122 THE EARLIEST GREEK GEOMETRY. THALES
fasteners’; and, while it is clear from the passage that the
persons referred to were clever geometers, the word reveals a
characteristic modus operandi. The Egyptians were ex
tremely careful about the orientation of their temples, and
the use of ropes and pegs for marking out the limits,
e. g. corners, of the sacred precincts is portrayed in all
pictures of the laying of foundation stones of temples. 1 The
operation of £ rope-stretching ’ is mentioned in an inscription on
leather in the Berlin Museum as having been in use as early
as Amenemhat I (say 2300 b.c.). 2 Now it was the practice
of ancient Indian and probably also of Chinese geometers
to make, for instance, a right angle by stretching a rope
divided into three lengths in the ratio of the sides of a right-
angled triangle in rational numbers, e.g. 3, 4, 5, in such a way
that the three portions formed a triangle, when of course a right
angle would be formed at the point where the two smaller
sides meet. There seems to be no doubt that the Egyptians
knew that the triangle (3, 4, 5), the sides of which are so
related that the square on the greatest side is equal to the
sum of the squares on the other two, is right-angled; if this
is so, they were acquainted with at least one case of the
famous proposition of Pythagoras.
Egyptian geometry, i. e. mensuration.
We might suppose, from Aristotle’s remark about the
Egyptian priests being the first to cultivate mathematics
because they had leisure, that their geometry would have
advanced beyond the purely practical stage to something
more like a theory or science of geometry. But the docu
ments which have survived do not give any ground for this
supposition; the art of geometry in the hands of the priests
never seems to have advanced beyond mere routine. The
most important available source of information about Egyptian
mathematics is the Papyrus Rhind, written probably about
1700 B.C. but copied from an original of the time of King
Amenemhat III (Twelfth Dynasty), say 2200 B.c. The geo
metry in this ‘ guide for calculation, a means of ascertaining
everything, of elucidating all obscurities, all mysteries, all
1 Brugsch, Steininschrift und Bibelwort, 2nd ed., p. 86,
2 Diimichen, Denderatempel, p. 33.
