Systematic Treatise on Arithmetic, Vol. 6 (1592) - Page 4

### Cutting the Length from a Rectangular Field

40 paces Original length: 48 paces Original width Length of the cut Area of the cut: 720 paces

The method states: Set the cut area of 720 paces as the dividend (shi). The shi is the total amount or area to be divided. Use the original width of 40 paces as the divisor (fa). The fa is the dimension used to divide the total area. Divide it to obtain the length of the cut, which is 18 paces. This matches the question.

Suppose there is a square field. From the southeast corner, a rectangular section with an area of 32 square paces is cut. The southern side is required to be 4 paces wide. The question asks: what is the length of the eastern side of the cut?

Answer: The length of the eastern cut is 8 paces.

Section C ### Cutting a Rectangle from a Square

South Width: 4 paces Length: 8 paces Area of the cut: 32 paces

The method states: Set the cut area of 32 paces as the dividend (shi). Use the southern width of 4 paces as the divisor (fa). Divide it to obtain the length of the eastern cut, which is 8 paces. This matches the question.

If the eastern length is a fixed number and the question asks for the southern width, simply use the length as the divisor and divide the cut area.

Suppose there is a rectangular field 15 paces long and 12 paces wide. Now, from the eastern side, an area of 50 The text concludes mid-sentence; based on the previous patterns, it likely continues to ask for the width of this 50-pace area.