Illustrated · 1 min
This can be done by meeting endpoints of different segments:
In the above diagram, the blue, red, and green lines all have the same length. Use a compass to measure the distance between B and C, and then draw the circle out (the pencil should start at B). The resulting circle should intersect the line in two places: B, which we started from, and D, our new point.
Since segments BC and BD are both radii of one circle, they have the same length. To get the next segment DE on the line, flip the compass (switch the two points C and D) and complete the circle to get E.