In some ways separating the Roman and Byzantine Empires is misleading.
"in some ways." This is one of the reasons I hate the shit out of Gibbon - he's the guy that makes people come up with a date that "Rome fell" rather than recognizing that its power and influence waned, its center of gravity shifted east, and European history became a messy string of uneasy confederations beheading each other over a thousand years for various and sundry reasons too complicated for modern history teachers to get into.
The concept of "Byzantium" is directly responsible for the modern assumptions that ancient civilizations went "poof! all gone!" instead of having their descendants looking back and saying "huh. Looks like we stopped running the world about 70 years ago."
Civilizations die not by murder, but from suicide.
- Arnold Toynbee