上下文：欧几里得关于毕德哥拉斯定理的证明利用了前已证明的命题41。

Context: Euclid's proof of the Pythagorean theorem made use of the previous proven theorem known as Proposition 41.

youdao

理解欧几里得对毕德哥拉斯定理的证明。

Understand Euclid's proof of the Pythagorean Theorem.

youdao

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。

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.

youdao

你给它渲染了一层浪漫主义色彩，简直就像是给欧几里得第五定理掺进了恋爱故事或私奔情节。

You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.

youdao

生活在公元前540年左右的毕达哥拉斯，便提出了闻名于世的关于直角三角形各边的 勾股定理 。古代最知名的几何学家欧几里得生活在公元前300年左右。

Pythagoras, who is remembered for his theorem about the sides of a right-angled triangle, lived around 540 BC, while Euclid, the best known geometer of the ancient world, lived around 300 BC.

youdao

生活在公元前540年左右的毕达哥拉斯，便提出了闻名于世的关于直角三角形各边的 勾股定理 。古代最知名的几何学家欧几里得生活在公元前300年左右。

Pythagoras, who is remembered for his theorem about the sides of a right-angled triangle, lived around 540 BC, while Euclid, the best known geometer of the ancient world, lived around 300 BC.

youdao