Famous problems of elementary geometry: the duplication of the cube; the trisection of an angle; the quadrature of the circle; an authorized translation of F. Klein's Vorträge über ausgewählte fragen der elementargeometrie, ausgearbeitet von F. Tägert (1897)
Klein, Felix, 1849-1925, Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, London, Ginn & company · leaf 29
e= 2 * Taking for the domain of rationality the totality of rationalfunctions of r, we know by the previous reasoning that theequation x3 = r is irreducible. Hence the problem of themultiplication of the cube does not admit, in general, of aconstruction by means of straight edge and compasses. II.… … Fig. 2. These roots are represented geometrically by the vertices ofan equilateral triangle inscribed in the circle with radiusunity and center at the origin. Thefigure shows that to the root xx cor-responds the argument -^. Hencethe equation x3 = cos <j> + i sin <£ is the analytic…
Geometry
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