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 Ptolemy Claudius Ptolemy (; , "Klaúdios Ptolemaîos" ; ; ) was a Greco-Roman mathematician, astronomer, geographer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, and held Roman citizenship. The 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou () in the Thebaid (). This attestation is quite late, however, and, according to Gerald Toomer, the translator of his "Almagest" into English, there is no reason to suppose he ever lived anywhere other than Alexandria. He died there around AD 168. Ptolemy wrote several scientific