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Encyclopedia Britannica - Main :: SOU-STE |
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STEINER, JAKOB (1796-1863) , Swiss mathematician, was born on the 18th of March 1796 at the village
Heidelberg
Heidelberg
Steiner's mathematical work
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 analytical methods. In his own field he surpassed all his contemporaries. His investigations are distinguished by their great
In his Systematische Entwickelung der Abadngigkeit geometrischer Gestalten von einander he laid the foundation of modern synthetic geometry. He introduces what are now called the geometrical forms (the row, flat pencil, &c.), and establishes between their elements a one-one correspondence, or, as he calls it, makes them projective. He next gives by aid of these projective rows' and pencils a new generation of conics and ruled 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
In a second little volume, 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. Poncelet, how all problems of the second 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 drawing- paper . He also wrote Vorlesungen fiber synthetische Geometrie, published posthumously at Leipzig
The 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 relating to algebraical curves and surfaces, especially the 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. Hesse, " they are, like P. Fermat's theorems, riddles to the present and future generations." Eminent analysts succeeded in proving some of the theorems, but it was reserved to L. Cremona to prove them all, and that by auniform synthetic method, in his book on algebraical curves. Other important investigations relate to maxima
Steiner's papers were collected and published in two volumes (Gesammelte Werke, 18811882) by the Berlin Academy
See C. F. Geiser's pamphlet Zur Erinnerung an J. Steiner (Zurich, 1874). End of Article: STEINER, JAKOB (1796-1863) If you wish, you can link directly to this article.
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