"Sun Tzŭ's Computational Classic: Volume II" 《孫子算經卷中》 §22

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
今有築城、上廣二丈、下廣五丈四尺、高三丈八尺、長五千五百五十尺。	Suppose there be [a] building of [a] wall, of upper breadth two rods, lower breadth five rods [and] four rules, height three rods [and] eight rules, [and] length five thousand five hundred [and] fifty rules.
秋程人功三百尺。問須功幾何。	[The] autumn quota [for a] person's output [is] three hundred rules. [We] ask, how many [people's] output [be] needed?	三百尺： three hundred rules In modern language these would be cubic rules. Version A has 湏 for 須.
答曰、二萬六千一十一功。	Answer saith: two myriad six thousand [and] eleven [people's] output.
術曰、并上下廣、得七十四尺、半之、得三十七尺。	Method saith: combining [the] upper [and] lower breadths, resulteth in seventy-four rules, [and] halving it, resulteth in thirty-seven rules.
以高乘之、得一千四百六尺。又以長乘之、得積七百八十萬三千三百尺。	Multiplying it by [the] height, resulteth in one thousand four hundred [and] six rules. And multiplying it by [the] length, resulteth in volume seven hundred [and] eighty myriad three thousand [and] three hundred rules.
以秋程人功三百尺除之、即得。	Dividing it by [the] autumn quota [for a] person's output, three hundred rules, [we] are done.	In modern notation, the effort required to build a trapezoidal prism of upper breadth A = 20 \unit{rules}, lower breadth B = 54 \unit{rules}, height H = 38 \unit{rules}, and length L = 5550 \unit{rules}, at rate R = 300 \unit{rules}^3 / \unit{person}, is \begin{aligned} W &= \frac{A + B}{2} \cdot H L \div R \\[\tallspace] &= \frac{20 \unit{rules} + 54 \unit{rules}}{2} \times 38 \unit{rules} \times 5550 \unit{rules} \div \frac{300 \unit{rules}^3}{\unit{person}} \\[\tallspace] &= 26011 \unit{people}. \end{aligned}

Source text

Target text

Notes

今有築城、上廣二丈、下廣五丈四尺、高三丈八尺、長五千五百五十尺。

Suppose there be [a] building of [a] wall, of upper breadth two rods, lower breadth five rods [and] four rules, height three rods [and] eight rules, [and] length five thousand five hundred [and] fifty rules.

秋程人功三百尺。問須功幾何。

[The] autumn quota [for a] person's output [is] three hundred rules. [We] ask, how many [people's] output [be] needed?

三百尺： three hundred rules
In modern language these would be cubic rules.
Version A has 湏 for 須.

答曰、二萬六千一十一功。

Answer saith: two myriad six thousand [and] eleven [people's] output.

術曰、并上下廣、得七十四尺、半之、得三十七尺。

Method saith: combining [the] upper [and] lower breadths, resulteth in seventy-four rules, [and] halving it, resulteth in thirty-seven rules.

以高乘之、得一千四百六尺。又以長乘之、得積七百八十萬三千三百尺。

Multiplying it by [the] height, resulteth in one thousand four hundred [and] six rules. And multiplying it by [the] length, resulteth in volume seven hundred [and] eighty myriad three thousand [and] three hundred rules.

以秋程人功三百尺除之、即得。

Dividing it by [the] autumn quota [for a] person's output, three hundred rules, [we] are done.

In modern notation, the effort required to build a trapezoidal prism of upper breadth A = 20 \unit{rules}, lower breadth B = 54 \unit{rules}, height H = 38 \unit{rules}, and length L = 5550 \unit{rules}, at rate R = 300 \unit{rules}^3 / \unit{person}, is
\begin{aligned} W &= \frac{A + B}{2} \cdot H L \div R \\[\tallspace] &= \frac{20 \unit{rules} + 54 \unit{rules}}{2} \times 38 \unit{rules} \times 5550 \unit{rules} \div \frac{300 \unit{rules}^3}{\unit{person}} \\[\tallspace] &= 26011 \unit{people}. \end{aligned}

《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§22. Volume of a trapezoidal prism (2)

Translation

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《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II" §22. Volume of a trapezoidal prism (2)

Translation

Cite this page

《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§22. Volume of a trapezoidal prism (2)