《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§11. Some equivalent fractions (1)

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
十分減一者、以二乘、二十除。
減二者、以四乘、二十除。
減三者、以六乘、二十除。
減四者、以八乘、二十除。
減五者、以十乘、二十除。
減六者、以十二乘、二十除。
減七者、以十四乘、二十除。
減八者、以十六乘、二十除。
減九者、以十八乘、二十除。		 Subtracting one of ten shares: multiply by two, [and] divide [by] twenty;
subtracting two: multiply by four, [and] divide [by] twenty;
subtracting three: multiply by six, [and] divide [by] twenty;
subtracting four: multiply by eight, [and] divide [by] twenty;
subtracting five: multiply by ten, [and] divide [by] twenty;
subtracting six: multiply by twelve, [and] divide [by] twenty;
subtracting seven: multiply by fourteen, [and] divide [by] twenty;
subtracting eight: multiply by sixteen, [and] divide [by] twenty;
subtracting nine: multiply by eighteen, [and] divide [by] twenty.
  • 分： shares

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

  • I think this is saying
    \begin{aligned} -\frac{1}{10} &= -\frac{2}{20} \\[\tallspace] -\frac{2}{10} &= -\frac{4}{20} \\ & \enspace \vdots \\ -\frac{9}{10} &= -\frac{18}{20}, \end{aligned}
    but I have no clue as to why this might be useful, and why it is phrased in terms of subtraction. Ditto for the next section (§12).

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §11". <https://yawnoc.github.io/sun-tzu/i/11> Accessed yyyy-mm-dd.