Page 1
General Source of Computational Methods, Volume 7

Newly Compiled Direct Guide to the General Source of Computational Methods, Volume 7

Compiled by Cheng Dawei (pseudonym Binqu, courtesy name Rusi) of Xin’an
Revised by his great-grandson Cheng Guangshen (pseudonym Suting, courtesy name Peiwei)
Reviewed by Cheng Maoguang and Cheng Mianhong (courtesy name Shengfu)

Methods for Dividing Fields and Partitioning Areas

This section deals with land surveying, specifically how to calculate the dimensions required to "cut out" a specific area of land from a larger plot for sale, taxation, or inheritance.

Rhyme for Partitioning Areas of Rectangular Fields

The method for partitioning rectangular fields is truly marvelous;
To cut along the length, divide the desired area by the width.
To cut along the width, dividing by the length is just as easy;
Once you obtain the distance in paces, have no further doubt.

The method states: If you wish to cut a section based on the original length, then divide the target area by the original width.
If you wish to cut a section based on the original width, then divide the target area by the original length.
In modern terms, this is the simple formula: Area = Length × Width. Therefore, to find the necessary length to reach a certain area, one uses Length = Area / Width. The "paces" (bu, a unit of length) refer to the measurement used by surveyors on the ground.