Systematic Treatise on Arithmetic

The middle [value] 4 The OCR reads 'one', but the context of the calculation $4 \times 20$ suggests the multiplier from the previous page's 'number of sections'. times 20 results in 80. Subtract the smaller from the larger; the remainder is 60, which serves as the divisor 法: fa, the number used to divide the dividend. ○ Next, take the upper-left 3 and multiply by the lower-right 3 to get 9. Then, take the upper-right 4 and multiply by the lower-left 9 These directions refer to positions on a counting board used for cross-multiplication.; combined, these result in 15 fen and 6 li. Subtract 9 fen; the remainder is 6 fen 6 li, which is the common difference 差數: the fixed increment or decrement in an arithmetic progression for each section. ○ Now, taking the 3 sheng 9 ge of rice contained in the lower three sections as the dividend 實: shi, the number to be divided, multiply it by the divisor of 60 to get 234. Divide this by 3 三歸: a division shortcut for dividing by three to get 78 fen, which is the second value In this sequence, this represents the value for the second section of this sub-group.. Adding 6 fen 6 li gives the amount for the first section. Subtracting 6 fen 6 li gives 71 fen 4 li, which is the amount for the third section. Subtracting 6 fen 6 li again leaves a remainder of 64 fen 8 li, which is the amount for the fourth section. For each subsequent section, successively subtract 6 fen 6 li to obtain the respective amounts. Divide each by the divisor of 60 to match the requirements of the problem.

Song
Mathematical treatises often used rhyming songs to help students memorize problem parameters or methods.

In the original method, the lower three sections stored 4 sheng of rice, but the remainder was too large.
It has now been changed to 3 sheng 9 ge, which allows the calculation to resolve perfectly.

Ten thousand, six hundred, and eight taels of silver,
Are divided among four merchants according to their rates.

This introduces a new problem involving the distribution of 10,608 taels of silver based on specified proportions for four individuals.