Transmission of the Greek Classics on music ("De institutione musica libri quinque", unfinished) contributed to medieval education. "De arithmetica", begins with modular arithmetic, such as even and odd, evenly even, evenly odd, and oddly even. He then turns to unpredicted complexity by categorizing numbers and parts of numbers. His translations of Euclid on geometry and Ptolemy on astronomy, if they were completed, no longer survive. Boethius made Latin translations of Aristotle's "De interpretation" and "Categories" with commentaries. These were widely used during the Middle Ages. In the Western Provinces (what today is considered the Western Europe's heartland), the collapsing Roman empire lost many Greek manuscripts
Cosmas I of Alexandria Cosmas I of Alexandria Cosmas I or Kosmas I () served as Greek Patriarch of Alexandria between ca. 727 and his death in 768. Cosmas was the first residential Chalcedonian (Melkite) patriarch to be established in Alexandria following the Muslim conquest of Egypt in the 640s. The see had remained vacant since, but Cosmas was appointed with the consent of both the Umayyad Caliph and the Byzantine Emperor. The chronicler Theophanes the Confessor reports that in 742/3, he abjured Monotheletism, the dominant doctrine among Alexandrian Melkites since it had been promulgated by Emperor Heraclius. As Cosmas himself was most likely