Outline of the History of Ancient Chinese Science

Author: Chief Editor: Lu Jiaxi / et al
Publisher:
Publishing Date: 1998-06-01
Features:
Fragment: Three. The invention of early measuring tools such as calipers and rulers had a direct impact on the development of Chinese measurement technology. After the Qin and Han dynasties, measuring tools became increasingly specialized and refined. To measure length, zhanggans (measuring rods) and measuring ropes were invented, with the former used for short distances and the latter for long distances. There was also a soft tape measure made of bamboo strips, similar in length to a measuring tape. The goniometer evolved from an unmarked tool to a marked right-angle ruler. Additionally, levels, level scales, and compasses for determining direction were invented. Naturally, measurement methods also became more sophisticated, allowing not only the measurement of reachable targets but also unreachable ones. The sophistication of measurement methods brought advanced calculation techniques, enriching the content of Chinese mathematics. According to the Zhoubi Suanjing, a book compiled around 100 BC, during the early Zhou Dynasty (approximately 1000 BC), the Duke of Zhou Ji Dan discussed the use of the goniometer with Shang Gao in measuring methods. Shang Gao's "method of using the goniometer" included rich mathematical content. Shang Gao said, "Level the goniometer to straighten the rope, invert the goniometer to measure height, turn it back to measure depth, and lay it flat to measure distance." The phrase "invert the goniometer to measure height" means that if the goniometer is placed vertically, as shown in Figure 1-1-17, from one end A of the goniometer, one looks up at a high point E. The line of sight AE intersects CB at D. According to the properties of similar triangles, we can derive that the height X = AF · CD / AC. Here, CD / AC is the tangent of the angle EAF, but ancient China did not pay special attention to it. If the goniometer scale BC is turned upside down (see Figure 1118), known as "turning it back," the same principle can be used to measure the distance to a deep target. Similarly, if the goniometer scale CB is placed flat on a horizontal surface, the distance between distant targets can be measured. Shang Gao's "method of using the goniometer" is essentially what is now called right-angle measurement, which involves the Pythagorean theorem. Therefore, the Zhoubi Suanjing specifically cites examples such as "3-4-5." After the Qin and Han dynasties, some people wrote books to discuss in detail the use of the similarity of right-angled triangles for measurement. These works include the Zhoubi Suanjing, the Nine Chapters on the Mathematical Art, the Sea Island Suanjing, the Record of Mathematical Methods, the Mathematical Treatise in Nine Sections, and the Four-Element Jade Mirror, which together form the unique measurement theory of ancient Chinese mathematics.
Four. Understanding and Applying Diagonal Concepts
China has long been an agricultural-based society, with agriculture and handicrafts developing quite early and maturely. Advanced agriculture and handicrafts brought advanced technology, much of which included mathematical knowledge. According to the Kao Gong Ji, a book compiled during the Warring States period, people at that time already had an understanding of the concept of angles and applied it in the production of agricultural tools, vehicles, weapons, and musical instruments. The Kao Gong Ji states, "The work of the wheelwright: half a goniometer is called xuan, one and a half xuan is called que, one and a half que is called ke, and one and a half ke is called qingzhe." Here, "goniometer" refers to a right angle. Thus, "one xuan" is 45°, "one que" is 67.5°, "one ke" is 101°15′, and "one qingzhe" would be 151°52.5′. However, this is not entirely accurate. In the same book, "qingzhe" is also described as "one and a half goniometers," which would make it 135°. The emergence of specialized names for various angles reflects the understanding and application of angles in handicraft technology but also shows the primitive and limited nature of this understanding, reflecting the lack of emphasis on the mathematical significance of angles in ancient China. As we will see later, the reason why ancient Chinese mathematics did not develop theories related to angles, such as the similarity theory of general triangles, the theory of parallel lines, the relationship between the sides and angles of triangles, and trigonometry, is largely due to the insufficient understanding of the concept of angles. This made ancient Chinese mathematics adopt another approach to solving practical problems.
Five. Area and Volume Calculations
Calculations of area and volume are directly related to the establishment of tax systems and the perfection of the system of weights and measures. The Spring and Autumn Annals, an important classic from the pre-Qin period, records that in the 15th year of the Xuan Gong reign (594 BC), taxes were collected based on land area, with a 10% levy. This indicates that during the Spring and Autumn and Warring States periods, China already had methods for measuring land and calculating area and volume. These methods later appeared in the Nine Chapters on the Mathematical Art. However, it is certain that before the book was compiled in the 1st century BC, these methods must have already existed. Recent discoveries of Han Dynasty bamboo slips at ancient sites such as Juyan County in Gansu and Yinque Mountain in Linyi County in Shandong also provide evidence. Regarding the achievements of Chinese mathematics in area and volume calculations, we will provide a detailed introduction below. It is important to emphasize that these achievements gradually formed during the early accumulation of mathematical knowledge and became the foundation for later theories of area and volume.
Section 5. Definitions of Mathematical Concepts in the Mo Jing (Early Mathematical Logical Forms)
Ancient Chinese mathematics differs from ancient Greek mathematics in that it is not a deductive conceptual system based on logical reasoning but rather an algorithmic theory that is non-deductive. In this theory, concepts generally appear directly in problems and algorithms rather than in the exploration of relationships between concepts. Therefore, when performing calculations or constructing theories, there is less need to apply logical methods for conceptual generalization, including defining concepts. However, this does not mean that ancient China did not have mathematical concept definitions. During the Spring and Autumn period of the Hundred Schools of Thought, the Mohists and the School of Names proposed many definitions of mathematical concepts for the sake of argumentation. Among these, the Mo Jing is the most concentrated. The Mo Jing consists of 35 chapters, with the four chapters "Jingshang," "Jingshuo Shang," "Jingxia," and "Jingshuo Xia" being collective works of later Mohists, compiled around the 4th to 3rd centuries BC. The "Jing" records definitions of mathematical concepts, while the "Jingshuo" provides necessary supplements and explanations. The following are the definitions of mathematical concepts mentioned in the book:
(1) [Jing] Ping, meaning the same height. [Jingshuo] Ping refers to the level of the platform, like brothers.
(2) [Jing] Zhong, meaning the same length. [Jingshuo] The heart, zhong, are mutually similar from this point onward.
(3) [Jing] Yuan, meaning one center with the same length. [Jingshuo] Yuan refers to the mark made by a compass.
(4) [Jing] Tongchang, meaning to extend to the same length. [Jingshuo] Tong refers to the same length as the madman.
Postscript:
China is one of the four ancient civilizations of the world and the Chinese nation is one of the greatest nations in the world. Our ancient and brilliant science and culture were the crystallization of the labor and powerful weapons of our ancestors in their struggle for survival, development, and against nature; they were also a valuable asset that made significant contributions to human civilization in history. Uncovering and organizing the history of science and technology undoubtedly has profound historical significance and important practical significance for promoting traditional national culture and for the advancement of human society that looks back on the past and forward to the future. This book is the result of years of collective effort by the editorial committee members. Professor Lu Jiaxi and Professor Lu Yongxiang served as the chief editors; the other chief editors for each discipline are as follows:
Outline of the History of Mathematics: Yuan Xiaoming
Outline of the History of Physics: Wang Jin Guang Hong Zhen Huan
Outline of the History of Chemistry: Zhou Jia Hua
Outline of the History of Astronomy: Zhao Cheng Qiu Liu Jin Yi
Outline of the History of Geography: Yu Xi Xian
Outline of the History of Biology: Wang Zi Chun
Outline of the History of Agriculture: Min Zong Dian
Outline of the History of Medicine: Li Jing Wei Wang Yu Sheng
Professor Wang Yu Sheng served as the executive editor, overseeing various aspects of the book.
In short, after years of effort and hard work, the book has been published in a timely manner. Of course, it also includes praise for the spirit of teamwork and selfless dedication, as well as a sense of remembrance for the authors who passed away prematurely due to overwork. This is the postscript, and it is hereby recorded.