《孫子算經卷下》 "Sun Tzŭ's Computational Classic: Volume III"
§21. Unit conversion (2)

This section gives a worked example of unit conversions.

The relevant unit conversions for length are

\begin{aligned} 1 \unit{length~(匹)} &= 4 \unit{rods~(丈)} \\ 1 \unit{rod~(丈)} &= 10 \unit{rules~(尺)} \\ 1 \unit{rule~(尺)} &= 10 \unit{inches~(寸)}. \end{aligned}

See Vol. I §1 (Units of length).

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
今有錦一匹、直錢一萬八千。問丈尺寸各直幾何。 Suppose there be brocade one length, worth coins one myriad [and] eight thousand. [We] ask, how much [be] each of [each] rod, [each] rule, [and each] inch worth?
答曰、丈四千五百錢、尺四百五十錢、寸四十五錢。 Answer saith: [each] rod four thousand five hundred coins, [each] rule four hundred [and] fifty coins, [and each] inch forty-five coins.
術曰、置錢一萬八千、以四除之、得一丈之直。 Method saith: put [down the] coins one myriad [and] eight thousand; dividing it by four, resulteth in [the] worth of [each] one rod.
  • Version C erroneously has 得尺寸之直 before 得一丈之直.
一退再退、得尺寸之直。 Retreating once [and] retreating again, resulteth in [the] worth of [each] rule [and each] inch.
  • 再： again; or twice
  • In modern notation,
    \begin{aligned} \frac{18000 \unit{coins}}{1 \unit{length}} &= \frac{18000 \unit{coins}}{4 \unit{rods}} \\[\tallspace] &= 4500 \unit{coins} / {\unit{rod}} \\ &= 450 \unit{coins} / {\unit{rule}} \\ &= 45 \unit{coins} / {\unit{inch}}. \end{aligned}

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume III §21". <https://yawnoc.github.io/sun-tzu/iii/21> Accessed yyyy-mm-dd.