Hebrews 7:15-28: "15 This becomes even more evident when another priest arises in the likeness of Melchizedek, 16 who has become a priest, not on the basis of a legal requirement concerning bodily descent, but by the power of an indestructible life. 17 For it is witnessed of him, 'You are a priest forever, after the order of Melchizedek.' 18 For on the one hand, a former commandment is set aside because of its weakness and uselessness 19 (for the law made nothing perfect); but on the other hand, a better hope is introduced, through which we draw near to God.
"20 And it was not without an oath. For those who formerly became priests were made such without an oath, 21 but this one was made a priest with an oath by the one who aid to him: 'The Lord has sworn and will not change his mind, "You are a priest forever."' 22 This makes Jesus the guarantor of a better covenant.
"23 The former priests were many in number, because they were prevented by death from continuing in office, 24 but he holds his priesthood permanently, because he continues forever. 25 Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.
"26 For it was indeed fitting that we should have such a high priest, holy, innocent, unstained, separated from sinners, and exalted above the heavens. 27 He has no need, like those high priests, to offer sacrifices daily, first for his own sins and then for those of the people, since he did this once for all when he offered up himself. 28 For the law appoints men in their weakness as high priests, but the word of the oath, which came later than the law, appoints a Son who has been made perfect forever."
Hebrews 9:11-15: "11 But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) 12 he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption. 13 For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, 14 how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God.
"15 Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant."
Hebrews 10:19-23: "19 Therefore, brothers, since we have confidence to enter the holy places by the blood of Jesus, 20 by the new and living way that he opened for us through the curtain, that is, through his flesh, 21 and since we have a great priest over the house of God, 22 let us draw near with a true heart in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodies washed with pure water. 23 Let us hold fast the confession of our hope without wavering, for he who promised is faithful."
Hebrews 4:14-16: "14 Since then we have a great high priest who has passed through the heavens, Jesus, the Son of God, let us hold fast our confession. 15 For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin. 16 Let us then with confidence draw near to the throne of grace, that we may receive mercy and find grace to help in time of need."
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The passages cited from Hebrews appear in this same order in the hymn. 7:15-28 appears in the second verse, particularly in the lines "'A priest forevermore,' / An oath God would not break, / 'A priest within the order of / Melchizedek.'" 9:11-15 is in the third verse, specifically "He shed a blood, unlike the blood / Of goat or calf." 10:19-23 seems to appear from the end of the third verse through the fifth verse, and 4:14-16 is in both the fifth and sixth verses.
The first verse, however, seems to come from the end of Ephesians 1. "Christ sits at God's right hand, / His saving work complete" from part of verse 20: "when he raised him from the dead and seated him at his right hand in the heavenly places," and "To reign till ev'ry foe will lie / Beneath His feet" from verses 21-22: "far above all rule and authority and power and dominion, and above every name that is named, not only in this age but also in the one to come. 22 And he put all things under his feet and gave him as head over all things to the church."