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 Telmessos, as he ruled from 206 BC to until at least 181 BC. According to surviving inscriptions at Telmessos, Ptolemy II didn’t seem to have a royal title nor it is clear his relationship with the Pharaohs in Alexandria. It seems likely that his family had relative autonomy from Ptolemaic control increased. As Ptolemaic power declined rapidly and dramatically outside of Egypt after the death of Ptolemy III Euergetes in 222 BC, probably Ptolemy II’s father with his family had the motive and opportunity for divorcing themselves from Ptolemaic suzerainty. At an unknown date during his father’s reign, Lysimachus with