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Mathematische Annalen (57 )

Mathematische Annalen (57 )


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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. 1903 edition. Auszug: ... die Betrachtungen des 2 noch nichts aus. (Es ist hier ubrigens noch eine Bemerkung einzuschalten. In der elliptischen Geometrie gibt es zwei Strecken endlicher Lange, welche zwei Punkte verbinden (wenn wir prinzipiell von Strecken, die langer sind als der Umfang der ganzen Geraden, sich aber teilweise selbst uberdecken, absehen). Unter diesen ist naturlich im allgemeinen nur die eine die wirklich kurzeste Verbindung der beiden Punkte. Trotzdem bleibt der Satz, dass im Dreieck jede Seite kurzer ist als die Summe der beiden andern immer bestehen, wenn wir nur unter allen Strecken, welche drei Punkte verbinden, solche Tripel auswahlen, die ein Stuck aus der Ebene ausschneiden. Dass dieser Satz richtig ist, solange die Normalgerade das Dreieck nicht schneidet, folgt aus den Betrachtungen des 2). Sou abe-in einem Breiecke die Summe zweier Seiten auch dann noch grosser sein als die dritte, falls das Dreieck von der Normalgeraden geschnitten wird, so ist, wie wir sofort erkennen werden, die hinreichende und notwendige Bedingung dafur die, dass alle Geraden dieselbe Gesamtlange haben. Wir wollen zunachst zeigen, dass die Bedingung notwendig ist. Betrachten wir die beiden Geraden gx und, die sich in A schneiden. Dann kann man auf einen Punkt so wahlen, dass AB s ist, wo eine beliebig kleine Zahl ist. Durch ziehe man eine Parallele p zu gt g und p schneiden sich also auf der Normalgeraden im Punkte C. Sei li die Lange der einen Strecke AC (also gx--die der andern) und die Lange der einen Strecke (a


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Product Details
  • ISBN-13: 9781234195458
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 166
  • Spine Width: 9 mm
  • Width: 189 mm
  • ISBN-10: 1234195453
  • Publisher Date: 30 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 308 gr


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