Proof for the equality of excentric and epicycle movement
Proof for the equality of excentric and epicycle movement for the illustration of the sun movement according to Ptolemäus explanation: Red slice: sun parallelogram diagonal (feather): ray earth-sun angular velocity of the sun at the epicycle antipodal identical to the angular velocity of the circulation of the epicycle center.
Showcase of this model is Case number U 54
Ptolemäus. Almagest, 3rd book, chapter 3.