The iron legs of the statue in Daniel chapter 2, the fourth unnamed beast of Daniel 7 and the unnamed beast of Revelation 13 are all the same and represent the Roman Empire at different stages of its future history.
It is clear from Daniel chapter 2 that from the time of the Babylonian kingdom until the Second Coming of Christ and the establishment of the Kingdom of God/ World Government, there are only 4 Empires that affect Jerusalem during the time of Israel/Judea. (The Ottoman Empire was during the Gentile period [see Luke 21:24] when the Jews were not a nation there).These are the Babylonian, Medo-Persian, Greek and the Roman Empires.
[Some say that it is the First Coming of Jesus that is depicted as the Stone that came during the Roman Empire. If this is true, then the 13th and 17th chapters of Revelation are irrelevant in 98-99 AD and also now].
There are some differences in the 4th beast from the time when Daniel saw it into the future in the 6th century BC to when John saw the same into the future in the 1st century AD; quite naturally because Rome was to progress in history into the future during that time.
Now it has 7 heads and 10 horns.
The 7 heads are:
1 Head of the Babylon area that was absorbed into the Roman Empire;
1 Head of the Medo-Persian area absorbed;
4 Heads of the divided Greek empire that happened after the death of Alexander the Great (Daniel 8:8). These were Seleucus (over Syria), Lysimachus, Ptolemy (Egypt) and Cassander. All absorbed into the Roman Empire.
1 Head of the Roman Empire.
So, 1 + 1 + 4 + 1 = 7 (This is what Rev 13:2 says).
The dragon is, of course, Satan who gives its power to this political kingdom. “And the great dragon was cast out, the old serpent (the one who deceived Eve in the Garden) being called devil, and, Satan” (Rev 12:9).
The Roman Empire was very famous for its war making ability. This is why “all the earth wondered after the beast” (Rev 13:3) “saying, Who is like the beast; who is able to make war with it?” (verse 4).
When John saw the beast, one of its heads (this is the 7th Roman head) was wounded to death (verse 3). This is the fall of the western Roman Empire in Rome in AD 476. (Historians mark the end of the Ancient History here). Rome continued only in the eastern Roman Empire centered in Byzantium .
This “deadly wound was healed” (verse 3) when Emperor Justinian from Byzantium recaptured Rome in AD535. This is known in history as ‘The Imperial Restoration’.
The 10 horns are to continue one after the other in the very seat of the Roman Empire, that is, Europe until the Second Coming of Christ.
(I would dare say that the 9th horn was the Hitler-Mussolini Axis Power that culminated in the Second World War; 8th horn being the Napoleon’s European Empire).