Earlier quoted context omitted.
Add enough epicycles and you've got a Fourier transform... Epicycles were a great idea but applied for the wrong reason.
Oh, they worked really well; they were still used for numerical calculation even after Galileo. But they weren't a "demonstration of knowledge and understanding" of planetary motion.
Epicycles gave a better description of the movement of the planets, based on the observations available, which was entirely falsifiable. They were eventually superseded, and that's science at work.