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the Kingdom of Babylonia,
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which is the most powerful one in the Tigris Euphrates Valley,
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what is now Iraq,
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the Kingdom of Lydia occupying
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sort of the western portion of Asia Minor,
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excluding at first the coast,which was occupied by Greeks,
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but which the Lydians then conquered the Greeks in the 540s--
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that's the picture.
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Then there is the people of Persia,
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the Persians themselves who are of not much account.
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But when Cyrus becomes King in 559
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he is a member of the dynasty which is the Achaemenid Dynasty,