《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§22. Results of multiplication & division: multiples of 2

§15 through §22 give the results of multiplications and divisions of the form

\begin{aligned} (m n) \times (m n) &= m^2 n^2 \\ (m^2 n^2) \div m &= m n^2, \end{aligned}

along with the result of the division

\Bigl[ n \times n + (n - 1) \times n + \dots + 1 \times n \Bigr]^2 \div n.

Since this gets rather repetitive and boring, you may wish to skip to §23.

This section corresponds to n = 2.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
二二如四、自相乘、得一十六。二人分之、人得八。 Two twos [are] as four, [which], multiplied with itself, resulteth in sixteen. [With] two people sharing it, [each] person getteth eight.
一二如二、自相乘、得四。一人得四。 One two [is] as two, [which], multiplied with itself, resulteth in four. One person getteth four.
右二二一條、得六、自相乘、得三十六。二人分之、人得十八。 [The] two twos above [as] one strand, result in six, [which], multiplied with itself, resulteth in thirty-six. [With] two people sharing it, [each] person getteth eighteen.
  • 右： above; lit. aright
  • Version B has 人得一十八 for 人得十八.
  • In modern notation:
    \begin{gathered} 2 \times 2 + 1 \times 2 = 6; \\ 6 \times 6 = 36; \quad 36 \div 2 = 18. \end{gathered}

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §22". <https://yawnoc.github.io/sun-tzu/i/22> Accessed yyyy-mm-dd.