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
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* 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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