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 Philadelphus and dissolute, intellectual and artificial, has been compared with the Palace of Versailles of Louis XIV of France. Ptolemy deified his parents and his sister-wife after their deaths. Ptolemy II began his reign as co-regent with his father, Ptolemy Soter, from c. 285 to c. 283 BCE, and maintained a splendid court in Alexandria. Egypt was involved in several wars during his reign. His maternal half-brother Magas had declared himself king of Cyrene in 276 and began a war against Ptolemy's government in 274 BCE. Magas managed to keep Cyrenaica independent of the Ptolemies until his death in 250 BCE.