Eccentric or Epicycle?
Apollonius’ Demonstration
by Pierre Paquette · 2023-01-02

Ptolemy doesn’t mention the name, but Apollonius of Perga [c.240–c.190 BCE] was the first to demonstrate that the movement of a point on a deferent offset from the observer and the movement of a point on an epicycle moving on a deferent that is centered on the observer will both appear the same to the observer.

The diagram to the right shows that, if the deferent is offset from the observer by an amount corresponding to the radius of the epicycle, then the offset will correspond to the epicycle’s offsetting of the body, as demonstrated by the grey line always pointing in the same direction and keeping the same length. Additionally, grey dots are added in the path of the body to the right; they eventually cover a full circle equivalent to the left deferent. In both diagrams, the observer is located at the blue point. Click anywhere in the diagram to start/stop the animation.


© 2024 EcliptiQc / Pierre Paquette
Last Updated 2023-09-29 at 02 h 50 UTC