ts, to the measurement of the earth's surface.
Herodotus tells us that the Egyptians were obliged to cultivate
the science because the periodical inundations washed away the
boundary-lines between their farms. The primitive geometer, then, was
a surveyor. The Egyptian records, as now revealed to us, show that the
science had not been carried far in the land of its birth. The
Egyptian geometer was able to measure irregular pieces of land only
approximately. He never fully grasped the idea of the perpendicular
as the true index of measurement for the triangle, but based his
calculations upon measurements of the actual side of that figure.
Nevertheless, he had learned to square the circle with a close
approximation to the truth, and, in general, his measurement sufficed
for all his practical needs. Just how much of the geometrical knowledge
which added to the fame of Thales was borrowed directly from the
Egyptians, and how much he actually created we cannot be sure. Nor is
the question raised in disparagement of his genius. Receptivity is the
first prerequisite to progressive thinking, and that Thales reached out
after and imbibed portions of Oriental wisdom argues in itself for
the creative character of his genius. Whether borrower of originator,
however, Thales is credited with the expression of the following
geometrical truths:

1. That the circle is bisected by its diameter.

2. That the angles at the base of an isosceles triangle are equal.

3. That when two straight lines cut each other the vertical opposite
angles are equal.

4. That the angle in a semicircle is a right angle.

5. That one side and one acute angle of a right-angle triangle determine
the other sides of the triangle.

It was by the application of the last of these principles that Thales is
said to have performed the really notable feat of measuring the distance
of a ship from the shore, his method being precisely the same in
principle as that by which the guns are sighted on a modern man-of-war.
Another practical demonstration which Thales was credited with making,
and to which also his geometrical studies led him, was the measurement
of any tall object, such as a pyramid or building or tree, by means
of its shadow. The method, though simple enough, was ingenious. It
consisted merely in observing the moment of the day when a perpendicular
stick casts a shadow equal to its own length. Obviously the tree or
monument would also cast a shadow equal