This chapter takes a step back and considers mathematics from a different angle: the mathematics closer to day-to-day practice. At the same time, the chapter brings forward the historical narrative by beginning to consider the science of the Roman era. The same duality will characterize the following (longer) chapter on astronomy, and both for a reason: in the centuries following the two breakout generations of Greek mathematics, most work in the exact sciences was concentrated on more “applied” mathematics and in particular on astronomy. It is therefore fitting that we begin with the author (not a mathematician but a historian) most emblematic of the turn from Greek to Roman: “Polybius, Introducing Applied Mathematics.”