Final answer:
The Byzantine Empire grew in power due to strategic capital relocation to Constantinople, preservation of Roman traditions, and the spread of Christianity and Greek language. Their use of diplomacy through the 'Bureau of Barbarians' was instrumental. However, they eventually fell to the Ottoman Turks, marking a cultural shift towards the Renaissance in Western Europe.
Step-by-step explanation:
The Byzantine Empire prospered while the Western Roman Empire faced decline due to several factors that granted them relative stability and power. The empire benefited from its strategic reorientation around the new capital in Constantinople, which became a cultural and economic powerhouse. In contrast to the fragmentation of the Western Roman Empire into various Germanic kingdoms, the Byzantines preserved Roman legal and cultural traditions, and spread Christianity and the Greek language throughout the eastern Mediterranean. The Byzantines saw themselves as part of a strong Mediterranean empire and managed to push back against Muslims to the east and Slavic peoples to the west during the reign of the Macedonian dynasty, which brought about the Macedonian Renaissance. However, over time, the Eastern Empire faced challenges from Turkic tribes like the Seljuks and, eventually, the rise of the Ottoman Empire led to the fall of Byzantium in 1453, which marked a significant cultural shift and contributed to the onset of the Renaissance in Western Europe.
An important aspect of the Byzantine Empire's resilience was its adept use of diplomacy and intelligence through the 'Bureau of Barbarians', which played a crucial role in forming strategic alliances and undermining rival states. Despite periods of stability, Byzantium faced threats leading to its conquest by the Turks, which led to the transformation of the Hagia Sophia from a cathedral into a mosque, and left a lasting impact on the Greek and Turkish histories.