## Dividing a Segment into N parts:

Al-Nayrizi's Construction

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Copyright © 1996-2018 Alexander Bogomolny## Dividing a Segment into N parts:

Al-Nayrizi's Construction

The algorithm below has been included into Al-Nayrizi's commentary on Euclid's *Elements*. Euclid solves the problem of finding an N^{th} of a segment in Proposition VI.9. Al-Nayrizi's construction being simpler is clearly superior to Euclid's.

Let BC be a given segment to be divided into N parts. Draw two parallel lines through B and C and measure N equal segments on each: BB_{1}, B_{1}B_{2}, and so on, on one, and CC_{1}, C_{1}C_{2}, and so on, on the other pointing in different directions. Join the first of the points B with the last of C's and vice versa and join the rest by parallel lines. Those lines will cut BC into N equal segments.

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Copyright © 1996-2018 Alexander Bogomolny