In the lower method, also place 50 the doubled value of the first part of the quotient below the Square Method; the total is 80. Both are then multiplied by the second quotient of 5. $\bigcirc$ The 5 on the left is matched against the 8 on the right. Call out "five times eight" to subtract from the dividend the 400 paces, which exhausts the amount exactly. Thus, the width is found to be 35 paces. Adding the excess of 15 paces [to the width]:

Another Method Called "Square Root Extraction by Area Reduction"

Alternative Procedure

Place the area of the field as the dividend Shi: the target number or "total" being divided or factored in the center position. $\bigcirc$ Separately, place the deficit of 15 paces the difference between the length and width in the right position as the "area reduction" value. $\bigcirc$
Place the first quotient of 30 in the left position. $\bigcirc$ In the lower method, also place 30 on the right as the "Square Method" Fang fa: the primary divisor in the root extraction process. Multiply this by the area reduction value of 15, which results in 450. Subtract this from the central dividend; the remaining dividend is 1,300 paces. $\bigcirc$ Next, correlate the initial quotient of 30 with the upper quotient of 30. "Three times three [is nine]," so subtract the product 900 from the area; the remaining dividend is 400 paces. $\bigcirc$ Immediately double the Square Method value of 30 to make 60, which serves as the "Side Method" Lian fa: a secondary divisor used in more complex root extractions. $\bigcirc$ Place the second quotient of 5 in the left position next to the 30. $\bigcirc$ In the lower position, also place 5 and multiply it by the area reduction value of 15, which results in 75 paces. Subtract this from the central area; the remaining dividend is 325 paces. $\bigcirc$ Then, [using...]

This "Area Reduction" method is a variation of the traditional Chinese method for solving quadratic equations. It adjusts the central "Shi" (area) by subtracting the product of the first quotient and the side-difference before proceeding with the standard square root steps.