The Ten Horns of Daniel's Fourth Beast and the Beast(s) of the Apocalypse
Old Testament: Daniel 7:7, 20, 24
...a fourth beast, terrible and wonderful, and exceeding strong, it had great iron teeth, eating and breaking in pieces, and treading down the rest with its feet: and it was unlike to the other beasts which I had seen before it, and had ten horns... concerning the other that came up, before which three horns fell: and of that horn that had eyes, and a mouth speaking great things, and was greater than the rest... the ten horns of the same kingdom, shall be ten kings: and another shall rise up after them, and he shall be mightier than the former, and he shall bring down three kings.
New Testament: Apocalypse 12:3; Apocalypse 13:1; Apocalypse 17:3, 7, 12, 16-17
...a great red dragon, having seven heads and ten horns: and on his heads seven diadems... a beast coming up out of the sea, having seven heads and ten horns: and upon his horns, ten diadems... a woman sitting upon a scarlet coloured beast... having seven heads and ten horns... the ten horns which thou sawest are ten kings, who have not yet received a kingdom: but shall receive power as kings, one hour after the beast... these shall hate the harlot and shall make her desolate and naked and shall eat her flesh and shall burn her with fire... For God hath given into their hearts to do that which pleaseth him: that they give their kingdom to the beast, till the words of God be fulfilled.
The connection
John doesn't borrow Daniel's image once; he returns to it three separate times across his whole vision, turning the same figure to catch different angles of light. The dragon of chapter 12 shows what stands behind it, the seven diadems still on the heads, the raw source of the power. The beast of chapter 13 shows what it becomes in history, the diadems have migrated to the horns now, ten kings actually wielding delegated authority. The scarlet beast of chapter 17 shows what it is finally used for, carrying the harlot, propping up a corrupt system that trades on its violence. Daniel supplies the shape for all three: one terrible kingdom, ten horns rising from it, and among them a further power that subdues its own. Daniel's little horn "shall bring down three kings" from within its own alliance (Daniel 7:24). John's ten horns go further: they don't just subdue a few of their own number, they turn on the very harlot they were carrying and devour her outright, "shall hate the harlot... and shall eat her flesh, and shall burn her with fire" (Apocalypse 17:16). Every worldly alliance built on this pattern is shown, twice, to be structurally unstable, power granted only to be turned, sooner or later, against whatever it was first granted to serve.
Moral sense
The ten kings "receive power... one hour" (Apocalypse 17:12), a deliberately brief span. Loyalty bought by shared spoils lasts only as long as the spoils do; the horns turn on the harlot the moment serving her stops paying. Nothing built on that foundation, in an empire or in a single soul, was ever going to hold.
Anagogical sense
Even this collapse is not outside the plan: "God hath given into their hearts to do that which pleaseth him: that they give their kingdom to the beast, till the words of God be fulfilled" (Apocalypse 17:17). The self-devouring of worldly power is not chaos escaping God's hand; it is, however strange to say, one of the instruments by which His word is being fulfilled on schedule.
The Fathers
Hippolytus, Treatise on Christ and Antichrist. Sections 25-28 read Daniel's ten horns as "the kingdoms that are yet to rise" with "the other little horn that grows up among them" as Antichrist; sections 36-42 extensively quote Apocalypse 17-18's scarlet beast and harlot as depicting the same reality from a later vantage. He does not fuse the citations into a single sentence, but the whole treatise is built on reading Daniel and the Apocalypse as one continuous prophecy. St Irenaeus, Against Heresies, Book 5, ch. 26, makes the fusion explicit: John "teaches us what the ten horns shall be which were seen by Daniel", quoting Apocalypse 17:12; the one to come "shall slay three, and subject the remainder to his power", and the kings "shall lay Babylon waste, and burn her with fire", so a Father writing before Hippolytus already reads Daniel's horns and John's beast as one prophecy. St Jerome, Commentary on Daniel, on Daniel 7:8, follows "the traditional interpretation of all the commentators of the Christian Church" that ten kings will divide the Roman world and an eleventh "will overcome three of the ten kings", after which the other seven bow to him.
Warrant
Checked in the Greek, and the beast is described in shared vocabulary throughout: deka and kerata at Daniel 7:7 and 7:20 in the Septuagint and at Apocalypse 12:3 and 13:1, therion across Daniel 7:7 and Apocalypse 13:1 and 17:3, and basileis across Daniel 7:24 and Apocalypse 17:12. The ten, the horns, the beast and the kings are one vocabulary.
Catechism of the Catholic Church, paragraph 675.
The verses
Daniel 7:7 · Daniel 7:20 · Daniel 7:24 · Apocalypse 12:3 · Apocalypse 13:1 · Apocalypse 17:3 · Apocalypse 17:7 · Apocalypse 17:12 · Apocalypse 17:16 · Apocalypse 17:17