The logic of Madison's Federalist Papers No. 10 is consistent with the imperial principle of divide and conquer in that it puts forward representative democracy as a means of combating the dangers of faction, thus separating the people from their elected representatives.
Whether Madison intended to advance the principle of divide and conquer is a moot point, but there's no doubt that the form of representative democracy he advanced is more conducive to that end than direct democracy, which, like the Founding Fathers in general, he feared as giving rise to mob rule.
Right from the outset, then, there was a general consensus among the political leadership of the American republic that the people would be easier to govern if they were effectively separated from their elected representatives. In this way, the people would lack the kind of cohesion possible in a direct democracy, theoretically making it easier for the governing classes to exert control over them.