Systematic Treatise on Arithmetic (1592) - Page 10

The Answer is: 1,414 taels, 1 mace, and 4 candareens. The original units are Liang 兩, Qian 錢, and Fen 分. In this system, 10 candareens equal 1 mace, and 10 mace equal 1 tael.

The Method states: Set the quantity of timber as the Multiplicand (Shi 實). Use the price of 6 candareens per log as the Multiplier (Fa 法). Multiply them together to satisfy the question.

Method ❻ Multiplication

End of the Multiplicand					Start of the Multiplicand
Units	Tens	Hundreds	Thousands	Ten-Thousands
Start by calling 6	6 times 6	6 times 5	6 times 3	6 times 2
Fifty-four	Thirty-six	Results in thirty	Eighteen	Twelve
Change 9 to 5	Change 6 to 3	Change 5 to 3	Change 3 to 1	Change 2 to 1
Add 4 to the position below	Add 6 to the position below		Add 8 to the position below	Add 2 to the position below

Determining the Place Value					Original Multiplicand
Units	Tens	Hundreds	Thousands	Ten-Thousands
These are candareens; move forward and ascend to find the result	Above the multiplier is 6 candareens per log; where the logs end, stop; the next position below is the candareens place				Start by calling "Ten-Thousand" at the end
❹	Mace	Tens	Hundreds	Thousands	Ten-Thousands
					Count in order down to the individual logs
					5

The table above illustrates the "Yin" (multiplication) method using a counting board or abacus. The "Change X to Y" instructions describe how to manipulate the beads or rods to reflect the products of the multiplication table (e.g., 6 x 2 = 12 is handled by changing the digit 2 to 1 and adding 2 to the next lower position).

General Source of Computational Methods original: "Suanfa Tongzong" 算法統宗, a seminal 16th-century mathematical treatise by Cheng Dawei. Volume 11