Let us begin with some of the earliest discoveries and correct hypotheses. Anaximander thought that the earth floats freely, and is not supported on anything. Aristotle, * who often rejected the best hypotheses of his time, objected to the theory of Anaximander, that the earth, being at the centre, remained immovable because there was
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* De Caelo, 295b.
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no reason for moving in one direction rather than another. If this were valid, he said, a man placed at the centre of a circle with food at various points of the circumference would starve to death for lack of reason to choose one portion of food rather than another. This argument reappears in scholastic philosophy, not in connection with astronomy, but with free will. It reappears in the form of «Buridan’s ass,» which was unable to choose between two bundles of hay placed at equal distances to right and left, and therefore died of hunger.
Pythagoras, in all probability, was the first to think the earth spherical, but his reasons were (one must suppose) aesthetic rather than scientific. Scientific reasons, however, were soon found. Anaxagoras discovered that the moon shines by reflected light, and gave the right theory of eclipses. He himself still thought the earth flat, but the shape of the earth’s shadow in lunar eclipses gave the Pythagoreans conclusive arguments in favour of its being spherical. They went further, and regarded the earth as one of the planets. They knew-from Pythagoras himself, it is said—that the morning star and the evening star are identical, and they thought that all the planets, including the earth, move in circles, not round the sun, but round the «central fire.» They had discovered that the moon always turns the same face to the earth, and they thought that the earth always turns the same face to the «central fire.» The Mediterranean regions were on the side turned away from the central fire, which was therefore always invisible. The central fire was called «the house of Zeus,» or «the Mother of the gods.» The sun was supposed to shine by light reflected from the central fire. In addition to the earth, there was another body, the counter-earth, at the same distance from the central fire. For this, they had two reasons, one scientific, one derived from their arithmetical mysticism. The scientific reason was the correct observation that an eclipse of the moon sometimes occurs when both sun and moon are above the horizon. Refraction, which is the cause of this phenomenon, was unknown to them, and they thought that, in such cases, the eclipse must be due to the shadow of a body other than the earth. The other reason was that the sun and moon, the five planets, the earth and counter-earth, and the central fire, made ten heavenly bodies, and ten was the mystic number of the Pythagoreans.
This Pythagorean theory is attributed to Philolaus, a Theban, who
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lived at the end of the fifth century B.C. Although it is fanciful and in part quite unscientific, it is very important, since it involves the greater part of the imaginative effort required for conceiving the Copernican hypothesis. To conceive of the earth, not as the centre of the universe, but as one among the planets, not as eternally fixed, but as wandering through space, showed an extraordinary emancipation from anthropocentric thinking. When once this jolt had been given to men’s natural picture of the universe, it was not so very difficult to be led by scientific arguments to a more accurate theory.
To this various observations contributed. Oenopides, who was slightly later than Anaxagoras, discovered the obliquity of the ecliptic. It soon became clear that the sun must be much larger than the earth, which fact supported those who denied that the earth is the centre of the universe. The central fire and the counter-earth were dropped by the Pythagoreans soon after the time of Plato. Heraclides of Pontus (whose dates are about 388 to 315 B.C., contemporary with Aristotle) discovered that Venus and Mercury revolve about the sun, and adopted the view that the earth rotates on its own axis once every twenty-four hours. This last was a very important step, which no predecessor had taken. Heraclides was of Plato’s school, and must have been a great man, but was not as much respected as one would expect; he is described as a fat dandy.
Aristarchus of Samos, who lived approximately from 310 to 230 B.C., and was thus about twenty-five years older than Archimedes, is the most interesting of all ancient astronomers, because he advanced the complete Copernican hypothesis, that all the planets, including the earth, revolve in circles round the sun, and that the earth rotates on its axis once in twenty-four hours. It is a little disappointing to find that the only extant work of Aristarchus, On the Sizes and Distances of the Sun and the Moon, adheres to the geocentric view. It is true that, for the problems with which this book deals, it makes no difference which theory is adopted, and he may therefore have thought it unwise to burden his calculations with an unnecessary opposition to the general opinion of astronomers; or he may have only arrived at the Copernican hypothesis after writing this book. Sir Thomas Heath, in his work on Aristarchus, * which contains the text of this book
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* Aristarchus of Samos, the Ancient Copernicus. By Sir Thomas Heath. Oxford 1913. What follows is based on this book.
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with a translation, inclines to the latter view. The evidence that Aristarchus suggested the Copernican view is, in any case, quite conclusive.
The first and best evidence is that of Archimedes, who, as we have seen, was a younger contemporary of Aristarchus. Writing to Gelon, King of Syracuse, he says that Aristarchus brought out «a book consisting of certain hypotheses,» and continues: «His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit.» There is a passage in Plutarch saying that Cleanthes «thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the Universe (i.e. the earth), this being the effect of his attempt to save the phenomena by supposing the heaven to remain at rest and the earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis.» Cleanthes was a contemporary of Aristarchus, and died about 232 B.C. In another passage, Plutarch says that Aristarchus advanced this view only as a hypothesis, but that his successor Seleucus maintained it as a definite opinion. ( Seleucus flourished about 150 B.C.). Aëtius and Sextus Empiricus also assert that Aristarchus advanced the heliocentric hypothesis, but do not say that it was set forth by him only as a hypothesis. Even if he did so, it seems not unlikely that he, like Galileo two thousand years later, was influenced by the fear of offending religious prejudices, a fear which the attitude of Cleanthes (mentioned above) shows to have been well grounded.
The Copernican hypothesis, after being advanced, whether positively or tentatively, by Aristarchus, was definitely adopted by Seleucus, but by no other ancient astronomer. This general rejection was mainly due to Hipparchus, who flourished from 161 to 126 B.C. He is described by Heath as «the greatest astronomer of antiquity.» * He was the first to write systematically on trigonometry; he discovered the precession of the equinoxes; he estimated the length of the lunar month with an error of less than one second; he improved Aristarchus’s estimates of the sizes and distances of the sun and moon; he made a catalogue of eight hundred and fifty fixed stars, giving
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* Greek Mathematics, Vol. II, p. 253.
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their latitude and longitude. As against the heliocentric hypothesis of Aristarchus, he adopted and improved the theory of epicycles which had been invented by Apollonius, who flourished about 220 B.C.; it was a development of this theory that came to be known, later, as the Ptolemaic system, after the astronomer Ptolemy, who flourished in the middle of the second century A.D. Copernicus came to know something, though not much, of the almost forgotten hypothesis of Aristarchus, and was encouraged by finding ancient authority for his innovation. Otherwise, the effect of this hypothesis on subsequent astronomy was practically nil.Ancient astronomers, in estimating the sizes of the earth, moon, and sun, and the distances of the moon and sun, used methods which were theoretically valid, but they were hampered by the lack of instruments of precision. Many of their results, in view of this lack, were surprisingly good. Eratosthenes estimated the earth’s diameter at 7850 miles, which is only about fifty miles short of the truth. Ptolemy estimated the mean distance of the moon at 29 ½ times the earth’s diameter; the correct figure is about 30.7. None of them got anywhere near the size and distance of the sun, which all underestimated. Their estimates, in terms of the earth’s diameter, were:
Aristarchus, 180;
Hipparchus, 1245;
Posidonius, 6545.
The correct figure is 11,726. It will be
