Systematic Treatise on Computational Methods: Volume 12

Divide the sum of all sides original: 弦和和, literally "Hypotenuse-Sum-Sum," referring to the sum of the base, height, and hypotenuse (27 + 36 + 45 = 108). by 108; this yields 60, which is the hypotenuse-difference sum. ○ Use this hypotenuse-difference sum to divide the previous dividend to obtain the sum of all sides. The value 60 likely refers to a different triangle example, such as the 30-40-50 triangle, used here as a general procedural placeholder.

Subtracting the height-hypotenuse difference (9) from the base-hypotenuse sum (72) results in 63, which is the base-height sum Calculation: (Hypotenuse + Base) - (Hypotenuse - Height) = Base + Height. Numerically: 72 - 9 = 63.. ○ Subtracting the base-height difference (9) from the base-hypotenuse sum (72) leaves 63, which is the hypotenuse-difference sum This term refers to the sum of the hypotenuse and the difference between the other two sides. In this specific set of calculations, the result 63 is used as a functional equivalent in the derivation..

Adding the base (27) to the sum of the hypotenuse and leg-difference (54) results in 81, which is the height-hypotenuse sum. ○ Adding the height (36) to the base-hypotenuse difference (18) results in 54, which is the sum of the hypotenuse and leg-difference. ○ Subtracting the base-hypotenuse difference (18) from the height (36) leaves 18, which is the base-hypotenuse difference.

Adding the height (36) to the height-hypotenuse difference (9) results in 45, which is the hypotenuse. ○ Adding the base-height difference (9) to the height-hypotenuse difference (9) results in 18, which is the base-hypotenuse difference.

Subtracting the base-height difference (9) from the height-hypotenuse sum (81) leaves 72, which is the base-hypotenuse sum. ○ Adding the base-height sum (63) to the height-hypotenuse difference (9) results in 72, which is the base-hypotenuse sum. ○ Subtracting the base-height sum (63) from the height-hypotenuse sum (81) leaves 18, which is the base-hypotenuse difference.

Adding the base-height difference (9) and the base-height sum (63) results in 72; halving this yields 36, which is the height. ○ For the base-height sum of 63...