<span>This image
show how to divide a given line segment into a number of equal parts by using a
compass and ruler. First, draw the line
AB. Secondly, draw a line above and divide into 5 equal distances to make a
line AC. Third, using a compass by getting the distance of point C and B to be
equal in the distance of point A and D, also getting the distance of point C to
A to be equal to point B and D, then to make the Line DB. Finally divide into 5
equal parts by compass</span>.
The construction creates a series of similar triangles where line segment AB represents one of the sides in each triangle. Because the top vertex of each similar triangle is drawn at a regular interval using a compass, the sides of each successive similar triangle increase in length at a constant rate. Therefore, each line segment created by the similar triangles will have the same length, breaking the given line segment into a series of equal parts.
