Two Problems of Geometry

Abstract

IN your issue of August 22, Mr. A. B. Basset asks for solutions of the two problems, the trisection of an angle by means of the cissoid, and the duplication of the cube by the conchoid. I happened to come across a solution of the latter in an old book, Leslie's “Geometrical Analysis” (1821), where the problem is solved also in several other ways—by means of the cissoid, two parabolas, a rectangular hyperbola and circle, and the logarithmic curve. The problem of the trisection of an angle is also solved in several ways—by means of the conchoid (two ways), an hyperbola (e = 2) and intersecting circle, a rectangular hyperbola and circle, the quadratrix, the companion to the cycloid, and the Archimedean spiral, but not by the cissoid.