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What is added in this verse is that the woman is riding the beast (Revelation 13:1-4). This is a position of control, much like the rider of a horse, and this woman is identified as "MYSTERY, BABYLON THE GREAT." For her to be riding the beast, there must be at least some relationship between the two, because after all, this beast is pretty wild. In fact, each—the woman and the beast—is part of the same general system—the Babylonish system. Remember, Babylon became a worldwide, anti-God system. The Greek word for this is cosmos, meaning an orderly system that is against God. Both the woman and the beast are part of that same system, but they are obviously separate and different, yet having a relationship within the system.
God clearly reveals two distinctly different aspects, applications, or approaches within the Babylonish system, and the woman and the beast represent these. The beast is depicted in Revelation 13:2 as consisting of the strongest parts of a leopard, a bear, and a lion. Each of these beasts is unarguably wild, and each one, on its own, is a very powerful animal that a woman on her own would be no match for.
A human approach to life and its events would certainly be different than a bestial approach, and this "human" way is represented by the woman. We see in Revelation 17 that the woman, who would appear on the surface to be the weaker, is riding the beast—the seemingly super-powerful beast. She, at the point of time in which the prophecy is shown here, is superior, greater, more powerful and influential than the beast.
John W. Ritenbaugh
Where Is the Beast? (Part 4)