"Half-width times positive" means that the area of a triangle is equal to half the product of height and base length. "Half-width Multiply with" comes from Nine Chapters of Arithmetic.
Nine Chapters Arithmetic is a mathematical monograph written by Zhang Cang and Geng Shouchang in ancient China. It is the most important of the ten computing classics, written about the first century A.D., and its author can no longer be examined. It is generally believed that it has gradually become the final version after several generations of supplement and modification. Zhang Cang and Geng Shouchang in the Western Han Dynasty had been supplemented and sorted out, and they were generally finalized at that time. The last book was written at the latest in the early years of the Eastern Han Dynasty, and most of it was circulated in the Three Kingdoms period, that is, the fourth year of Jingyuan (263).
"Nine Chapters Arithmetic" is very rich in content and summarizes the mathematical achievements in the Warring States, Qin and Han Dynasties. At the same time, Nine Chapters Arithmetic has its unique achievements in mathematics. It not only mentioned the problem of score at the earliest, but also recorded the problem of surplus and deficiency at the earliest. Zhang Equation also expounded the negative number and its addition and subtraction algorithm for the first time in the history of world mathematics. It is a comprehensive historical work and the most concise and effective applied mathematics in the world at that time. Its appearance marks the formation of a complete system of ancient mathematics in China.
Appreciation of works:
"Nine Chapters Arithmetic" defines the framework of ancient mathematics in China, which is characterized by focusing on calculation, closely linking with practice and aiming at solving mathematical problems in people's production and life. Its influence is so profound that China's mathematical works will generally take two forms in the future: either taking notes for it or writing books in its style; Even after the introduction of western calculus into China, people often put mathematical knowledge including western calculus in the framework of nine chapters when writing books.
However, Nine Chapters Arithmetic also has its shortcomings that can not be ignored: there is no definition of any mathematical concept, and no derivation and proof are given. In the fourth year of Wei Jingyuan (263), Liu Hui made comments on Nine Chapters Arithmetic, which greatly made up for this defect.