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The only thing that an ancient greek, a renaissance italian, and a modern american share is that the american thinks they are all white. Otherwise these groups share almost nothing in culture, religion, ancestry, worldview.
Being able to have this open-ended ability to cherry pick things from highly disparate times and places and consider them "white" is white supremacy. A modern palestinian is culturally closer to an ancient greek than you are. These things simply are not yours to claim, or at least not any more than they are all of ours.