The connection between exacting revenge and an exact measurement is not obvious, but Latin makes it clear. Both senses flow from exigere, a verb meaning 'to drive out, demand, or weigh thoroughly,' combining ex- ('out') and agere ('to drive'). A Roman tax collector exacted payments by driving out every last coin. A Roman engineer demanded exact measurements by weighing with thoroughness. The past participle exactus carried both flavours: something fully driven out, and something precisely determined. English inherited the dual personality intact. The verb to exact (demand forcefully) entered the language alongside the adjective exact (perfectly precise) in the 15th century, and both have remained in active use. The Latin root agere was extraordinarily productive — it also generated agent, essay, examine, and exigent, all centred on the concept of driving or doing. An exacting task and an exact result are, at their Latin core, the same idea: thoroughness pushed to its limit.