It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.

Your Highness, I have no need of this hypothesis.

To Napoleon on why his works on celestial mechanics make no mention of God: Your Highness, I have no need of this hypothesis.

The word 'chance' then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.

I have lived long enough to know what I did not at one time believe--that no society can be upheld in happiness and honor without the sentiment of religion.

The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.

We are so far from knowing all the forces of nature and their various modes of action that it would be unworthy of the philosopher to deny phenomena simply because they are inexplicable at the present state of our knowledge. The more difficult it is to acknowledge their existence, the greater the care with which we must study these phenomena.