Systematic Treatise on Arithmetic

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The Explanation says:

For eight horses, nine oxen, and fourteen sheep, it was collectively agreed to compensate the victim with six shi A unit of volume; see previous page note. of grain. The ratios are set at one part per sheep, two parts per ox, and four parts per horse.

The Method says:

○ The method says: Set the 6 shi of grain as the dividend original: 實 (shí). ○ Separately, take the 8 horses and multiply by 4 the horse's ratio to obtain a proportional weight original: 衰 (shuāi) of 32; take the 9 oxen and multiply by 2 to obtain a proportional weight of 18; and take the 14 sheep multiplied by 1. Adding these together gives 64 as the divisor original: 法 (fǎ); the text notes the character 'four' is faded here. Dividing [the dividend by the divisor] yields 9 sheng, 3 ge, 7 shao, and 5 chao, which is the compensation amount required for a single unit of weight.

Multiply this unit value across each proportional weight: First, multiply by the sheep’s weight of 14 to get 1 shi, 3 dou, 1 sheng, 2 ge, and 5 shao, which is the amount the sheep owner must pay. ○ Next, multiply by the oxen’s weight of 18 to get 1 shi, 6 dou, 8 sheng, 7 ge, and 5 shao, which is the amount the ox owner must pay. ○ Finally, multiply by the horse’s weight of 32 to get 3 shi, which is the amount the horse owner must pay. These calculations satisfy the requirements of the question.