Each problem that I solved became a rule, which served afterwards to solve other problems.
Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.
When I consider this carefully, I find not a single property which with certainty separates the waking state from the dream. How can you be certain that your whole life is not a dream?
We call infinite that thing whose limits we have not perceived, and so by that word we do not signify what we understand about a thing, but rather what we do not understand.
Although my knowledge grows more and more, nevertheless I do not for that reason believe that it can ever be actually infinite, since it can never reach a point so high that it will be unable to attain any greater increase.
Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can always imagine as many roots for each equation as I have assigned, yet there is not always a definite quantity corresponding to each root we have imagined.
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