《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§12. Some equivalent fractions (2)

This section gives some equivalent fractions.

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
九分減一者、以二乘、十八除。
八分減一者、以二乘、十六除。
七分減一者、以二乘、十四除。
六分減一者、以二乘、十二除。
五分減一者、以二乘、十除。		 Subtracting one of nine shares: multiply by two, [and] divide [by] eighteen;
subtracting one of eight shares: multiply by two, [and] divide [by] sixteen;
subtracting one of seven shares: multiply by two, [and] divide [by] fourteen;
subtracting one of six shares: multiply by two, [and] divide [by] twelve;
subtracting one of five shares: multiply by two, [and] divide [by] ten.
  • 分： shares

    In Chinese, the fraction a/b is referred to as b 分之 a, literally "a of b shares".

  • Like the previous section (§11), I think this is saying
    \begin{aligned} -\frac{1}{9} &= -\frac{2}{18} \\[\tallspace] -\frac{1}{8} &= -\frac{2}{16} \\ & \enspace \vdots \\ -\frac{1}{5} &= -\frac{2}{10} \end{aligned}
    and again I have no clue as to why this might be useful, and why it is phrased in terms of subtraction.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §12". <https://yawnoc.github.io/sun-tzu/i/12> Accessed yyyy-mm-dd.