While there is a linear relation between radius and the angle, the distance between the windings is constant.
P times the the length of a given line.
P the radius is equal to this P . With the trisection was meant the quest to divide an angle in three equal parts. This is easy with the Archimedes' spiral, too. While the angle is linear with the radius, a division of the radius in n equal parts gives n equal angles in the spiral. Rotating this device with constant speed about its center results in a uniform linear motion at the crossing with the y-axis.