
How to divide a given line into an arbitrary number of equal parts?

1. 
 Start with two points defining the given line.


2. 
 Draw an auxiliary line of suitable length, making an (acute) angle with line 1.


3. 
 Construct an arc with its center at the angular point, and with a suitable radius. It must intersect the auxiliary line.


4. 
 Construct an arc with the same radius and orientation as arc 3, with its center at the intersection of arc 3 and the auxiliary line.


5. 
 Repeat this the required number of times...


6. 
 ...(in this example five times in total)...


7. 
 ...for each successive intersection.


8. 
 Draw the connecting line between the last intersection (of arc 7) with the auxiliary line and the opposite (righthand) endpoint of line 1.


9. 
 Construct a line through the preceding intersection (of arc 6) with the auxiliary line, parallel to line 8. It must intersect line 1.


10. 
 Repeat this...


11. 
 ...for all preceding...


12. 
 ...intersections with the auxiliary line.


13. 
 Mark the intersections of all parallel lines with line 1.


14. 
 Marks 13 define the divisions to be constructed. They divide the given line into the required number (here five) of equal parts.

