<P> Besides these advanced philosophical works, Boethius is also reported to have translated important Greek texts for the topics of the quadrivium . His loose translation of Nicomachus's treatise on arithmetic (De institutione arithmetica libri duo) and his textbook 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 . </P> <P> 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 . </P> <P> In the Western Provinces (what today is considered the Western Europe's heartland), the collapsing Roman empire lost many Greek manuscripts which were not preserved by monasteries . However, due to the expense and dearth of writing materials, monastic scribes could recycle old parchments . The parchments could be reused after scraping off the ink of the old texts, and writing new books on the previously used parchment, creating what is called a palimpsest . Fortunately for modern scholars, the old writing can still be retrieved, and many extremely valuable works, which would have otherwise been lost, have been recovered in this way . As the language of Roman aristocrats and scholars, Greek died off along with the Roman Empire in the West, and by 500 CE, almost no one in Western Europe was able to read (or translate) Greek texts, and with the rise of the Islamic Empire, the west was further cut off from the language . After a while, only a few monasteries in the west had Greek works, and even fewer of them copied these works (mainly the Irish). Some Irish monks had been taught by Greek and Latin missionaries who probably had brought Greek texts with them . </P> <P> William of Moerbeke was one of the most prolific and influential translators of Greek philosophical texts in the middle half of the thirteenth century . Very little is known of William's life . He was born probably in 1215 in the village of Moerbeke, now in Belgium, and probably entered the Dominican priory in Leuven as a young man . Most of his surviving work was done during 1259 - 72 . </P>

Who saved much of the learning after the fall of the roman empire