Illustrated Commentary on Nine Chapters, Vol. 1

The lü ratio/rate of three constitutes the "given number," and four constitutes the "required number." Regarding the gougu right-angled triangle (lit. base and altitude), they are collectively categorized under lü. Master Liu's referring to Liu Hui, the third-century mathematician commentary states: "The gou-lü base-ratio and gu-lü altitude-ratio are seen in the base and altitude." Now, simply stating that they are of the same form is done for brevity and simplicity. The method of "multiplying differently and dividing the same" original: "異乘同除" a technique for solving proportions by cross-multiplication yields the same result. Zhongxiang, Li Huang.