In The American Republic: Its Constitution, Tendencies, and Destiny (1865), Orestes Brownson claims (ch. 1 introduction):
Aristotle* knew only four forms of government: Monarchy, Aristocracy, Democracy, and Mixed Governments. The American form is none of these, nor any combination of them.
*cf. Politics III
Why did Orestes Brownson think that "The American form is none of these, nor any combination of them"? Why is it not a "Mixed Government"?
What St. Thomas Aquinas says about the best form of government in Summa Theologica I-II q. 105 a. 1 c. seems to describe the United States's form of government, a mixed government:
the best form of government [ordinatio principum, lit. “ordering of princes”] is in a state or kingdom, where one is given the power to preside over all; while under him are others having governing powers: and yet a government of this kind is shared by all, both because all are eligible to govern, and because the rules are chosen by all. For this is the best form of polity, being partly kingdom, since there is one at the head of all; partly aristocracy, in so far as a number of persons are set in authority; partly democracy, i.e. government by the people, in so far as the rulers can be chosen from the people, and the people have the right to choose their rulers.
Similarly, St. Robert Bellarmine, S.J., considers monarchy the theoretically best form of government, but that "Monarchy Mixed with Aristocracy and Democracy, Should be More Useful in this Life" (De Romano Pontifice ch. 3; cf. the ch. "Cardinal Bellarmine's Books De Summo Pontifice Considered" of Hobbes's Leviathan).