New PDF release: A treatise on the analytical geometry of the point, line,

By John Casey

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Additional info for A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples

Example text

J2 K = K 2 (-J5) mit erzeugendem Polynom f3(X) = X2 - 5 E E K) [x], K 2 [x]. 8: FUhren Sie die Konstruktion der Zahl IX mit Zirkel und Lineal durch. Bemerkung: Mit eiIigeschriinkten "Werkzeugen" (z. B. Lineal allein, Zirkel allein) oder speziellen "Werkzeugen" (z. B. 2 erkliirt) oder Ellipsenzirkel) lassen sich andere Zahlenmengen (je nach dem weniger oder mehr als bei den klassischen Konstruktionen mit Zirkel und Lineal) konstruieren (vgl. Bieberbach, 1952). 3 Das Delische Problem der Wurfelverdopplung Der zu verdoppelnde Wfufel moge ohne Beschriinkung der Allgemeinheit eine Kantenlange von 1 haben.

Beim Satz von Pappus gibt es zwei Tragergeraden, die sich schneiden (P = "groBer Pappus") oder die parallel sind (p = "kleiner Pappus"). Es wird jeweils aus gewissen Parallelitaten auf eine weitere Parallelitat geschlossen, wodurch die sich schlieBende Figur entsteht. In den folgenden Figuren sind die Voraussetzungen der Satze zu entnehmen; verschieden gezeichnete Punkte und Geraden seien als verschieden vorausgesetzt. 19 (D = "groBer Desargues" mit 3 copunktalen Tragergeraden t\, t2 und t3) bzw.

U < ... < b24 < b l2 < b6 fur den Kreisumfang U entstehen. Manchmal verwendet man auch die Folge A 6, A 7, A g, ist dies etwas problematisch? ••• der n-Ecke zur Approximation. 2 5-Eck gerechnet und fur 1t die sehr gute Abschiitzung 10 10 3,141", 3- < 1t < 3 - '" 3,143 71 70 gefunden (vgl. Dorbrand, 2001). 13: Wei sen Sie die Intervallschachtelungs-Eigenschaft nach und bestatigen Sie das Ergebnis von Archimedes! Ludolph van Ceulen (1540 - 1610) ging sogar bis zum 3·2 62 _Eck und fand damit 1t auf 35 Stellen genau.

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A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples by John Casey


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