Nine Chapters on Mathematical Art, Vol. 1

[If the] circumference is 30 bu and the diameter is 10 bu, now follow the dense ratio The dense ratio uses a diameter of 9 bu and 6/11 of a bu. Ask: What is the area of the field?

Answer: 75 bu According to the Hui method, this should be an area of 71 and 112/157 bu.

We, Chunfeng and others, respectfully note: The dense ratio results in an area of 71 and 13/22 bu.

There is another circular field with a circumference of 181 bu and a diameter of 60 and 1/3 bu.

We, Chunfeng and others, respectfully note: For a circumference of 3 and diameter of 1, a circumference of 181 bu results in a diameter of 60 and 1/3 bu; according to the dense ratio, the diameter is 57 and 22/23 bu.

Ask: What is the area of the field?

Answer: 11 mu and 90 and 1/12 bu According to the Hui method, this should be an area of 10 mu and 113/314 of 208 bu.