My point was that trying to express epicycles in the new terminology is not possible.
This is false in an amusing way: expressing motion in terms of epicycles is mathematically equivalent to decomposing functions into Fourier series -- a central concept in both physics and mathematics since the nineteenth century.
To be perfectly fair, AFAIK Ptolemy thought in terms of a finite (and small) number of epicycles, not an infinite series.
Here's the new thread for posting quotes, with the usual rules: