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
Library of Alexandria scrolls in its collection, so, during the reign of Ptolemy III Euergetes, it opened a satellite collection in the Serapeum of Alexandria, a temple to the Greco-Egyptian god Serapis located near the royal palace. Aristophanes of Byzantium (lived 257– 180 BC) became the fourth head librarian sometime around 200 BC. According to a legend recorded by the Roman writer Vitruvius, Aristophanes was one of seven judges appointed for a poetry competition hosted by Ptolemy III Euergetes. All six of the other judges favored one competitor, but Aristophanes favored the one whom the audience had liked the least. Aristophanes declared that