Rev 13:1 "having seven heads and ten horns"
The Horns are upcoming nations.
And the ten horns out of this kingdom are ten kings that shall arise. (Dan 7:24)
And the ten horns which thou sawest are ten kings, which have received no kingdom as yet. (Rev 17:12)
Ostrogoths
Heruli
Vandals
Visigoths (Spain)
Franks (France)
Suevi (Portugal)
Burgundians (Switzerland)
Anglo-Saxons (Britian)
Lombards (Italy)
Huns or Alemani (Germany)
This gives a good time frame of when we see this Beast.
With the ten horns on this Beast this is sometime after the Kingdom has split.
The ten crowns because the kingdom would be split into different nations.
Satan could now work through the different kingdoms under it.
And yes in Daniel three horns were uprooted but we must also note that 10 is also a symbol for Complete or Entire.
So the entire kingdom of Rome would give homage unto the Beast.