"[T]he application of algebra to geometry... far more than any of his metaphysical speculations, has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences."

“Now, such a theory of life excites in many minds...inveterate dislike. To suppose that life has (as they express it) no higher end than pleasure—no better and nobler object of desire and pursuit—they designate as utterly mean and grovelling; as a doctrine worthy only of swine, to whom the followers of Epicurus were, at a very early period, contemptuously likened; and modern holders of the doctrine are occasionally made the subject of equally polite comparisons by its German, French, and English assailants.”

“Everybody knows that the same sum of money is of much greater value to a poor man that to a rich one. Give £10 a year to the man who has but £10 a year, you double his income, and you nearly double his enjoyments. Add £10 more, you do not add to his enjoyments so much as you did by the first £10. The third £10 is less valuable than the second, and the fourth less valuable than the third. To the possessor of £1,000 a year the addition of £10 would be scarcely perceptible; to the possessor of £10,000 it would not be worth slooping for.The richer a man is the less he is benefited by any further addition to his income. The man of £4,000 a year has four times the income of the man who has but £1,000; but does anybody suppose that he has four times the happiness?”

“No longer enslaved or made dependent by force of law, the great majority are so by force of poverty; they are still chained to a place, to an occupation, and to conformity with the will of an employer, and debarred, by the accident of birth both from the enjoyments, and from the mental and moral advantages, which others inherit without exertion and independently of desert. That this is an evil equal to almost any of those against which mankind have hitherto struggled, the poor are not wrong in believing.”

“A Turk thinks, or used to think (for even Turks are wiser now-a-days), that society would be on a sandbank if women were suffered to walk about the streets with their faces uncovered. Taught by these and many similar examples, I look upon this expression of loosening the foundations of society, unless a person tells in unambiguous terms what he means by it, as a mere bugbear to frighten imbeciles with.”

“The remedies for all our diseases will be discovered long after we are dead; and the world will be made a fit place to live in, after the death of most of those by whose exertions it will have been made so. It is to be hoped that those who live in those days will look back with sympathy to their known and unknown benefactors.”

“We are not so absurd as to propose that the teacher should not set forth his own opinions as the true ones and exert his utmost powers to exhibit their truth in the strongest light. To abstain from this would be to nourish the worst intellectual habit of all, that of not finding, and not looking for, certainty in any teacher. But the teacher himself should not be held to any creed; nor should the question be whether his own opinions are the true ones, but whether he is well instructed in those of other people, and, in enforcing his own, states the arguments for all conflicting opinions fairly.”