Parallel (geometry) as a pair of straight lines in a plane which do not meet appears as Definition 23 in Book I of Euclid's Elements. Alternative definitions were discussed by other Greeks, often as part of an attempt to prove the parallel postulate. Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein. Simplicius also mentions Posidonius' definition as well as its modification by the philosopher Aganis. At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary schools. The traditional treatment of geometry was being
Ptolemy II of Telmessos a paternal first cousin called Antipater Epigonos and likely he had a paternal second cousin called Epigonos. Through his father, Ptolemy II was a direct descendant of Lysimachus who was one of the Diadochi of the Greek King Alexander the Great who was King of Thrace, Asia Minor and Macedonia and Ptolemy I Soter another of the Diadochi of the Greek King Alexander the Great who was the founder of the Ptolemaic dynasty of Ancient Egypt and his wife, Berenice I of Egypt. Berenice I was the great-niece of the powerful Regent Antipater, through her maternal grandfather Cassander, the brother