re preserved only as rules of thumb by the craftsmen and experts, who
would jealously hide them as secrets of trade. Men of genius were not
wanting in the long history of Egypt; two doctors, Imhotp (Imuthes), the
architect of Zoser, in the IIIrd Dynasty, and Amenophis (Amenhotp), son
of Hap, the wise scribe under Amenophis III. in the XVIIIth, eventually
received the honours of deification; and Hardadf under Cheops of the
IVth Dynasty was little behind these two in the estimation of posterity.
Such men, who, capable in every field, designed the Great Pyramids and
bestowed the highest monumental fame on their masters, must surely have
had an insight into scientific principles that would hardly be credited
to the Egyptians from the written documents alone.

_Mathematics._--The Egyptian notation for whole numbers was decimal,
each power of 10 up to 100,000 being represented by a different figure,
on much the same principle as the Roman numerals. Fractions except 2/3
were all primary, i.e. with the numerator unity: in order to express
such an idea as 9/13 the Egyptians were obliged to reduce it to a series
of primary fractions through double fractions 2/13 + 2/13 + 2/13 + 2/13
+ 1/13 = 4(1/8 + 1/52 + 1/104) + 1/13 = 1/2 + 2/13 + 1/26 = 1/2 + 1/8 +
1/26 + 1/52 + 1/104; this operation was performed in the head, only the
result being written down, and to facilitate it tables were drawn up of
the division of 2 by odd numbers. With integers, besides adding and
subtracting, it was easy to double and to multiply by 10: multiplying
and dividing by 5 and finding the 1-1/2 value were also among the
fundamental instruments of calculation, and all multiplication proceeded
by repetitions of these processes with addition, e.g. 9 x 7 = (9 x 2 x
2) + (9 x 2) + 9. Division was accomplished by multiplying the divisor
until the dividend was reached; the answer being the number of times the
divisor was so multiplied. Weights and measures proceeded generally on
either a decimal or a doubling system or a combination of the two. Apart
from a few calculations and accounts, practically all the materials for
our knowledge of Egyptian mathematics before the Hellenistic period date
from the Middle Kingdom.

The principal text is the Rhind Mathematical Papyrus in the British
Museum, written under a Hyksos king c. 1600 B.C.; unfortunately it is
full of gross errors. Its contents fall roughly into the following
scheme, but the main headings are n