Illustrated Commentary on the Nine Chapters on the Mathematical Art, Volume 1, Field Measurement

It is not possible to speak of the "power" in general terms; it is based on the single plane of the width and length. The term "product" refers to the total number of accumulated steps. The Classic says "multiplying gets the square steps," which is the clear text for the total number. The commentary says it is "called a power," which fully captures the original intention of multiplying for square steps. The previous commentary said "the product is the field's power," which is understandable in principle. But then it says "it is called a power," which is redundant and inaccurate. Now, I will preserve the commentary, remove the incorrect parts, and briefly simplify it for the benefit of later students.

Divide by the mu method of 240 steps to get the number of mu; 100 mu make one qing.

I, Chunfeng, and the others, respectfully observe that this is the beginning of the chapter, so we specifically list the two methods of qing a larger unit of land area and mu a smaller unit of land area. Other rules are not repeated, as they can be understood from this. For every mu of land, if the width is 10 steps and we distribute the length, we make 15 rows. If each row is 1 step wide and we cross-cut it into 16 rows, each row is 1 step wide and 16 steps long. This is the result of distributing and cross-cutting, with each step forming a square. There are 240 steps in total; the number of steps is exactly the same. Speaking from this, the multiplication of width and length to get square steps is verified. The 240 steps constitute the mu method. The 100 mu constitute the qing method. Therefore, by dividing by these, one obtains the mu.

The calculation procedure states: Place the width of 15 steps in the upper position, and also place the length of 16 steps in the lower position. In the upper position, there are ten steps; for ten or more, call out: once for the lower, one, one, one, like one.