Thales, it is said, was the first to inscribe a right-angled triangle into a circle. He is said to have sacrificed an ox in honour of his discovery.
Thales Theorum: if A,B and C are points on a circle where the line AC is a diameter of the circle , the the angle ABC is a right-angle.
Plato divides the world into realms. The realm of the forms was the highest, an intelligible, rather than experiential realm of truths. These forms, for Plato were more real than the everyday world because of their immutability and singularity, as opposed to the multiplicity and ever changing character of the world of men, analogised as the wall of flickering shadows in plato's cave.
"Plato has a system in which he makes a division between the material sensible world and what he terms, an other worldly realm of forms; of perfect, eternal, ideal, non-sensible principles. And those are the things that are truly real and everything in this world is simply representing it or imitating it. The ideas is that somehow we must try to get as close to the forms as we can and particularly the form of the good." Angie HobbsFrom In Our Time Neoplatonism BBC Radio 4 First Broadcast 19th April 2012
I was watching the star and the star was watching me. We were poised, exactly equal weights, if one can think of awareness as a weight, held level in a balance. This seemed to endure and endure, I don't know how long, two entities equally suspended in a void, equally opposite, devoid of any meaning or feeling. There was no sensation of beauty, of morality, of divinity, of physical geometry; simply the sensation of the situation.
John Fowles, The Magus p.237
On the fields of Troy a fallen soldier pleaded with Achilles the Greek hero to save his life. According to Homer Achilles replied,
'Do you not see what a man I am, how huge, how splendid, and born of a great father, and the Mother who bore me immortal? But even I have also my death and strong destiny, and there shall be a dawn or an afternoon or noontide, when some man in the fighting will take the life from me also. Either with a spear cast or an arrow flown from the bow-string.'
With that, Achilles killed him.
Cited on In Our Time 'Heroism', First Broadcast BBC Radio 4, 9:00AM Thu, 6 May 2004