The structure of the Social Contract presents an intriguing puzzle. While the first three books argue for a republic of free and equal citizens, the fourth book seems to praise the Roman Republic, a state based on military expansion, slavery, class division, and an inegalitarian voting system. I argue that this puzzle can be solved if we understand the fourth book to be making an a fortiori argument in which Rousseau counterintuitively uses the flawed example of the Roman Republic to show the possibility of large republics in modern circumstances.