 | Morris Kline - 1990 - 434 páginas
...(See Chap. 25, sec. 4.) Fermat stated and sketched13 the proof by infinite descent of the theorem: The area of a right.angled triangle the sides of which...are rational numbers cannot be a square number. This sketch is the only detailed one ever given by him, and it follows as a corollary that the solution... | |
 | John Stillwell - 2004 - 576 páginas
...these are important threads throughout the whole of this book. 11.4 Rational Right-angled Triangles The area of a right-angled triangle the sides of which...developments to be made in the theory of numbers. [Fermat(1670), p. 271] This is number 45 of Fermat's Observations on Diophantus, responding to a problem... | |
 | Thomas L. Heath - 1910 - 406 páginas
...") is the occasion of Fermat's remarkable note upon the theorem discovered by him to the effect that The area of a rightangled triangle the sides of which...are rational numbers cannot be a square number. This note will be given in full, with other information on the same subject, in the Supplement.] ON POLYGONAL... | |
| |
The area of a right-angled triangle the sides of which are rational numbers cannot be a square number. This proposition, which is my own discovery, I have at length succeeded in proving, though not without much labour and hard thinking. I give the proof... 