The computation of the stations of the planets in the epicyclic theory was reduced by Apollonius to the geometrical problem of drawing a line intersecting the epicycle such that the sections have a definite ratio.
Through the revolution of the entire epicycle towards the left side, the planet situated on its circumference moves from point 1 to point 2 over a distance equal to the angular velocity of this revolution times the distance earth-planet. At the same time the planet on its epicycle moves toward the right side, from point 1 to point 3 over a distance equal to the angular velocity on the epicycle times the radius of the epicycle. The latter displacement viewed is foreshortened in the same ratio as that between the distance planet-footprint of the perpendicular and center-planet. The planet seems at rest when the two displacements are seen from the earth to compensate. This occurs when the two distances, planet-footprint and planet-earth, have the inverse ratio of the angular velocities. In other words, the planet has a station then the distance earth-planet and half the chord in the epicycle have the same ratio as the period of revolution and the synodic period.