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 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