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Analytische Geometrie Der Kegelschnitte; Mit Besonderer Berucksichtigung Der Neueren Methoden (1 )

Analytische Geometrie Der Kegelschnitte; Mit Besonderer Berucksichtigung Der Neueren Methoden (1 )


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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. 1898 edition. Auszug: ...Werte je einer Variabein sin y 'v ' cos y 'v Der Kreis und die Gerade. 207 In rationaler Form sind diese Gleichungen quadratisch und liefern die Wurzeln sin y Yq2--p2, y', y" = P sin v + cos YIV--P2, wo die Paare x'y' und x"y" so zusammengehoren, dafs die oberen bez. unteren Vorzeichen gleichzeitig gelten. Falls ein imaginarer Kreis gegeben war, ist nur p2 durch--p'2 zu ersetzen. Es bleibt also, wenn die Gerade reell ist, auch dann noch Summe und Product der Wurzeln reell (x' + x") = p cos y, W + y") = P sin y, x'x" = p2--p2 sin2 y, y'y" = p2--p2 cos2 y. Weil wir so durch quadratische Gleichungen die gemeinsamen Wertepaare erhalten, so mussen wir ( 23) sagen: Eine Gerade und ein Kreis besitzen stets zwei Schnittpunkte.Es sind aber drei Falle zu unterscheiden. Ist erstens der Kreis reell und p p, d. h. der Abstand der Geraden vom Kreiscentrum kleiner als der Radius, so sind die Wurzelpaare reell: die Gerade schneidet den Kreis in zwei reellen und verschiedenen Punkten. Ist dagegen zweitens p p, d. h. der Abstand grofser als der Radius, oder ist der Kreis imaginar, so sind, anschaulich gesprochen, keine Schnittpunkte vorhanden. Weil aber die Wurzelwerte als conjugirt complexe Zahlen existiren, so sagen wir: die Gerade schneidet den Kreis in zwei conjugirt imaginaren Punkten ( 16). Ist endlich drittens p = p, d. h. das Perpendikel vom Centrum auf die Gerade gleich dem Radius, so fallen die Schnittpunkte in einen reellen Punkt x--p cos y, y = p sin y zusammen. Man spricht dann bekanntlich von einer Beruhrung des Kreises durch die Gerade. Allgemein bezeichnet die analytische Geometrie eine Gerade als Tangente..."


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Product Details
  • ISBN-13: 9781234510480
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 130
  • Spine Width: 7 mm
  • Width: 189 mm
  • ISBN-10: 1234510480
  • Publisher Date: 24 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 245 gr


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