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See also:STEINER, See also:JAKOB (1796-1863) , Swiss mathematician, was See also:born on the 18th of See also:March 1796 at the See also:village of Utzendorf (See also:canton See also:Bern). At eighteen he became a See also:- PUPIL (Lat. pupillus, orphan, minor, dim. of pupus, boy, allied to puer, from root pm- or peu-, to beget, cf. "pupa," Lat. for " doll," the name given to the stage intervening between the larval and imaginal stages in certain insects)
pupil of Heinrich See also:Pestalozzi, and afterwards studied at See also:Heidelberg. Thence he went to See also:Berlin, earning a livelihood there, as in Heidelberg, by giving private lessons. Here he became acquainted with A. L. Crelle, who, encouraged by his ability and by that of N. H. See also:Abel, then also staying at Berlin, founded his famous See also:Journal (1826). After Steiner's publication (1832) of his Systematische Entwickelungen he received, through See also:Jacobi's exertions, who was then See also:professor at See also:Konigsberg, an honorary degree of that university; and through the See also:influence of G. J. Jacobi and of the See also:brothers See also:Alexander and Wilhelm von See also:Humboldt a new See also:chair of See also:geometry was founded for him at Berlin (1834). This he occupied till his See also:death, which took See also:place in Bern on the 1st of See also:April 1863.
Steiner's mathematical See also:work was confined to geometry. This he treated synthetically, to the See also:total exclusion of See also:analysis, which he hated, and he is said to have considered it a disgrace to synthetical geometry if equal or higher results were obtained by See also:analytical methods. In his own See also:- FIELD (a word common to many West German languages, cf. Ger. Feld, Dutch veld, possibly cognate with O.E. f olde, the earth, and ultimately with root of the Gr. irAaror, broad)
- FIELD, CYRUS WEST (1819-1892)
- FIELD, DAVID DUDLEY (18o5-1894)
- FIELD, EUGENE (1850-1895)
- FIELD, FREDERICK (18o1—1885)
- FIELD, HENRY MARTYN (1822-1907)
- FIELD, JOHN (1782—1837)
- FIELD, MARSHALL (183 1906)
- FIELD, NATHAN (1587—1633)
- FIELD, STEPHEN JOHNSON (1816-1899)
- FIELD, WILLIAM VENTRIS FIELD, BARON (1813-1907)
field he surpassed all his contemporaries. His investigations are distinguished by their See also:great generality, by the fertility of his resources, and by such a rigour in his proofs that he has been considered the greatest geometrical See also:genius since 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 of See also:Apollonius.
In his Systematische Entwickelung der Abadngigkeit geometrischer Gestalten von einander he laid the See also:foundation of See also:modern synthetic geometry. He introduces what are now called the geometrical forms (the See also:row, See also:flat See also:pencil, &c.), and establishes between their elements a one-one See also:correspondence, or, as he calls it, makes them projective. He next gives by aid of these projective rows' and pencils a new See also:generation of conics and ruled See also:quadric surfaces, " which leads quicker and more directly than former methods into the inner nature of conics and reveals to us the organic connexion of their innumerable properties and mysteries." In this work also, of which unfortunately only one See also:volume appeared instead of the projected five, we see for the first time the principle of duality introduced from the very beginning as an immediate outflow of the most fundamental properties of the See also:plane, the See also:line and the point.
In a second little volume, See also:Die geometrischen Constructionen ausgefuhrt mittelst der geraden Linie and eines festen Kreises (1833), republished in 1895 by Ottingen, he shows, what had been already suggested by J. V. See also:Poncelet, how all problems of the second 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 can be solved by aid of the straight-edge alone without the use of compasses, as soon as one circle is given on the See also:drawing-See also:paper. He also wrote Vorlesungen fiber synthetische Geometrie, published posthumously at See also:Leipzig by C. F. Geiser and H. Schroeter in 1867; a third edition by R. See also:Sturm was published in 1887–1898.
The See also:rest of Steiner's writings are found in numerous papers mostly published in Crelle's Journal, the first volume of which contains his first four papers. The most important are those See also:relating to algebraical curves and surfaces, especially the See also:short paper Allgemeine Eigenschaften algebraischer Curven. This contains only results, and there is no indication of the method by which they were obtained, so that, according to L. O. See also:Hesse, " they are, like P. See also:Fermat's theorems, See also:riddles to the See also:present and future generations." Eminent analysts succeeded in proving some of the theorems, but it was reserved to L. See also:Cremona to prove them all, and that by auniform synthetic method, in his See also:book on algebraical curves. Other important investigations relate to See also:maxima and minima. Starting from See also:simple elementary propositions, Steiner advances to the See also:solution of problems which analytically require the calculus of variation, but which at the time altogether surpassed the See also:powers of that calculus. Connected with this is the paper Vom Krummungsschwerpuncte ebener Curven, which contains numerous properties of pedals and roulettes, especially of their areas.
Steiner's papers were collected and published in two volumes (Gesammelte Werke, 1881–1882) by the Berlin See also:Academy.
See C. F. Geiser's pamphlet Zur Erinnerung an J. Steiner (See also:Zurich, 1874).
End of Article: STEINER, JAKOB (1796-1863)
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