Is that the <standard> way of "improving" this discussion? What I remember
from _A History of Ancient Mathematical Astronomy_ is that he said
something like "there is no need to discuss Egyptians, Maya, or the
Chinese." And in practice he didn't discuss so much about the Indians
either, more than saying that they got everything they had from the
Greeks.
I think, perhaps, a more humble attitude--found in <other> authors'
work--would "improve" not only the discussion of the Egyptians, but also
the discussion of all other non-Western scientific cultures.
Bo Klintberg (from a snowy, -20 degrees Toronto) Brrrr!
------------------------
On Sat, 2 Jan 1999, Manoel de Campos Almeida
wrote:
> I would like to quote Neugebauer's opinion on the matter, to improve
> the discussion:
>
> "Problems concerning areas or volumes do not constitute an independent
> field of mathematical research but are only one of the many applications
> of numerical methods to practical problems. There is no essential
> difference between the determination of the acreage of a field in
> special measures and the distribution of beer to temple personal
> according to different ratings. This is a state of affairs which holds to
> a large extent even in the Hellenistic period and far beyond it. In
> Arabic mathematics, the "inheritance" problems play an important role,
> while similar examples are found already in Old-Babylonian texts. The
> geometrical writings of Heron, whether authentic or merely ascribed to
> him, contain whole chapters on units, weights, measurements, etc. Of
> course, since the Hellenistic period, even the writings of Heron and
> related documents show the influence of scientific Greek geometry. But,
> by and large, one has to distinguish two widely separate types of
> "Greek" mathematics. One is represented by the strictly logical approach
> of Euclid, Archimedes, Apollonius, etc.; the other group is only a part
> of general Hellenistic mathematics, the roots of which lie in the
> Babylonian and Egyptian procedures. The writings of Heron and Diophantus
> and works know only from fragments or from papyrus documents form part
> of this oriental tradition which can be followed into the Middle Ages
> both in Arabic and in the western world. "Geometry" in the modern sense
> of this word owes very little to the modest amount of basic geometrical
> knowledge which was needed to satisfy practicals ends. ..." (The Exact
> Sciences in Antiquity, O. Neugebauer, Dover, 1969, p. 82-3).
>
> Then, how much was really Egyptian mathematics, and how far was its
> influence on each of Greek's mathematical trends, are questions that,
> I think, still deserve better evaluation. Maybe we need to wait for more
> findings on Egyptian mathematics in such times.
>
> Manoel de Campos Almeida
> Pontificia Universidade Catolica do Parana
> Rua Hermes Fontes, 1282
> Curitiba - 80.440-070
> Parana - Brasil
> manoel@rla01.pucpr.br