《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§9. Area of a rectangle

This section gives a worked example of computing the area of a rectangle.

The relevant unit conversion for length is

1 \unit{rod~(丈)} = 10 \unit{rules~(尺)}.

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
今有屋基、南北三丈、東西六丈、欲以甎砌之。凡積二尺、用甎五枚。問計幾何。	Suppose there be [an] house foundation, three rods north–south, [and] six rods east–west, [and we] wish to assemble it with bricks. Every two rules of area, useth five bricks. [We] ask, how many amounteth [this] to?	南北： north–south; lit. south–north Version C erroneously has ● `U+25CF` for both instances of 甎. 枚 Classifier for bricks, omitted in the English.
答曰、四千五百枚。	Answer saith: four thousand five hundred [bricks].
術曰、置東西六丈、以南北三丈乘之、得一千八百尺。以五乘之、得九千尺。以二除之、即得。	Method saith: put [down the] six rods east–west; multiplying it by [the] three rods north–south, resulteth in one thousand eight hundred rules. Multiplying it by five, resulteth in nine thousand rules. Dividing it by two, [we] are done.	九千尺： nine thousand rules This is area, but Literary Chinese does not distinguish square units from linear units. In modern notation, the number of bricks required to fill a rectangle of length L = 3 \unit{rods} and width W = 6 \unit{rods} at number density \rho = 5 / (2 \unit{rules}^2) is \begin{aligned} N &= L W \rho \\ &= 3 \unit{rods} \times 6 \unit{rods} \times \frac{5}{2 \unit{rules}^2} \\ &= 4500. \end{aligned}

Conway (2023). "Sun Tzŭ's Computational Classic: Volume II §9". <https://yawnoc.github.io/sun-tzu/ii/9> Accessed yyyy-mm-dd.