It's an underworld filled with gold that a brigade of fallen angels begins to extract with spades and pick axes.

在这个地狱一群堕落天使们可以拿着铲子和锤子,挖取地下的金矿。

耶鲁公开课 - 弥尔顿课程节选

Perhaps it's clear to you that no matter how your axes are oriented, when you ask, "How long is this arrow?"

这应该是比较显然的,无论坐标轴指向哪里,当你问,"这个矢量有多长"

耶鲁公开课 - 基础物理课程节选

Now as I did last time, let me put in two axes to make the picture a little easier to draw.

和我上次做的一样,画两个纵轴来帮助我们作图

耶鲁公开课 - 博弈论课程节选

px So we're talking about pi carbon 2 p x, 2px because it's the x axes combining to carbon 2 p x.

我们讨论的是π碳，因为它在x轴结合成碳。

麻省理工公开课 - 化学原理课程节选

People make really stupid decisions and so as you know in this course with P sets there are three axes that we look at when evaluating your code.

人们做了一个愚蠢的决定,在这个课程上，通过习题集，当执行你的代码的时候,有三个评估方面。

哈佛公开课 - 计算机科学课程节选

They are simply analytical tools. They're not inherently biased. They can be applied fairly to the text, and they're extraordinarily useful. It's just that some of the earlier practitioners of these methods did have ideological axes to grind, and we need to be aware of that.

所以它们只是分析工具，本身并不带有偏见,它们是十分有用的，完全可以运用于文本,但一些早期实施者并没有将其,融会贯通，我们必须意识到这一点。

耶鲁公开课 - 旧约导论课程节选

Here are the axes again.

再画一个坐标系。

耶鲁公开课 - 死亡课程节选

Time. Okay, pitch and time and pitch and duration, excellent, so those are the two dimensions of music and well, indeed we could even call them the axes of music because we tend to think of pitch on a vertical axis.

时间,音高和时间,或者是音高和时值,非常好,它们是音乐的两个维度,其实我们可以称呼它们为音乐的两轴,因为我们趋向于将音高放在竖轴上来考虑

耶鲁公开课 - 聆听音乐课程节选

When you go from one set of axes to another set of axes, the numbers change.

当你将一组坐标轴变换到另一组坐标轴时,坐标值会发生变化

耶鲁公开课 - 基础物理课程节选

Actually, the view of vectors we take nowadays is that vectors are associated with a pair of numbers which, on the rotation of axes, transform like this.

实际上,今天我们讲矢量所用的观点是,矢量是和一组坐标值相对应的,在坐标轴旋转的过程中像这样变换

耶鲁公开课 - 基础物理课程节选

But you agree that there is no reason why somebody else couldn't come along and say, "You know what, I want to use a different set of axes.

但是你们得认识到,没有人会站出来说,"我想要用一套不同的坐标系

耶鲁公开课 - 基础物理课程节选

On the vertical axis I'll put two vertical axes in, just for the sake of things on the vertical axis I'll put my expected payoffs.

坐标系的纵轴,由于种种原因,我花了两个纵轴,纵轴表示我的预期收益

耶鲁公开课 - 博弈论课程节选

Well,if you go back to the formation of musical notation from the ninth through the twelfth centuries we see that very early on these two dimensions of music the two axes of music that we talked about before pitch vertically and duration horizontally, are in place and we have these spots in this grid.

回顾一下从公元九世纪至二十世纪,音乐记谱法的历史形成过程,我们可以看出,音乐的两个维度,就是我们之前提到的音乐的两个轴,纵轴是音高,横轴是时值,在早期已经存在了,我们在这样的网格上用点记录

耶鲁公开课 - 聆听音乐课程节选

I mentioned something of increasing importance only later, which is that you are free to pick another set of axes, not in the traditional x and y direction, but as an oblique direction.

后来我又讲了更重要的知识点,你可以随意选取另外一个坐标系,不再是传统的 x 和 y 方向,而是倾斜过的方向

耶鲁公开课 - 基础物理课程节选

For most of us, gravity acts this way, defines a vertical direction very naturally and the blackboard is oriented this way, so very natural to call that x and call that y and line up our axes.

对我们多数人来说,重力作用下,很自然地确定了竖直方向,而我们的黑板又是这个指向的,所以很自然地定出 x 轴和 y 轴,并标出我们的坐标系

耶鲁公开课 - 基础物理课程节选