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
Political and military events in Scotland during the reign of David I of Scotland and England", a title which acknowledged the new Scoto-Northumbrian identity of David's realm. Political and military events in Scotland during the reign of David I Political and military events in Scotland during the reign of David I are the events which took place in Scotland during David I of Scotland's reign as King of Scots, from 1124 to 1153. When his brother Alexander I of Scotland died in 1124, David chose, with the backing of Henry I of England, to take the Kingdom of Alba for himself. David was forced to engage in warfare against his rival and