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

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.

How do we know that anything really exists, that anything is really the way it seems ot us through our senses?

At last I will devote myself sincerely and without reservation to the general demolition of my opinions.

Omnia apud me mathematica fiunt.

Here I beg you to observe in passing that the scruples that prevented ancient writers from using arithmetical terms in geometry, and which can only be a consequence of their inability to perceive clearly the relation between these two subjects, introduced much obscurity and confusion into their explanations.

On the one hand I have a clear and distinct idea of myself, in so far as I am a thinking, non-extended thing; and on the other hand I have a distinct idea of body, in so far a this is simply an extended, non-thinking thing. And, accordingly, it is certain that I am really distinct from my body, and exist without it.