《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§10. Volume exchange rates for grain & rice

This section gives exchange rates for trading various types of grain and rice.

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
以粟求糲米、三之、五而一。
以糲米求粟、五之、三而一。
以糲米求飯、五之、二而一。
以粟米求糲飯、六之、四而一。
以糲飯求糲米、二之、五而一。
以糳米求飯、八之、四而一。		 Seeking coarse grain with grain: triple it, [with] five [being] one.
Seeking grain with coarse grain: quintuple it, [with] three [being] one.
Seeking [coarse] rice with coarse grain: quintuple it, [with] two [being] one.
Seeking coarse rice with grain: sextuple it, [with] four [being] one.
Seeking coarse grain with coarse rice: double it, [with] five [being] one.
Seeking [intricate] rice with intricate grain: octuple it, [with] four [being] one.
  • Version A erroneously has 米粟求糲米 for 以粟求糲米.
  • 粟： grain

    As opposed to 糲 "coarse-grain", or 糳 "intricate-grain", to follow.

  • 糲： coarse(-grain)

    糲、力制切、音勵、 Cantonese: lai6, Mandarin: lì

  • 粟米： grain

    This is not a nice paragraph to render into English (hence the colours). I am overloading the word "grain" with both 粟 "grain" (in contrast to 糲 "coarse-grain", and 糳 "intricate-grain") and 米 "grain", i.e. "uncooked rice" (in contrast to 飯 "cooked-rice", which I am just calling "rice" for brevity).

  • Version C erroneously has 绺 for 糳.
  • 糳： intricate(-grain)

    糳、 Cantonese: tsok9 (post-merger: chok9), Mandarin: zuò

  • These are volume exchange rates to be used when trading grain and rice; I'm not sure why 6/4 and 8/4 haven't been simplified. In modern notation:
    \gdef\vol#1{V(\text{#1})} \begin{aligned} \vol{coarse grain} &= \frac{3}{5} \cdot \vol{grain} \\[\tallspace] \vol{grain} &= \frac{5}{3} \cdot \vol{coarse grain} \\[\tallspace] \vol{coarse rice} &= \frac{5}{2} \cdot \vol{coarse grain} \\[\tallspace] \vol{coarse rice} &= \frac{6}{4} \cdot \vol{grain} \\[\tallspace] \vol{coarse grain} &= \frac{2}{5} \cdot \vol{coarse rice} \\[\tallspace] \vol{intricate rice} &= \frac{8}{4} \cdot \vol{intricate grain}. \end{aligned}

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §10". <https://yawnoc.github.io/sun-tzu/i/10> Accessed yyyy-mm-dd.