The inaugural lecture, or oration, delivered by Regiomontanus at the University of Padua in 1464 is deemed a document of remarkable significance in the history of science. Although it has attracted much scholarly attention, few efforts have been directed towards identifying the traces of Byzantine influence it might carry; that is to say, the extent to which Regiomontanus might have been influenced by the views of his patron, Bessarion. This paper responds to the need for such a study, arriving at the following conclusions. First, Regiomontanus's praise of astrology is in line with Bessarion's reaction to the official decisions taken against astrology in Constantinople at the Council of 1351 - decisions which were ultimately rooted in the hesychast controversy and in the confessional struggles between the Churches of Constantinople and Rome. Second, the legitimation of the Graeco-Arabic roots of astronomy in an institutional context, as undertaken by Regiomontanus, is in accordance with the intellectual influences Bessarion had absorbed in his youth in Constantinople. Third, contrary to some claims, it is likely that Regiomontanus does not adhere to a humanist anti-Arab agenda; rather, his views on the history of mathematics are a consequence of the Graeco-Arabic heritage of his patron, and of his lack of access to Arabic translations.