Systematic Treatise on Arithmetic, Vol. 6

General Source of Computational Methods: Volume 7

...western height original: 股 (gu), the longer leg of a right triangle is 9 paces. Question: what is the width of the base of the cut?

The method states: Set the area of the cut, 31 and 5 tenths paces, and double it to get 63 paces. Use the western height of 9 paces as the divisor (fa: the measure used to divide the area). Divide to obtain the width of the northern base of the cut, which is 7 paces. This matches the question.

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Calculating Rectangular Fields

Suppose there is a rectangular field original: 直田 (zhi tian), literally "straight field" with an area of 1,920 paces. It is stated only that the length is 60 paces. Question: What is the width?

The method states: Set the area 1,920 paces as the dividend (shi: the total value to be divided). Use the length 60 paces as the divisor (fa). Divide to obtain the width.

If the problem only stated the width as 32 paces and asked for the length: simply use the width as the divisor (fa) to obtain the length.

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Calculating Triangular Fields

Suppose there is a triangular field original: 圭田 (gui tian), literally a "tablet field" shaped like a ritual jade tablet with an area of 225 paces. It is stated only that the length is 30 paces. Question: What is the width?