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 to its own height at the same moment. It remains then but to measure the length of this shadow to determine the height of the object. Such feats as this evidence the practicality of the genius of Thales. They suggest that Greek science, guided by imagination, was starting on the high-road of observation. We are told that Thales conceived for the first time the geometry of lines, and that this, indeed, constituted his real advance upon the Egyptians. We are told also that he conceived the eclipse of the sun as a purely natural phenomenon, and that herein lay his advance upon the Chaldean point of view. But if this be true Thales was greatly in advance of his time, for it will be recalled that fully two hundred years later the Greeks under Nicias before Syracuse were so disconcerted by the appearance of an eclipse, which was interpreted as a direct omen and warning, that Nicias threw away the last opportunity to rescue his army. Thucydides, it is true, in recording this fact speaks disparagingly of the superstitious bent of the mind of Nicias, but Thucydides also was a man far in advance of his time.
All that we know of the psychology of Thales is summed up in the famous maxim, "Know thyself," a maxim which, taken in connection with the proven receptivity of the philosopher's mind, suggests to us a marvellously rounded personality.
The disciples or successors of Thales, Anaximander and Anaximenes, were credited with advancing knowledge through the invention or introduction of the sundial. We may be sure, however, that the gnomon, which is the rudimentary sundial, had been known and used from remote periods in the Orient, and the most that is probable is that Anaximander may have elaborated some special design, possibly the bowl-shaped sundial, through which the shadow of the gnomon would indicate the time. The same philosopher is said to have made the first sketch of a geographical map, but this again is a statement which modern researches have shown to be fallacious, since a Babylonian attempt at depicting the geography of the world is still preserved to us on a clay tablet. Anaximander may, however, have been the first Greek to make an attempt of this kind. Here again the influence of Babylonian science upon the germinating Western thought is suggested.
It is said that Anaximander departed from Thales's conception of the earth, and, it may be added, from the Babylonian conception also, in that he conceived it as a cylinder, or rather as a truncated cone, the upper end of which is the habitable portion. This conception is perhaps the first of these guesses through which the Greek mind attempted to explain the apparent fixity of the earth. To ask what supports the earth in space is most natural, but the answer given by Anaximander, like that more familiar Greek solution which transformed the cone, or cylinder, into the giant Atlas, is but another illustration of that substitution of unwarranted inference for scientific induction which we have already so often pointed out as characteristic of the primitive stages of thought.
Anaximander held at least one theory which, as vouched for by various copyists and commentators, entitles him to be considered perhaps the first teacher of the idea of organic evolution. According to this idea, man developed from a fishlike ancestor, "growing up as sharks do until able to help himself and then coming forth on dry land."(1) The thought here expressed finds its germ, perhaps, in the Babylonian conception that everything came forth from a chaos of waters. Yet the fact that the thought of Anaximander has come down to posterity through such various channels suggests that the Greek thinker had got far enough away from the Oriental conception to make his view seem to his contemporaries a novel and individual one. Indeed, nothing we know of the Oriental line of thought conveys any suggestion of the idea of transformation of species, whereas that idea is distinctly formulated in the traditional views of Anaximander.