以物理学观点评中国古代数学著作

COMMENTARY ON ANCIENT CHINESE MATH-BOOKS IN THE LIGHT OF PHYSICS

该文从中国古代数学著作中梳理出与物理学相关的某些算题,它们的物理内容包括运动学、斜面、螺旋、堤坝设计与流体静力学、固体的比重、横梁高宽比数等。从历史观和价值观上分别对这些算题作出评述,同时也对古代数学与物理学相关性作出评估。

This paper points out the mathematical problems concerned with physics from ancient Chinese math-books, which include kinematics, oblique plane, spiral, and design of dykes and dams, as well as hydrostatics, specific gravity of solid, and ratio between the length and width of crossbeam. It comments on these problems in the view of history and value, respectively, and estimates the coherence between mathematics and physics in ancient times. In the mathematical problem about kinematics, not only time, distance, velocity and its direction, but also the concept of acceleration are included. The concepts of Yi Ji Li (益疾里) and Jian Chi Li (减迟里), which is equal to the concept of acceleration in physics, are put forward in the Jiu Zhang Suan Shu (Nine Chapters on the Mathematical Art). Although in resolving oblique plane problem the method similar to parallelogram analysing calculation was used by the ancient Chinese, the variety of acting force was first applied by them in the oblique plane movement. Over a long period of time, the problem of helix was not thought to belong to traditional Chinese science. However, an interesting problem about this is given in the ancient math-books. The strategy of design and the calculation method of screw-pitch about helix in Jiu Zhang Suan Shu are also described in the paper. The problem about the relation between distance and wheel perimeter in the Sun Zi Suan ding (Master Sun's Mathematical Manual) provides the evidence for Ji Li Gu Che (记里鼓车) invented during the Han and Jin Dynasties. Many concrete data about the design of dams are also found in the problems, which show that the ancients had profound knowledge of hydrostatics. Especially, the ancients knew that the thickness of dam bottom increases with the depth of water increasing, which is just the scientific understanding about the static pressure of water increasing with the depth of water increasing. In this paper, the specific gravity of 7 substances (gold, silver, lead, copper, iron, jade and stone)measured by the ancients and their history are illustrated. And measuring the specific gravity of some compound or calculating the content of each substance in it are difficult to some extent. Several methods for measuring specific gravity and their value in history are also included in the paper. In ancient mathematics, the concrete data about rectangular crossbeam intercepted from log are also recorded, which are no doubt the summing-up of experience by construction craftsmen. These records and the analyses of crossbeam about building in different dynasties indicate ancient China's scientific knowledge and development in understanding the ratio between the height and width of crossbeam. Lastly,the paper estimates the coherence between ancient mathematics and physics, and analyses the reason why ancient Chinese mathematicians failed to promote physics from experience to theory.