论文标题
在Desargues仿射平面上的4分的交叉比率的不变和保存转换
Invariant and Preserving Transforms for Cross Ratio of 4-Points in a line on Desargues Affine Plane
论文作者
论文摘要
本文介绍了在Desargues仿生平面中的一条线的交叉比的变换的几何形状的进步。此处给出的结果具有干净的，基于干净的DESARGUES AXPINE PLAN AXIOMATION和该平面线上点的添加和乘法的定义，以及用于偏斜的场属性。在本文中，研究了与四点的交叉比例的某些变换有关的属性和结果，我们将其分为两类，分为\ emph {不变}和\ emph {保留}的交叉比率。本文的结果是（1）四个点的交叉比例为\ emph {不变}下的变换：反转，自然翻译，天然扩张，mobiüs变换，在Desargues仿射平面的一系列中。 （2）在变换下，四个点的交叉比例为\ emph {保留}：平行投影，翻译和扩张在desargues仿射平面中。
This paper introduces advances in the geometry of the transforms for cross ratio of four points in a line in the Desargues affine plane. The results given here have a clean, based Desargues affine plan axiomatic's and definitions of addition and multiplication of points on a line in this plane, and for skew field properties. In this paper are studied, properties and results related to the some transforms for cross ratio for 4-points, in a line, which we divide into two categories, \emph{Invariant} and \emph{Preserving} transforms for cross ratio. The results in this paper are (1) the cross-ratio of four points is \emph{Invariant} under transforms: Inversion, Natural Translation, Natural Dilation, Mobiüs Transform, in a line of Desargues affine plane. (2) the cross-ratio of four points is \emph{Preserved} under transforms: parallel projection, translations and dilation's in the Desargues affine plane.
