帕普斯问题中的算术术语使用——从笛卡尔《几何》的视角  

The Arithmetical Terminology in Pappus' Example: From the Perspective of Geometry of Rene Descartes

作　　者：高剑平[1] 罗栋[2] 何玉艳[1] 

机构地区：[1]广西民族大学政治学与国际关系学院,广西南宁530006 [2]中国科学院大学人文学院,北京100049

出　　处：《自然辩证法通讯》2014年第1期97-102,128,共6页Journal of Dialectics of Nature

基　　金：教育部人文社会科学研究2011年规划基金项目(11YJA720009);广西教育厅2012年重点项目"笛卡尔的解析几何思想与近代科学认识论"阶段性成果

摘　　要：对数学术语的理解和使用方式的变化,往往蕴含着数学思想的重大转变。笛卡尔《几何》中对于帕普斯问题的相关论述显示:古代数学家未能区分清楚表征几何对象自身属性的算术术语和表征几何对象与其它几何对象之间关系的算术术语。对于五线及更多数目直线的情形,古代数学家一方面认为存在确定的待求线,但不能确定待求曲线是什么,同时又声称无法确定它们的存在。对陌生的或尚未被研究的几何曲线,古人使用算术术语描述几何问题时很容易造成费解。笛卡尔与古代数学家对几何中算术术语使用的不同态度,以及直尺和圆规作图的运动解释,有助消除这种费解。这些从侧面反映出:笛卡尔《几何》一书蕴含并反映了数学思想的重大转变。Terminology changes tend to indicate the great transformation of mathematical thoughts. Pappus' example is one of the key problems which are discussed in Geometry of Rene Descartes. In Pappus' example, it was not explained that how and why ancient mathematicians used arithmetical terms in geometry. What explanations ancient mathematician made and why they caused obscurity and embarrassment are not very clear. The analysis of passages on Pappus' example shows that there are different kinds of arithmetical term use in geometry, and ancient mathematicians misused them. It not only limited the range of the study, but also made the use of arithmetical terms in geometry obscure in ancient mathematics. When ancient mathematicians could not find the properties of a geometrical object, their presentations about the object could be very incomprehensive. Descartes made the antiquity's descriptions understandable by redefining the arithmetical terminology in geometry. It reflected the transformation of mathematical thoughts.

关 键 词：笛卡尔 《几何》算术 几何 算术术语 

分 类 号：O11[理学—数学]