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?
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.
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.
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