Head of Assyria and head of the Northern kingdom of Israel, circa 790 B.C:
Isaiah 7:8-9
"For the head of Syria is Damascus, and the head of Damascus is (king) Rezin; and within sixty-five years Ephraim shall be broken so that it shall not be a people. And the head of Ephraim is Samaria, and the head of Samaria is Remaliah's son. If you will not believe, surely you shall not be established."
In Isaiah 7:8-9 (above) HEAD/S = the seat of power / authority.
Jesus called Satan
"the ruler of this world", and the apostle Paul called him
"the prince of the power of the air, the spirit that now works in the children of disobedience", who we are told
will give the beast of Revelation Chapter 13 his seat, power and great authority.
This is reflected in the crowns on the dragon's seven heads in Revelation 12:3, and on the horns of the ten kings in Revelation 13:1.
Seat of Satan, 1st century, A.D: Pergamon:
There was a temple to Zeus in Pergamon. Zeus-worship was widespread in the ancient world, the Roman Empire being no exception. Zeus was the ancient Greek god of the sky and thunder, who ruled as 'king of the gods' of Mount Olympus.
The Roman equivalent is Jupiter, who was chief deity of Roman state religion throughout the Republican and Imperial eras, until the spread of Christianity killed Zeus-worship.
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Revelation 13:3
And I saw one of his heads as it were wounded to death; and his deadly wound was healed: and all the world wondered after the beast.
The head of the Roman Empire was Rome, and the head of Rome was Caesar, the seat of the Roman Empire - yet Pargamon is called the seat / throne of Satan in Revelation 2:13, therefore since Zeus was the king of (all) the gods, we may want to look for another throne of the beast in the 1st century A.D, and in the Revelation.
Jesus tells the church at Pergamos:
"I know your works, and where you live, even where Satan's seat [Greek: thrónos] is. And you hold fast My name and have not denied My faith, even in those days in which Antipas was My faithful martyr, who was slain among you, where Satan dwells.
But I have a few things against you, because you have there those who hold the teachings of Balaam, who taught Balak to cast a stumbling-block before the sons of Israel, to eat things sacrificed to idols and to commit fornication.
So you also have those who hold the teaching of the Nicolaitans, which thing I hate.
Repent! But if not I will come to you quickly, and will fight with them by the sword of My mouth."
Seat of the beast, Revelation 13:1-4
And the beast which I saw was like a leopard, and its feet like those of a bear, and its mouth like the mouth of a lion. And the dragon gave him his power and his seat [Greek: thrónos] and great authority.
Seat of the beast, Revelation 16:10-11
And the fifth angel poured out his vial
on the throne [Greek: thrónos] of the beast, and its kingdom became darkened. And they gnawed their tongues from the pain. And they blasphemed the God of Heaven because of their pains and their sores. And they did not repent of their deeds.
Revelation 13:3
"And I saw one of his heads as it were wounded to death; and his deadly wound was healed: and all the world wondered after the beast."
Note: The seat / throne of Satan is the head of the beast.
Revelation 17
10 And there are seven kings; five have fallen, and one is, and the other has not yet come. And when he comes, he must continue a short time.
11 And the beast that was, and is not, even he is the eighth, and is of the seven, and goes into perdition.
12 And the ten horns which you saw are ten kings, who have received no kingdom yet, but
will receive authority as kings one hour with the beast.
13 These have one mind, and they will give their power and authority to the beast.
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Since the 8th king
is one of the seven, which head is it? The 6th or the 7th?
The 10 kings, who rule with the 8th king for "one hour",
had not yet received their kingdoms when John received the Revelation, so the ten kings are not the 6th head.
Therefore the beast ascending out of the abyss (i.e the 8th king) can only be the 7th head of the beast (since it is one of the seven).
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If we want to know where the throne of Satan / the beast is, We may want to look at what the saints in Pargamon were rebuked for, and at the fact that Jesus warned them to:
Repent! But if not I will come to you quickly, and will fight with them by the sword of My mouth.