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
Piri Reis map Alexandria, Ptolemy I, who ruled Alexandria in the 4th century BC, and Claudius Ptolemy, the Greek geographer and cartographer who lived in Alexandria during the 2nd century AD. Gregory McIntosh states "Arab writers often confused Claudius Ptolemy, the geographer of the second century C.E., with Ptolemy I, one of Alexander's generals... Piri Reis has undoubtedly made the same error, resulting in his believing the charts and maps were from the time of Ptolemy I instead of Claudius Ptolemy." The map was discovered serendipitously on 9 October 1929, through the philological work of the German theologian Gustav Adolf Deissmann (1866–1937). He