I thought fit to... explain in detail in the same book the peculiarity of a certain method, by which it will be possible... to investigate some of the problems in mathematics by means of mechanics. This procedure is... no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards... But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.
ArchimedesRelated topics
book certain clear course easy find fit geometry knowledge less mathematics mechanics possible procedure proof thought means things questionsRelated 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
Pictures are the idea in visual or pictorial form; and the idea has to be legible, both in the individual picture and in the collective context - which presupposes, of course, that words are used to convey information about the idea and the context. However, none of this means that pictures function as illustrations of an idea: ultimately, they are the idea. Nor is the verbal formulation of the idea a translation of the visual: it simply bears a certain resemblance to the meaning of the idea. It is an interpretation, literally a reflection.
Gerhard Richter
Throughout his last half-dozen books, for example, Arthur Koestler has been conducting a campaign against his own misunderstanding of Darwinism. He hopes to find some ordering force, constraining evolution to certain directions and overriding the influence of natural selection. [...] Darwinism is not the theory of capricious change that Koestler imagines. Random variation may be the raw material of change, but natural selection builds good design by rejecting most variants while accepting and accumulating the few that improve adaptation to local environments.
Stephen Jay Gould
Modern man, seeking a middle position in the evaluation of sense impression and thought, can, following Plato, interpret the process of understanding nature as a correspondence, that is, a coming into congruence of pre-existing images of the human psyche with external objects and their behaviour. Modern man, of course, unlike Plato, looks on the pre-existent original images also as not invariable, but as relative to the development of a conscious point of view, so that the word "dialectic" which Plato is fond of using may be applied to the process of development of human knowledge.
Wolfgang Pauli
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Pierre-Simon Laplace