And we learned how to prove the Pythagorean Theorem in Euclidean geometry, starting with the various axioms in Euclidean geometry, ba, ba-ba, ba-ba, ba-ba, ba bum.

我们都学习过,欧几里得几何中对勾股定理的证明方法,从繁杂的欧氏几何的公理开始,邦,邦邦,邦邦,邦邦

耶鲁公开课 - 死亡课程节选

And it turns out there's a variety of proofs of the Pythagorean Theorem.

其实有很多种证明勾股定理的方法

耶鲁公开课 - 死亡课程节选

And as a result of writing it down and keeping track, he produced a very clear record, and scientific evidence, that using this procedure could protect a population of people from the disease.

凭借他的持续关注和追踪,他做出了十分清晰的记录,留下了科学证据,证明这种方法,可以让人们不再得这种病

耶鲁公开课 - 生物医学工程探索课程节选

It is found that the most effective way of dealing with this phenomenon was actually to cultivate the positive,to cultivate personal strengths, to cultivate and identify one's passions, ? to ask a question such as "what is meaningful to me in my life?

事实证明，处理这种现象,最有效的方法是,培养积极性和个人优点，培育激情，提出这种问题“我人生中什么是有意义的？

哈佛公开课 - 幸福课课程节选

We prove things in mathematics that have never been proven before or we find new ways to prove these theorems or what have you and we can be creative.

我们用数学去证明从未被证明过的事物,我们探寻新的方法去证明那些定理,或其他诸如此类,总之,我们具有创造力

耶鲁公开课 - 死亡课程节选

That approach pretty clearly isn't going to work for souls, because a soul--and again, we've got in mind this metaphysical view, according to which it's something immaterial-- isn't something we see.

但这种方法显然不能用来证明灵魂的存在,因为灵魂,我再一次说明,从这种形而上学的角度来看,灵魂是非物质实体,我们看不到它

耶鲁公开课 - 死亡课程节选