  Egyptologists and historians of mathematics around 1930 did an admirable job
in showing that problem 14 of the newly discovered Moscow Papyrus from around
1850 BCE amounts to a general and exact calculation of the volume of a
truncated pyramid (frustum). They were less successful in giving tentative
explanations of what convinced the Egyptians of its correctness. In particular,
they never looked into the possibility of dissecting three identical copies of
the frustum and recomposing them into three boxes of differing sizes whose
volumes can be easily calculated. This is surprising because the formula at
which the historians arrived seems to suggest this procedure. About 2000 years
after the Egyptians, the Chinese scholar Liu Hui did exactly this for the
almost identical problem from the Nine Chapters. If those historians of
mathematics around 1930 had known Liu Hui's algorithm they could have easily
drawn tentative conclusions also for the Egyptian case. The present paper
suggests that it was their knowledge of rigorous Euclidean geometry and of
relatively modern algebra which distorted the judgment of those historians,
something which could not have been the case for Liu Hui. Their failure seems
to have discouraged later Egyptologists to look for explanations or to even
point to Liu Hui when his work had become known. Thus a chance was missed to
use the great intuitive and pedagogic potential of a remarkable piece of
Egyptian mathematics. This paper is not a contribution to the historiography of
Egyptian mathematics for which the author is no specialist but argues primarily
on a methodological level using secondary historical sources. The paper is
partly inspired by a more recent publication of Paul Shutler (2009) who
suggests an intuitive and historically possible proof also for the special, and
mathematically crucial case of the second formula, which is related to the full
pyramid.

History and Overview