Systematic Treatise on Arithmetic, Vol. 3

For a trapezoid original: 梯斜 (tixie), literally "ladder slant.", combine the widths of both ends and halve the sum;
Multiply by the length, and the area will be clearly revealed.

For a triple-width field Likely a drum-shaped field where the width is measured at both ends and the middle., double the middle width and add the two end widths;
Divide the total by four and multiply by the length to find the area.

For an arc-segment original: 弧矢 (hushi), "bow and arrow." This refers to a circular segment where the chord is the bowstring and the sagitta is the arrow., combine the chord length with the height of the arc;
Halve this sum and multiply it again by the height.

For ox-horn or eyebrow-shaped fields Crescent-shaped fields or lunes., combine the arc lengths;
Halve the result and multiply by the half-diameter The radius or the distance from the center of the curve to the edge..

For a quadrilateral with two unequal sides, add the East and West dimensions;
Halve the sum and multiply by the width.

For a snake-boat field A shape tapered at both ends, similar to a spindle., add the three measured widths together;
Divide by three to find the average width, then multiply by the length.

For a field with four unequal sides, divide it into two sections;
One becomes a right-angled triangle Gougu The "Gougu" theorem is the Chinese equivalent of the Pythagorean theorem., and the other a slanted shape.

Field shapes vary, so you must categorize them by type;
Divide the total area by 240 original: 二四 (two-four). In the Ming dynasty, 240 square paces (bu) equaled 1 mu. to make the number of mu clear.

○ The method of measurement: five feet chi equal one pace bu. Each square pace is five feet by five feet, totaling twenty-five square feet. To calculate based on a five-foot pace: a value below the pace of five [inches] is one tenth-pace one [inch] is two hundredth-paces This provides a conversion for decimal arithmetic. Since 1 pace = 5 feet, then 0.5 feet = 0.1 paces (1 fen), and 1 inch (0.1 feet) = 0.02 paces (2 li).. If the length and width are asked in units of ten-foot rods (zhang) and feet (chi), simply apply the method of setting the positions and doubling to multiply them.