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How to construct a line parallel to a given line, passing through a given point?
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| 1. |
| Start with two lines forming an (acute) angle, one of which (the upgoing line) defines the given line. The other one is an auxiliary line.
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| 2. |
| On the auxiliary line, determine the given point. (The auxiliary line must pass through the given point).
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| 3. |
| Construct an arc with its center at the angular point, and with a suitable radius. It must intersect with both lines.
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| 4. |
| Construct an arc with the same radius and orientation as arc 3, with its center at point 2.
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| 5. |
| Construct an arc with its center at the intersection of arc 3 and the auxiliary line, passing through the intersection of arc 3 and the upgoing line.
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| 6. |
| Construct an arc with the same radius and orientation as arc 5, with its center at the intersection of arc 4 and the auxiliary line.
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| 7. |
| Draw a line through point 2 and the intersection of arcs 4 and 6, and extend it where necessary.
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| 8. |
| Line 7 is the line to be constructed. It runs parallel to the given line, and passes through the given point.
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