EGYPTIAN GEOMETRY 
123 
difficulties ’, as it calls itself, is rough mensuration. The 
following are the cases dealt with which concern us here. 
(1) There is the rectangle, the area of which is of course 
obtained by multiplying together the numbers representing 
the sides. (2) The measure of a triangle is given as the pro 
duct of half the base into the side. And here there is a differ 
ence of opinion as to the kind of triangle measured, Eisenlohr 
and Cantor, taking the diagram to represent an isosceles tri 
angle rather inaccurately drawn, have to assume error on 
the part of the writer in making the area \ah instead of 
\aV{b 2 — %a 2 ) where a is the base and b the ‘side’, an error 
which of course becomes less serious as a becomes smaller 
relatively to h (in the case taken a = 4, h = 10, and the area 
as given according to the rule, i.e. 20, is not greatly different 
from the true value 19-5959). But other authorities take the 
triangle to be right-angled and h to be the side perpendicular 
to the base, their argument being that the triangle as drawn 
is not a worse representation of a right-angled triangle than 
other triangles purporting to be right-angled which are found 
in other manuscripts, and indeed is a better representation of 
a right-angled triangle than it is of an isosceles triangle, while 
the number representing the side is shown in the figure along 
side one only of the sides, namely that adjacent to the angle 
which the more nearly represents a right angle. The advan 
tage of this interpretation is that the rule is then correct 
instead of being more inaccurate than one would expect from 
a people who had expert land surveyors to measure land for 
the purpose of assessing it to tax. The same doubt arises 
with reference to (3) the formula for the area of a trapezium, 
namely ■|(a + c) x b, where a, c are the base and the opposite 
parallel side respectively, while b is the ‘ side ’, i.e. one of the 
non-parallel sides. In this case the figure seems to have been 
intended to be isosceles, whereas the formula is only accurate 
if b, one of the non-parallel sides, is at right angles to the base, 
in which case of course the side opposite to b is not, at right 
angles to the base. As the parallel sides (6, 4) in the case 
taken are short relatively to the £ side ’ (20), the angles at the 
base are not far short of being right angles, and it is possible 
that one of them, adjacent to the particular side which is 
marked 20, was intended to be right. The hypothesis that