Obtaining the width difference 6 paces and subtracting it from the lower width 22 paces leaves 16 paces, which is the middle width that fits the question.

General Source of Computational Methods, Volume 7

Page 4

Suppose there is a trapezoidal field original: 梯田 (titian). A field shaped like a ladder, which is the traditional Chinese term for a trapezoid. with an area of 1,500 paces, a northern width The "northern" width refers to the top horizontal side of the trapezoid in a standard orientation. of 40 paces, and a central length of 50 paces. What is the southern width?

The method states: Take the area 1,500 paces and double it to get 3,000 paces as the dividend (shi: the total value to be divided). Use the length 50 paces as the divisor (fa: the measure used to divide). Dividing results in 60 paces. From this, subtract the northern width 40 paces; the remainder is the southern width of 20 paces, which fits the question.

Suppose there is an original slanted field with a southern width of 4 paces, a northern width of 10 paces, and a length of 12 paces. Now, one wishes to extend it into the form of a right-angled triangle gougu: the traditional Chinese mathematical term for a right triangle, where "gou" is the base and "gu" is the height/leg. How long is the extension of the leg?

The method states: Multiply the southern width 4 paces by the length 12 paces to get 48 paces as the dividend. Separately, subtract the two widths from each other; the remainder of 6 paces is the divisor. Dividing the dividend by the divisor yields a leg extension of 8 paces, which fits the question. This calculation uses the principle of similar triangles to find how far the sides must be extended to meet at a single point (the vertex of the triangle).

梯田 (titian): Trapezoidal field, 廣 (guang): Width, 長 (chang): Length, 積 (ji): Area, 步 (bu): Paces (a unit of measurement), 實 (shi): Dividend, 法 (fa): Divisor, 勾股 (gougu): Right-angled triangle