It would be inconvenient to interrupt the account of Menaechmus's solution of the problem of the two mean proportionals in order to consider the way in which he may have discovered the conic sections and their fundamental properties. It seems to me much better to give the complete story of the origin and development of the geometry of the conic sections in one place, and this has been done in the chapter on conic sections associated with the name of Apollonius of Perga. Similarly a chapter has been devoted to algebra (in connexion with Diophantus) and another to trigonometry.
Thomas Little HeathRelated topics
account algebra conic connexion development done fundamental geometry mean name order place problem story trigonometry wayRelated quotes
Some students of philosophy have unreasonably high expectations of the subject. They expect it to provide them with a complete and detailed picture of the human predicament. They think that philosophy will reveal to them the meaning of life, and explain to them every facet of our complex existences. Now, although studying philosophy can illuminate fundamental questions about our lives, it does not provide anything like a complete picture, if indeed there could be such a thing. Studying philosophy isn't an alternative to studying art, literature, history, psychology, anthropology, sociology, politics, and science.
Nigel Warburton
Man's quest for knowledge is an expanding series whose limit is infinity, but philosophy seeks to attain that limit at one blow, by a short circuit providing the certainty of complete and inalterable truth. Science meanwhile advances at its gradual pace, often slowing to a crawl, and for periods it even walks in place, but eventually it reaches the various ultimate trenches dug by philosophical thought, and, quite heedless of the fact that it is not supposed to be able to cross those final barriers to the intellect, goes right on.
Stanisław Lem
How can anyone expect to be understood unless he presents his thoughts with complete honesty? This situation is unfair because it asks too much of the world. In effect, we say, "I don't dare show you what I am because I don't trust you for a minute but please love me anyway because I so need you to. And, of course, if you don't love me anyway, you're a dirty dog, just as I suspected, so I was right in the first place." Yet, every time God's children have thrown away fear in pursuit of honesty-trying to communicate themselves, understood or not, miracles have happened.
Duke Ellington
The nude gains its enduring value from the fact that it reconciles several contrary states. It takes the most sensual and immediately interesting object, the human body, and puts it out of reach of time and desire; it takes the most purely rational concept of which mankind is capable, mathematical order, and makes it a delight to the senses; and it takes the vague fears of the unknown and sweetens them by showing that the gods are like men and may be worshiped for their life-giving beauty rather than their death-dealing powers.
Kenneth Clark
If every day a man takes orders in silence from an incompetent superior, if every day he solemnly performs ritual acts which he privately finds ridiculous, if he unhesitatingly gives answers to questionnaires which are contrary to his real opinions and is prepared to deny his own self in public, if he sees no difficulty in feigning sympathy or even affection where, in fact, he feels only indifference or aversion, it still does not mean that he has entirely lost the use of one of the basic human senses, namely, the sense of humiliation.
Václav Havel