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How to divide a given line into an arbitrary number of equal parts?
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| 1. |
| Start with two points defining the given line.
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| 2. |
| Draw an auxiliary line of suitable length, making an (acute) angle with line 1.
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| 3. |
| Construct an arc with its center at the angular point, and with a suitable radius. It must intersect the auxiliary line.
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| 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.
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| 5. |
| Repeat this the required number of times...
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| 6. |
| ...(in this example five times in total)...
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| 7. |
| ...for each successive intersection.
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| 8. |
| Draw the connecting line between the last intersection (of arc 7) with the auxiliary line and the opposite (righthand) end-point of line 1.
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| 9. |
| Construct a line through the preceding intersection (of arc 6) with the auxiliary line, parallel to line 8. It must intersect line 1.
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| 10. |
| Repeat this...
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| 11. |
| ...for all preceding...
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| 12. |
| ...intersections with the auxiliary line.
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| 13. |
| Mark the intersections of all parallel lines with line 1.
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| 14. |
| Marks 13 define the divisions to be constructed. They divide the given line into the required number (here five) of equal parts.
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