126 THE EARLIEST GREEK GEOMETRY. THALES
in form ‘ 9 in height and 6 in breadth The word qa, here
translated ‘height’, is apparently used in other documents
for ‘length’ or ‘greatest dimension’, and must in this case
mean the diameter of the base, while the ‘ breadth ’ is the
height in our sense. If we denote the diameter of the circular
base by k, and the height by h, the formula used in this
problem for finding the volume is (| • §&) 2 • Here it is
not f h, but |/i, which is taken as the last factor of the
product. Eisenlohr suggests that the analogy of the formula
for a hemisphere, Trr 2 .|r, may have operated to make the
calculator take | of the height, although the height is not
in the particular case the same as the radius of the base, but
different. But there remains the difficulty that (f) 2 or —■
times the area of the circle of diameter k is taken instead
of the area itself. As to this Eisenlohr can only suggest that
the circle of diameter k which was accessible for measurement
was not the real or mean circular section, and that allowance
had to be made for this, or that the base was not a circle of
diameter k but an ellipse with -^-k and k as major and minor
axes. But such explanations can hardly be applied to the
factor (|) 2 in the Kahun case if the latter is really the case
of a hemispherical space as suggested. Whatever the true
explanation may be, it is clear that these rules of measure
ment must have been empirical and that there was little or
no geometry about them.
Much more important geometrically are certain calculations
with reference to the proportions of pyramids (Nos. 56-9 of
the Papyrus Rhind) and a monu
ment (No. 60). In the case
of the pyramid two lines in the
figure are distinguished, (1)
ukha-thebt, which is evidently
some line in the base, and
(2) pir-em-us or per-em-us
(‘height’), a word from which
the name Trapa/ny may have
been derived. 1 The object of
H
A
B
1 Another view is that the words nvpnpis and nvpapovs, meaning a kind
of cake made from roasted wheat and honey, are derived from nvpoi,
‘ wheat and are thus of purely Greek origin.