对於所謂“初等”数学来說,还保存着来自希腊科学的,一方面是代数方法而另一方面又是直观的几何概念的这种彼此分裂的特征。誠然,在解几何問題时常常要用到某些代数方法,但是在初等数学中,沒有把几何問題归結为代数問題的一般方法,同样也沒有对代数公式和代数关系式作几何解釋的一般方法。这样的一般方法中最簡單的是在空間中引入坐标系。这就使我們有可能在空間中的每一个点与三个实数x,y,z的数組之間建立起对应,与量x,y,z有关的每一个方程可以解釋为空間中的某一个面等等。这样一来,坐标法首先使我們能按照完全确定的法則,系統地利用代数以解决几何問題,分类和討論各种不同的几何形象(曲線,曲面等),其次使我們有可能按照非常一般的法則,对各种不同的代数关系式作几何解釋,例如,任何一个線性方程 For the so-called “elementary” mathematics, this is also a separate feature from the Greek science, on the one hand, algebraic methods and on the other hand intuitive geometric concepts. It is true that some algebraic methods are often used to solve geometric problems, but in elementary mathematics, there is no general method for reducing geometric problems to algebraic problems, nor is there any general explanation for algebraic formulas and algebraic relations. method. The simplest of such general methods is to introduce coordinate systems in space. This makes it possible to establish a correspondence between each point in space and an array of three real numbers x, y, z. Each equation related to the quantities x, y, z can be interpreted as a space One side and so on. In this way, the coordinate method first allows us to systematically use algebra to solve geometric problems, classify and discuss various geometric images (curves, surfaces, etc.) in accordance with fully-determined rules, and secondarily make it possible to follow very general Laws, geometric interpretation of various algebraic relations, for example, any linear equation