The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.

The principal effect of the passions is that they incite and persuade the mind to will the events for which they prepared the body.

Everybody thinks himself so well supplied with common sense that even those most difficult to please. . . never desire more of it than they already have.

All is to be doubted.

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.

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.

Good sense is, of all things among men, the most equally distributed; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess.