Abstract: A touch of Hellenistic culture on Muslims was apparent in the first Umayyah caliph era, Mu'a>wiyah ibn Abi Sufya>n (41-60 H), who was kind to officially appoint high officers and his personal physician of the Roman scientists. At that very moment, the translation of books from Greco-Roman to Arabic had not been done, but the absorption of Greco-Roman culture was done by regular interaction or everyday conversation (social interaction). The aim of the paper is to track when the absorption of the Muslims started concerning on the Greco-Roman philosophy, because there is information that they, in first century of Hijriyah, had started copying Greek books into Arabic. According to historical data, at the time of the Umayah, the Caliph...