Byzantium/Constantinople was conquered in 1451, but the empire continued to decline starting around the 18th or 19th centuries. It officially died in WWI. As for how long it was a major threat to Europe, the empire's prime was the 16th century, under Suleiman the Magnificent.
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It was a oil-exporting nation and it lost too much of an important resource, thus crippling the economy.
They both controlled all aspects of daily life
