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
Piri Reis map Alexandria, Ptolemy I, who ruled Alexandria in the 4th century BC, and Claudius Ptolemy, the Greek geographer and cartographer who lived in Alexandria during the 2nd century AD. Gregory McIntosh states "Arab writers often confused Claudius Ptolemy, the geographer of the second century C.E., with Ptolemy I, one of Alexander's generals... Piri Reis has undoubtedly made the same error, resulting in his believing the charts and maps were from the time of Ptolemy I instead of Claudius Ptolemy." The map was discovered serendipitously on 9 October 1929, through the philological work of the German theologian Gustav Adolf Deissmann (1866–1937). He