The first definite knowledge that we have of Egyptian mathematics comes
to us from a manuscript copied on papyrus, a kind of paper used about
the Mediterranean in early times. This copy was made by one Aah-mesu
(The Moon-born), commonly called Ahmes, who probably flourished about
1700 B.C. The original from which he copied, written about 2300 B.C.,
has been lost, but the papyrus of Ahmes, written nearly four thousand
years ago, is still preserved, and is now in the British Museum. In this
manuscript, which is devoted chiefly to fractions and to a crude
algebra, is found some work on mensuration. Among the curious rules are
the incorrect ones that the area of an isosceles triangle equals half
the product of the base and one of the equal sides; and that the area of
a trapezoid having bases _b_, _b'_, and the nonparallel sides each equal
to _a_, is 1/2_a_(_b_ + _b'_). One noteworthy advance appears, however.
Ahmes gives a rule for finding the area of a circle, substantially as
follows: Multiply the square on the radius by (16/9)^2, which is
equivalent to taking for [pi] the value 3.1605. This papyrus also
contains some treatment of the mensuration of solids, particularly with
reference to the capacity of granaries. There is also some slight
mention of similar figures, and an extensive treatment of unit
fractions,--fractions that were quite universal among the ancients. In
the line of algebra it contains a brief treatment of the equation of the
first degree with one unknown, and of progressions.[16]
Herodotus tells us that Sesostris, king of Egypt,[17] divided the land
among his people and marked out the boundaries after the overflow of the
Nile, so that surveying must have been well known in his day. Indeed,
the _harpedonaptae_, or rope stretchers, acquired their name because they
stretched cords, in which were knots, so as to make the right triangle
3, 4, 5, when they wished to erect a perpendicular. This is a plan
occasionally used by surveyors to-day, and it shows that the practical
application of the Pythagorean Theorem was known long before Pythagoras
gave what seems to have been the first general proof of the proposition.
Public-domain text, read in full here on John Shaqi.
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