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A Circle Within a Square
Method for square fields
For the method of cubic measurement original: 三乘方 (sanchengfang), literally "three-multiplied square," referring to volume or higher-order calculations, multiply the value by itself twice and divide by three.
To find the area: multiply the diameter by itself, then multiply by three and divide by four.
The area of a circle within a square is three-fourths
A Hexagon Within a Circle
To find the area: divide by seven and multiply by six.
The area of a hexagon within a circle is six-sevenths
A Square Within a Circle
To find the area: divide by three and multiply by two.
The area of a square within a circle is two-thirds
A Circle Within a Hexagon
Method: divide by seven and multiply by six.
The area of a circle within a hexagon is six-sevenths
A Circle Within a Triangle
To find the area: divide by seven and multiply by four.
The area of a circle within a triangle is four-sevenths
A Triangle Within a Circle
To find the area: divide by sixteen and multiply by seven.
The area of a triangle within a circle is seven-sixteenths
Suppose there is now a square field with a length and width of fifty steps bu: a unit of length based on a double-pace, approx. 1.5 meters each. What is the total area?
Answer: The area is 2,500 square steps.
The tax is 10 mu, 4 fen, 1 li, and 6.6 hao mu: a unit of land area where 1 mu = 240 square steps; fen, li, and hao are decimal subdivisions of the mu. The calculation 2,500 ÷ 240 equals 10.4166... mu, matching the text's tax figure.
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