The problem of the trisection of an angle, analytically considered, depends on the solution of a cubic equation, say 4x3−3x−cos a = 0, which is in general irreducible, and therefore not soluble by means of quadratic radicals. It follows that the trisection of an angle cannot be effected by means of the ruler and compass alone. This, in fact if not in theory, appears to have been known to the early Greek geometers, and they proposed the use of various curves, the continuous mechanical construction of which must, of course, be postulated, for the solution of the problem. The Quadratrix and the Spiral of Archimedes, both transcendental curves, may be mentioned. It was early discovered that the conic sections could be used for the purpose, and in modern times various solutions have been suggested involving their use.