MEASUREMENT OF PYRAMIDS
127
the problems is to find a certain relation called se-qet,
literally ‘ that which makes the nature i. e. that which
determines the proportions of the pyramid. The relation
se-qet
\ ukha-thebt
In the case of the monument we have
piremus
two other names for lines in the figure, (1) senti, ‘ foundation
or base, (2) qay en hern, ‘ vertical length ’, or height; the
■| senti
or
same term se-qet is used for the relation .
1 ' qay en heru
the same inverted. Eisenlohr and Cantor took the lines
(1) and (2) in the case of the pyramid to be different from
the lines (1) and (2) called by different names in the monument.
Suppose A BCD to be the square base of a pyramid, E its
centre, R the vertex, and F the middle point of the side AD
of the base. According to Eisenlohr and Cantor the ukha-
thebt is the diagonal, say AC, of the base, and the pir-em-us
is the edge, as AH. On this assumption the se-qet
AE
AH
= cos HAE.
In the case of the monument they took the senti to be the
side of the base, as AB, the qay en heru to be the height of
the pyramid EH, and the se-qet to be the ratio of EH to
^AB or of EH to EF, i. e. the tangent of the angle HFE
which is the slope of the faces of the pyramid. According
to Eisenlohr and Cantor, therefore, the one term se-qet was
used in two different senses, namely, in Nos. 56—9 for cos HAE
and in No. 60 for tan HFE. Borchardt has, however, proved
that the se-qet in all the cases has one meaning, and represents
the cotangent of the slope of the faces of the pyramid,
i. e. cot HFE or the ratio of FE to EH. There is no difficulty
in the use of the different words ukha-thebt and senti to
express the same thing, namely, the side of the base, and
of the different words pel‘-em-us and qay en heru in the same
sense of ‘ height ’; such synonyms are common in Egypt, and,
moreover, the word mer used of the pyramids is different
from the word an for the monument. Again, it is clear that,
while the slope, the angle HFE, is what the builder would
want to know, the cosine of the angle HAE, formed by the
edge with the plane of the base, would be of no direct use
