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Their first and most eminent representative was Protagoras ; other notable sophists include Gorgias of Leontini, Prodicus, Hippias, Antiphon, Thrasymachus, and Critias.

毕达哥拉斯是智者中最有名的代表,其他智者包括伦蒂尼的高尔吉亚,普罗迪科,希庇阿斯、安提丰、特拉叙马霍斯和克里提阿。

It is considered that in China, the mathematician of fust proof of the Pythagorean theorem is Zhao shuang, who live in the third century a.

但毕达哥拉斯并没有著作流传于世,也没有任何后世的文献记载毕达哥拉斯所给出的证明方法,有的只是种种猜测。

First, when the Pythagoreans discovered the irrationality of the square root of two … Second, when the philosophical Bishop, Berkeley the Bear, pointed out the contradiction of dividing by zero … But Cantor the Goat, by his General Set Theory, has shown us how to resolve these problems, and to dispel crisis from the Foundations of Mathematics!

每一次危机是毕达哥拉斯学派发现了2的平方根是一个无理数……第二次危机是作为哲学家的毕晓普这只贝克莱大熊指出了用0做除数所具有的矛盾性……而康托尔山羊在它的《普通集合论》里向我们证明了它是如何解决这个问题的,并且消除了数学基础的危机!

In Plato's "Symposium", Aristophanes argues that the origins of love lie in the search for symmetry, while Pythagoras and Theaetetus—who discovered the icosahedron, the geometric shape with 20 triangular faces—explored the symmetries of geometric figures.

在柏拉图的《会饮篇》中,阿里斯托芬提出爱的缘起就在于对对称的寻觅,而毕达哥拉斯和发现由二十个三角形面组成的二十面体的泰阿泰德则探究几何形体的对称。

Gnosticism-that is, the cabalistic "okmah", translated into "Madda'"(Aramaic,"Manda'"= knowledge of things divine)-seems to have been the first attempt on the part of the Jewish sages to give the empirical mystic lore, with the help of Platonic and Pythagorean or Stoic ideas, a speculative turn; hence the danger of heresy from which Akiba and Ben Zoma strove to extricate themselves, and of which the systems of Philo, an adept in Cabala (see "De Cherubim," 14;"De Sacrificiis Abelis et Caini," 15;"De Eo Quod Deterius Potiori Insidiatur," 48;"Quis Rerum Divinarum Heres Sit," 22), and of Paul see Matter,"History of Gnosticism," ii.

诺斯替主义,也就是说, cabalistic " okmah ",翻译成" Madda "(阿拉姆,"曼达"=知识的神圣的东西)似乎是第一次尝试对部分犹太圣人给实证神秘传说的帮助下,柏拉图和毕达哥拉斯或斯多葛思想,投机反过来,因此危险的异端邪说从秋叶忠利和本祖马力求脱困,以及该系统的哲学,一个善於Cabala (见"德革鲁宾," 14 ";德Sacrificiis Abelis等彩妮," 15 ;"德御宁狱吏Deterius Potiori Insidiatur ," 48 "; Quis事物Divinarum继承人坐下," 22 )和保罗(见物,"历史的诺斯替主义"二。

For my purpose is not to furnish mere matter of much talk, but to throw light upon the number of years from the foundation of the world, and to condemn the empty labour and trifling of these authors, because there have neither been twenty thousand times ten thousand years from the flood to the present time, as Plato said, affirming that there had been so many years; nor yet 15 times 10,375 years, as we have already mentioned Apollonius the Egyptian gave out; nor is the world uncreated, nor is there a spontaneous production of all things, as Pythagoras and the rest dreamed; but, being indeed created, it is also governed by the providence of God, who made all things; and the whole course of time and the years are made plain to those who wish to obey the truth.

我的目的不是为了提供单纯的事多谈,但以投掷轻后数年内,从基础的世界,并谴责空洞的劳动和琐碎的这些作者,因为那里既没有得到20000倍, 10 1000年,从洪水到现在的时间,正如柏拉图说,肯定有过了这么多年,也尚未15倍10375年,正如我们已经提到apollonius埃及了,也不是世界uncreated ,也不是有自发生产的所有事情,因为毕达哥拉斯和其余梦想,但目前确实造成了,它也是由普罗维登斯的上帝,谁做好了各种东西,以及整个过程中的时间及年资,都是平原那些要服从真理。

Greek philosopher and mathematician who founded in southern Italy a school that emphasized the study of musical harmony and geometry. He proved the universal validity of the Pythagorean theorem and is considered the first true mathematician.

毕达哥拉斯古希腊哲学家和数学家,在意大利南部创立学派,强调对音乐和谐及几何的研究:他证明了毕达哥拉斯定理的广泛有效,性并且被认为是世界是第一位真正的数学家

From a synthesis of pre-Hellenic beliefs with the Thracian cult of Zagreus and soon becoming mingled with the Eleusinian mysteries and the doctrines of Pythagoras.

俄耳甫斯教:起源于公元前 6世纪的古希腊神秘宗教,它综合了前希腊信仰和扎格列欧斯的色雷斯教并且很快与衣洛西斯奥义和毕达哥拉斯教义相混合

BC, Pythagoras came to Miletus, may Loos and other places, visited Thales, Anaximander, and Phil Quds, and became their students.

公元前551年,毕达哥拉斯来到米利都、得洛斯等地,拜访了泰勒斯、阿那克西曼德和菲尔库德斯,并成为了他们的学生。

Now turn thy thoughts to the other kinds of men. To that place then we must remove, where there are so many great orators, and so many noble philosophers, Heraclitus, Pythagoras, Socrates; so many heroes of former days, and so many generals after them, and tyrants; besides these, Eudoxus, Hipparchus, Archimedes, and other men of acute natural talents, great minds, lovers of labour, versatile, confident, mockers even of the perishable and ephemeral life of man, as Menippus and such as are like him.

现在把思绪转向其他一类人,进入这样一个世界,在这里有如此多杰出的演说家、如此多高贵的哲人,赫拉克利特、毕达哥拉斯、苏格拉底,如此多昨日的英雄,以及如此多跟随他们的将军,还有那些暴君,除了这些,还有欧多克索斯,希琶斯,阿基米德,以及其他具有真正自然天赋者、具有伟大思想者、热爱劳作者、多才多艺者、自负的人以及嘲讽堕落、朝生暮死生活的人,就像梅尼普以及类似于他的人。

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