suaded by such
reasoning.

When all things were ready, the army commenced its march and moved
eastward, through one province of Asia Minor after another, until they
reached the Halys. This river is a considerable stream, which rises in
the interior of the country, and flows northward into the Euxine Sea.
The army encamped on the banks of it, and some plan was to be formed
for crossing the stream. In accomplishing this object, Croesus was
aided by a very celebrated engineer who accompanied his army, named
Thales. Thales was a native of Miletus, and is generally called in
history, Thales the Milesian. He was a very able mathematician and
calculator, and many accounts remain of the discoveries and
performances by which he acquired his renown.

For example, in the course of his travels, he at one time visited
Egypt, and while there, he contrived a very simple way of measuring
the height of the pyramids. He set up a pole on the plain in an
upright position, and then measured the pole and also its shadow. He
also measured the length of the shadow of the pyramid. He then
calculated the height of the pyramid by this proportion: as the
length of shadow of the pole is to that of the pole itself, so is
the length of the shadow of the pyramid to its height.

Thales was an astronomer as well as a philosopher and engineer. He
learned more exactly the true length of the year than it had been
known before; and he also made some calculations of eclipses, at least
so far as to predict the year in which they would happen. One eclipse
which he predicted happened to occur on the day of a great battle
between two contending armies. It was cloudy, so that the combatants
could not see the sun. This circumstance, however, which concealed the
eclipse itself, only made the darkness which was caused by it the more
intense. The armies were much terrified at this sudden cessation of
the light of day, and supposed it to be a warning from heaven that
they should desist from the combat.

Thales the Milesian was the author of several of the geometrical
theorems and demonstrations now included in the Elements of Euclid.
The celebrated fifth proposition of the first book, so famous among
all the modern nations of Europe as the great stumbling block in the
way of beginners in the study of geometry, was his. The discovery of
the truth expressed in this proposition, and of the complicated
demonstration which establishes it, was certainly a much greater