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Coeus was an obscure figure, and like most of the Titans he played no active part in Greek mythology—he appears only in lists of Titans—but was primarily important for his descendants. With his sister, "shining" Phoebe, Coeus fathered two daughters, Leto and Asteria. Leto copulated with Zeus (the son of fellow Titans Cronus and Rhea) and bore Artemis and Apollo. Asteria became the mother of Hecate by Perses (son of fellow Titan Crius and half-sister Eurybia).
Along with the other Titans, Coeus was overthrown by Zeus and the other Olympians in the Titanomachy. Afterwards, he and all his brothers (sans Oceanus) were imprisoned in Tartarus by Zeus. Coeus, later overcome with madness, broke free from his bonds and attempted to escape his imprisonment, but was repelled by Cerberus.
Tacitus wrote that Coeus was the first inhabitant of the island of Kos, which claimed to be the birthplace of his daughter Leto. Coeus's name was modified from Κοῖος (Koîos) to Κῶιος (Kōios), leading to his association with the island.
Eventually Zeus freed the Titans, presumably including Coeus.
Ovid in Metamorphoses (VI.185) alludes to Coeus' obscure nature: "Latona, that Titaness whom Coeus sired, whoever he may be." (nescio quoque audete satam Titanida Coeo): M. L. West, in "Hesiod's Titans" (The Journal of Hellenic Studies105 ) remarks that Phoibe's "consort Koios is an even more obscure quantity. Perhaps he too had originally to with Delphic divination", and he suspects that Phoebe, Koios and Themis were Delphic additions to the list of Titanes, drawn from various archaic sources.
Hesiod included among his descendants Hekate, daughter of Asteriē, as Apostolos N. Athanassakis, noted, correcting the OCD, noted (Athanassakis, "Hekate Is Not the Daughter of Koios and Phoibe" The Classical World71.2 ); R. Renehan expanded the note in "Hekate, H. J. Rose, and C. M. Bowra", The Classical World,73.5 (February 1980:302–304).
Although usually the daughter of Hyperion and Theia, as in Hesiod, Theogony371–374, in the Homeric Hymn to Hermes (4), 99–100, Selene is instead made the daughter of Pallas the son of Megamedes.
Gaius Valerius Flaccus, Argonautica translated by Mozley, J H. Loeb Classical Library Volume 286. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1928. Online version at theoi.com.
Tacitus, Complete Works of Tacitus. Tacitus. Alfred John Church. William Jackson Brodribb. Sara Bryant. edited for Perseus. New York. : Random House, Inc. Random House, Inc. reprinted 1942. Online text available at Perseus.tufts.
The Hymns of Orpheus. Translated by Taylor, Thomas (1792). University of Pennsylvania Press, 1999. Online version at theoi.com