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.

The curve also permits the solution of the problems of duplicating a cube and trisecting an angle.

His investigation of the properties of amicable numbers and of the problem of trisecting an angle, are of importance.