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.

Thus each truth discovered was a rule available in the discovery of subsequent ones.

But in my opinion, all things in nature occur mathematically.

Nothing comes out of nothing.

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.

Illusory joy is often worth more than genuine sorrow.

To live without philosophizing is in truth the same as keeping the eyes closed without attempting to open them.