Subject: Re: [HM] History of negative numbers
From: Franz Lemmermeyer (lemmerm@mpim-bonn.mpg.de)
Date: Fri Jan 21 2000 - 05:45:47 EST
On Thu, 20 Jan 2000, Douglas Jimenez wrote:
> I want to know if somebody in the list knows a good book about the
> evolution of the concept of negative number.
Gericke, Helmuth
Zur Geschichte der negativen Zahlen.
Dauben, Joseph W. (ed.) et al., History of mathematics: states of the art.
Flores quadrivii -- Studies in honor of Christoph J. Scriba.
San Diego, CA: Academic Press. 279-306 (1996).
is cited in Klaus Barner's preprint "Diophant und die negativen
Zahlen", where he tries to credit Diophantus with the invention
of negative numbers (not successfully in my view, but I'll save
my remarks for another occasion). Gericke has actually written a
book on the history of the notion of numbers:
Geschichte des Zahlbegriffs, BI Mannheim, 1970.
Then there's
Vredenduin, P. G. J.
Gleanings from the history of the negative number. (Dutch)
Euclides (Groningen) 61 (1985/86), no. 10, 331--337
which mentions that the _number line_ representing positive
and negative numbers can be found in the work of Wallis (1657)
and Newton. I recall having read something to that effect
in the very useful
J. Tropfke, Geschichte der Elementarmathematik
which has been reprinted in 1980. See also
J. Sesiano, The appearance of negative solutions in mediaeval mathematics.
Arch. Hist. Exact Sci. 32 (1985), no. 2, 105--150.
Kurt Elfering, Die negativen Zahlen und die Rechenregeln mit
ihnen bei Brahmagupta, Festschrift fuer Helmuth Gericke (1985), 83-86
There's also an article
Hlawka, Edmund
Zum Zahlbegriff, Philos. Natur. 19 (1982), no. 3-4, 413--470
which I haven't seen yet; according to the review in MR, he lets the
history of negative numbers start with Diophantus.
franz
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