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 god Serapis. Despite the widespread modern belief that the Library was "burned" once and cataclysmically destroyed, the Library actually declined gradually over the course of several centuries, starting with the purging of intellectuals from Alexandria in 145 BC during the reign of Ptolemy VIII Physcon, which resulted in Aristarchus of Samothrace, the head librarian, resigning from his position and exiling himself to Cyprus. Many other scholars, including Dionysius Thrax and Apollodorus of Athens, fled to other cities, where they continued teaching and conducting scholarship. The Library, or part of its collection, was accidentally burned by Julius Caesar during his civil