Eudoxus’s Theory Of Proportions And Its Influence

Eudoxus’s theory of proportion is a kind of method in order to clear the irrational number brings the mathematical crisis.lt had an irreplaceable role on the structure of real number. In this article. through reading related books.using historical ana lysis.comparative approach.on the basis if the predecessors.the author of the paper has done a detailed analysis and study of the evolution of ideas from Eudoxus theory of proportions to the Dedekin segmentation.The main work is as follows:Firstly.the paper elaborates the background of Eudoxus’s theory of proportions in detail.and makes a further research of the idea of mathematics and geometry tradition of the ancient Greek.Secondly.the writer reads up Euclid’s "Elements of Geometry" part of the theory of proportions.so the writer has carrying out a comprehensive interpretation to the theory of proportions.Describes the theory of proportion’s system.content and the difference or contact with the other parts. We can see that the theory of proportion is the most wonderful chapter in Elements of Geometry.Thirdly.the paper elaborates the background of the Dedekin segmentation.excavates the the source of thought of Dedekin segmentation.it was derived from the understanding of linear continuous.defined the irrational number by using the the method of segmentation of all rational number.The paper also has giving a comparative study on Eudoxus theory of proportions and Dedekin segmentation,points out their basic thought are the same.