**MR1698404**

**(2000j:01009)**

Clagett, Marshall(1-IASP)

Ancient Egyptian science: a source book. Vol. 3.

Ancient Egyptian mathematics. Memoirs of the American Philosophical Society, 232.

*American Philosophical Society, Philadelphia, PA,*1999. xii+462 pp. ISBN: 0-87169-232-5

01A16

This third volume of Marshall Clagett's *Ancient Egyptian science* is
dedicated to the mathematics of the Pharaonic period, mostly to that of the
second millennium BCE. Ancient Egyptian medicine and biology and the Egyptian
ways to represent nature (including the rather mathematical use of square grids
and proportion) have been postponed to a forthcoming volume.

This volume
consists of four parts. Part I is a general discussion of the topic, whereas
Part II consists of the major sources in Clagett's own translation (as in
previous volumes, always made with an eye to the best extant translations, but
at least adjusted in the interest of consistency). Part III contains the
bibliography together with an index of Egyptian (more or less) technical
terminology and another index of names and subjects; Part IV consists of
illustrations which, as in earlier volumes, also encompass facsimile
reproductions of sources, hieroglyphic transcriptions of these, and excerpts
from earlier secondary literature on the topic.

Beyond the source
material and the author's own interpretations (always well argued), the volume
gives a very full presentation of the opinions and reasoning of earlier authors,
from founding fathers like Lepsius, Eisenlohr, Griffith, Hultsch and Borchardt,
over Sethe, Peet, Neugebauer, Gillings and many others, to those of the latest
decade (Couchoud, Caveing, Guillemot, Ritter). Apart from presenting a fine
overview of the history of the historiography of the field, it also serves the
purpose of leaving ultimate judgement to readers while providing them with all
available tools for informed decision.

Part I starts by summing up what
can be concluded from Early Dynastic and Old Kingdom documents and practices
about counting and measurement during these epochs, emphasizing also how little
can actually be known. In contrast to what can be found even in serious
Egyptological work (but in full agreement with Clagett's truly historical
approach in preceding volumes), no claim is made that the mathematics of the
second millennium must already have been present during the Old Kingdom simply
because this is regarded as "the Golden Age of Egyptian knowledge and wisdom"
(p. 6). Almost $95%$ of general discussion is therefore dedicated to the
mathematics of the second millennium, from metrology and tables, over basic
concepts and arithmetical techniques, to particular arithmetical and geometrical
problem types. The Demotic period is not discussed (R. A. Parker's *Demotic
mathematical papyri* \ref[Brown Univ. Press, Providence, RI, 1972; Zbl
283.01001] renders it superfluous, and it is anyhow not central to Clagett's
project), and the 7th--8th-c. CE Akhmîm papyrus is only referred to in a
comparative note.

The sources presented in Part II are the following:
the Rhind mathematical papyrus; the Moscow mathematical papyrus; the Kahun
mathematical fragments; the Berlin papyrus 6619; the mathematical leather roll;
and, as a representative of the application of mathematical techniques in
real-life scribal accounting, Sections G--I from Reisner papyrus I.

The
translation of the Rhind papyrus follows Chace's literal translation from 1929
closely; Chace's corresponding hieratic text and hieroglyphic and phonetic
transcriptions are rendered in full in Part IV (readers who are not strongly
myopic may nevertheless need a magnifying glass: for understandable economic
reasons, Chace's large plates are strongly reduced); Struve's entire hieratic
text and hieroglyphic transcription of the Moscow papyrus are also reproduced;
so are the texts and published transcriptions of the remaining smaller
documents.

Even though the volume is not intended to displace preceding
publications---often the reader is invited to take advantage of their
discussions---it will provide anyone interested in ancient Egyptian mathematics
with a very convenient vade mecum, and it may guide readers taking up the topic
for the first time along a significant part of the route.

\{Volume II
has been reviewed \ref [MR1332718
(96i:01007)].\}