General Source of Computational Methods: Volume 7

...4 paces and 6 tenths, with the northern end required to be 4 paces wide. Question: what is the southern width of the cut?

Answer: The southern width of the cut is 3 paces.

Cutting a Slant from a Rectangular Field

The method states: Set the area of the cut, 54.6 paces, as the dividend (shi: the total value to be divided). Use the original length of 15.6 paces as the divisor (fa: the measure used to divide the area). Divide to obtain the width of the cut, 3.5 paces. This represents the average width of the two ends. Double this to get 7 paces. Subtract the northern width of 4 paces, and the remainder is the southern width of the cut, which is 3 paces.

Another method: Double the area of the cut to get 109.2 paces as the dividend (shi). Use the original length of 15.6 paces as the divisor (fa). Divide to obtain the combined width of the two ends, which is 7 paces. Subtract the northern width of 4 paces, and the remainder is the southern width of the cut, 3 paces. This also works.

Suppose there is a rectangular field 15 paces long and 12 paces wide. Now, from the northwest corner, a right-angled triangular section (gou-gu: a triangle where the 'gou' is the base and 'gu' is the height) is cut, with an area of 31.5 paces. The length of the western side (gu) is 9 paces. The question asks for the width of the northern side... The text ends here; the calculation would typically involve doubling the area and dividing by the known side to find the other side of the triangle.