Every failure is a step to success. Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error.

The object of science is knowledge; the objects of art are works. In art, truth is the means to an end; in science, it is the only end. Hence the practical arts are not to be classed among the sciences

We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed.

Those who have obtained the farthest insight into Nature have been, in all ages, firm believers in God.

The hypotheses we accept ought to explain phenomena which we have observed. But they ought to do more than this: our hypotheses ought to foretell phenomena which have not yet been observed.

The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made mechanics analytical; I mean Euler.

Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but halfway comprehends the meaning.