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 60
raw a line from the origin to the tangent x = 1. The inter-cept on this tangent equals f/2. 4. The conchoid of Nicomedes (c. 150 b.c.) is constructedas follows : Let 0 be a fixed point, a its distance from a fixed 46 FAMOUS PROBLEMS. line. If we pass a pencil of rays through 0 and lay off oneach… … jugate point; for b = a it is a cusp (Fig. 13). Taking for axes of X a the perpendicular and paral- lei through 0 to the fixed line, we have r_ b X X — c i whence (x2-fy2)(x-a)2-b2x2 = 0.. The conchoid is then of thefourth order, has a doublepoint at the origin, and iscomposed of two brancheshaving…
Geometry
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