"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