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Constantine never had a thing to do with the "eastern" empire or the "western" empire. He moved the capital of the Roman empire to the eastern city of Constantinople. The connotation of eastern and western was not made by the ancients, but is a term invented by historians to clarify the part of the empire they would be writing about. The ancients considered the empire one, and they all considered themselves Roman.
Tsar Peter the Great built St. Petersburg from scratch on land taken from the Swedes. Even before it was completed, Peter moved his court from Moscow to St. Petersburg making it the capital of the Russian Empire until after the 1917 October Revolution.
Tsar Peter I (the Great) conceived and built St.Petersburg, thumbing his nose at the Swedes, and moved his capital there when St.Petersburg was finished in 1712. He named it for his patron saint, St.Peter, it was not a mark of vanity on his part. After the October Revolution in 1917, Vladimir Lenin moved the capital back to Moscow.
Initially, it was Rome. The capital was moved by Emperor Constantine to Constantople (modern Istanbul) for strategic reasons: it was more easily defended. He named it Nova Roma; it was named after Constantine following his death.
Baghdad.
At first it was Baghdad, but later I believe the capital was moved to Damascus.
The first Islam State Capital was Medina, then Damascus, then Baghdad. Never Mecca was an Islamic state capital although Mecca is the most sacred Islamic city.
Baghdad, Iraq was the capital of the Abbassid Caliphate, which was largest and most powerful Islamic Empire at that time (of the several that existed). Córdoba, Spain was the capital of the Umayyad Caliphate and Fez, Morocco was the capital of the Idrissid Caliphate.
The Abbasids moved their capital to Baghdad because they wanted to move it closer to Damascus during the time when Umayyad's capital was Damascus. In which means that the Abbasid empire wants to overthrow the Umayyad empire.
The Abbassid Caliphate capital was moved to BAGHDAD, IRAQ, because Syria had an Umayyad power-base and Baghdad was much closer to Persia, which was the Abbassid power-base.
The Abbasid Dynasty
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After the capital of the Roman Empire was moved to Constantinople, the Empire lasted over 1000 years.
The Abbassids moved their capital to Baghdad because their base of support was among the Persians and Mesopotamian Arabs (as opposed to Damascus, which was the base of support for their Umayyad rivals).
To end the power of the caliph, which is the Islamic religious or political leader of Islam.
THEBES