PART I.GREEK ASTRONOMY TO ARISTARCHUS.
Thetitle-page of this book necessarily bears the name of one man; but the reader will find in its pages the story, or part of the story, of many other Pioneers of Progress. The crowning achievement of anticipating the hypothesis of Copernicus belongs to Aristarchus of Samos alone; but to see it in its proper setting it is necessary to have followed in the footsteps of the earlier pioneers who, by one bold speculation after another, brought the solution of the problem nearer, though no one before Aristarchus actually hit upon the truth. This is why the writer has thought it useful to prefix to his account of Aristarchus a short sketch of the history of the development of astronomy in Greece down to Aristarchus’s time, which is indeed the most fascinating portion of the story of Greek astronomy.
The extraordinary advance in astronomy made by the Greeks in a period of little more than three centuries is a worthy parallel to the rapid development, in their hands, of pure geometry, which, created by them as a theoretical science about the same time, had by the time of Aristarchus covered the ground of the Elements (including solid geometry and the geometry of the sphere), had established the main properties of the three conic sections, had solved problems which were beyond the geometry of the straight line and circle, and finally, before the end ofthe third centuryB.C., had been carried to its highest perfection by the genius of Archimedes, who measured the areas of curves and the surfaces and volumes of curved surfaces by geometrical methods practically anticipating the integral calculus.
To understand how all this was possible we have to remember that the Greeks, pre-eminently among all the nations of the world, possessed just those gifts which are essential to the initiation and development of philosophy and science. They had in the first place a remarkable power of accurate observation; and to this were added clearness of intellect to see things as they are, a passionate love of knowledge for its own sake, and a genius for speculation which stands unrivalled to this day. Nothing that is perceptible to the senses seems to have escaped them; and when the apparent facts had been accurately ascertained, they wanted to know thewhyand thewherefore, never resting satisfied until they had given a rational explanation, or what seemed to them to be such, of the phenomena observed. Observation or experiment and theory went hand in hand. So it was that they developed such subjects as medicine and astronomy. In astronomy their guiding principle was, in their own expressive words, to “save the phenomena”. This meant that, as more and more facts became known, their theories were continually revised to fit them.
It would be easy to multiply instances; it must suffice in this place to mention one, which illustrates not only the certainty with which the Greeks detected the occurrence of even the rarest phenomena, but also the persistence with which they sought for the true explanation.
Cleomedes (second centuryA.D.) mentions that there were stories of extraordinary eclipses which “the more ancient of the mathematicians” had vainly tried toexplain; the supposed “paradoxical” case was that in which, while the sun seems to be still above the western horizon, theeclipsedmoon is seen to rise in the east. The phenomenon appeared to be inconsistent with the explanation of lunar eclipses by the entry of the moon into the earth’s shadow; how could this be if both bodies were above the horizon at the same time? The “more ancient” mathematicians essayed a geometrical explanation; they tried to argue that it was possible that a spectator standing on aneminenceof the spherical earth might see along the generators of aconei.e. a little downwards on all sides instead of merely in the plane of the horizon, and so might see both the sun and the moon even when the latter was in the earth’s shadow. Cleomedes denies this and prefers to regard the whole story of such cases as a fiction designed merely for the purpose of plaguing astronomers and philosophers; no Chaldæan, he says, no Egyptian, and no mathematician or philosopher has recorded such a case. But the phenomenon is possible, and it is certain that it had been observed in Greece and that the Greek astronomers did not rest until they had found out the solution of the puzzle; for Cleomedes himself gives the explanation, namely that the phenomenon is due to atmospheric refraction. Observing that such cases of atmospheric refraction were especially noticeable in the neighbourhood of the Black Sea, Cleomedes goes on to say that it is possible that the visual rays going out from our eyes are refracted through falling on wet and damp air, and so reach the sun although it is already below the horizon; and he compares the well-known experiment of the ring at the bottom of a jug, where the ring, just out of sight when the jug is empty, is brought into view when water is poured in.
The genius of the race being what it was, the Greeksmust from the earliest times have been in the habit of scanning the heavens, and, as might be expected, we find the beginnings of astronomical knowledge in the earliest Greek literature.
In the Homeric poems and in Hesiod the earth is a flat circular disc; round this disc runs the river Oceanus, encircling the earth and flowing back into itself. The flat earth has above it the vault of heaven, like a sort of hemispherical dome exactly covering it; this vault remains for ever in one position; the sun, moon and stars move round under it, rising from Oceanus in the east and plunging into it again in the west.
Homer mentions, in addition to the sun and moon, the Morning Star, the Evening Star, the Pleiades, the Hyades, Orion, the Great Bear (“which is also called by the name of the Wain”), Sirius, the late-setting Boötes (the ploughman driving the Wain), i.e. Arcturus, as it was first called by Hesiod. Of the Great Bear Homer says that it turns round on the same spot and watches Orion; it alone is without lot in Oceanus’s bath (i.e. it never sets). With regard to the last statement it is to be noted that some of the principal stars of the Great Bear do now set in the Mediterranean, e.g. in places further south than Rhodes (lat. 36°), γ, the hind foot, and η, the tip of the tail, and at Alexandria all the seven stars except α, the head. It might be supposed that here was a case of Homer “nodding”. But no; the old poet was perfectly right; the difference between the facts as observed by him and as seen by us respectively is due to the Precession of the Equinoxes, the gradual movement of the fixed stars themselves about the pole of the ecliptic, which was discovered by Hipparchus (second centuryB.C.). We know from the original writings of the Greek astronomers that in Eudoxus’s time (say 380B.C.) the whole of the Great Bear remained always wellabove the horizon, while in the time of Proclus (sayA.D.460) the Great Bear “grazed” the horizon.
In Homer astronomical phenomena are only vaguely used for such purposes as fixing localities or marking times of day or night. Sometimes constellations are used in giving sailing directions, as when Calypso directs Odysseus to sail in such a way as always to keep the Great Bear on his left.
Hesiod mentions practically the same stars as Homer, but makes more use of celestial phenomena for determining times and seasons. For example, he marked the time for sowing at the beginning of winter by the setting of the Pleiades in the early twilight, or again by the early setting of the Hyades or Orion, which means the 3rd, 7th, or 15th November in the Julian calendar according to the particular stars taken; the time for harvest he fixed by the early rising of the Pleiades (19th May), threshing time by the early rising of Orion (9th July), vintage time by the early rising of Arcturus (18th September), and so on. Hesiod makes spring begin sixty days after the winter solstice, and the early summer fifty days after the summer solstice. Thus he knew about the solstices, though he says nothing of the equinoxes. He had an approximate notion of the moon’s period, which he put at thirty days.
But this use of astronomical facts for the purpose of determining times and seasons or deducing weather indications is a very different thing from the science of astronomy, which seeks to explain the heavenly phenomena and their causes. The history of this science, as of Greek philosophy in general, begins with Thales.
The Ionian Greeks were in the most favourable position for initiating philosophy. Foremost among the Greeks in the love of adventure and the instinct of newdiscovery (as is shown by their leaving their homes to found settlements in distant lands), and fired, like all Greeks, with a passion for knowledge, they needed little impulse to set them on the road of independent thought and speculation. This impulse was furnished by their contact with two ancient civilisations, the Egyptian and the Babylonian. Acquiring from them certain elementary facts and rules in mathematics and astronomy which had been handed down through the priesthood from remote antiquity, they built upon them the foundation of the science, as distinct from the mere routine, of the subjects in question.
Thales of Miletus (about 624–547B.C.) was a man of extraordinary versatility; philosopher, mathematician, astronomer, statesman, engineer, and man of business, he was declared one of the Seven Wise Men in 582–581B.C.His propensity to star-gazing is attested by the story of his having fallen into a well while watching the stars, insomuch that (as Plato has it) he was rallied by a clever and pretty maidservant from Thrace for being so “eager to know what goes on in the heavens when he could not see what was in front of him, nay at his very feet”.
Thales’s claim to a place in the history of scientific astronomy rests on one achievement attributed to him, that of predicting an eclipse of the sun. The evidence for this is fairly conclusive, though the accounts of it differ slightly. Eudemus, the pupil of Aristotle, who wrote histories of Greek geometry and astronomy, is quoted by three different Greek writers as the authority for the story. But there is testimony much earlier than this. Herodotus, speaking of a war between the Lydians and the Medes, says that, “when in the sixth year theyencountered one another, it fell out that, after they had joined battle, the day suddenly turned into night. Now that this change of day into night would occur was foretold to the Ionians by Thales of Miletus, who fixed as the limit of time this very year in which the change took place.” Moreover Xenophanes, who was born some twenty-three years before Thales’s death, is said to have lauded Thales’s achievement; this would amount to almost contemporary evidence.
Could Thales have known the cause of solar eclipses? Aëtius (A.D.100), the author of an epitome of an older collection of the opinions of philosophers, says that Thales was the first to declare that the sun is eclipsed when the moon comes in a direct line below it, the image of the moon then appearing on the sun’s disc as on a mirror; he also associates Thales with Anaxagoras, Plato, Aristotle, and the Stoics as holding that the moon is eclipsed by reason of its falling into the shadow made by the earth when the earth is between the sun and the moon. But, as regards the eclipse of the moon, Thales could not have given this explanation, because he held that the earth (which he presumably regarded as a flat disc) floated on the water like a log. And if he had given the true explanation of a solar eclipse, it is impossible that all the succeeding Ionian philosophers should have exhausted their imaginations in other fanciful explanations such as we find recorded.
The key to the puzzle may be afforded by the passage of Herodotus according to which the prediction was a rough one, only specifying that the eclipse would occur within a certain year. The prediction was probably one of the same kind as had long been made by the Chaldæans. The Chaldæans, no doubt as the result of observations continued through many centuries, had discovered the period of 223 lunations after which lunareclipses recur. (This method would very often fail for solar eclipses because no account was taken of parallax; and Assyrian cuneiform inscriptions record failures as well as successful predictions.) Thales, then, probably learnt about the period of 223 lunations either in Egypt or more directly through Lydia, which was an outpost of Assyrio-Babylonian culture. If there happened to be a number ofpossiblesolar eclipses in the year which (according to Herodotus) Thales fixed for the eclipse, he was, in using the Chaldæan rule, not taking an undue risk; but it was great luck that the eclipse should have been total. It seems practically certain that the eclipse in question was that of the (Julian) 28th May, 585.
Thales, as we have seen, made the earth a circular or cylindrical disc floating on the water like a log or a cork and, so far as we can judge of his general conception of the universe, he would appear to have regarded it as a mass of water (that on which the earth floats) with the heavens encircling it in the form of a hemisphere and also bounded by the primeval water. This view of the world has been compared with that found in ancient Egyptian papyri. In the beginning existed theNū, a primordial liquid mass in the limitless depths of which floated the germs of things. When the sun began to shine, the earth was flattened out and the water separated into two masses. The one gave rise to the rivers and the ocean, the other, suspended above, formed the vault of heaven, the waters above, on which the stars and the gods, borne by an eternal current, began to float. The sun, standing upright in his sacred barque which had endured for millions of years, glides slowly, conducted by an army of secondary gods, the planets and the fixed stars. The assumption of an upper and lower ocean is also old Babylonian (cf. thedivision in Genesis 1. 7 of the waters which were under the firmament from the waters which were above the firmament).
It would follow from Thales’s general view of the universe that the sun, moon and stars did not, between their setting and rising again, continue their circular path below the earth but (as with Anaximenes later) moved laterally round the earth.
Thales’s further contributions to observational astronomy may be shortly stated. He wrote two worksOn the solsticeandOn the equinox, and he is said by Eudemus to have discovered that “the period of the sun with respect to the solstices is not always the same,” which probably means that he discovered the inequality of the four astronomical seasons. His division of the year into 365 days he probably learnt from the Egyptians. He said of the Hyades that there are two, one north and the other south. He observed the Little Bear and used it as a means of finding the pole; he advised the Greeks to follow the Phœnician plan of sailing by the Little Bear in preference to their own habit of steering by the Great Bear.
Limited as the certain contributions of Thales to astronomy are, it became the habit of the GreekDoxographi, or retailers of the opinions of philosophers, to attribute to Thales, in common with other astronomers in each case, a number of discoveries which were not made till later. The following is a list, with (in brackets) the names of the astronomers to whom the respective discoveries may with most certainty be assigned: (1) the fact that the moon takes its light from the sun (Anaxagoras), (2) the sphericity of the earth (Pythagoras), (3) the division of the heavenly sphere into five zones (Pythagoras and Parmenides), (4) the obliquity of the ecliptic (Œnopides of Chios), and (5) the estimate ofthe sun’s apparent diameter as 1/720th of the sun’s circle (Aristarchus of Samos).
Anaximander (about 611–547B.C.), a contemporary and fellow-citizen of Thales, was a remarkably original thinker. He was the first Greek philosopher who ventured to put forward his views in a formal written treatise. This was a workAbout Natureand was not given to the world till he was about sixty-four years old. His originality is illustrated by his theory of evolution. According to him animals first arose from slime evaporated by the sun; they lived in the sea and had prickly coverings; men at first resembled fishes.
But his astronomical views were not less remarkable. Anaximander boldly maintained that the earth is in the centre of the universe, suspended freely and without support, whereas Thales regarded it as resting on the water and Anaximenes as supported by the air. It remains in its position, said Anaximander, because it is at an equal distance from all the rest of the heavenly bodies. The earth was, according to him, cylinder-shaped, round “like a stone pillar”; one of its two plane faces is that on which we stand; its depth is one-third of its breadth.
Anaximander postulated as his first principle, not water (like Thales) or any of the elements, but the Infinite; this was a substance, not further defined, from which all the heavens and the worlds in them were produced; according to him the worlds themselves were infinite in number, and there were always some worlds coming into being and others passing awayad infinitum. The origin of the stars, and their nature, he explained as follows. “That which is capable of begetting thehot and the cold out of the eternal was separated off during the coming into being of our world, and from the flame thus produced a sort of sphere was made which grew round the air about the earth as the bark round the tree; then this sphere was torn off and became enclosed in certain circles or rings, and thus were formed the sun, the moon and the stars.” “The stars are produced as a circle of fire, separated off from the fire in the universe and enclosed by air. They have as vents certain pipe-shaped passages at which the stars are seen.” “The stars are compressed portions of air, in the shape of wheels filled with fire, and they emit flames at some point from small openings.” “The stars are borne round by the circles in which they are enclosed.” “The sun is a circle twenty-eight times (v. l.27 times) the size of the earth; it is like a wheel of a chariot the rim of which is hollow and full of fire and lets the fire shine out at a certain point in it through an opening like the tube of a blow-pipe; such is the sun.” “The sun is equal to the earth.” “The eclipses of the sun occur through the opening by which the fire finds vent being shut up.” “The moon is a circle nineteen times the size of the earth; it is similar to a chariot-wheel the rim of which is hollow and full of fire like the circle of the sun, and it is placed obliquely like the other; it has one vent like the tube of a blow-pipe; the eclipses of the moon depend on the turnings of the wheel.” “The moon is eclipsed when the opening in the rim of the wheel is stopped up.” “The moon appears sometimes as waxing, sometimes as waning, to an extent corresponding to the closing or opening of the passages.” “The sun is placed highest of all, after it the moon, and under them the fixed stars and the planets.”
It has been pointed out that the idea of the formation of tubes of compressed air within which the fire of eachstar is shut up except for the one opening through which the flame shows (like a gas-jet, as it were) is not unlike Laplace’s hypothesis with reference to the origin of Saturn’s rings. In any case it is a sufficiently original conception.
When Anaximander says that the hoops carrying the sun and moon “lie obliquely,” this is no doubt an attempt to explain, in addition to the daily rotation, the annual movement of the sun and the monthly movement of the moon.
We have here too the first speculation about the sizes and distances of the heavenly bodies. The sun is as large as the earth. The ambiguity between the estimates of the size of the sun’s circle as twenty-seven or twenty-eight times the size of the earth suggests that it is a question between taking the inner and outer circumferences of the sun’s ring respectively, and a similar ambiguity may account for the circle of the moon being stated to be nineteen times, not eighteen times, the size of the earth. No estimate is given of the distance of the planets from the earth, but as, according to Anaximander, they are nearer to the earth than the sun and moon are, it is possible that, if a figure had been stated, it would have been nine times the size of the earth, in which case we should have had the numbers 9, 18, 27, three terms in arithmetical progression and all of them multiples of 9, the square of 3. It seems probable that these figures were not arrived at by any calculation based on geometrical considerations, but that we have here merely an illustration of the ancient cult of the sacred numbers 3 and 9. Three is the sacred number in Homer, 9 in Theognis. The cult of 3 and its multiples 9 and 27 is found among the Aryans, then among the Finns and Tartars and then again among the Etruscans. Therefore Anaximander’s figures probablysay little more than what the Indians tell us, namely, that three Vishnu-steps reach from earth to heaven.
Anaximander is said to have been the first to discover thegnomon(or sun-dial with a vertical needle). This is, however, incorrect, for Herodotus says that the Greeks learnt the use of thegnomonand thepolosfrom the Babylonians. Anaximander may have been the first to introduce the gnomon into Greece. He is said to have set it up in Sparta and to have shown on it “the solstices, the times, the seasons, and the equinox”.
But Anaximander has another title to fame. He was the first who ventured to draw a map of the inhabited earth. The Egyptians indeed had drawn maps before, but only of special districts. Anaximander boldly planned out the whole world with “the circumference of the earth and of the sea”. Hecataeus, a much-travelled man, is said to have corrected Anaximander’s map so that it became the object of general admiration.
With Anaximenes of Miletus (about 585–528/4B.C.) the earth is still flat like a table, but, instead of being suspended freely without support as with Anaximander, it is supported by the air, riding on it as it were. The sun, moon and stars are all made of fire and (like the earth) they ride on the air because of their breadth. The sun is flat like a leaf. Anaximenes also held that the stars are fastened on a crystal sphere like nails or studs. It seems clear therefore that by the stars which “ride on the air because of their breadth” he meant the planets only. A like apparent inconsistency applies to the motion of the stars. If the stars are fixed in the crystal sphere like nails, they must be carried round complete circles by the revolution of the sphere about a diameter.Yet Anaximenes also said that the stars do not move or revolveunderthe earth as some suppose, butroundthe earth, just as a cap can be turned round on the head. The sun is hidden from sight, not because it is under the earth, but because it is covered by the higher parts of the earth and because its distance from us is greater. Aristotle adds the detail that the sun is carried round the northern portion of the earth and produces night because the earth is lofty towards the north. We must again conclude that the stars which, like the sun and moon, move laterally round the earth between their setting and rising again are the planets, as distinct from the fixed stars. It would therefore seem that Anaximenes was the first to distinguish the planets from the fixed stars in respect of their irregular movements. He improved on Anaximander in that he relegated the fixed stars to the region most distant from the earth.
Anaximenes was also original in holding that, in the region occupied by the stars, bodies of an earthy nature are carried round along with them. The object of these invisible bodies of an earthy nature carried round along with the stars is clearly to explain the eclipses and phases of the moon. It was doubtless this conception which, in the hands of Anaxagoras and others, ultimately led to the true explanation of eclipses.
The one feature of Anaximenes’s system which was destined to an enduring triumph was the conception of the stars being fixed on a crystal sphere as in a rigid frame. This really remained the fundamental principle in all astronomy down to Copernicus.
With Pythagoras and the Pythagoreans we come to a different order of things. Pythagoras, born at Samosabout 572B.C., is undoubtedly one of the greatest names in the history of science. He was a mathematician of brilliant achievements; he was also the inventor of the science of acoustics, an astronomer of great originality, a theologian and moral reformer, and the founder of a brotherhood which admits comparison with the orders of mediæval chivalry. Perhaps his most epoch-making discovery was that of the dependence of musical tones on numerical proportions, the octave representing the proportion of 2 : 1 in length of string at the same tension, the fifth 3 : 2, and the fourth 4 : 3. Mathematicians know him as the reputed discoverer of the famous theorem about the square on the hypotenuse of a right-angled triangle (= Euclid I. 47); but he was also the first to make geometry a part of a liberal education and to explore its first principles (definitions, etc.).
Pythagoras is said to have been the first to maintain that the earth is spherical in shape; on what ground, is uncertain. One suggestion is that he may have argued from the roundness of the shadow cast by the earth in the eclipses of the moon; but Anaxagoras was the first to give the true explanation of such eclipses. Probably Pythagoras attributed spherical shape to the earth for the mathematical or mathematico-æsthetical reason that the sphere is the most beautiful of all solid figures. It is probable too, and for the same reason, that Pythagoras gave the same spherical shape to the sun and moon, and even to the stars, in which case the way lay open for the discovery of the true cause of eclipses and of the phases of the moon. Pythagoras is also said to have distinguished five zones in the earth. It is true that the first declaration that the earth is spherical and that it has five zones is alternatively attributed to Parmenides (born perhaps about 516 or 514B.C.), on the good authority of Theophrastus. It is possible that, although Pythagoraswas the real author of these views, Parmenides was the first to state them in public.
Pythagoras regarded the universe as living, intelligent, spherical, enclosing the earth at the centre, and rotating about an axis passing through the centre of the earth, the earth remaining at rest.
He is said to have been the first to observe that the planets have an independent motion of their own in a direction opposite to that of the fixed stars, i.e. the daily rotation. Alternatively with Parmenides he is said to have been the first to recognise that the Morning and the Evening Stars are one and the same. Pythagoras is hardly likely to have known this as the result of observations of his own; he may have learnt it from Egypt or Chaldæa along with other facts about the planets.
We have seen that certain views are alternatively ascribed to Pythagoras and Parmenides. The system of Parmenides was in fact a kind of blend of the theories of Pythagoras and Anaximander. In giving the earth spherical form with five zones he agreed with Pythagoras. Pythagoras, however, made the spherical universe rotate about an axis through the centre of the earth; this implied that the universe is itself limited, but that something exists round it, and in fact that beyond the finite rotating sphere there is limitless void or empty space. Parmenides, on the other hand, denied the existence of the infinite void and was therefore obliged to make his finite sphere motionless and to hold that its apparent rotation is only an illusion.
In other portions of his system Parmenides followed the lead of Anaximander. Like Anaximander (and Democritus later) he argued that the earth remains in the centre because, being equidistant from all points onthe sphere of the universe, it is in equilibrium and there is no more reason why it should tend to move in one direction than in another. Parmenides also had a system of wreaths or bands round the sphere of the universe which contained the sun, the moon and the stars; the wreaths remind us of the hoops of Anaximander, but their nature is different. The wreaths, according to the most probable interpretation of the texts, are, starting from the outside, (1) a solid envelope like a wall; (2) a band of fire (the æther-fire); (3) mixed bands, made up of light and darkness in combination, which exhibit the phenomenon of “fire shining out here and there,” these mixed bands including the Milky Way as well as the sun, moon and planets; (4) a band of fire, the inner side of which is our atmosphere, touching the earth. Except that Parmenides placed the Morning Star first in the æther and therefore above the sun, he did not apparently differ from Anaximander’s view of the relative distances of the heavenly bodies, according to which both the planets and the other stars are all placed below the sun and moon.
Two lines from Parmenides’s poem have been quoted to show that he declared that the moon is illuminated by the sun. The first line speaks of the moon as “a night-shining foreign light wandering round the earth”; but, even if the line is genuine, “foreign” need not mean “borrowed”. The other line speaks of the moon as “always fixing its gaze on the sun”; but, though this states an observed fact, it is far from explaining the cause. We have, moreover, positive evidence against the attribution of the discovery of the opacity of the moon to Parmenides. It is part of the connected prose description of his system that the moon is a mixture of air and fire, and in other passages we are told that he held the moon to be of fire. Lastly, Plato speaks of“the fact which Anaxagoraslately asserted, that the moon has its light from the sun”. It seems impossible that Plato would speak in such terms if the fact in question had been stated for the first time either by Parmenides or by the Pythagoreans.
Anaxagoras, a man of science if ever there was one, was born at Clazomenae in the neighbourhood of Smyrna about 500B.C.He neglected his possessions, which were considerable, in order to devote himself to science. Someone once asked him what was the object of being born, and he replied, “The investigation of sun, moon and heaven”. He took up his abode at Athens, where he enjoyed the friendship of Pericles. When Pericles became unpopular shortly before the outbreak of the Peloponnesian war, he was attacked through his friends, and Anaxagoras was accused of impiety for declaring that the sun was a red-hot stone and the moon made of earth. One account says that he was fined and banished; another that he was imprisoned, and that it was intended to put him to death, but that Pericles obtained his release; he retired to Lampsacus, where he died at the age of seventy-two.
One epoch-making discovery belongs to him, namely, that the moon does not shine by its own light but receives its light from the sun: Plato, as we have seen, is one authority for this statement. Plutarch also in hisDe facie in orbe lunaesays, “Now when our comrade in his discourse had expounded that proposition of Anaxagoras that ‘the sun places the brightness in the moon,’ he was greatly applauded”.
This discovery enabled Anaxagoras to say that “the obscurations of the moon month by month were due to its following the course of the sun by which it is illuminated,and the eclipses of the moon were caused by its falling within the shadow of the earth which then comes between the sun and the moon, while the eclipses of the sun were due to the interposition of the moon”. Anaxagoras was therefore the first to give the true explanation of eclipses. As regards the phases of the moon, his explanation could only have been complete if he had known that the moon is spherical; in fact, however, he considered the earth (and doubtless the other heavenly bodies also) to be flat. To his true theory of eclipses Anaxagoras added the unnecessary assumption that the moon was sometimes eclipsed by other earthy bodies below the moon but invisible to us. In this latter assumption he followed the lead of Anaximenes. The other bodies in question were probably invented to explain why the eclipses of the moon are seen oftener than those of the sun.
Anaxagoras’s cosmogony contained some fruitful ideas. According to him, the formation of the world began with a vortex set up, in a portion of the mixed mass in which “all things were together,” by Mind. This rotatory movement began at one point and then gradually spread, taking in wider and wider circles. The first effect was to separate two great masses, one consisting of the rare, hot, light, dry, called the æther, and the other of the opposite categories and called air. The æther took the outer place, the air the inner. Out of the air were separated successively clouds, water, earth, and stones. The dense, the moist, the dark and cold, and all the heaviest things, collect in the centre as the result of the circular motion, and it is from these elements when consolidated that the earth is formed. But after this, “in consequence of the violence of the whirling motion, the surrounding fiery æther tore stones away from the earth and kindled them into stars”. Anaxagoras conceivedtherefore the idea of acentrifugalforce, as distinct from that of concentration brought about by the motion of the vortex, and he assumed a series of projections or “hurlings-off” of precisely the same kind as the theory of Kant and Laplace assumed for the formation of the solar system.
In other matters than the above Anaxagoras did not make much advance on the crude Ionian theories. “The sun is a red-hot mass or a stone on fire.” “It is larger (or ‘many times larger’) than the Peloponnese.” He considered that “the stars were originally carried round (laterally) like a dome, the pole which is always visible being thus vertically above the earth, and it was only afterwards that their course became inclined”.
But he put forward a remarkable and original hypothesis to explain the Milky Way. He thought the sun to be smaller than the earth. Consequently, when the sun in its revolution passes below the earth, the shadow cast by the earth extends without limit. The trace of this shadow on the heavens is the Milky Way. The stars within this shadow are not interfered with by the light of the sun, and we therefore see them shining; those stars, on the other hand, which are outside the shadow are overpowered by the light of the sun which shines on them even during the night, so that we cannot see them. Aristotle easily disposes of this theory by observing that, the sun being much larger than the earth, and the distance of the stars from the earth being many times greater than the distance of the sun, the sun’s shadow would form a cone with its vertex not very far from the earth, so that the shadow of the earth, which we call night, would not reach the stars at all.
Empedocles of Agrigentum (about 494–434B.C.) would hardly deserve mention for his astronomy alone, so crude were his views where they differed from those of his predecessors. The earth, according to Empedocles, is kept in its place by the swiftness of the revolution of the heaven, just as we may swing a cup with water in it round and round so that in some positions the top of the cup may even be turned downwards without the water escaping. Day and night he explained as follows. Within the crystal sphere to which the fixed stars are attached (as Anaximenes held), and filling it, is a sphere consisting of two hemispheres, one of which is wholly of fire and therefore light, while the other is a mixture of air with a little fire, which mixture is darkness or night. The revolution of these two hemispheres round the earth produces at each point on its surface the succession of day and night. Empedocles held the sun to be, not fire, but a reflection of fire similar to that which takes place from the surface of water, the fire of a whole hemisphere of the world being bent back from the earth, which is circular, and concentrated into the crystalline sun which is carried round by the motion of the fiery hemisphere.
Empedocles’s one important scientific achievement was his theory that light travels and takes time to pass from one point to another. The theory is alluded to by Aristotle, who says that, according to Empedocles, the light from the sun reaches the intervening space before it reaches the eye or the earth; there was therefore a time when the ray was not yet seen, but was being transmitted through the medium.
We have seen that Pythagoras was the first to give spherical form to the earth and probably to the heavenly bodies generally, and to assign to the planets a revolution of their own in a sense opposite to that of the daily rotation of the fixed stars about the earth as centre.
But a much more remarkable development was to follow in the Pythagorean school. This was nothing less than the abandonment of the geocentric hypothesis and the reduction of the earth to the status of a planet like the others. The resulting system, known as the Pythagorean, is attributed (on the authority probably of Theophrastus) to Philolaus; but Diogenes Laertius and Aëtius refer to one Hicetas of Syracuse in this connection; Aristotle attributes the system to “the Pythagoreans”. It is a partial anticipation of the theory of Copernicus but differs from it in that the earth and the planets do not revolve round the sun but about an assumed “central fire,” and the sun itself as well as the moon does the same. There were thus eight heavenly bodies, in addition to the sphere of the fixed stars, all revolving about the central fire. The number of revolutions being thus increased to nine, the Pythagoreans postulated yet another, making ten. The tenth body they called the counter-earth, and its character and object will appear from the following general description of the system.
The universe is spherical in shape and finite in size. Outside it is infinite void, which enables the universe to breathe, as it were. At the centre is the central fire, the Hearth of the Universe, called by various names such as the Tower or Watch-tower of Zeus, the Throne of Zeus, the Mother of the Gods. In this central fire is located the governing principle, the force which directs the movementand activity of the universe. The outside boundary of the sphere is an envelope of fire; this is called Olympus, and in this region the elements are found in all their purity; below this is the universe. In the universe there revolve in circles round the central fire the following bodies: nearest to the central fire the counter-earth which always accompanies the earth, then the earth, then the moon, then the sun, next to the sun the five planets, and last of all, outside the orbits of the planets, the sphere of the fixed stars. The counter-earth, which accompanies the earth but revolves in a smaller orbit, is not seen by us because the hemisphere on which we live is turned away from the counter-earth. It follows that our hemisphere is always turned away from the central fire, that is, it faces outwards from the orbit towards Olympus (the analogy of the moon which always turns one side towards us may have suggested this); this involves a rotation of the earth about its axis completed in the same time as it takes the earth to complete a revolution about the central fire.
Although there was a theory that the counter-earth was introduced in order to bring the number of the moving bodies up to ten, the perfect number according to the Pythagoreans, it is clear from a passage of Aristotle that this was not the real reason. Aristotle says, namely, that the eclipses of the moon were considered to be due sometimes to the interposition of the earth, sometimes to the interposition of the counter-earth. Evidently therefore the purpose of the counter-earth was to explain the frequency with which eclipses of the moon occur.
The Pythagoreans held that the earth, revolving, like one of the stars, about the central fire, makes night and day according to its position relatively to the sun; it is therefore day in that region which is lit up by the sunand night in the cone formed by the earth’s shadow. As the same hemisphere is always turned outwards, it follows that the earth completes one revolution about the central fire in a day and a night or in about twenty-four hours. This would account for the apparent diurnal rotation of the heavens from east to west; but for parallax (of which, if we may believe Aristotle, the Pythagoreans made light), it would be equivalent to the rotation of the earth on its own axis once in twenty-four hours. This would make the revolution of the sphere of the fixed stars unnecessary. Yet the Pythagoreans certainly gave some motion to the latter sphere. What it was remains a puzzle. It cannot have been the precession of the equinoxes, for that was first discovered by Hipparchus (second centuryB.C.). Perhaps there was a real incompatibility between the two revolutions which was unnoticed by the authors of the system.
Œnopides of Chios (a little younger than Anaxagoras) is credited with two discoveries. The first, which was important, was that of the obliquity of the zodiac circle or the ecliptic; the second was that of a Great Year, which Œnopides put at fifty-nine years. He also (so we are told) found the length of the year to be 365-22/59 days. He seems to have obtained this figure by a sort of circular argument. Starting first with 365 days as the length of a year and 29½ days as the length of the lunar month, approximate figures known before his time, he had to find the least integral number of complete years containing an exact number of lunar months; this is clearly fifty-nine years, which contain twice 365 or 730 lunar months. Œnopides seems by his knowledge of the calendar to have determined the number of days in 730 lunar months to be 21,557, and this numberdivided by fifty-nine, the number of years, gives 365-22/59 as the number of days in the year.
We come now to Plato (427–347B.C.). In the astronomy of Plato, as we find it in the Dialogues, there is so large an admixture of myth and poetry that it is impossible to be sure what his real views were on certain points of detail. In thePhædowe have certain statements about the earth to the effect that it is of very large dimensions, the apparent hollow (according to Plato) in which we live being a very small portion of the whole, and that it is in the middle of the heaven, in equilibrium, without any support, by virtue of the uniformity in the substance of the heaven. In theRepublicwe have a glimpse of a more complete astronomical system. The outermost revolution is that of the sphere of the fixed stars, which carries round with it the whole universe including the sun, moon and planets; the latter seven bodies, while they are so carried round by the general rotation, have slower revolutions of their own in addition, one inside the other, these revolutions being at different speeds but all in the opposite sense to the general rotation of the universe. The quickest rotation is that of the fixed stars and the universe, which takes place once in about twenty-four hours. The slower speeds of the sun, moon and planets are not absolute but relative to the sphere of the fixed stars regarded as stationary. The earth in the centre is unmoved; the successive revolutions about it and within the sphere of the fixed stars are (reckoning from the earth outwards) those of the moon, the sun, Venus, Mercury, Mars, Jupiter, Saturn; the speed of the moon is the quickest, that of the sun the next quickest, while Venus and Mercury travel with the sun and have the same speed, takingabout a year to describe their orbits; after these in speed comes Mars, then Jupiter and, last and slowest of all, Saturn. There is nothing said in theRepublicabout the seven bodies revolving in a circle different from and inclined to the equator of the sphere of the fixed stars; that is, the obliquity of the ecliptic does not appear; hence the standpoint of the whole system is that of Pythagoras as distinct from that of the Pythagoreans.
Plato’s astronomical system is, however, most fully developed in theTimæus. While other details remain substantially the same, the zodiac circle in which the sun, moon and planets revolve is distinguished from the equator of the sphere of the fixed stars. The latter is called the circle of the Same, the former that of the Other, and we are told (quite correctly) that, since the revolution of the universe in the circle of the Same carries all the other revolutions with it, the effect on each of the seven bodies is to turn their actual motions in space into spirals. There is a difficulty in interpreting a phrase in Plato’s description which says that Venus and Mercury, though moving in a circle having equal speed with the sun, “have the contrary tendency to it”. Literally this would seem to mean that Venus and Mercury describe their circles the opposite way to the sun, but this is so contradicted by observation that Plato could hardly have maintained it; hence the words have been thought to convey a vague reference to the apparent irregularities in the motion of Venus and Mercury, their standings-still and retrogradations.
But the most disputed point in the system is the part assigned in it to the earth. An expression is used with regard to its relation to the axis of the heavenly sphere which might mean either (1) that it is wrapped or globed about that axis but without motion, or (2) that it revolves round the axis. If the word meansrevolvingabout the axis of the sphere, the revolution would be either (a) rotation about its own axis supposed to be identical with that of the sphere, or (b) revolution about the axis of the heavenly sphere in the same way that the sun, moon and planets revolve about an axis obliquely inclined to that axis. But (a) if the earth rotated about its own axis, this would make unnecessary the rotation of the sphere of the fixed stars once in twenty-four hours, which, however, is expressly included as part of the system. The hypothesis (b) would make the system similar to the Pythagorean except that the earth would revolve about the axis of the heavenly sphere instead of round the central fire. The supporters of this hypothesis cite two passages of Plutarch to the effect that Plato was said in his old age to have repented of having given the earth the middle place in the universe instead of placing it elsewhere and giving the middle and chiefest place to some worthier occupant. It is a sufficient answer to this argument that, if Plato really meant in the passage of theTimæusto say that the earth revolves about the axis of the heavenly sphere, he had nothing to repent of. We must therefore, for our part, conclude that in his written Dialogues Plato regarded the earth asat restin the centre of the universe.
We have it on good authority that Plato set it as a problem to all earnest students “to find what are the uniform and ordered movements by the assumption of which the apparent movements of the planets can be accounted for”. The same authority adds that Eudoxus was the first to formulate a theory with this object; and Heraclides of Pontus followed with an entirely new hypothesis. Both were pupils of Plato and, in so far as the statement of his problem was a stimulus to these speculations, he rendered an important service to the science of astronomy.
Eudoxus of Cnidos (about 408–355B.C.) was one of the very greatest of the Greek mathematicians. He was the discoverer and elaborator of the great theory of proportion applicable to all magnitudes whether commensurable or incommensurable which is given in Euclid’s Book V. He was also the originator of the powerfulmethod of exhaustionused by all later Greek geometers for the purpose of finding the areas of curves and the volumes of pyramids, cones, spheres and other curved surfaces. It is not therefore surprising that he should have invented a remarkable geometrical hypothesis for explaining the irregular movements of the planets. The problem was to find the necessary number of circular motions which by their combination would produce the motions of the planets as actually observed, and in particular the variations in their apparent speeds, their stations and retrogradations and their movements in latitude. This Eudoxus endeavoured to do by combining the motions of several concentric spheres, one inside the other, and revolving about different axes, each sphere revolving on its own account but also being carried round bodily by the revolution of the next sphere encircling it. We are dependent on passages from Aristotle and Simplicius for our knowledge of Eudoxus’s system, which he had set out in a workOn Speeds, now lost. Eudoxus assumed three revolving spheres for producing the apparent motions of the sun and moon respectively, and four for that of each of the planets. In his hypothesis for the sun he seems deliberately to have ignored the discovery made by Meton and Euctemon some sixty or seventy years before that the sun does not take the same time to describe the four quadrants of its orbit between the equinoctial and solstitial points.
It should be observed that the whole hypothesis of the concentric spheres is pure geometry, and there is no mechanics in it. We will shortly describe the arrangement of the four spheres which by their revolution produced the motion of a planet. The first and outermost sphere produced the daily rotation in twenty-four hours; the second sphere revolved about an axis perpendicular to the plane of the zodiac or ecliptic, thereby producing the motion along the zodiac “in the respective periods in which the planets appear to describe the zodiac circle,” i.e. in the case of the superior planets, the sidereal periods of revolution, and in the case of Mercury and Venus (on a geocentric system) one year. The third sphere had its poles at two opposite points on the zodiac circle, the poles being carried round in the motion of the second sphere; the revolution of the third sphere about the axis connecting the two poles was again uniform and took place in a period equal to the synodic period of the planet, or the time elapsing between two successive oppositions or conjunctions with the sun.
The poles of the third sphere were different for all the planets, except that for Mercury and Venus they were the same. On the surface of the third sphere the poles of the fourth sphere were fixed, and its axis of revolution was inclined to that of the former at an angle constant for each planet but different for the different planets. The planet was fixed at a point on the equator of the fourth sphere. The third and fourth spheres together cause the planet’s movement in latitude. Simplicius explains clearly the effect of these two rotations. If, he says, the planet had been on the third sphere (by itself), it would actually have arrived at the poles of the zodiac circle; but, as things are, the fourth sphere, which turns about the poles of the inclined circle carrying the planet and rotates in the opposite sense to the third, i.e. from eastto west, but in the same period, will prevent any considerable divergence on the part of the planet from the zodiac circle, and will cause the planet to describe about this same zodiac circle the curve called by Eudoxus thehippopede(horse-fetter), so that the breadth of this curve will be the maximum amount of the apparent deviation of the planet in latitude. The curve in question is an elongated figure-of-eight lying along and bisected by the zodiac circle. The motion then round this figure-of-eight combined with the motion in the zodiac circle produces the acceleration and retardation of the motion of the planet, causing the stations and retrogradations. Mathematicians will appreciate the wonderful ingenuity and beauty of the construction.
Eudoxus spent sixteen months in Egypt about 381–380B.C., and, while there, he assimilated the astronomical knowledge of the priests of Heliopolis and himself made observations. The Observatory between Heliopolis and Cercesura used by him was still pointed out in Augustus’s time; he also had one built at Cnidos. He wrote two books entitled respectively theMirrorand thePhænomena; the poem of Aratus was, so far as verses 19–732 are concerned, drawn from thePhænomenaof Eudoxus. He is also credited with the invention of thearachne(spider’s web) which, however, is alternatively attributed to Apollonius, and which seems to have been a sun-clock of some kind.
Eudoxus’s system of concentric spheres was improved upon by Callippus (about 370–300B.C.), who added two more spheres for the sun and the moon, and one more in the case of each of the three nearer planets, Mercury, Venus and Mars. The two additional spheres in the case of the sun were introduced in order to account for the unequal motion of the sun in longitude; and the purpose in the case of the moon was presumably similar.Callippus made the length of the seasons, beginning with the vernal equinox, ninety-four, ninety-two, eighty-nine and ninety days respectively, figures much more accurate than those given by Euctemon a hundred years earlier, which were ninety-three, ninety, ninety and ninety-two days respectively.
With Callippus as well as Eudoxus the system of concentric spheres was purely geometrical. Aristotle (384–322B.C.) thought it necessary to alter it in a mechanical sense; he made the spheres into spherical shells actually in contact with one another, and this made it almost necessary, instead of having independent sets of spheres, one set for each planet, to make all the sets part of one continuous system of spheres. For this purpose he assumed sets ofreactingspheres between successive sets of the original spheres. E.g. Saturn being carried by a set of four spheres, he had three reacting spheres to neutralise the last three, in order to restore the outermost sphere to act as the first of the four spheres producing the motion of the next lower planet, Jupiter, and so on. The change was hardly an improvement.
Aristotle’s other ideas in astronomy do not require detailed notice, except his views about the earth. Although he held firmly to the old belief that the earth is in the centre and remains motionless, he was clear that its shape (like that of the stars and the universe) is spherical, and he had arrived at views about its size sounder than those of Plato. In support of the spherical shape of the earth he used some good arguments based on observation. (1) In partial eclipses of the moon the line separating the dark and bright portions is always circular—unlike the line of demarcation in the phases of the moon which may be straight. (2) Certain stars seen above the horizon in Egypt and in Cyprus are not visible further north, and, on the other hand, certainstars set there which in more northern latitudes remain always above the horizon. As there is so perceptible a change of horizon between places so near to each other, it follows not only that the earth is spherical but also that it is not a very large sphere. Aristotle adds that people are not improbably right when they say that the region about the Pillars of Heracles is joined on to India, one sea connecting them. He quotes a result arrived at by the mathematicians of his time, that the circumference of the earth is 400,000 stades. He is clear that the earth is much smaller than some of the stars, but that the moon is smaller than the earth.
The systems of concentric spheres were not destined to hold their ground for long. In these systems the sun, moon and planets were of necessity always at the same distances from the earth respectively. But it was soon recognised that they did not “save the phenomena,” since it was seen that the planets appeared to be at one time nearer and at another time further off. Autolycus of Pitane (who flourished about 310B.C.) knew this and is said to have tried to explain it; indeed it can hardly have been unknown even to the authors of the concentric theory themselves, for Polemarchus of Cyzicus, almost contemporary with Eudoxus, is said to have been aware of it but to have minimised the difficulty because he preferred the hypothesis of the concentric spheres to others.
Development along the lines of Eudoxus’s theory being thus blocked, the alternative was open of seeing whether any modification of the Pythagorean system would give better results. We actually have evidence of revisions of the Pythagorean theory. The first step was to get rid of the counter-earth, and some Pythagoreans did this by identifying the counter-earth with the moon. We hear too of a Pythagorean system in which the central fire was not outside the earth but in the centre of theearth itself. The descriptions of this system rather indicate that in it the earth was supposed to be at rest, without any rotation, in the centre of the universe. This was practically a return to the standpoint of Pythagoras himself. But it is clear that, if the system of Philolaus (or Hicetas) be taken and the central fire be transferred to the centre of the earth (the counter-earth being also eliminated), and if the movements of the earth, sun, moon and planets round the centre be retained without any modification save that which is mathematically involved by the transfer of the central fire to the centre of the earth, the daily revolution of the earth about the central fire is necessarily transformed into a rotation of the earth about its own axis in about twenty-four hours.
All authorities agree that the theory of the daily rotation of the earth about its own axis was put forward by Heraclides of Pontus (about 388–315B.C.), a pupil of Plato; with him in some accounts is associated the name of one Ecphantus, a Pythagorean. We are told that Ecphantus asserted “that the earth, being in the centre of the universe, moves about its own centre in an eastward direction,” and that “Heraclides of Pontus and Ecphantus the Pythagorean make the earth move, not in the sense of translation, but by way of turning as on an axle, like a wheel, from west to east, about its own centre”.
Heraclides was born at Heraclea in Pontus. He went to Athens not later than 364B.C., and there met Speusippus, who introduced him into the school of Plato. On the death of Speusippus (then at the head of the school) in 338, Xenocrates was elected to succeed him; at this election Heraclides was also a candidate and was onlydefeated by a few votes. He was the author of dialogues, brilliant and original, on all sorts of subjects, which were much read and imitated at Rome, e.g. by Varro and Cicero. Two of them “On Nature” and “On the Heavens” may have dealt with astronomy.
In his view that the earth rotates about its own axis Heraclides is associated with Aristarchus of Samos; thus Simplicius says: “There have been some, like Heraclides of Pontus and Aristarchus, who supposed that the phenomena can be saved if the heaven and the stars are at rest while the earth moves about the poles of the equinoctial circle from the west to the east, completing one revolution each day, approximately; the ‘approximately’ is added because of the daily motion of the sun to the extent of one degree”.
Heraclides made another important advance towards the Copernican hypothesis. He discovered the fact that Venus and Mercury revolve about the sun as centre. So much is certain; but a further question naturally arises. Having made Venus and Mercury revolve round the sun like satellites, did Heraclides proceed to draw the same inference with regard to the other, the superior, planets? The question is interesting because, had it been laid down that all the five planets alike revolve round the sun, the combination of this hypothesis with Heraclides’s assumption that the earth rotates about its own axis in twenty-four hours would have amounted to an anticipation of the system of Tycho Brahe, but with the improvement of the substitution of the daily rotation of the earth for the daily revolution of the whole system about the earth supposed at rest. Schiaparelli dealt with the question in two papers entitledI precursori di Copernico nell’ antichità(1873), andOrigine del sistema planetario eliocentrico presso i Greci(1898). Schiaparelli tried to show that Heraclides did arrive at theconclusion that the superior planets as well as Mercury and Venus revolve round the sun; but most persons will probably agree that his argument is not convincing. The difficulties seem too great. The circles described by Mercury and Venus about the sun are relatively small circles and are entirely on one side of the earth. But when the possibility of, say, Mars revolving about the sun came to be considered, it would be at once obvious that the precise hypothesis adopted for Mercury and Venus would not apply. It would be seen that Mars is brightest when it occupies a position in the zodiacoppositeto the sun; it must therefore be nearest to the earth at that time. Consequently the circle described by Mars, instead of being on one side of the earth, must comprehend the earth which is inside it. Whereas therefore the circles described by Mercury and Venus were what the Greeks calledepicyclesabout a material centre, the sun (itself moving in a circle round the earth), what was wanted in the case of Mars (if the circle described by Mars was to have the sun for centre) was what the Greeks called aneccentriccircle, with a centre which itself moves in a circle about the earth, and with a radius greater than that of the sun’s orbit. Though the same motion could have been produced by anepicycle, the epicycle would have had to have a mathematical point (not the material sun) as centre. But the idea of using non-material points as centres for epicycles was probably first thought of, at a later stage, by some of the great mathematicians such as Apollonius of Perga (about 265–190B.C.).
Not only does Schiaparelli maintain that the complete (but improved) Tychonic hypothesis was put forward by Heraclides or at least in Heraclides’s time; he goes further and makes a still greater claim on behalf of Heraclides, namely, that it was he, and not Aristarchus ofSamos, who first stated as a possibility the Copernican hypothesis. Now it was much to discover, as Heraclides did, that the earth rotates about its own axis and that Mercury and Venus revolve round the sun like satellites; and it seemsa prioriincredible that one man should not only have reached, and improved upon, the hypothesis of Tycho Brahe but shouldalsohave suggested the Copernican hypothesis. It is therefore necessary to examine briefly the evidence on which Schiaparelli relied. His argument rests entirely upon one passage, a sentence forming part of a quotation from a summary by Geminus of theMeteorologicaof Posidonius, which Simplicius copied from Alexander Aphrodisiensis and embodied in his commentary on thePhysicsof Aristotle. The sentence in question, according to the reading of the MSS., is as follows: “Hence we actually find a certain person, Heraclides of Pontus, coming forward and saying that, even on the assumption that the earth moves in a certain way, while the sun is in a certain way at rest, the apparent irregularity with reference to the sun can be saved”. (The preceding sentence is about possible answers to the question, why do the sun, the moon and the planets appear to move irregularly? and says, “we may answer that, if we assume that their orbits are eccentric circles or that the stars describe an epicycle, their apparent irregularity will be saved, and it will be necessary to go further and examine in how many different ways it is possible for these phenomena to be brought about”.)
Now it is impossible that Geminus himself can have spoken of an astronomer of the distinction of Heraclides as “a certainHeraclides of Pontus”. Consequently there have been different attempts made to emend the reading of the MSS. All the emendations proposed are open to serious objections, and we are thrown back onthe reading of the MSS. Now it “leaps to the eyes” that, if the name of Heraclides of Pontus is left out, everything is in order. “This is why one astronomer has actually suggested that, by assuming the earth to move in a certain way, and the sun to be in a certain way at rest, the apparent irregularity with reference to the sun will be saved.” This seems to be the solution of the puzzle suggested by the ordinary principles of textual criticism, and is so simple and natural that it will surely carry conviction to the minds of unbiassed persons. Geminus, in fact, mentioned no name but meant Aristarchus of Samos, and some scholiast, remembering that Heraclides had given a certain motion to the earth (namely, rotation about its axis), immediately thought of Heraclides and inserted his name in the margin, from which it afterwards crept into the text.
It is only necessary to add that Archimedes is not likely to have been wrong when he attributed the first suggestion of the Copernican hypothesis to Aristarchus of Samos in express terms; and this is confirmed by another positive statement by Aëtius, already quoted, that “Heraclides of Pontus and Ecphantus the Pythagorean made the earth move,notin the sense of translation, but with a movement of rotation”.