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Einleitung in Die Synthetische Geometrie; Ein Leitfaden Beim Unterrichte an Hoheren Realschulen Und Gymnasien

Einleitung in Die Synthetische Geometrie; Ein Leitfaden Beim Unterrichte an Hoheren Realschulen Und Gymnasien


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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. 1869 edition. Auszug: ... eine ahnliche conjugirt, wie man sich aus Fig. 57 uberzeugt. Da zwei concentrische Kreise die unendlich entfernte Gerade der Ebene zur Potenzlinie haben, so kann man annehmen, dass die sammtlichen Kreise, welche einen gegebenen Punkt M zum Mittelpunkt haben, eine Kreisschaar bilden, deren Axe unbestimmt ist, d. h. jede durch M gehende Gerade kann als Axe angesehen werden, insofern sie die sammtlichen Mittelpunkte der Kreise (welche sich in M vereinigen) enthalt. Um die conjugirte Schaar zu finden, bemerke man, dass die Mittelpunkte ihrer Kreise im Unendlichen liegen, so dass also diese Kreise, insofern sie uberhaupt in das endliche Gebiet der Ebene hineinragen, aus Geraden bestehen. Wenn eine Gerade einen Kreis unter rechten Winkeln schneiden soll, so muss sie durch den Mittelpunkt des Kreises gehen, woraus durch Umkehrung folgt, dass die sammtlichen Geraden, die durch M gehen, und von denen jede mit der unendlich entfernten Geraden der Ebene zusammengenommen wird, als eine Kreisschaar aufgefasst werden konnen, die conjugirt ist zu der Schaar concentrischer Kreise mit dem Mittelpunkte M. Die betrachtete Schaar concentrischer Kreise wird, wie jede Kreisschaar, von einer Transversalen G in einem Punktsysteme geschnitten. Dieses Punktsystem ist immer ein gleichseitig hyperbolisches ( 11), dessen einer Asymptotenpunkt der Fusspunkt des von M auf G gefallten Perpendikels ist, wahrend der andere Asymptotenpunkt im Unendlichen liegt. Das Punktsystem, in welchem die zur concentrischen Kreisschaar conjur girte Schaar geschnitten wird, ist ein parabolisches, dessen vereinigte Asymptotenpunkte sich auf der unendlich entfernten Geraden der Ebene...


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Product Details
  • ISBN-13: 9781234871925
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 56
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1234871920
  • Publisher Date: 25 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 118 gr


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