Plato Quotes

In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.

Men are not born equal in themselves, so I think it beneath a man to postulate that they are. If I thought myself as good as Sokrates I should be a fool; and if, not really believing it, I asked you to make me happy by assuring me of it, you would rightly despise me. So why should I insult my fellow-citizens by treating them as fools and cowards? A man who thinks himself as good as everyone else will be at no pains to grow better. On the other hand, I might think myself as good as Sokrates, and even persuade other fools to agree with me; but under a democracy, Sokrates is there in the Agora to prove me wrong. I want a city where I can find my equals and respect my betters, whoever they are; and where no one can tell me to swallow a lie because it is expedient, or some other man's will.

Manlius ... took care in his invitations, actively sought to exclude from his circle crude and vulgar men like Caius Valerius. But they were all around; it was Manlius who lived in a dream world, and his bubble of civility was becoming smaller and smaller. Caius Valerius, powerful member of a powerful family, had never even heard of Plato. A hundred, even fifty years before, such an absurdity would have been inconceivable. Now it was surprising if such a man did know anything of philosophy, and even if it was explained, he would not wish to understand.