The Roman Empire reached its greatest territorial extent during the 2nd century AD; the following two centuries witnessed the slow decline of Roman control over its outlying territories. Economic issues, including inflation, and external pressure on the frontiers combined to make the 3rd century politically unstable, with emperors coming to the throne only to be rapidly replaced by new usurpers. Military expenses increased steadily during the 3rd century, mainly in response to the war with Sassanid Persia, which revived in the middle of the 3rd century. The army doubled in size, and cavalry and smaller units replaced the legion as the main tactical unit. The need for revenue led to increased taxes and a decline in numbers of the curial, or landowning, class, and decreasing numbers of them willing to shoulder the burdens of holding office in their native towns. More bureaucrats were needed in the central administration to deal with the needs of the army, which led to complaints from civilians that there were more tax-collectors in the empire than tax-payers.

In what century did the Roman Empire achieve its greatest extent?