Science 173
general method might have been discovered by cutting up a
solid model into simple solids of easily determined volumes.
Perhaps the volumes were found by a weighing method similar
to that used later by Heron of Alexandria (c. 250 B.C.).
There is no direct evidence that the Egyptians knew how to
calculate the volume of a pyramid, yet it is difficult to imagine
that they did not. The volume might have been determined
by constructing a pyramid in model blocks and then rearranging
the blocks in the shape of a solid prism. The formula 'Volume =
| X area of base X height' is first used by Democritus (c. 460 B.C.)*
Heron uses various formulae for the volumes of cones and pyra-
mids—some correct, others incorrect. It is significant that the
incorrect formulae were derived, in part, at any rate, from
Babylonia, where they originated in problems of everyday life,
such as the contents of baskets, tree-trunks, and dikes. These
incorrect formulae lingered in use for a long time, for practical
purposes.
If the Egyptian did know how to find the volume of a pyramid,
the volume of a truncated pyramid would have been easily
determined as the difference between the volumes of two
pyramids.
The statement is frequently made that one problem indicates
with certainty that the Egyptian of 2000 B.C. knew the formula
for the area of a hemisphere. There are sound reasons, however,
for rejecting this interpretation, which would place Egyptian
mathematics on a far higher level than the evidence from other
sources warrants.
From the foregoing summary, it will be clear that mathe-
matical knowledge in ancient Egypt was essentially practical in
character and must have developed as occasion arose in dealing
with problems encountered in daily life. Most of the problems
deal with the concrete—7 loaves, 5 men—rarely with abstract
numbers. While the Egyptian .knew how to deal with particular
cases, there is little evidence that he realized the underlying