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1·Understand Euclid's proof of the Pythagorean Theorem.

理解欧几里得对毕德哥拉斯定理的证明。

2·He is best known for the Pythagorean theorem, which bears his name.

他因以自己名字命名的毕达哥拉斯定理而最为知名。

3·He even came up on his own with a way to prove the Pythagorean theory.

甚至相出了一个自己的方法来证明勾股定理。

4·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。

5·They are Pythagorean proposition, Chinese residual theorem and Oula theorem.

它们是勾股定理、中国剩余定理、欧拉定理。

6·The most complicated part, Devlin says, is our good old friend the Pythagorean theorem.

Devlin说，最复杂的部分便是我们熟知的毕达哥拉斯定理。

7·The method of deducing Pythagorean Triples (irreducible and reducible) is explained.

并说明了互素勾股数组的导出方法。

8·The method of calculation is exactly the same as that used for the Pythagorean 12 tones.

这种计算方法与毕达哥拉斯的12音计算法完全一致。

9·In addition, Pythagorean School explored art from the perspective of harmonious proportion.

毕达哥拉斯学派还从和谐的比例的角度，研究了艺术问题。

10·And I have tried to grasp the * Pythagorean power by which number holds control above the change.

我还想明白毕达哥拉斯的乘方，通过乘方数控制万物的变化。