15. The division of the line segment

To divide a given segment AB into two equal parts, the points of its beginning and end are taken as the centers from which arcs of radius exceeding half of segment AB are taken . Arcs are carried out before intersection, where they get points C and D. A line connecting these points will divide the segment at point K into two equal parts (Fig. 30, a).

Fig. thirty

In order to divide the segment AB into a given number of equal sections n, an auxiliary straight line is drawn at any acute angle to AB , on which n equal sections of arbitrary length are laid out from the common given point (Fig. 30b). From the last point (in the drawing - the sixth) they draw a straight line to point B and, through points 5, 4, 3, 2, 1, they draw straight lines parallel to the segment 6B. These straight lines will cut off on the segment AB a specified number of equal segments (in this case, 6).