...trailing on the ground by 2 feet. Use this "hypotenuse-difference" The difference between the length of the rope (hypotenuse) and the height of the pole (vertical side). as the divisor. The result is 30. Add the hypotenuse-difference of 2 feet to get 32. Halve this to get the rope length of 12 feet original: "1 zhang 2 chi." Note: There appears to be a minor calculation or transcription error in the original source here; mathematically, if the base were 8 and the difference 2, the length should be 17.. Subtract the difference of 2 feet from the hypotenuse to get the timber height of 15 feet original: "1 zhang 5 chi.", which is the vertical side.

Method for Finding the Hypotenuse-Difference

Suppose there is a curtain hanging outside a hall door. When hanging straight down, the bottom of the curtain is 5 inches 寸 (cun): a Chinese inch, 1/10th of a foot above the ground. If you pull the curtain 6 feet away from the door, the bottom is then 2 feet 5 inches above the ground. What is the height of the curtain?

The method says: Set the 6-foot distance from the door as the base side 勾 (Gou): the horizontal side of a right triangle. Multiply it by itself to obtain 36. Take the 2 feet 5 inches distance from the ground and subtract the original 5-inch distance; the remainder of 2 feet is the hypotenuse-difference. Divide the squared base (36) by this difference to obtain 18 feet. Add the hypotenuse-difference of 2 feet to get a total of 20 feet. Halve this result to get the curtain height of 10 feet. This matches the problem.

Suppose there is a door being opened. When pulled 1 foot away from the frame, the gap is 2 inches... This text cuts off and likely continues on the following page.