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
Reign of Cleopatra Reign of Cleopatra The reign of Cleopatra VII of the Ptolemaic Kingdom of Egypt began with the death of her father, the ruling pharaoh Ptolemy XII Auletes, by March 51 BC. It ended with her death on 10 or 12 August 30 BC. Following the reign of Cleopatra, the country of Egypt was transformed into a province of the Roman Empire and the Hellenistic period came to an end. During her reign she ruled Egypt and other territories as an absolute monarch, in the tradition of the Ptolemaic dynasty's founder Ptolemy I Soter (r. 305–283 BC) as well as Alexander