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.
Prussia was a strange little country. For most of its life, it was all split up. Ducal Prussia in the East was held by the Elector of Brandenburg, while royal Prussia in the West was part of Poland. By the beginning of the 18th century, the Hohenzollern family held firm control over both Brandenburg and Ducal Prussia, but it was always seeking to expand and collect more territory. In 1701, Elector Frederick III received the title 'King in Prussia' as a reward for helping the Holy Roman Emperor and Austrian ruler Leopold I, and the Kingdom of Prussia officially began.
Over the next several decades, Prussia grew in power, politically and militarily. The next king, Frederick William I, who reigned from 1713 to 1740, built up a massive army. He started out with about 38,000 soldiers in 1713, but by the time of his death, Prussia was a military powerhouse with over 80,000 well-trained soldiers.
The king's successor, Frederick II, at first seemed unlikely to make good use of all that military might. The new king styled himself as an 'enlightened' monarch. He studied the ideas of the Enlightenment, wrote essays on political philosophy, played and composed music and patronized the arts. Frederick II, however, was no wimp. He had an aggressive side, as we shall soon see.
B. The actual number of farmers increased between 1840 and 1900.
