Illustrated Commentary on Nine Chapters, Vol. 1

...the roots of arithmetic. During my leisure from examining these deep mysteries, I realized their intent. Therefore, I dared to exhaust my stubborn ignorance to gather what I have seen and compose a commentary. When the various matters are inferred by their categories, each has a place to return. Although the branches may divide, they share the same root; one only needs to trigger a single end to understand the rest. Furthermore, the principles I have analyzed are explained with words, and the applications are illustrated with diagrams, so that they might be concise yet comprehensive, clear yet not exhaustive. The reader who contemplates this will understand more than half of it. Moreover, arithmetic is among the Six Arts. In antiquity, the government promoted the virtuous and capable and taught them in the national schools. Although it is called the Nine Numbers, it can penetrate the subtle and enter the minute, exploring without limitation. As for how the methods are passed down, they are like using a compass and a square; they can be mastered together, and it is not particularly difficult. Today, those who love this are few. Therefore, even if the world has many talented scholars, they may not necessarily be able to master this. The Office of the Grand Minister of Instruction in the Rites of Zhou states that at the summer solstice, at midday, one erects a gnomon A rod used to measure shadows. of eight feet; its shadow is one foot and five inches, which is called the "Earth's Center." The commentary says that to the south, one wears the sun at a distance of 15,000 miles. Regarding this statement, one can deduce it through mathematical methods. According to the Nine Chapters, one establishes four...