Geometry is the art of correct reasoning from incorrectly drawn figures.

It is far better to foresee even without certainty than not to foresee at all.

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?