“Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.”

p, 125
Achimedes (1920)

p, 125
Achimedes (1920)

Mathematics Magazine, Vol. 23-24. (1949), p. 161
Context: Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid's notorious oversights drove this lesson home.

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.

Mathematics and Mathematicians (1992); published in Is Mathematics Inevitable? A Miscellany (2008), edited by Underwood Dudley, p. 3. ISBN 0883855666

Curriculum Vitae - an autobiographical statement written when Eisenstein was 20, often referred to as his "Autobiography" (1843)

Note written on the margins of his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus, this was taken as an indication of what became known as Fermat's last theorem, a correct proof for which would be found only 357 years later; as quoted in Number Theory in Science and Communication (1997) by Manfred Robert Schroeder

XVII, 11
The Kitáb-I-Asmá
Context: Should a person lay claim to a cause and produce his proofs, then those who seek to repudiate him are required to produce proofs like unto his. If they succeed in doing so, his words will prove vain and they will prevail; otherwise neither his words will cease nor the proofs he hath set forth will become void. I admonish you, O ye who are invested with the Bayán, if ye would fain assert your ascendancy, confront not any soul unless ye give proofs similar to that which he hath adduced; for Truth shall be firmly established, while aught else besides it is sure to perish.

The Judge
"Beyond" (1933)