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For the Greeks of Plato's time, as can be seen in Herodotus' Histories, IV, 42-45, Libya was the name of the third part of the known world, after Europe and Asia, that is, our modern Africa, or at least its northern part along the Mediterranean. Indeed, the Greek world was organized with the Mediterrranean in its center and split into three parts when rounding it :

• Europe from the Pillars of Heracles (today's Strait of Gibraltar) west all the way to the Phasis east, a river (today's Rion, in the Republic of Georgia) flowing from Caucasus down to the easternmost coast of the Euxine Pontus (today's Black Sea), including the countries along the northern coasts of the Mediterranean (Spain, France, Italy, Greece) and the countries north of the Black Sea (Thracia, Scythia and, further north, the half-mythical country of the Hyperboreans, whose name means "those who live past Boreus, the cold wind from north") ;
• Asia from the Phasis north to the Nile south, including the countries along the eastern coasts of the Mediterranean : Asia Minor, Syria and Egypt, and the countries further east ;
• Libya from the Nile east back to the Pillars of Heracles west, including the countries south of the Mediterranean, hardly known to the Greeks aside from Egypt, Cyrenaica and the Phoenician settlement of Carthage.

Libya owed its name to a daughter of Epaphus, a king of Tyre (or Sidon) and a son of Io and Zeus, born after Io, under the form of a white heifer, had fled Argos and reached the coast of Syria in the area that was to become the country of the Phoenicians. This daughter named Libya was loved by Poseidon from whom she had two sons, Agenor, the mythical hero of Phoenicia, and Belus, the mythical hero of Egypt. Agenor in turn was the father of Europa and her brothers Cadmus (the founder of the Greek Thebes), Phoenix (the eponym of Phoenicia), Cilix (the eponym of Cilicia and Thasus (the eponym of the island of Thasos), all of whom founded settlements and cities during their quest for their sister after she had been loved and abducted by Zeus taking the guise of a bull to become the mother of the Cretan king Minos. Belus, for his part, gave birth to Danaus and Egyptus, whose offspring returned to Argos.