Look at line fifty-five: "Ay me, I fondly dream! / ?" Had ye been there -- for what could that have done?"

看第55行：“哎，我啊！，我在痴呆的幻想/,如果你们女神们在那儿，又能怎样呢“

耶鲁公开课 - 弥尔顿课程节选

Therefore, the vector A that you gave me, I have managed to write as i times Ax plus j times Ay.

这样,你给我的矢量 A,我已把它写成 i ? Ax + j ? Ay的形式

耶鲁公开课 - 基础物理课程节选

You can ask yourself, "If you gave me a particular vector, what do I use for Ax and Ay?"

你可以问问自己,"如果给定一个矢量,该怎么确定 Ax 和 Ay"

耶鲁公开课 - 基础物理课程节选

But this is the same vector we are calling i times Ax plus j times Ay.

这和矢量 i ? Ax + j ? Ay 是一样的

耶鲁公开课 - 基础物理课程节选

The point is the arrow A, somebody has chosen to write in terms of i prime and j prime as Ax prime and Ay prime.

解决问题的关键在于矢量 A,可以用这样的形式来描述,i' ? Ax' + j' ? Ay'

耶鲁公开课 - 基础物理课程节选

If the Ax and Ay, some are positive and some are negative, this is the way by which we have learned we should combine multiples of i.

如果 Ax 和 Ay 有正有负,这就要用到我们所学过的方法,将所有 i 的倍数加起来

耶鲁公开课 - 基础物理课程节选

If you give me a pair of numbers, Ax and Ay, that's as good as giving me this arrow, because I can find the length of the arrow by Pythagoras' theorem.

如果给我一组数字,Ax 和 Ay,就相当于给了我这个箭头示意图,因为我可以利用毕达哥拉斯定理定理求出模长

耶鲁公开课 - 基础物理课程节选

That would come by saying, "I'm taking i times Ax + j times Ay + i times Bx + j times By, " and I'm trying to add all these guys.

那就这样做,"i ? Ax + j ? Ay + i ? Bx + j ? By",然后把它们都加起来

耶鲁公开课 - 基础物理课程节选

Now, when you work with components, Ax and Ay, if I didn't mention it, they are the components of the vector, you can do all your bookkeeping in terms of Ax and Ay.

当你们在计算分量 Ax 和 Ay 的时候,即使我没有说明,你们也要记得它们是矢量的分量,你们可以都用 Ax 和 Ay 的形式来表示

耶鲁公开课 - 基础物理课程节选

I gave you a law of transformation of the components; namely, if the vector has components Ax and Ay in one reference frame and Ax prime and Ay prime in another reference frame, how are the two related?

我介绍过分量变换的法则,即如果矢量在一个坐标系的分量为 Ax 和 Ay,在另一坐标系中的分量为 Ax' 与 Ay',它们有着什么样的联系

耶鲁公开课 - 基础物理课程节选