Diagram of Geometric Evolution: One Square, Four Side-Strips, and Corners

200 60 8 Total

Square: White Method: Square Area: 40,000 paces Original: 方白法方積四萬步. This represents the central square of 200 x 200. One side-strip: Length 200 Width 60 Area 12,000 Corner square: Side 60 Area 3,600 One side-strip: Length 200 Width 60 Area 12,000 200 60 8 Total One side-strip: Length 200 Width 60 Area 12,000 Corner square: Side 60 Area 3,600 One side-strip: Length 200 Width 60 Area 12,000 200 60 8 Total

Area of the small side-strip. ◯ Then, for the third quotient of 8 paces, multiply it by itself to get an area of 64 paces; this is the area of the small corner square. ◯ For a flat circle, first use the square root method, then divide by twelve to find the width.

The value 520 becomes the Side-Strip Method Lian fa: The divisor used to calculate the area of the rectangular strips added to the square. ◯ Below the third quotient of 8, also place an 8 below the Side-Strip Method of 580. Align these with the top quotient of 8 to perform the subtraction. First, use the 8 on the left against the 5 on the right: "Five times eight is forty," subtracting 40,000 paces from the Dividend, which exhausts that part. Then call out:
Two paces; call out and subtract sixteen 8 x 2 = 16; this refers to subtracting 1,600 from the remaining area.
Then call out:
Eight times eight; subtract sixty-four.

The Geometric Evolution Explanation says: The first quotient of 200, when multiplied by itself, yields an area of 40,000; this is the Great Square Area. For the second quotient of 60, there is a width of 60 and a length of 200; therefore, double the first quotient of 200 to make 400 as the Side-Strip Method. Multiplied by the second quotient on the left, this yields 24,000, which is the area of the two side-strips with length 200 and width 60. ◯ Then, the third quotient of 8 paces: the second quotient of 60 multiplied by itself yields 3,600, which is the Middle Square Area The corner square created by the second step.. ◯ Within the third quotient of 8 paces, there is a width of 8 paces and a length of 260 paces. Therefore, doubling the combined first and second quotients (260) gives 520. Multiplying this length of 520 by the width of 8 yields an area of 4,160 paces. ◯ The third quotient of 8 paces multiplied by itself yields an area of 64 paces. ◯ These two widths of 8 paces and lengths of 260 paces are...