The ancient Romans preferred to leave the pursuit of the sciences to the Greeks, but they were formidable engineers. Physics can give us perspective on feats of ancient Roman civil engineering, among which are the aqueducts which supplied Rome (and other cities) with water beginning in 312 BC. The rows of stone arches that characterize many famous aqueducts (though the majority of Roman aqueducts were underground) lean on one another for support. But are they stable on their own? I will present a mathematical model for the stability of freestanding stone arches, and a complementary Styrofoam model, to answer the question of whether aqueduct arches had to be braced during construction.