When the Lamb takes the book, the angels sing a new song, a song of kingship (Revelation 5:8-10). In it, the sum up the work of the Lamb in a triadic formula that expands to a quaternity.

The Lamb 1) was slain 2) to purchase for God from every tribe, tongue, people, and nation and, having purchased, 3) to make them kingdom and priests. The subject shifts in the final clause of verse 10: It is a statement not about the Lamb but about the purchased ones who 4) reign upon the earth.

It's a neatly triune formulation. The Lamb is the subject of a threefold sequence, both passion (was slain) and action (purchase and make). The triadic structure itself suggests that the Lamb's work is a prism through which the Trinity shines. And that structural hint is evident in the substance of the statements, which match the three Persons.

1) Clearly, the Son, the Lamb, was the one slain.

2) He was slain to purchase a people for God, the Father.

3) Jesus makes a kingdom and priests, but we know from elsewhere in the New Testament that He makes this royal priesthood through His Spirit.

The passion and action are the Lamb's, but His work is directed toward or in concert with His Father and His Spirit. It's significant that this summary of redemption doesn't end with the purchase. What the Lamb purchases He transforms, making them into a kingdom and priests.

Even that full triadic sequence doesn't reach the telos of the Lamb's work. The passion and action of the Lamb, as the action and passion of the Triune God, is fulfilled in a fourth, in the reign of the saints on earth. Jonathan Edwards said that God created the world to provide a Bride for His Son, to bring her into the Triune family. We might say here that the Lamb died and rose again to share the Triune throne with the people of God. The Lamb was slain, purchased, and made in order to form a human fourth who would enter into the enthronement of the Trinity.