And that happened because the Fourth Crusade sacked Constantinople and shattered the Byzantine Empire, and they were able to do so because they were invited in by some imbecile rivals to the Byzantine throne. Moreover, the ultimate reason (almost certainly) that the Byzantines were not in control of the lands where the Crusaders originated was because of the earlier Arab conquest of the southeastern provinces. Finally, had the Byzantines fended off the Arabs in, say, the 650s, the Turks would probably not have been Muslims anyhow.
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