“Any desired geometrical mean between two sines has for its Logarithm the corresponding arithmetical mean between the Logarithms of the sines.”

Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)

Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, The Pell Equation http://books.google.com/books?id=L6QKAAAAYAAJ (1912)
Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square.

Letter published in the Manchester Advertiser (3 March 1911), quoted in A People's History of the United States (1980) page 345.
Context: Our democracy is but a name. We vote? What does that mean? It means that we choose between two bodies of real, though not avowed, autocrats. We choose between Tweedledum and Tweedledee.… You ask for votes for women. What good can votes do when ten-elevenths of the land of Great Britain belongs to 200,000 and only one-eleventh to the rest of the 40,000,000? Have your men with their millions of votes freed themselves from this injustice?

Source: House of Leaves

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

p, 125
Stetigkeit und irrationale Zahlen (1872)

Source: The Ballad of the Sad Café and Other Stories

Oscar Iden Lecture Series, Lecture 3: "The State of Individuals" (1976)

No. 78
The Federalist Papers (1787–1788)
Context: There is no position which depends on clearer principles, than that every act of a delegated authority, contrary to the tenor of the commission under which it is exercised, is void. No Legislative act, therefore, contrary to the Constitution, can be valid. To deny this, would be to affirm, that the deputy is greater than his principal; that the servant is above his master; that the Representatives of the People are superior to the People themselves; that men acting by virtue of powers, may do not only what their powers do not authorize, but what they forbid. If it be said that the Legislative body are themselves the constitutional judges of their own powers, and that the construction they put upon them is conclusive upon the other departments, it may be answered, that this cannot be the natural presumption, where it is not to be collected from any particular provisions in the Constitution. It is not otherwise to be supposed, that the Constitution could intend to enable the Representatives of the People to substitute their will to that of their constituents. It is far more rational to suppose, that the Courts were designed to be an intermediate body between the People and the Legislature, in order, among other things, to keep the latter within the limits assigned to their authority. The interpretation of the laws is the proper and peculiar province of the Courts. A Constitution is, in fact, and must be regarded by the Judges, as a fundamental law. It therefore belongs to them to ascertain its meaning, as well as the meaning of any particular Act proceeding from the Legislative body. If there should happen to be an irreconcilable variance between the two, that which has the superior obligation and validity ought, of course, to be preferred; or in other words, the Constitution ought to be preferred to the statute, the intention of the People to the intention of their agents. Nor does this conclusion by any means suppose a superiority of the Judicial to the Legislative power. It only supposes that the power of the People is superior to both; and that where the will of the Legislature, declared in its statutes, stands in opposition to that of the People, declared in the Constitution, the Judges ought to be governed by the latter rather than the former. They ought to regulate their decisions by the fundamental laws, rather than by those which are not fundamental. [... ] whenever a particular statute contravenes the Constitution, it will be the duty of the Judicial tribunals to adhere to the latter and disregard the former.