ot shown in the original:--

I. _Arithmetic._--A. Tables and rule to facilitate the employment of
fractions.

(a) Table of the divisions of 2 by odd numbers from 3 to 99 (e.g. 2
: 11 = 1/6 + 1/66), see above.
(b) Conversions of compound fractions (e.g. 2/3 x 1/3 = 1/6 + 1/18),
with rule for finding 2/3 of a fraction.

B. The "bread" calculation--a division by 10 of the units 1 to 9.

C. "Completing" calculations.

(a) Adding multiples of a fraction to produce a more convenient
fraction (perhaps connected with the use of palms and
cubits in decoration in a proportion based on the number 8).
(b) Finding the difference between a given fraction and a given
whole number.

D. _Ahe_[9] or "mass"-problems (of the form x + x/n = a, to find the
_ahe_ x).

E. _Tooun_-problems (_tooun_, "rising," seems to be the difference
between the shares of two sets of persons dividing an amount between
them on a lower and a higher scale).

II. _Geometry._--A. Measurement of volume (amounts of grain in
cylindrical and rectangular spaces of different dimensions and vice
versa).

B. Measurement of area (areas of square, circular, triangular, &c.,
fields).

C. Proportions of pyramids and other monuments with sloping sides.

III. _Miscellaneous problems_ (and tables) such as are met with in
bread-making, beer-making, food of live-stock, &c. &c.

The method of estimating the area of irregular fields and the cubic
contents of granaries, &c., is very faulty. It would be interesting to
find material of later date, such as Pythagoras is reported to have
studied.

See A. Eisenlohr, _Ein mathematisches Handbuch der alten Agypter_
(Leipzig, 1877); F. Ll. Griffith, "The Rhind Mathematical Papyrus" in
_Proceedings of the Soc. of Biblical Archaeology_, Nov. 1891, March,
May and June 1894.

_Astronomy._--The brilliant skies of day and night in Egypt favoured the
development of astronomy. A papyrus of the Roman period in the British
Museum attributes the invention of horoscopes to the Egyptians, but no
early instance is known. Professor Petrie has indeed suggested, chiefly
on chronological grounds, that a table of stars on the ceiling of the
Ramesseum temple and another in the tomb of Rameses VI. (repeated in
that of Rameses IX. without alteration) were horoscopes of Rameses II.
and VI.; but Mahler's interpretation of the tables