approximation to TT now known to be 3*1415. . .. The Babylonians
used 3, as did the writer of I Kings vii. 23.
8. Find the content of a cylinder of diameter 12 and height
The area of the base is found as in No. 7 above. This is then
multiplied by the height.
The question whether the Egyptians knew that a triangle
whose sides are proportional to 3, 4, and 5 is right-angled has
been much discussed. It seems inconceivable that they should
not have made this discovery. Yet there is no direct evidence
that they did so. We find equations of the form 32+4z = 52,
but there is no statement of the general relation nor any evidence
such as three rods of lengths 3, 4, and 5 cubits bundled together,
or a cord knotted at points dividing it in the same ratios.
One example indicates that the Egyptian had a clear con-
ception of the nature of a geometrical series, of which the first
term is unity. The sum of 5 terms is correctly given. It is not
clear from the solution that any general formula was known.
Problems dealing with pyramids illustrate the Egyptian method
of measuring an angle of slope by the horizontal offset per unit
vertical height (the seked), a measure of what we now call the
co-tangent of the angle. In the practical application to the
cutting of casing stones to the required angle, the stone mason
would mark off one cubit vertically and then set out the seked
horizontally. He then drew the line indicating the direction in
which the stone should be cut. Such lines have often been found
on stone blocks.
The problem most widely discussed in modern times is one
dealing with the volume of a truncated pyramid. It is far in
advance of anything we know of Egyptian geometry. Many
attempts have been made to reconstruct the mentai processes
required for the sequence of operations, which follows the use
of the modern formula V = %h (a2-\-ab+b2)9 where b is the