The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. ...Simplicius.
Morris KlineRelated topics
affirmation attempt axiom believe euclid find good nine parallel prove reason self-sufficiency straight try using wayRelated quotes
I would rather have as my patron a host of anonymous citizens digging into their own pockets for the price of a book or a magazine than a small body of enlightened and responsible men administering public funds. I would rather chance my personal vision of truth striking home here and there in the chaos of publication that exists than attempt to filter it through a few sets of official, honorably public-spirited scruples.
John Updike
A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
Paul Dirac
Recipe for greatness To bear up under loss, to fight the bitterness of defeat and the weakness of grief, to be victor over anger, to smile when tears are close, to resist evil men and base instincts, to hate hate and to love love, to go on when it would seem good to die, to seek ever after the glory and the dream, to look up with unquenchable faith in something evermore about to be, that is what any man can do, and so be great.
Zane Grey
We must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity.
Marie Curie
Looking back the great American ‘stabilisation' [and boom] of 1922-1929 was really a vast attempt to destabilise the value of money in terms of human effort by means of a colossal programme of investment [driven by too easy credit]... which succeeded for a surprisingly long period, but which no human ingenuity could have managed to direct indefinitely on sound and balanced lines. [and therefore it ended dramatically in the huge 1929 stock market crash followed by the Great Depression. ].
Dennis Holme Robertson