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 I Soter Ptolemy I Soter Ptolemy I Soter (; , "Ptolemaĩos Sōtḗr" "Ptolemy the Savior"; c. 367 BC – January 282 BC) was a companion and historian of Alexander the Great who succeeded to his empire. Ptolemy became ruler of Egypt (323–282 BC) and founded the Ptolemaic dynasty which ruled it for the next three centuries, turning Egypt into a Hellenistic kingdom and Alexandria into a center of Greek culture. Ptolemy was the son of Arsinoe of Macedon by either her husband Lagus or Philip II of Macedon, the father of Alexander. Ptolemy was one of Alexander's most trusted companions and military