Dividing a Segment into N parts:
Euclid's Segment Division
A Mathematical Droodle: What Is This About?

Explanation

Euclid offered an lagorithm for finding N^th part of a given segment in Elements VI.9.

Let BC be a given segment to be divided into N equal parts. Draw any line through B at a positive angle to BC. Measure on that line equal segments BB₁, B₁B₂, ..., B_N-1B_N. Join B_N to C and through the rest of points B draw the lines parallel to B_NC. They will cross BC in the points dividing BC into N equal parts.

• How to divide a segment into n equal parts
• Al-Nayrizi's Construction
• Besteman's Construction
• Besteman Construction II
• Dividing a Segment by Paper Folding
• Euclid's Segment Division
• The GLaD Construction
• The SaRD Construction
• Similar Right Triangles