General Source of Computational Methods, Volume 7
Page 9

If Cutting an Area from the Narrower End of a Field

If cutting an area from the narrow end of the field	Use square root extraction to find the width of the cut	Half of the sum becomes the divisor rule
Square the narrow width and add it to the side of the dividend	Combine the two widths and halve the sum	Divide the cut area by the rule to find the length

Suppose there is a titian: trapezoidal field literally "ladder field" with a length of 90 paces. The south width is 20 paces and the north width is 38 paces. Now, from the south side (the narrower end), an area of 822.5 square paces is cut. Question: What is the length and the width of this cut section?

Answer: The length of the cut is 35 paces. The width at the point of the cut is 27 paces.

Cutting the Narrower End of a Trapezoid

North width: 38 paces Total length (C to midpoint): 90 paces

Cut length: 35 paces
Width at the cut: 27 paces
South width: 20 paces

The method states: Set the cut area of 822.5 square paces and double it to obtain 1,645 paces. Subtract the two widths 38 minus 20 to find a difference of 18 paces, which is the kuocha: width difference. Multiply the doubled area by this difference to get 29,610 paces. Divide this by the original length of 90 paces to obtain 329 paces This represents the change in the square of the width over the cut section. Separately, take the narrow end...

The text concludes on the next page, but the calculation involves adding the square of the narrow width (20² = 400) to the result (329) to get 729, then taking the square root to find the new width (27). From there, the length is found by dividing the doubled area by the sum of the two widths.