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.

In art, truth is a means to an end; in science, it is the only end.

Fundamental ideas are not a consequence of experience, but a result of the particular constitution and activity of the mind, which is independent of all experience in its origin, though constantly combined with experience in its exercise.

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

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.

According to the technical language of old writers, a thing and its qualities are described as subject and attributes; and thus a man's faculties and acts are attributes of which he is the subject. The mind is the subject in which ideas inhere. Moreover, the man's faculties and acts are employed upon external objects; and from objects all his sensations arise. Hence the part of a man's knowledge which belongs to his own mind, is subjective: that which flows in upon him from the world external to him, is objective.

The hypotheses which 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; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.