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
Ptolemy Philadelphus (son of Cleopatra) Ptolemy Philadelphus (son of Cleopatra) Ptolemy Philadelphus (, "Ptolemy the brother-loving", August/September 36 BC – 29 BC) was a Ptolemaic prince and was the youngest and fourth child of Greek Ptolemaic Queen Cleopatra VII of Egypt, and her third with Roman Triumvir Mark Antony. Ptolemy was of Greek and Roman heritage. He was born in Antioch, Syria (now a part of modern Turkey). Ptolemy was named after the original Ptolemy II Philadelphus (the second Pharaoh of the Ptolemaic dynasty) and Cleopatra's intention was recreating the former Ptolemaic Kingdom. In late 34 BC, at the Donations of Alexandria, Ptolemy was made