Augustus De Morgan quotes:

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

The Astronomer's Drinking Song Astronomers! What can avail Those who calumniate us; Experiment can never fail With such an apparatus...

The sacred writings excepted, no Greek has been so much read and so variously translated as Euclid.

Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum, And the great fleas themselves, in turn, have greater fleas to go on, While these again have greater still, and greater still, and so on.

I don't quite hear what you say, but I beg to differ entirely with you.

All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses.

Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.

I was x years old in the year x2.

Mathematicians care no more for logic than logicians for mathematics.

The moving power of mathematical invention is not reasoning but imagination.

Common integration is only the memory of differentiation...

It is easier to square a circle than to get round a mathematician.

We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

Isaac Newton was born at Woolsthorpe, near Grantham, in Lincolnshire, on Christmas Day, 1642: a weakly and diminutive infant, of whom it is related that, at his birth, he might have found room in a quart mug. He died on March the 20th, 1727, after more than eighty-four years of more than average bodily health and vigour; it is a proper pendant to the story of the quart mug to state that he never lost more than one of his second teeth.

I am perfectly convinced that I have both seen, and heard in a manner which should make unbelief impossible, things called spiritual which cannot be taken by a rational being to be capable of explanation by imposture, coincidence, or mistake.

Wrong hypotheses, rightly worked from, have produced more useful results than unguided observations.

The gambling reasoner is incorrigible; if he would but take to the squaring of the circle, what a load of misery would be saved.

I did not hear what you said, but I absolutely disagree with you.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]

It was long before I got at the maxim, that in reading an old mathematician you will not read his riddle unless you plough with his heifer; you must see with his light, if you want to know how much he saw.

I end with a word on the new symbols which I have employed. Most writers on logic strongly object to all symbols. ... I should advise the reader not to make up his mind on this point until he has well weighed two facts which nobody disputes, both separately and in connexion. First, logic is the only science which has made no progress since the revival of letters; secondly, logic is the only science which has produced no growth of symbols.

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.

[About Francis Baily] The history of the astronomy of the nineteenth century will be incomplete without a catalogue of his labours. He was one of the founders of the Astronomical Society, and his attention to its affairs was as accurate and minute as if it had been a firm of which he was the chief clerk, with expectation of being taken into partnership.

During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true

My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.

Common integration is only the memory of differentiation... The different artifices by which integration is effected, are changes, not from the known to the unknown, but from forms in which memory does not serve us to those in which it does.