10:38 live by faith. This is the last of the three quotations in the New Testament of Habakkuk 2:4 (see Romans 1:17; Galatians 3:11).
10:39 believe. “Believe” here is the same as “have faith.” The emphasis throughout Hebrews 11 on “faith” is simply a recital of the outworking of the faith introduced into the discussion here in Hebrews 10:38-39 (there were no chapter divisions in the original manuscript). Thus the working faith of Hebrews 11 is the living faith of Hebrews 10:38 and the saving faith of Hebrews 10:39, and that faith must be exercised first of all on the creation as the work of God (Hebrews 11:3).