Meh, this sounds so deterministic.
Arab dominance over the Middle East certainly helped the trade, but it also led to the destruction and displacement of the previous civilizations. I imagine there was some population decline and great deal of damage to the existing societies.
For Europe, the main problem would be the fact that Crusades would have never happened - and all the wealth, experience and knowledge the Crusaders acquired there would have never get back to Europe. The same goes for Spain, through which the ancient knowledge made its way to Western European universities.
On the other hand, we can't simply say that nothing else would change. For example, Spain might be conquered by the Byzantines eventually and they could be the ones who would bring the old texts back to the Latins. Without losing Egypt/Levant/North Africa, the Byzantines might be strong enough to expand in the Balkans. It's possible that Byzantine influence could have stopped the eastwards expansion of Catholic Christianity and the whole Central Europe might become Orthodox.
A strong Byzantine Empire might even establish strong trade ties with India (
Egypt->Red Sea->Yemen->Indian ocean->India route). It's also likely that Christianity would travel south to East African coast, just as Islam did.
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One important question - with absence of a "common enemy", do you believe that Catholic and Orthodox Christianity would be more hostile to each other?
I read the 1st one, but can't get my hands on the 2nd. Our librarians probably never heard about it

BTW, there is a chapter about 1938 Munich Treaty in the 2nd volume, right?