Stepped reckoner

Gottfried Wilhelm Leibniz's Step Reckoner of 1673 is often called the first true four-function calculator. Its secret is the stepped drum, a cylinder whose teeth run partway along its length in graded steps, so that sliding a small gear along it chooses how many teeth it meets. One revolution can enter any digit from 0 to 9, and repeated turns of the crank multiply. That drum-shaped gear underpinned calculator designs for roughly 275 years, an unbroken record for a single mechanism, and it reappears in the arithmometer and the Curta further down this list. Leibniz spent about 45 years building versions of the machine and only one survives.