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 42
magnitudeof the different periods. For this purpose we shall employthe following artifice : We divide the semicircle of unit radiusinto 17 equal parts and denote by Si, S2, . . . SJ7 the distances 28 FAMOUS PROBLEMS. of the consecutive points of division A1? A2, . . . A17 from the jinitial point of… … That this may be identical with k+p 2tt a,4 2 cos h —, we must have 17: 4h = 17 = 17 —4h. Giving to h the values 1, 2, 3, 4, 5, 6, 7, 8, we find for k thevalues 13, 9, 5, 1, — 3, — 7, — 11, — 15. Hence Zl == Si3,Z2 = Si, Z3 :== Sg, Z4 = Si5, z5~ S7, z6 — Sn, Z7 = S3, Z8 = S5. The figure shows that…
Geometry
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