I recently read a history-book written in the 60s and there it was the "Byzantine Empire" ...
I did not intend to say that the Muslims were some sort of masterminds and the medieval Europeans barbarians. Of course the Middle-East has a rich philosophical tradition, dating back to the Egyptians, Persians and Babylonians. I just wanted to ridicule the author's notion that the Christians were supposed to be the masterminds and the Muslims the barbarians.
You are right on the Renaissance: It was deeply christian, but it was a new branch, an occult, magic-related Christianity. "New-Age" so-to-speak. Some of these new ideas got adopted into the christian mainstream, others were declared heretical. I doubt that the author would accept hermetic magic as christian.
The Volkswanderung was the tipping-point for the West-Roman Empire: The Roman Empire had always financed itself by expanding and pillaging other countries. This meant they needed a bigger army, which meant they needed even more money. Then a certain point was reached when Rome could no longer expand: In Scotland they needed Hadrian's Wall and in Germany they needed the Limes as bulwarks against barbarians that were too strong to conquer. And the kingdoms of the Middle-East were too strong as well.
Rome was running out of soldiers to protect what they had conquered. They started hiring local tribes. At the same time, Rome had a bad tax-system, where tax-evasion was normal for rich people. Without money to supply their army, the Roman Empire shrunk. I imagine, the Volkswanderung put lots of pressure on their remaining troops. The power and territory of Rome shrunk until they were totally dependent on their german allies for administration and protection. And then the Germans simply took over.