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Koordinaten-Geometrie: Erster Band: Die Ebene by Hans Beck

Koordinaten-Geometrie: Erster Band: Die Ebene

by Hans Beck
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Book cover type: Paperback
  • ISBN13: 9783642895227
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 432
  • Original Price: EUR 46.68
  • Language: German
  • Edition: 1919
  • Item Weight: 590 grams
  • BISAC Subject(s): Geometry / General

An Lehrbiichern der analytischen Geometrie herrscht kein Mangel. Sie gehen im allgemeinen nicht zu weit iiber das hinaus, was der Studierende bereits von der Schule mitbringt, und wollen meist offenbar nur eine Vorbereitung fiir die Differentialrechnung sein. Daher befolgen sie eine gemischte Methode, insofern sie die synthe- tische Elementargeometrie voraussetzen und sich darauf beschranken, deren Aussagen nachtraglich in das neue Gewand des Koordinaten- apparats zu kleiden. Der in dieser Weise behandelte Stoff ist im wesentlichen seit zwei J ahrhunderten bekannt, und man konnte daraus schlieBen, daB die analytische Geometrie seit jener Zeit erstarrt sei. Tatsachlich hat wahrend der groBeren Halfte des verflossenen Jahrhunderts die synthetische Geometrie, in Deutschland die Steinersche Schule, das Hauptinteresse absorbiert. Dariiber ist einmal die analytiEche Geo- metrie, die gleiche Erfolge nicbt aufzuweisen hatte, in MiBkredit gekommen, und andererseits hat eine gewisse Vereinseitigung statt- gefunden, insofern die Synthetiker nur ein Sondergebiet, die projek- tive Geometrie, pflegten und sich um andere Dinge, insonderheit um die Elementargeometrie kaum kiimmerten. Fiir die Koordinatengeometrie wurde der erste neue Gedanke nach langer Zeit 1872 von F. Klein in seinem Erlanger Programm ausgesprocben (vgl. S. 199 bis 202 dieses Buches). Klein erkannte wie sich die uniibersehbare Fiille geometrifcher Einzelerscheinungen in eine Reihe von Systemen einordnen laBt. Damit wurden die Invariantentheorie und die Lehre von den Transformationsgruppen Hilfswissenschaften der analytischen Geometrie, und es wurde u. a. auch der Nichteuklidischen Geometrie, die sich bis dahin nur zag- haft entwickelt hatte, ein fester Platz angewiesen.

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