The curve also permits the solution of the problems of duplicating a cube and trisecting an angle.
It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."
Although Hippocrates could not determine the proportionals, his statement of the problem in this form was a great advance, for it was perceived that the problem of trisecting an angle was reducible to a similar form which, in the language of algebraic geometry, is to solve geometrically a cubic equation.
TRISECTRI X, a curve which is a variety of the limacon of Pascal, and named from its property of trisecting an angle.
His investigation of the properties of amicable numbers and of the problem of trisecting an angle, are of importance.