Rafael Bombelli da Bologna, L'Algebra. Prima edizione integrale. Introduzione
di U. Forti - Prefazione di E. Bortolotti. Feltrinelli editore, Milano 1966
I know what I have to do this evening.
Thanks a lot, Heinz Lueneburg
>
> Professor Lueneburg asks for a more precise citation of Rafael Bombelli's
> exposition of synthetic division of polynomials.
>
> The following is from my notes on the second edition of 1579, the copy
> at American University in Washington, DC. I believe that this same material is
> in the 1572 edition as well, but that the page numbers are different.
> Bombelli follows the three book style popular at the time. He wrote
> five books, but, according to the Dictionary of Scientific Biography (DSB), the
> last two books weren't published until the 20th Century.
> Book I is about the arithmetic of radicals, and an introduction to
> notation. The notation is rather "Cossist", R.q.21, for example, meanin the
> square root of 21. This is described on page 335 of Victor Katz' book on the
> history of mathematics (1st ed.) Book I also includes some arithmetic
> involving square roots of negative numbers (Bombelli, p 169), with mnemonic
> poetry to help the reader remember the rules.
> The issue at hand, though, is polynomial arithmetic. That is in Book
> II, starting with a peculiar notation that Burton has used as the cover
> illustration on the latest edition of his History of Mathematics. After a few
> pages on the addition, subtraction and multiplication of polynomials, on page
> 229, Bombelli does the traditional long division of polynomials, almost exactly
> the way that I learned it in school, with the example dividing x^3+8 by x+2,
> and getting x^2-2x+4, as one would hope that he would.
> Then, Bombelli moves on to other topics, especially the solution of
> cubic equations.
>
> I hope this is what you were looking for.
>
> Ed Sandifer
>
> *************************************************************************
> * Ed Sandifer * sandifer@wcsu.ctstateu.edu *
> * Professor of Mathematics * *
> * Western Connecticut State University* www.wcsu.ctstateu.edu/~SANDIFER/*
> * Danbury, CT 06810 * *
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>