Square [the narrow width] to get 400 square paces. Add this to the 329 square paces [calculated previously] to get a total of 729 square paces. This is the shi: dividend.

Perform kaipingfang: square root extraction on this value to find the width at the point of the cut, which is 27 paces. Take this 27-pace width at the cut and add it to the original width of the narrow end, which was 20 paces.

The sum is 47 paces. Halve this to get 23.5 paces, which serves as the fa: divisor rule. Divide the cut area of 822.5 square paces by this rule to find the length of the cut, which is 35 paces. This matches the question.

Suppose there is a trapezoidal field with a length of 90 paces. The narrow end is 20 paces wide and the wide end is 38 paces wide. Now, from the wide end, an area of 1,787.5 square paces is cut. Question: What are the length and width of the cut section? how much?

Answer: The length cut off is 55 paces. The width at the point of the cut is 27 paces.

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Cutting from the Wide End of a Trapezoid

Narrow end: 20 paces Cut length: 35 paces This likely refers to the previous example's result or a remaining section Wide end: 38 paces

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The method states: Set the cut area and double it to get 3,575 square paces. Subtract the narrow width from the wide width to find the remainder of 18 paces, which is the kuocha: width difference.

Multiply the doubled area by this width difference to get 64,350 paces. Divide this by the original length of 90 paces...

This calculation is the first step in finding the width of the cut section when starting from the wider base. The scribe uses the doubled area and the rate of narrowing (width difference over total length) to determine how much the squared width decreases.