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Fausset's Bible Dictionary
1. One of Lamech's (See ; see ZILLAH) wives (Genesis 4:19).
2. Daughter of Elon the Hittite; one of Esau's three wives; mother of his firstborn, Eliphaz; ancestress of six of the Edomite tribes (Genesis 36:2-4; (Genesis 36:15-16); called Βashemath (Genesis 26:34), ("the fragrant"). Esau's third wife, daughter of Ishmael, also is called Bashemath, but Mahalath in Genesis 28:9. Moses drew the genealogy from documents of Esau's tribe, without altering them. Eastern and especially Arabian custom gives surnames (founded on some memorable event in one's life), which gradually supersede the other name; for instance, Edom, Genesis 25:30. Women received new names when married; so both might be called Bashemath.
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Fausset, Andrew R. Entry for 'Adah'. Fausset's Bible Dictionary. https://www.studylight.org/dictionaries/eng/fbd/a/adah.html. 1949.