Aristotle's argument for slavery was mostly about reason, not strength. He argued that certain populations were incapable of proper reason and required somebody more "rational" (more Greek, in practice) to exercise it for them, creating not only a right but a sort of duty among "rational" populations to enslave the irrational. For their own good, ken?
(Ironically, Aristotle would have regarded a lot of the people involved in the Atlantic slave trade, who were by the 18th century mostly Dutch, Scots and English, as falling under the heading of "naturally slave-y".)
As Lord Baal says, slavers didn't tend to appeal to realist theories of authority, because realism and racism don't tend to fit together very well unless you construct some Hitlerian theory of race war, which really wasn't what the slavers were interested in. Their preference was for corporate theories of slavery, which justified the institution in terms of a benevolent relationship between the master and slave, and between the plantation and society at large. Even the most nakedly bigoted of them would merely assert that the African was possessed of no rights and therefore it didn't matter what was done to them; it would be far too dangerous to suggest that, if their positions were reversed, the African would be within his rights treat the European in the same way.