Music is the pleasure the human mind experiences from counting without being aware that it is counting.
Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.
He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.
Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it.
When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.
The art of discovering the causes of phenomena, or true hypotheses, is like the art of deciphering, in which an ingenious conjecture often greatly shortens the road.
In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.
The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.
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