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 X Alexander I throne, and replacing the former sarcophagus with one made of glass. The citizens of Alexandria were so outraged at this act that they exiled him again almost immediately and attempted to wipe out all record of him. He would later be killed on his way to Cyprus. When Ptolemy X died, Ptolemy IX regained the throne. When Ptolemy IX died in 81 BC, Ptolemy X's wife Berenice III took over the throne for six months. Ptolemy X Alexander I Ptolemy X Alexander I (, "Ptolemaĩos Aléxandros") was King of Egypt from 110 BC to 109 BC and 107 BC till