Eurynome is an Okeanid, i.e. she is one of the three thousand daughters of Okeanos (Ocean) and Tethys. (Theogony, line 358)
Eurynome and Zeus are the parents of the three Graces: Euphrosyne, Aglaia and Thalia (Theogony, line 907). Eurynome and her consort, Ophion, were the first to occupy Mount Olympos (Olympus) but returned to the sea after they were forced off the mountain by the Titans, Kronos (Cronos) and Rheia (Rhea).
Eurynome and the Nereid, Thetis, earned the eternal gratitude of the smith of the gods, Hephaistos (Hephaestus), when they cared for him after he had been ejected from Mount Olympos. After a violent dispute with Hera, Zeus threw Hephaistos from Mount Olympos and he landed halfway across the Aegean Sea on the island of Lemnos. After finding the abandoned young god, Eurynome and Thetis cared for him but the terrible fall had injured Hephaistos’ legs and left him permanently lame. The two goddesses nursed and raised Hephaistos in secret. They provided him with a cave where he could practice and perfect his craft until, after nine years, he returned to Mount Olympos to rejoin his mother and take his rightful place among the Olympians.
The line numbers listed here correspond fairly well with the Lattimore and Murray/Wyatt translations of The Iliad. Other translations (Fitzgerald, Fagles et al) do not correspond as well but, with a small amount of effort, you should be able to find the reference you need regardless of the translation you use. Lattimore (ISBN 0226469409); A.T. Murray/William F. Wyatt Vol. I & II (ISBN 0674995791 and 0674995805); Robert Fitzgerald (ISBN 0374529051); Robert Fagles (ISBN 0140275363)
