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 Ptolemy II Philadelphus Ptolemy II Philadelphus (, "Ptolemaîos Philádelphos" "Ptolemy, lover of his sister"; 308/9–246 BCE) was the king of Ptolemaic Egypt from 283 to 246 BCE. He was the son of Ptolemy I Soter, the Macedonian Greek general of Alexander the Great who founded the Ptolemaic Kingdom after the death of Alexander, and queen Berenice I, originally from Macedon in northern Greece. During Ptolemy II's reign, the material and literary splendour of the Alexandrian court was at its height. He promoted the Museum and Library of Alexandria. He erected a commemorative stele, the Great Mendes Stela. He also led