And thereby make ourselves, as it were, the lords and masters of nature.

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.

If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.

The rainbow is such a remarkable phenomenon of nature, and its cause has been so meticulously sought after by inquiring minds throughout the ages, that I could not choose a more appropriate subject for demonstrating how, with the method I am using, we can arrive at knowledge not possessed at all by those whose writings are available to us.

Omnia apud me mathematica fiunt.

Give me extension and motion and I will construct the universe.

The only thing that I know, is that I know nothing