Schizm,
Surely the 'little horn' of Daniel 7 must be the same as the 'little horn' of Daniel 8?
And out of one of them there came forth another horn, a small one [Rome]
This horn comes out of one of the four horns on the Greek male goat. These four horns were the Empires set up after the death of Alexander, including the Seleucid and Ptolemaic Empires. The 'little horn' cannot be Rome simply because Rome did not come out of the Greek Empire and can hardly be described as 'small'.
whereas the little horn of Daniel 7 arises after Rome has ruled
A common mistake is to think Daniel says anything about Rome at all. What is the last Empire actually named in the book of Daniel? It's Greece. (Daniel 11). The 'king of the north' and 'king of the south' also come out of this divided Greek Empire.
Most people know what Rome did to Jerusalem and its temple in 70.
It's a shame not as many people know what Seleucid King Antiochus IV Epiphanes did to the temple in 167 BC.(1 Maccabees 1:57)
CF.