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 50
y4 = 0, with roots z1 and z2; zx > z2.These will furnish Zl = 2 cos —, whence it is easy to construct the polygon desired. Wenotice further that to construct zx it is sufficient to construct xi? x2> yi? y<t« We then lay off the following segments : upon the uppertangent, y = 2, £ j4 £ xi… … THE REGULAR POLYGON OF 17 SIDES. 37 two points, the projection of which from the point A (0, 2),the upper vertex of the circle, gives the two roots x1? x2 of thefirst quadratic equation as intercepts upon the axis of X. 4To solve the second equation we have to lay off — above xi and below. Xl To…
Geometry
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