当考虑到古代的数学时，我们往往首先想到的是毕达哥拉斯和欧几里德。

When we think of ancient mathematics, the first names that come to mind are Pythagoras and Euclid.

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我们发现，在希腊哲学家中，毕达哥拉斯和柏拉图以及他们的追随者相信灵魂轮回或转生。

Among the Greek philosophers we find that Pythagoras, Plato and their followers believed in this theory of Metempsychosis or Transmigration of souls.

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毕达哥拉斯学派开始通过这些研究探索合弦与声学。

The Pythagorean School began the scientific exploration of harmony and acoustics through these studies.

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First of all, it's clear from the Pythagoras' theorem that a is the square root of ^2 + ^2.

首先,根据毕达哥拉斯定理,勾股定理在西方被称为"毕达哥拉斯定理"

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I take the difference in the x-values, squared, the difference in the y-values, squared, add them up, take the square root of that.

好，是毕达哥拉斯定力对不对？,求x坐标的差，然后平方，求y坐标的差，然后平方，把它们加起来，开平方。

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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

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