This problem, also termed the " **Apollonian** problem," was demonstrated with the aid of conic sections by Apollonius in his book on Contacts or Tangencies; geometrical solutions involving the conic sections were also given by Adrianus Romanus, Vieta, Newton and others.

This problem, which is sometimes known as the **Apollonian** Problem, was proposed by Vieta in the 16th century to Adrianus Romanus, who gave a solution by means of a hyperbola.

In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or **Apollonian** parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.