N2 p1297 to He. 8.8.  “I. The Eight Covenants Summary: [This is all copied in The New Covenant file.] “I. The Eight Covenants, Summary: (1) The Edenic Covenant Cmt. on Ge 1:26conditioned the life of man in innocency. (2) The Adamic Covenant Cmt. on Ge 3:14 conditions the life of fallen man and gives promise of a Redeemer. (3) The Noahic Covenant Cmt. on Ge 9:1. establishes the principle of human government. (4) The Abrahamic Covenant Cmt. on Ge 15:18 founds the nation of Israel, and confirms, with specific additions, the Adamic promise of redemption. (5) The Mosaic Covenant Cmt. on Ex 19:25. condemns all men, ‘for that all have sinned.’ (6) The Palestinian Covenant Cmt. on De 30:3 secures the final restoration and conversion of Israel. (7) The Davidic Covenant Cmt. on 2Sa 7:16 establishes the perpetuity of the Davidic family (fulfilled in Christ, Mt 1:1; Lu 1:31-33; Ro 1:3 and of the Davidic kingdom, over Israel, and over the whole earth; to be fulfilled in and by Christ 2Sa 7:8-17; Zec 12:8; Lu 1:31-33; Ac 15:14-17; 1Co 15:24. (8) The New covenant rests upon the sacrifice of Christ, and secures the eternal blessedness, under the Abrahamic Covenant Ga 3:13-29 of all who believe. It is absolutely unconditional, and, since no responsibility is by it committed to man, it is final and irreversible.
“II. The relation of Christ to the eight covenants is as follows: (1) To the Edenic Covenant, Christ, as the ‘second Man,’ the ‘last Adam’ 1Co 15:45-47 takes the place over all things which the first Adam lost Col 2:10; Heb 2:7-8. (2) He is the ‘Seed of the woman’ of the Adamic Covenant Ge 3:15; Joh 12:31; 1Jo 3:8; Ga 4:4; Re 20:10 and fulfilled its conditions of toil Mr 6:3 and obedience. (3) As the greatest son of Shem, in Him was fulfilled supremely the promise to Shem in the Noahic Covenant. Col 2:9. (4) He is the “Seed to whom the promises were made” in the Abrahamic Covenant; the son of Abraham obedient unto death Ge 22:18; Ga 3:16; Php 2:8. (5) He lived sinlessly under the Mosaic covenant and bore for us its curse. Ga 3:10-13. (6) He lived obediently as a Jew in the land under the Palestinian Covenant, and will yet perform it gracious promises De 28:1-30:9. (7) He is the ‘Seed,’ ‘Heir,’ and ‘King’ under the Davidic Covenant Mt 1:1; Lu 1:31-33. (8) His sacrifice is the foundation of the New Covenant Mt 26:28; 1Co 11:25.”

N1 p9 to Genesis 3.14. “The Adamic Covenant conditions the life of fallen man—conditions which must remain till, in the kingdom age, ‘the creation also shall be delivered from the bondage of corruption into the glorious liberty of the sons of God’ (Rom. 8.21). The elements of the Adamic Covenant are:
The serpent, Satan’s tool, is cursed (v.14), and becomes God’s illustration in nature of the effects of sin—from the most beautiful and subtle of creatures to a loathsome reptile? The deepest mystery of the atonement is intimated here. Christ, ‘made sin for us,’ in bearing our judgment, is typified by the brazen serpent (Nu. 21.5-9; John 3.14, 15; 2 Cor. 5.21). Brass  speaks of judgment—in the brazen altar, of God’s judgment, and in the laver, of self-judgment.
The first promise of a Redeemer (v.15). Here begins the ‘highway of the Seed,’ Abel, Seth, Noah (Gen. 6.8-10), Shen (Gen. 9.26, 27)), Abrahan (Gen. 12.1-4), Isaac (Gen. 17.19-21), Jacob (Gen. 28.10-14), Judah (Gen. 49.10), David (2 Sam. 7.5-17), Immanuel-Christ (Isa. 7.9-14; Mt. 1.1, 20-23; 1 John 3.8; John 12.31).
(1) The changed state of the woman (v16). In  three  particulars: (a) Multiplied conception; (b) motherhood linked with sorrow; (c) the headship of the man (cf. Gen. 1.26, 27). The entrance of sin, which  is disorder, makes necessary a  headship, and  it is vested in man (1 Tim. 2.11-14; Eph. 5.22-25; 1 Cor. 11.7-9)).
(2) The earth  cursed  (v17) for man’s sake. It is better for fallen man to battle with a reluctant earth than  to live without toil.
(3)The inevitable sorrow of life (v17).
(4)The light occupation of Eden (Gen. 2.15) changed to burdensome labour (vs. 18, 19).
(5)Physical death (v19; Rom. 5.12-21). See “Death (spiritual’ (Gen. 2.17; Eph. 2.5, note).

See, for the other seven covenants: Edenic, Gen. 1.28; Noahic, Gen. 9.1; Abrahamic, Gen. 15.18; Mosaic, Ex. 19.25; Palestinian, Deut. 30.3; Davidic, 2 Sam. 7.1-17; New, Heb. 8.8.

N1 p19 (* * * Israel was called to be a witness to the unity of God in the midst of universal idolatry (Deut. 6.4; Isa. 43.10-12); to illustrate the blessedness of serving the true God (Deut. 33.26-29); to receive and preserve the divine revelations (Rom. 3.1,2; Deut. 4.5-8); and to produce the Messiah (Gen. 3.15; 21.3; 28.10-14; 49.10; 2 Sam. 7.16, 17; Isa. 4.3, 4; Mt. 1.1.  The reader of scripture should hold firmly in mind: (1) that from Gen. 12. to Mt. 12.45 the Scriptures have primarily in view Israel, the little rill, not the great Gentile river, though again and again the universality of the ultimate divine intent breaks into view (e.g. Gen. 12.3; Isa. 2.2, 4; 5.26, 9.1, 2; 11.10-12; 42.1-6; 49.6, 12; 52.15; 54.3; 55.5; 60.3, 5, 11-16; 61.6, 9; 62.2; 66.12, 18, 19; Jer. 16.19; Joel 3, 9, 10; Mal. 1.11; Rom. 9., 10., 11.; Gal. 3.8-14); (2) that the human race, henceforth called Gentile in distinction from Israel, goes on under the Adamic and Noahic covenants; and that for the race (outside Israel) the dispensations of Conscience and Human Government continue. The moral history of the great Gentile world is told in Rom. 1.21-32, and its moral accountability in Rom. 2.1-16.  Conscience never acquits: it either “accuses” or “excuses.”  Where the law is known to the Gentiles it is to them, as to Israel, “a ministration  of death, “ a “curse” (Rom. 3.19.20; 7.9, 10; 2 Cor. 3.7; Gal. 3.10). A wholly new responsibility arises when either Jew or Gentile knows the Gospel (John 3.18, 19, 36; 15.22-24; 16.9; John 5.9-12).

N1 p263 to Joshua 5.2: “Circumcision is the “sign” of the Abrahamic Covenant Ge 17:7-14 Ro 4:11. “The reproach of Egypt” was that, during the later years of the Egyptian bondage, this separating sign had been neglected (cf. Ex 4:24-26 and this neglect had continued during the wilderness wanderings. The N.T. analogue is world conformity; the failure openly to take a believer’s place with Christ in death and resurrection. Ro 6:2-11; Ga 6:14-16. Spiritually it is mortifying the deeds of the body through the Spirit. Ro 8:13; Ga 5:16-17; Col 2:11; 3:5-10.”