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Problem 584

Divide a given line segment into parts proportional to given line segments.

Expert verified

To divide a given line segment AB into parts proportional to given line segments m, n, etc., follow these steps:
1. Draw a parallel line and mark points C, D, ... such that BC, CD, ... are equal to the line segments m, n, ... .
2. Connect the points C, D, ... to the point B, forming a series of similar triangles with bases on AB.
3. Use the property of similar triangles to find the lengths of the segments BP, PQ, and QE.
4. Verify that the sum of the segments BP, PQ, and QE is equal to the total length of AB.
The lengths of the segments BP, PQ, and QE will be the proportional divisions of the given line segment AB.

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