A tangent is a straight line that just touches a curve, so the concept of "running the tangents" is to run the shortest distance possible by running straight from one curve to the next.

切线是一条直线，刚好接触到曲线，所以跑切线是从一个弯道跑到另一个最短的距离。

youdao

To solve the problem about determinant and solution to tangent line of curve of second order in Analytic Geometry with viewpoint and methods of Higher Geometry.

利用《高等几何》的观点、方法解决《解析几何》中的二次曲线的切线的存在性与求法问题。

youdao

The procedure used to define the derivative has a geometric interpretation which leads in a natural way to the idea of a tangent line to a curve.

微分的定义步骤有一个几何解释，最简单的观念就是一条曲线的切线。

youdao

I don't know how well you can see it in this figure here, is the slope of a straight line connecting these two points, and as the points come closer and closer, the straight line would become tangent to the curve.

我不清楚你们对于这个图像的理解,这条连接两点的斜线,随着两点距离逐渐缩小,两点连线会变成曲线的切线

耶鲁公开课 - 基础物理课程节选