The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.
The ordinary operations of algebra suffice to resolve problems in the theory of curves.
[said about the chemist Lavoisier:]
It took the mob only a moment to remove his head; a century will not suffice to reproduce it.
I do not know.
[summarising his life's work]
When we ask advice, we are usually looking for an accomplice.
If I had not inherited a fortune I should probably not have cast my lot with mathematics.
[a quotation from De Morgan]
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 which 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.]
One day after [Laplace] had invited Lagrange to dinner, Lagrange asked: "Will it be necessary to wear the costume of a senator?" in a mocking tone, of which everyone sensed the malice, except the amphityron [=host] senator.
I regard as quite useless the reading of large treatises of pure analysis: too large a number of methods pass at once before the eyes. It is in the works of applications that one must study them; one judges their ability there and one apprises the manner of making use of them.
As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.
I am delighted at the contrast between your modesty and the good opinion that other geometers have of themselves, although they have certainly nothing like the same claim. You are a living instance of what you said to me some time ago, that pretensions are ever in an inverse ratio to merit. (letter from d'Alembert).