"e may fancy that we see or feel what we in reality infer. Newton saw the truth of many propositions of geometry without reading the demonstrations, but not, we may be sure, without their flashing through his mind. A truth, or supposed truth, which is really the result of a very rapid inference, may seem to be apprehended intuitively. It has long been agreed by thinkers of the most opposite schools, that this mistake is actually made in so familiar an instance as that of the eyesight. There is nothing of which we appear to ourselves to be more directly conscious, than the distance of an object from us. Yet it has long been ascertained, that what is perceived by the eye, is at most nothing more than a variously coloured surface; that when we fancy we see distance, all we really see is certain variations of apparent size, and degrees of faintness of colour; and that our estimate of the object's distance from us is the result of a comparison between the size and colour of the object as they appear at the time, and the size and colour of the same or of similar objects as they appeared when close at hand, or when their degree of remoteness was known by other evidence. The perception of distance by the eye, which seems so like intuition, is thus, in reality, an inference grounded on experience; an inference, too, which we learn to make; and which we make with more and more correctness as our experience increases; though in familiar cases it takes place, so rapidly as to appear exactly on a par with those perceptions of sight which are really intuitive, our perceptions of colour."

“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.”

“[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.”

“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.”