## Dividing a Segment into N parts:

Euclid's Segment Division

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

Euclid's Segment Division

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

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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 BB_{1}, B_{1}B_{2}, ..., B_{N-1}B_{N}. Join B_{N} to C and through the rest of points B draw the lines parallel to B_{N}C. 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
- Divide Triangle by Lines Parallel to Base

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Copyright © 1996-2018 Alexander Bogomolny64969268 |