论古希腊的“无理线段”——对《几何原本》第十卷内容的分析

On Irrational Lines of Ancient Greece——Analysis of Tenth Book of Euclid's Elements

本文用现行数学符号重现了欧几里得《几何原本》第十卷中的十三类无理线段,并论述了它们之间的内在联系.结论中指出,欧几里得研究的无理线段仅限于建立在毕达哥拉斯定理以及线段的有理运算上.虽然本卷内容丰富,结构严谨,但由于没有摆脱几何的约束,因而对无理数理论的发展没有实质性的突破.

In this paper,we reappear thirteen irrational lines in tenth book ofEucld's Elements with now mathematical symbols,and discuss theirinternal relations.we point out Eucbid's study established only on pyt-hagoras' theorem and rational operation of lines.Although it's rich incontent and its structure is strict,but it had not essence developmenton irrational number theory.