The verb to tread is one of the oldest words known in the English language and its forebears, being found in that most ancient of Anglo-Saxon writings, Beowulf, which dates to the seventh century A.D.
It, or rather, its close relatives, are also known in all the languages of the Teutonic group, with the general meaning of “to step upon, to walk on.”
The noun is less old, and that particular sense of the noun applying to the steps of a set of stairs is as recent as about the eighteenth century.
Yet it is this sense that has entered into treadmill, for this machine, invented about 1820 as a means of employing prisoners, was a large cylinder, or wheel, arranged with a series of horizontal treads around its circumference.
As the wheel was rotated by means of men “climbing” these steps, the resultant movement of the axle was used to operate a mill, thus giving us the compound term treadmill.