The army begins to march.
Thales the Milesian.
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, Crœsus 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.
Mathematical skill of Thales.
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.
His theorems.
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 mathematical performance than the measuring of the altitude of the pyramids by their shadow.
Ingenious plan of Thales for crossing the Halys.
But to return to Crœsus. Thales undertook the work of transporting the army across the river. He examined the banks, and found, at length, a spot where the land was low and level for some distance from the stream. He caused the army to be brought up to the river at this point, and to be encamped there, as near to the bank as possible, and in as compact a form. He then employed a vast number of laborers to cut a new channel for the waters, behind the army, leading out from the river above, and rejoining it again at a little distance below. When this channel was finished, he turned the river into its new course, and then the army passed without difficulty over the former bed of the stream.
Advance of Cyrus.