Line Division in Euclidean Geometry

One of the earliest problem when teaching euclidean geometry using just ruler and compass is how to divide a line into n equal parts using only straight edge and compass. The following snapshots using KSEG illustrates this idea.
 It makes it clear that it doesn't matter what is the side of the division we use on the line. Also the helping line on which divisions are made can be at any angle other than 180 and 360 degrees.