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
History of Alexandria wealth and power of the Ptolemies, but also celebrated and affirmed Greekness. These processions were used to shout Greek superiority over any non-Greeks that were watching, thereby widening the divide between cultures. From this division arose much of the later turbulence, which began to manifest itself under the rule of Ptolemy Philopater (221–204 BC). The reign of Ptolemy VIII Physcon from 144–116 BC was marked by purges and civil warfare (including the expulsion of intellectuals such as Apollodorus of Athens), as well as intrigues associated with the king's wives and sons. Alexandria was also home to the largest Jewish community