Kullman wrote:
> In response to a question posed in a precalculus class, about the
> origins of the method of synthetic division for polynomials, a
> student claims that it is due to William Horner in 1819, but I
> believe that the student is confusing synthetic division with
> "Horner's method."
>
> Can anyone suggest a source for synthetic division?
>
> Thank you,
>
> David Kullman
> Miami University
> Oxford, Ohio
>
The oldest occurrence of synthetic division I know of is in
Pedro Nun~ez, Libro de Algebra en Arithmetica y Geometria. Anvers 1567
folio 32r. I have put my excerpts of the book with the complete quotation
of the (portuguese) foreword and the (spanish) chapter II on my homepage.
It is a dvi-file. The example of the synthetic division is on page 18.
Nunes teaches in this chapter the manipulation of polynomials and their
quotients. The way he works with these things shows that he is near to the
algebraist's understanding of polynomials in contrast to the analyst's
understanding of polynomial functions. He also makes it clear that one
needs negative numbers for the synthetic division of polynomials.
My comments are, of course, in German. Here the address:
http://www.mathematik.uni-kl.de/~luene/miszellen/Stammblatt.html
There is also a picture of the portuguese 100 Escudo coin on my homepage.
Heinz Lueneburg