... divide by the method to obtain a cut length of 40 paces. Multiply this by the original width of 30 paces to get 1,200 The OCR reads 1,003, but mathematically 40 multiplied by 30 is 1,200. as the shi: dividend. Divide this by the original length of 75 paces, acting as the fa: divisor, to obtain a cut width of 18 paces. This matches the question.

Suppose there is a right-angled triangular field with a length of 40 paces and a width of 20 paces. Now, a section with an area of 175 square paces is to be cut from the wide end. The question asks: what are the length and width of this cut section?

Cutting Area from a Right-Angled Triangle

The answer states:
The cut length is 10 paces.
The upper width of the cut is 15 paces.

The method states: First multiply the width original: 勾 (gou) and the length original: 股 (gu) together and halve the result to find the total area of 400 paces. Subtract the cut area of 175 paces; the remaining area of 225 paces will serve as the zhu: primary value.

Determining the Dimensions of the Cut when the Area of the Small Tip is Known

〇 Set the area of the small tip, 225 paces, and double it to get 450.
Multiply this by the original length of 40 paces to get 18,000. Divide this by the original width of 20 paces to get 900 as the shi: dividend. Using the method of extracting the square root original: 開平方法 (kai ping fang fa), we find the length of the remaining upper tip to be 30 paces. Then, using this value as a divisor...