The study of treatises on Nature of the Late Antiquity and the mid-byzantine period offers us the tracing path that leads from ancient Greek science to the late medieval period achievements. We intend to focus on the astronomical principles presented in some byzantine treatises which indicate the living tradition of the ancient Greek scientific spirit within the Greek-speaking, Christianized, Byzantine Empire. Mainly, we will present certain astronomical principles which can be found at Cosmas Indicopleustes’ Christian Topography (6th century), at Symeon Seth’s Summary of Physics (11th century) and Nickephorus Blemmydes’ Summary of Physics (13th century). The quotes which can be found in these essays indicate the wide knowledge of the authors on fundamental issues of the Astronomy as they had been derived from ancient Greek astronomical texts which were preserved in the byzantine territories. Also, the extended timeline of these references outlines that the Greek tradition on Astronomy had been active all the medieval period in the areas that were ruled by the Byzantine Empire and consequently could be transferred beyond the frontiers, to the territories of the eastern Empires through travelers and diplomatic missions.