Genealogy - Vine's Expository Dictionary of New Testament Words
Genealogy[ A-1,Noun,G1076, genealogia ]
is used in 1 Timothy 1:4; Titus 3:9, with reference to such genealogies" as are found in Philo, Josephus and the book of Jubilees, by which Jews traced their descent from the patriarchs and their families, and perhaps also to Gnostic "genealogies" and orders of aeons and spirits. Amongst the Greeks, as well as other nations, mythological stories gathered round the birth and "genealogy" of their heroes. Probably Jewish "genealogical" tales crept into Christian communities. Hence the warnings to Timothy and Titus.
[ B-1,Verb,G1075, genealogeo ]
"to reckon or trace a genealogy" (from genea, "a race," and lego, "to choose, pick out"), is used, in the Passive Voice, of Melchizedek in Hebrews 7:6, RV, "whose genealogy (AV, 'descent') is not counted."
[ C-1,Adjective (negative),G35, agenealogetos ]
denoting "without recorded pedigree" (a, negative, and an adjectival form from B), is rendered "without genealogy" in Hebrews 7:3. The narrative in Gen. 14 is so framed in facts and omissions as to foreshadow the person of Christ.