the highest mathematical knowledge reached by the Egyptians of that day.
Geometry is treated very superficially and as of subsidiary interest
to arithmetic; there is no ordered series of reasoned geometrical
propositions given--nothing, indeed, beyond isolated rules,
and of these some are wanting in accuracy.


[1] See AUGUST EISENLOHR: _Ein mathematisches Handbuch der
alten Aegypter_ (1877); J. Gow: _A Short History of Greek Mathematics_
(1884); and V. E. JOHNSON: _Egyptian Science from the Monuments
and Ancient Books_ (1891).


One geometrical fact known to the Egyptians was that if a triangle
be constructed having its sides 3, 4, and 5 units long respectively,
then the angle opposite the longest side is exactly a right angle; and the
Egyptian builders used this rule for constructing walls perpendicular
to each other, employing a cord graduated in the required manner.
The Greek mind was not, however, satisfied with the bald statement
of mere facts--it cared little for practical applications,
but sought above all for the underlying REASON of everything.
Nowadays we are beginning to realise that the results achieved by this
type of mind, the general laws of Nature's behaviour formulated
by its endeavours, are frequently of immense practical importance--
of far more importance than the mere rules-of-thumb beyond which
so-called practical minds never advance. The classic example
of the utility of seemingly useless knowledge is afforded by
Sir WILLIAM HAMILTON'S discovery, or, rather, invention of Quarternions,
but no better example of the utilitarian triumph of the theoretical
over the so-called practical mind can be adduced than that afforded