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 (name) Ptolemy (name) The name Ptolemy or Ptolemaeus may refer to: Ptolemy, or Ptolemaeus, or Tolomeo (Italian spelling) may also refer to: According to Georg Autenrieth, the English name Ptolemy comes from the Ancient Greek name Πτολεμαῖος ("Ptolemaios"), "warlike" or "son of war". Autienrieth renders the meaning of the name to be an adjective from πτόλεμος ("ptólemos"), explained as a Homeric Greek form of πόλεμος ("pólemos"), "war". A nephew of Antigonus I Monophthalmus was called "Polemaeus", the normal form of the adjective. "Ptolemaios" is first attested in Homer's Iliad and is the name of an Achaean warrior, son of Piraeus, father