试论《九章算术》的问题设计

A TENTATIVE DISCUSSION ON THE DESIGN OF PROBLEMS IN NINE CHAPTERS ON THE MATHEMATICAL ART

该文对《九章算术》中问题的设计和组织，以及编著者设计和组织问题的总目标进行了研究，认为：（１）《九章算术》的题设有“表”、“里”两层含义。从表面上看，《九章算术》是应用题集；从深层看，它是一部钩沉索隐，把握群数之赜，展开为数之道，并以象征形式表达“赜”与“道”的著作。（２）两层含义间的关系是，表层看到的实际应用问题是深层探讨和表达数之“赜”、数之“道”时观象的对象、取象的借鉴和表象的形式。（３）《九章算术》以题设为主体构成全书，术文服从题设。（４）《九章算术》具有美学价值，它要求研读者与编著者的创作心态共鸣，以透过可见的表象，领悟作品的深层内涵。（５）从中西科学对比来看，中国传统精密科学的这种整体的、象征的思维和表达方式，对于离开抽象和分析就寸步难行的西方现代思维方式的转化可能有借鉴的意义。

After inquiring into the design and organization of 'problems' in Nine Chapters on the Mathematical Art, and the main goal of its compiler in designing and organizing them, this paper deems that:(1)The 'prpblems' of the work have two levels ofmeaning.So,on the surface, this is a book on applied mathematics i but as regards what ishidden obscurely under the surface, this is a book dealing with the 'Ze' of numbers and the'Way' of mathematics which are expressed in a symbolic manner;(2) The practical 'problems' on the surface are symbols for observing facts, taking images and expressing the 'Ze'and 'Way' in the depths under the surface;(3)The main body of the book consists of 246'problems', and the part on 'methods' is subordinated to the 'problems'; (4) The book,which has aesthetical value,asks its readers to sympathize with the compiler's creative frameof mind and to grasp the latent meaning under the surface.