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 58
tangent on the right)and the diameter perpendicular to it.Draw lines from 0, the vertex of thecircle thus determined, to points uponthe tangent, and lay off from 0 uponeach the segment lying between itsintersection with the circle and thetangent. The locus of points so deter-mined is the cissoid.… … Fig. 12. the total segment equals cos 6 circle is cos 0.hence * The difference of the two segments is r, and cos 6 cos 0 = sin2 0cos 6 ALGEBRAIC CONSTRUCTIONS. 45 By transformation of coordinates we obtain the Cartesianequation, (x2 + y2)x-y2 = 0. The curve is of the third order, has a cusp at the…
Geometry
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