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坐标几何和微積分的发明,使十七世纪的数学大大地改变旧观。取相互垂直而直線做坐标轴,於是平面上任一点的位置可以其和這而直線的垂直距雕x,y做坐标而决定。这在今天已经成为一般人的常识;但当时发明确实是一件艰难的工作。设x,y为由某方程式所联系,如y~2=x~3则适合於这个方程式的点一般是在一曲線上。这种方法使平面上的曲線和x,y的方程式发生了一对一的对应关系,可以使几何问题化为代数问题,然后由代数的运算推出几何的结论;因为方程式的每一性质可变换为几何图形的性质。因此我们所研究的曲線范围大加扩充了。古代几何学中一些无
The invention of coordinate geometry and calculus allowed the seventeenth century mathematics to greatly change the old concept. Take the axes perpendicular to each other and make the axes, so the position of any point on the plane can be determined by the coordinates x and y of the vertical distance from the straight line. This has become the common sense of the people today; but at that time, the invention was indeed a difficult task. Let x and y be linked by an equation. If y~2=x~3, the point that is suitable for this equation is generally on a curve. This method makes a one-to-one correspondence between the curve on the plane and the x, y equations, which can make the geometry problem an algebraic problem, and then push the algebraic operation to derive the geometric conclusion; because each property of the equation can be transformed The nature of the geometry. Therefore, the range of the curve we have studied has been greatly expanded. Some of the ancient geometry