Now, in modern times, we call this Pythagoras' theorem.

在现代，我们称之哥拉定理。

One classic proof often attributed to Pythagoras himself uses a strategy called proof by rearrangement.

经典证明是哥拉自己做出的，他利用了一种名叫排列的证明方法。

Pythagoras, a Greek philosopher who lived around 500BC, is said to have discovered that notes that sound harmonious together have simple ratios between their frequencies: for example, one that is an octave higher than another has double the frequency.

据说公元前500年左右，希腊哲学家哥拉已经发现了发音和谐的音符在频率之间成简单比例：例如，高一个八度的音符具有两倍的频率。

Pythagoras didn't write down his beliefs but communicated them orally to a select few men, so it's hard to know if what we have is his original teachings.

哥拉并没有把他的信仰写下来，而是把它们口头传给少数几个人，所以很难知道我们所拥有的是否是他的原教义。

Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh.

哥拉被误解了，苏格拉底、耶稣、路德、哥白尼、伽利略、牛顿，以及所有有史以来纯洁与睿智的灵魂都被误解过。

Pythagoras was born the longest time ago in 570 B.C. and might have had the first laboratory ever recorded.

哥拉出生于公元前570年，可能是有史以来第一个拥有有记载的实验室的人。

Empedocles thought he was a God and jumped into a volcano. And Pythagoras had an irrational fear of beans.

恩培多克勒以他是天神，跳进了火山，哥拉对豆子有莫名的恐惧。

And according to his follower Philolaus of Croton, Pythagoras believed that the planets moved in set patterns according to mathematical principles of harmony and did not " wander the sky" as their Greek name planetes meaning 'wanderer' suggests.

根据他的追随者克罗顿的菲洛劳的说法，哥拉行星按照和谐的数学原理以固定的模式运行，而不是像他们的希腊名字“漫游者”所暗示的那样“漫游天空”。

The theorem is named for Pythagoras, a Greek philosopher and mathematician in the 6th century B.C., but it was known more than a thousand years earlier.

该定理是以公元前 6 世纪的希腊哲学家和数学家哥拉命名的，但它早在一千多年前就被人所知。

According to Pythagoras Theorem, the diagonal length would be square root of two; but try as he might, Hippasus could not express this as a ratio of two integers.

根据哥拉的理论，这个正方形的对角线长度应该根号二；但是无论希帕索如何尝试，都不能将根号二变两个整数的比例形式。

Pythagoras, who lived between circa 571 and 497 BCE, developed a mathematical system to explain the movements of the planets, and so often, is considered the first Greek astronomer.

哥拉生活在公元前 571 年至 497 年之间，他发明了一套数学系统来解释行星的运行，因此经常被是第一位希腊天文学家。

Pythagoras is credited with being the person to identify Venus as one single planet, not two — one appearing in the morning and one in the evening.

哥拉被是确定金星是一颗行星的人，而不是两颗——一颗在早上出现，一颗在晚上出现。

And it's actually a very old idea; it goes back over 2,000 years to Pythagoras.

这实际上是一个非常古老的想法；它可以追溯到 2000 多年前的哥拉。

Scoots, I think you're thinking of tulip, not euclids, and Pythagoras.

库茨，我想你是在想郁金香，而不是欧几里得和哥拉。

And so there's all these very important people, Aristotle, Plato, Socrates, Pythagoras, et cetera.

所以这里有许多非常重要的人物，如亚里士多德、柏拉图、苏格拉底、哥拉等等。

Ancient philosophers, going back to Pythagoras, believed that your breath contained your soul.

追溯到哥拉的古代哲学家相信你的呼吸包含你的灵魂。

Building on ideas first put forward by Pythagoras and Ptolemy, Kepler suggested that each planet was responsible for an inaudible musical note that had a frequency proportional to the velocity of the planet along its orbit.

基于哥拉和托勒密最初提出的思想，开普勒提出， 每个行星都对应着一个无声的音乐音符， 其频率与行星在其轨道上的速度成正比。

If Newton's imagination had been of the same vividly dramatic kind he might have seen the ghost of Pythagoras walk into the orchard and explain why the apples were falling.

如果牛顿的想象力同样具有生动的戏剧性， 他可能会看到哥拉的鬼魂走进果园并解释什么苹果会掉下来。

From Pythagoras to Herbert Spencer, every one had done it, although commonly science had explored an ocean which it preferred to regard as Unity or a Universe, and called Order.

从哥拉到赫伯特·宾塞，每个人都做到了，尽管科学通常探索的是一片海洋，它更愿意将其视统一体或宇宙，并称之秩序。

One of the first people to come up with the idea that the Earth was round was a person by the name of Pythagoras.

最早提出地球是圆形的人之一名叫哥拉。