And insist on not spotting other outdated terms.
When I grew up in the '70s, the Byzantine Empire was still the eastern Roman Empire. And in many languages spoken by Muslims, Xians are still "Romans", but the only Xians the early Muslims had access to were either the intellectual descendants of early non-Catholic/Orthodox Xians or Byzantines.
Arabs inherited a lot of medicine and math from the Greeks, by which I don't mean "those living in Greece" but those who spoke koine. Same for astronomy. Many of the facts they inherited came from Babylonia or Alexandria. They got other parts from conquests and raids in areas of Asia further east. Muslims tend to be maximalist in their claims.
A lot of the Renaissance thought was an expansion of ideas and views that formed in the High Middle Ages.
I consider Xianity by 350 AD to be utterly apostate and foreign to what the first generation or two of Xians believed. In other words, the difference between the Middle Ages and the utter break you see later on is pretty much non-existent. Shift your frame of reference in the other direction--i.e., don't adopt your definitions--and you get the opposing view, that the Renaissance was still highly Xian, just not doctrinaire Catholic.
As for the take-over of the Roman Empire, I suspects that the Volkswanderung is at the heart of the contention. In the East it led to the spread of Slavs into Byzantine territories, and in the West the spread of various East Germanic tribes west and south.
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