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Science                                     175
gyptian has not always been given full credit for what he did.
efore 2000 B.C. he had developed a practical system of numera-
on and could carry out arithmetical calculations (involving the
lanipulation of complicated fractional expressions) with ease
ad accuracy. He evolved methods of solution, some of which
irvive in modern text-books—in particular those connected
/ith division in given proportions, and 'work' problems (by the
aethod of adding reciprocals). He could solve problems involv-
ng two unknown quantities and had elementary notions of
Arithmetical progression using fractions, as well as of geometrical
progression. He was familiar with the elementary properties of
rectangles, triangles, circles, and pyramids.   Thus he could deal
successfully with mathematical problems encountered in his
daily life. The examples we have throw light on the methods
of trading, the feeding of live stock, the raising of taxes, and the
determination of the values of food and drink in terms of the
amount which can be made from a given quantity of material.
How far, if at all, Egypt was indebted to Babylonia in regard
to mathematics and astronomy is a matter for conjecture in the
present state of our knowledge.   In both subjects there are
indications of independent evolution and as yet there is no evi-
dence that the early Egyptians owed anything to other sources.
Weights and Measures
The prototype of the beam balance is frequently represented
in scenes depicting the weighing of precious metals in Egypt,
from the Fifth Dynasty onwards. It is sometimes accompanied
by a tray with numbered weights. The earliest examples employ
a simple beam drilled at the centre for a loop suspension, as well
as near the ends for a single cord and hook on which hangs a
basket or pan to take the weights on one side and the object
to be weighed on the other. The design shows gradual improve-
ment with time. The plummet makes its appearance about
2500 B.C. Later four suspension cords for each scale pan are