Charles, here is a reference for my first point above:

http://www.amazon.com/Sailing-Byzantium-Empire-Shaped-World/dp/0553803816

In truth, the Arabs world had very few of the ancient text whilst the Eatern Empire had all of the text that survived the collapse of Antiquity.

These Arabic translations, BTW, were really the work of western Dhimmis and hardly major currents in Islamic intellectual life. A possible exception here being the Arab commentaries on Galen.

For an earlier reference to the Eastern Empire’s transmission of Ancient Greek knowledge in late Medieval Italy, see this:

http://books.google.com/books?id=Qzc8OeuSXFMC&pg=PA266&lpg=PA266&dq=dissemination+of+greek+text+early+middle+ages&source=bl&ots=iIHf7hToWo&sig=TZoQszCYpXaUmdPHD7YZG-UlSHg&hl=en&ei=ZRkhSoX5LInFtgfutdW6Bg&sa=X&oi=book_result&ct=result&resnum=3

But again, recent scholarship is questioning the very notion that Ancient knowledge was ever really “lost” completely in the West, or at least pushed back the discovery date my centuries. (I will dig around for an online link to support this assertion.)

Whatever the case, we must not confuse Western Gothic Europe with European Civilization as a whole. “Western Civilization” lies west of the Urals, not west of the Alps.