The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.

All political revolutions, not affected by foreign conquest, originate in moral revolutions. The subversion of established institutions is merely one consequence of the previous subversion of established opinions.

Next to selfishness the principal cause which makes life unsatisfactory is want of mental cultivation.

The art of music is good, for the reason, among others, that it produces pleasure; but what proof is it possible to give that pleasure is good? If, then, it is asserted that there is a comprehensive formula, including all things which are in themselves good, and that whatever else is good, is not so as an end, but as a mean, the formula may be accepted or rejected, but is not a subject of what is commonly understood by proof.

A person should be free to do as he likes in his own concerns; but he ought not to be free to do as he likes in acting for another, under the pretext that the affairs of the other are his own affairs.

There is always need of persons not only to discover new truths, and point out when what were once truths are true no longer, but also to commence new practices, and set the example of more enlightened conduct, and better taste and sense in human life.

We have hitherto considered only two possibilities: that the received opinion may be false, and some other opinion, consequently, true; or that, the received opinion being true, a conflict with the opposite error is essential to a clear apprehension and deep feeling of its truth. But there is a commoner case than either of these; when the conflicting doctrines, instead of being one true and the other false, share the truth between them.