He wasn't American. Washington was a British colonist who became a citizen of a confederate states (1781 articles of confederation) until he became a US citizen (1789 when the constitution created the federation of states). The first born "American" president was actually John Tyler who was born in 1790. So yes, Washington wasn't American.
And since Washington was a member of the Virginia plantation elite, as well as educated in British schools (as well as fought in the French-Indian War), he cannot be considered American through any form of influence. While Washington is considered a war hero he won three major engagements (decisive but not many) and lost many more.
Alexander however would be considered greek because of his religion, etymology, military tactics, education, etc. He would be considered Macedonian but Greek influence and culture spread well beyond the city-states. Besides, even Byzantium was considered Greek when it was in Thrace.
Anyway, historical myths? I like the one about how the Spanish Conquistadors destroyed the Aztec Empire with 160 soldiers. They had steel, cannon, horses, and bio-weapons (smallpox) but they still enlisted the help of the Mexicans (yes, the native american tribe) and attacked the Aztec with well over 4,000 men (I believe that is the number, maybe more.)
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