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 II of Telmessos of Antipater. Ptolemy II was born and raised in Telmessos in Lycia at an unknown date during his father’s reign of Telmessos. His father Lysimachus ruled as the Ptolemaic Client King of Telmessos from February 240 BC until his death in 206 BC. Little is known on his early life prior to succeeding his father. When his father died in 206 BC, Ptolemy II became the fourth and final ruler from the Lysimachid dynasty, which is also known as the Ptolemaic/Lysimachid dynasty in Lycia to rule the city. Ptolemy II also, was the third and final Ptolemaic Client King of