Systematic Treatise on Arithmetic, Vol. 6

...divide by the total length to get 715 paces. Separately, take the width of the wide end, 38 paces, and square it to get 1,444 square paces. Subtract

the 715 paces [calculated above]; the remainder is 729 square paces, which serves as the shi: dividend. Perform kaipingfang: square root extraction on this value to find 27 paces, which is

the width at the point of the cut. Then, take this width of 27 paces and add it to the original width of the wide end, 38 paces, for a total of 65 paces.

Halve this to get 32.5 paces, which serves as the fa: divisor rule. Use this to divide the cut area of 1,787.5 square paces to find the length of the cut, which is 55 paces. This matches the question.

◯ If the field is to be divided into three segments, first determine the lengths to be cut from the wide and narrow ends. Subtracting these from the total length

will give the length of the middle segment.

In cases where the field is divided into four or five segments, also begin by cutting away the lengths from the wide and narrow ends. Then,

take the remaining length (after subtracting the two end sections from the original total length) and the widths at those two cut points, and apply the

tifa: trapezoidal method again to perform the remaining cuts.

The method for cutting diagonal shapes follows the same principles as the trapezoidal method. For instance, the method for cutting areas from the east and west sides is fully recorded in the "Section on Rare and Difficult Problems" original: "Shaomo zhang" in the original: "Zhen ben" "Zhen" volume of this work.