Genealogy...traced (1075) (genealogeo from genea [from ginomai = to become] = a generation, a race, posterity, that which has been begotten + lego = to choose, to pick out, to reckon) means to reckon or trace a genealogy or ancestry. The only other use of genealogeo in Scripture is in the Septuagint (LXX)... 1 Chronicles 5:1 Now the sons of Reuben the first-born of Israel (for he was the first-born, but because he defiled his father's bed, his birthright was given to the sons of Joseph the son of Israel; so that he is not enrolled in the genealogy (Hebrew = yachas = to reckon genealogically ; Lxx = genealogeo) according to the birthright. The one whose genealogy is not traced from them - More literally this reads "he who is not genealogically derived from them". Obviously, this description refers to Melchizedek who was not a descendant of Abraham. In this verse the writer substantiates the fact that the Melchizedekian priesthood and thus Christ's priesthood is superior to the Aaronic (Levitical) priesthood because Levi's great-grandfather Abraham paid tithes to Melchizedek and Levi, though as yet unborn, was involved in this transaction (see Hebrews 7:9 note). Obviously Levi was not born until many years after the event in Genesis 14 and yet as the Jews well knew Abraham was the father the Hebrew race. It follows that all twelve tribes including the tribe of Levi (and the priestly family) were represented in Abraham in Genesis 14 when he recognized the superiority of Melchizedek by paying a tenth to him and receiving Melchizedek's priestly blessing. And as he goes on to state in the next verse no one disputes the fact that "the lesser is blessed by the greater". Thus in this dual manner the surpassing greatness of the royal priesthood of Melchizedek is emphasized.