So, the total work that we can get out must be zero, out of the whole sum of them.

因此，我们可以从这两个热机,得到的总功，一定是零。

麻省理工公开课 - 热力学与动力学课程节选

To get the best fitting line, you find the line that minimizes the sum of squared distances.

要找到最切合的直线,就是要使,这些距离的平方和最小

耶鲁公开课 - 金融市场课程节选

Okay, so that tells you how to add two vectors and get a sum.

这就是矢量的加法法则

耶鲁公开课 - 基础物理课程节选

The sum of path number 2 and path number 3 get me to the same place, so the energy change by going through this time path, this intermediate point here back all the way to final state should be the same the red path.

而经过路径2和3可以3,到达同样的末态，因此经过路径,2和3带来的能量的变化，与路径1带来的,能量变化相同。

麻省理工公开课 - 热力学与动力学课程节选

If you want to add two vectors, you can add the arrows by the rule I gave you or just add the components of x of the two guys to get the component of the sum and likewise for the y.

如果要把两个矢量相加,你可以用我教给你们的箭头相接的方法,或者就将二者的 x 分量相加,得到和矢量的 x 分量,y 方向也是这样

耶鲁公开课 - 基础物理课程节选