Cut a line into N segments

How to Cut a line into N segments
using just a compass and a straightedge

Here we cut a line into 3 segments, but the same approach can be used to cut a line into any number of segments:

Steps:

• Draw a line from the start point, heading somewhat upwards
• Use the compass to divide it into 3 segments
• Use the compass to create a parallel line heading backwards and down from the end point.
• Use the compass to divide it into 3 segments
• Connect the intersection points of the two new lines, and where they cross the original line it will be neatly subdivided.