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
Reign of Cleopatra could be classified as Greeks if they abandoned their original cultures, received a Greek education, labeled their gods and goddesses with Greek names, and embraced the Greek lifestyle. Native Egyptians had been largely excluded from serving in the military by the reign of Ptolemy II, replaced by Greek and Jewish landholders called cleruchs. By the reign of Ptolemy IV in the late 3rd century BC they were reintroduced as phalangite soldiers. Large migrations of Greeks to Egypt ceased by the 2nd century BC, so that the Greek minority in Ptolemaic Egypt remained demographically small. Although Egyptian priests were often wealthy