epicycle-deferent model

accepted: 15/03/2021) Abstract Planets occasionally quit their prograde motions and go against their normal direction, said retrogression. Happening for differences in orbital velocities of planets and earth, retrogression loops not only are unequal at forms and scales but appear everywhere in the sky. Applying the concentric epicycle-deferent model makes the similar regular loops, but it does not correspond to observations; thus, employing eccentre deferent is needed. Description of the phenomenon is the subject of Book XII of the Almagest. Ptolemy explained some necessary lemmas for his geometrical explanations and examined his justifications by few specified positions for every planet. This paper studies contents of a treatise note on retrogression attributed to Muʾayyad al‐Dīn al‐ʿUrḍī, one of the invited scholars to founding Maragha observatory. Apart from his skills and achievements in designing and manufacturing astronomical instruments, he was a proficient theorist astronomer with educational experiences. The present treatise is an informative text similar to other known works of ʿUrḍī in precision and consideration of the matter’s geometrical aspects.He has attempted to encounter the phenomenon holistically instead of checking parameters in the case studies to present regulation using Apollonius’ theorem