Gesellschaft der Wissenschaften) at Gottingen . His first memoir on the theory of See also:

• MAGNETISM
• MAGNETISM, TERRESTRIAL

magnetism, Intensitas vis magneticae terrestris ad mensuram absolutam revocata, was published in 1833, and he shortly afterwards proceeded, in See also:

• CONJUNCTION (from Lat. conjungere, to join together)

conjunction with Wilhelm See also:

• WEBER, CARL MARIA FRIEDRICH ERNEST VON (1786–1826)
• WEBER, WILHELM EDUARD (1804-1891)

Weber, to invent new apparatus for observing the See also:

• EARTH
• EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. 'pq'e, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in
• EARTH, FIGURE OF
• EARTH, FIGURE OF THE

earth's magnetism and its changes; the See also:

• INSTRUMENTS

instruments devised by them were the See also:

• DECLINATION (from Lat. declinare, to decline)

declination See also:

• INSTRUMENT (Lat. instrumentum, from insincere, to build up, furnish, arrange, prepare)

instrument and the bifilar See also:

• MAGNETOMETER

magnetometer . With Weber's assistance he' erected in 1833 at Gottingen a magnetic observatory See also:

• FREE

free from See also:

• IRON [symbol Fe, atomic weight 55.85 (0=16)]

iron (as Humboldt and F . J . D . See also:

• ARAGO, DOMINIQUE FRANCOIS JEAN (1786-1853)

Arago had previously done on a smaller See also:

• SCALE
• SCALE (1) A

scale), where he made magnetic observations, and from this same observatory he sent telegraphic signals to the neighbouring See also:

• TOWN

town, thus showing the practicability of an electromagnetic See also:

• TELEGRAPH (Gr. Tike, far, and rypaq5eiv, to write)

telegraph . He further instituted an association (Magnetischer Verein), composed at first almost entirely of Germans, whose continuous observations on fixed See also:

• TERM

term-days extended from See also:

• HOLLAND
• HOLLAND, CHARLES (1733–1769)
• HOLLAND, COUNTY AND PROVINCE OF
• HOLLAND, HENRY FOX, 1ST BARON (1705–1774)
• HOLLAND, HENRY RICH, 1ST EARL OF (1S9o-,649)
• HOLLAND, HENRY RICHARD VASSALL FOX, 3RD
• HOLLAND, JOSIAH GILBERT (1819-1881)
• HOLLAND, PHILEMON (1552-1637)
• HOLLAND, RICHARD, or RICHARD DE HOLANDE (fl. 1450)
• HOLLAND, SIR HENRY, BART

Holland to See also:

• SICILY (Ital. Sicilia)

Sicily . The volumes of their publication, Resultate aus den Beobachtungen See also:

• DES

des magnetischen Vereins, extend from 1836 to 1839; and in those for 1838 and 1839 are contained the two important memoirs by See also:

• GAUSS, KARL FRIEDRICH (1777-1855)

Gauss, Allgemeine Theorie des Erd- . magnetismus, and the Allgemeine Lehrsatze—on the theory of forces attracting according to the inverse square of the distance .

The instruments and methods thus due to him are substantially those employed in the magnetic observatories throughout the See also:

• WORLD

world.' He co-operated in the Danish and Hanoverian measurements of an arc and trigonometrical operations (1821-1848), and wrote (1843, 1846) the two memoirs Uber Gegenstande der hoheren Geoddsie . Connected with observations in See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general we have (1812-1826) the memoir Theoria combinationis observationum erroribus minimis obnoxia, with a second See also:

• PART

part and a supplement . Another memoir of applied See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics is the Dioptrische Untersuchungen (1840) . Gauss was well versed in general literature and the See also:

• CHIEF (from Fr. chef, head, Lat. caput)

chief See also:

• LANGUAGES

languages of See also:

• MODERN

modern See also:

• EUROPE

Europe, and was a member of nearly all the leading scientific See also:

• SOCIETIES, LEARNED

societies in Europe . He died at Gottingen on the 23rd of See also:

• FEBRUARY

February 1855 . The See also:

• CENTENARY (from Lat. centenarius, of or belonging to a hundred, from centeni, distributive of centum, hundred)

centenary of his See also:

• BIRTH (a word common in various forms to Teutonic languages from the root of the verb " to bear ")

birth was celebrated (1877) at his native See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place, Brunswick . Gauss's collected See also:

• WORKS

works were published by the Royal Society of Gottingen, in 7 vols . 4to (Gott., 1863-1871), edited by E . J.Schering —(1) the Disquisitiones arithmeticae, (2) Theory of Numbers, (3) See also:

• ANALYSIS (Gr. avci and Meta, to break up into parts)

Analysis, (4) See also:

• GEOMETRY

Geometry and Method of Least Squares, (5) Mathematical Physics, (6) See also:

• ASTRONOMY (from Gr. &arpov, a star, and v ,usiv, to classify or arrange)

Astronomy, and (7) the Theoria motus corporum coelestium . Additional volumes have since been published, Fu'zdamente der Geometrie usw . (1900), and Geodatische Nachtrage zu See also:

• BAND

Band iv . (1903) .

They include, besides his various works and memoirs, notices by him of many of these, and of works of other authors in the Gottingen gelehrte Anzeigen, and a considerable amount of previously unpublished See also:

• MATTER

matter, Nachlass . Of the memoirs in pure mathematics, comprised for the most part in vols. ii., iii. and iv . (but to these must be added those on Attractions in vol. v.), it may be safely said there is not one which has not signally contributed to the progress of the See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

branch of mathematics to which it belongs, or which would not require to be carefully analysed in a See also:

• HISTORY

history of the subject . See also:

• RUNNING

Running through these volumes in See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order, we have in the second the memoir, Summatio quarundam serierum singularium, the memoirs on the theory of See also:

• BIQUADRATIC (from the Lat. bi-, bis, twice, and quadratus, squared)

biquadratic residues, in which the notion of complex numbers of the See also:

• FORM (Lat. forma)

form a+bi was first introduced into the theory of numbers; and included in the Nachlass are some valuable tables . That for the See also:

• CONVERSION (Lat. conversio, from convertere, to turn or ,change)

conversion of a fraction into decimals (giving the See also:

• COMPLETE

complete See also:

• PERIOD
• PERIOD (Gr. irepioSos, a going or way round, circuit, aepi, round, and &Sis, way, road)

period for all the See also:

• PRIME, PRIMER AND PRIMING

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 . In vol. iii. we have memoirs See also:

• RELATING

relating to the See also:

• PROOF (in M. Eng. preove, proeve, preve, &°c., from O. Fr . prueve, proeve, &c., mod. preuve, Late. Lat. proba, probate, to prove, to test the goodness of anything, probus, good)

proof of the theorem that every numerical See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation has a real or imaginary See also:

• ROOT (late O.E. rot, adopted from Scand., cf. Norw. and Swed. rot, Dan. rod; the true O.E. word was wyrt, plant, represented in Ger. Wurz or Wurzel; the ultimate root is the same in both words, and is seen in Lat. radix)
• ROOT, ELIHU (1845– )

root, the memoir on. the Hypergeometric Series, that on See also:

• INTERPOLATION (from Lat. interpolare, to alter, or insert something fresh, connected with pollee, a polish)

Interpolation, and the memoir Determinatio attractionis—in which a planetary See also:

• MASS (O.E. maesse; Fr. messe; Ger. Messe; Ital. messa; from eccl. Lat. missa)
• MASS, IN

mass is considered as distributed over its See also:

• ORBIT (from Lat. orbita, a track, orbis, a wheel)

orbit according to the See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time in which each portion of the orbit is described, and the question (having an implied reference to the theory of See also:

• SECULAR (Lat. saecularis, of or belonging to an age or generation, saeculum)

secular perturbations) is to find the attraction of such a See also:

• RING (O.E. hring; a word common to Teutonic languages; and probably cognate with the Lat. circus, Gr. KtpKOS or KpLKOS, Skt'. chakra, wheel, circle, cf. also " harangue "); in art, a band of circular shape of varying sizes, made of any material and used f

ring . In the See also:

• SOLUTION (from Lat. solvere, to loosen, dissolve)

solution the value of an elliptic See also:

• FUNCTION

function is found by means of the arithmetico-geometrical mean . The Nachlass contains further re-searches on this subject, and also researches (unfortunately very fragmentary) on the See also:

• LEMNISCATE (from Gr. X wLo coc, ribbon)

lemniscate-function, &c., showing that Gauss was, even before 'Soo, in See also:

• POSSESSION
• POSSESSION (Lat. possessio, possidere, to possess)

possession of many of the discoveries which have made the names of N . H . See also:

• ABEL (better ABELL), THOMAS (d. 1540)
• ABEL (Hebrew for breath)
• ABEL, KARL FRIEDRICH (1725-1787)
• ABEL, NIELS HENRIK (1802-1829)
• ABEL, SIR FREDERICK AUGUSTUS, BART

Abel and K . G . J .

See also:

• JACOBI, FRIEDRICH HEINRICH (1743-1819)
• JACOBI, JOHANN GEORG (1740-1814)
• JACOBI, KARL GUSTAV JACOB (1804-1851)

Jacobi illustrious . In vol. iv. we have the memoirAllgemeine Auflosung, on the graphical See also:

• REPRESENTATION

representation of one See also:

• SURFACE

surface upon another, and the Disquisitiones generales circa superficics curvas . (An See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of the treatment of surfaces which he originated in this See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper will be found in the See also:

• ARTICLE (from Lat. articulus, a joint)

article SURFACE.) And in vol. v. we have a memoir On the Attraction of Homogeneous Ellipsoids, and the already mentioned memoir Allgemeine Lehrsdtze, on the theory of forces attracting according to the inverse square of the distance . (A .