A History of Science-1 [46]
of the convexity of the earth's surface is furnished by observation of an approaching ship at sea. On a clear day a keen eye may discern the mast and sails rising gradually above the horizon, to be followed in due course by the hull. Similarly, on approaching the shore, high objects become visible before those that lie nearer the water. It is at least a plausible supposition that Pythagoras may have made such observations as these during the voyage in question, and that therein may lie the germ of that wonderful conception of the world as a sphere. To what extent further proof, based on the fact that the earth's shadow when the moon is eclipsed is always convex, may have been known to Pythagoras we cannot say. There is no proof that any of the Italic philosophers made extensive records of astronomical observations as did the Egyptians and Babylonians; but we must constantly recall that the writings of classical antiquity have been almost altogether destroyed. The absence of astronomical records is, therefore, no proof that such records never existed. Pythagoras, it should be said, is reported to have travelled in Egypt, and he must there have gained an inkling of astronomical methods. Indeed, he speaks of himself specifically, in a letter quoted by Diogenes, as one who is accustomed to study astronomy. Yet a later sentence of the letter, which asserts that the philosopher is not always occupied about speculations of his own fancy, suggesting, as it does, the dreamer rather than the observer, gives us probably a truer glimpse into the philosopher's mind. There is, indeed, reason to suppose that the doctrine of the sphericity of the earth appealed to Pythagoras chiefly because it accorded with his conception that the sphere is the most perfect solid, just as the circle is the most perfect plane surface. Be that as it may, the fact remains that we have here, as far as we can trace its origin, the first expression of the scientific theory that the earth is round. Had the Italic philosophers accomplished nothing more than this, their accomplishment would none the less mark an epoch in the progress of thought. That Pythagoras was an observer of the heavens is further evidenced by the statement made by Diogenes, on the authority of Parmenides, that Pythagoras was the first person who discovered or asserted the identity of Hesperus and Lucifer--that is to say, of the morning and the evening star. This was really a remarkable discovery, and one that was no doubt instrumental later on in determining that theory of the mechanics of the heavens which we shall see elaborated presently. To have made such a discovery argues again for the practicality of the mind of Pythagoras. His, indeed, would seem to have been a mind in which practical common-sense was strangely blended with the capacity for wide and imaginative generalization. As further evidence of his practicality, it is asserted that he was the first person who introduced measures and weights among the Greeks, this assertion being made on the authority of Aristoxenus. It will be observed that he is said to have introduced, not to have invented, weights and measures, a statement which suggests a knowledge on the part of the Greeks that weights and measures were previously employed in Egypt and Babylonia. The mind that could conceive the world as a sphere and that interested itself in weights and measures was, obviously, a mind of the visualizing type. It is characteristic of this type of mind to be interested in the tangibilities of geometry, hence it is not surprising to be told that Pythagoras "carried that science to perfection." The most famous discovery of Pythagoras in this field was that the square of the hypotenuse of a right-angled triangle is equal to the squares of the other sides of the triangle. We have already noted the fable that his enthusiasm over this discovery led him to sacrifice a hecatomb. Doubtless the story is apocryphal, but doubtless, also, it expresses the truth as to the fervid joy with which the philosopher must have contemplated the results of his creative