HTML (142 kb) DVI (75 kb) PDF (185 kb) Compressed PostScript (72 kb) A5 PS booklet (67 kb) What are these? [12 Feb 2009] | by Carl Friedrich Gauss (1815); the Latin original appears in Volume 3, pages 33-56, of his collected works. Any polynomial of even degree m is transformed into one of degree ^{1}/_{2}m(m−1); notice that, although this is typically a larger number, it contains one fewer factor of 2. Each root of the derived polynomial determines a pair of roots of the original one via a quadratic equation. Any odd-degree equation has a real root. This English translation was made by Paul Taylor in December 1983 and corrected by Bernard Leak. A summary of the proof, together with a note by Martin Hyland on its logical significance, appeared in Eureka 45 (1985). The L^{A}T_{E}X version was produced in August 2003. Thanks to Mark Wainwright for finding my notes in an old box of papers in Cambridge and returning them to me. |
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