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.