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Die Elemente Der Neueren Geometrie Und Der Algebra Der Binaren Formen; Ein Beitrag Zur Einfuhrung in Die Algebra Der Linearen Transformationen

Die Elemente Der Neueren Geometrie Und Der Algebra Der Binaren Formen; Ein Beitrag Zur Einfuhrung in Die Algebra Der Linearen Transformationen


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About the Book

Dieses historische Buch kann zahlreiche Tippfehler und fehlende Textpassagen aufweisen. Kaufer konnen in der Regel eine kostenlose eingescannte Kopie des originalen Buches vom Verleger herunterladen (ohne Tippfehler). Ohne Indizes. Nicht dargestellt. 1862 edition. Auszug: ...die allgemeinen Gleichungen des men und n'en Grades zu fuhren. Denn, da die Resultante das Product sammtlicher m n Differenzen ist, die man aus den Wurzeln der einen und denen der anderen Gleichung bilden kann, so wird sie mit c'Hn multipliciert, wenn jede der Wurzeln -i, a2, ' ' -, i, -2', ... aa' mit dem constanten Factor c multipliciert ist. T)amit diess aber geschehe, mussen in den Coefficienten der Gleichungen a0) 1 ) aw und ebenso in a0 y ai; an nach ihrer Natur als symmetrische Functionen der Wurzeln (Art. 6) die Factoren c, c1, c, . c ', cn respective hinzutreten, Factoren also, deren Exponenten respective mit den Indices der Coefficienten, zu welchen sie treten, identisch sind. Die Resultante der beiden Gleichungen wird also mit cnln multipliciert, indem zu jedem ihrer Glieder eine Potenz von c als Factor tritt, deren Exponent mit der Summe der Indices des Gliedes ubereinstimmt; diese Summe muss also constant und =m-, d.i. gleich dem Product der Grade beider Gleichungen sein, oder nach der Ausdrucksweise des Artikels 7, das Gewicht eines jeden Gliedes der Resultante zweier Gleichungen als Function ihrer Coefficienten ist dem Product ihrer Grade gleich. Man kann nach diesen allgemeinen Gesetzen in jedem gegebenen Falle die litterale Form der Resultante entwickelt darstellen. Fur den Fall m = n schliesst man aus der Natur der Resultante als Product aller Wurzeldifferenzen auch auf die Gleichheit der numerischen Coefficienten derjenigen ihrer Glieder, welche das eine aus dem anderen durch Vertauschung der Coefficienten der einen Gleichung mit den entsprechenden der anderen oder durch Vertauschung der Coefficienten jeder..."


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Product Details
  • ISBN-13: 9781234511531
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 42
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1234511533
  • Publisher Date: 24 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 95 gr


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Die Elemente Der Neueren Geometrie Und Der Algebra Der Binaren Formen; Ein Beitrag Zur Einfuhrung in Die Algebra Der Linearen Transformationen
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