```The epistemology concepts in Descartes’
coordinate geometry

LUO Dong, GAO Jianping
Center for Studies of STS，Guangxi
University for Nationalities

[email protected]
I. Differences between Descartes’ geometry and
Euclidean geometry

II. Epistemology basis of Descartes’ geometry

I. Differences between Descartes’ geometry and
Euclidean geometry

1. Geometric constructions need Algebraic operations
1、几何作图要求对线段作加减乘除，对特别的线段取平方根，这几种运算均

2. Differences between Descartes’ geometry and Euclidean
geometry
a. Different points
Euclidean geometry: points indiscernible
Descartes’ geometry: points discernible
2、笛卡尔解析几何与欧几里德几何之间的差异
a.点的差异

I. Differences between Descartes’ geometry and
Euclidean geometry

2. Differences between Descartes’ geometry and Euclidean geometry
b. relationship between point and lines
Euclidean geometry: points are on lines
Descartes’ geometry: lines are the traces of points’ movements
2、笛卡尔解析几何与欧几里德几何之间的差异
b.点与线之间关系差异

I. Differences between Descartes’ geometry and
Euclidean geometry

2. Differences between Descartes’ geometry and Euclidean geometry
c. Quantization of space in coordinate systems
Euclidean geometry: geometrical figures’ relationship is base on
their own properties
Descartes’ geometry: geometrical figures’ relationship is base on
coordinate system
2、笛卡尔解析几何与欧几里德几何之间的差异
c.几何图形之间关系差异

I. Differences between Descartes’ geometry and
Euclidean geometry

2. Differences between Descartes’ geometry and Euclidean geometry
d. Intuitiveness of geometrical figures
Euclidean geometry: the figures are in mind when we solve geometrical
puzzles
Descartes’ geometry: we face algebraic equations when we solve
geometrical puzzles
2、笛卡尔解析几何与欧几里德几何之间的差异
d.几何直观性之间的差异

II. What do these differences mean

1. Ontology and epistemology in Euclidian geometry
(1)Most of the laws in Elements could be from the school of Plato
(2)points, lines and surfaces are ideas
(3)these geometrical ideas are being, and not come into being.
1、欧几里德几何中的本体论和认识论
（1）几何原本中大部分定律来自柏拉图学派
（2）点、线、面均是理念
（3）几何理念作为一种存在者而存在，而不解释这些线、图形如何形成(点线面

II. What do these differences mean

2. Epistemology in Descartes’ geometry
(1)Lines are the traces of the motion of points.
(2)Lines and figures come into being.
(3)Relationship of geometrical figures are the relationship of points, and the
geometrical space turns to be algebraic space
2、笛卡尔解析几何中的认识论
（1）受伽利略研究抛物运动影响将曲线当成质点运动轨迹。
（2）曲线和图形不是既定的存在者，而是形成的，存在着。
（3）几何空间关系时是点与点之间关系，是代数方程（组）内变量之间关系，空间数

Conclusion

Descartes’ geometry is his critics of ontology in geometry.
Being turns to coming into being, and ontology turns
into epistemology in geometry

Thanks!

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