But others say the earth floats upon water. This view we consider the most ancient: it is ascribed to Thales the Milesian. It regards the earth as upheld in its place because it floats like a piece of wood or anything else of the same kind....But water itself cannot remain suspended on high, but must be upheld in its turn by something. Further, as air is lighter than water, so water is lighter than earth. How then can they fancy that what is lighter lies below and supports what is heavier? Again, were the whole earth able to float upon water, this would also be the case with its fragments. But this seems not so, for any piece of earth sinks to the bottom of water, and larger fragments sink more swiftly.

ARISTARCHUS AND ARCHIMEDES

ARISTARCHUS of Samos, who flourished about 280 to 264 B.C., and Archimedes of Syracuse, born about 287 B.C., are the most modern in mind of the Greek physicists. Aristarchus alone directly concerns us here. The Pythagoreans had imagined a fire at the centre of the universe, but Aristarchus was the first to frame in a definite way the theory that the sun is the centre round which the earth and the other planets revolve. This does not appear in the only one of his works which survives, but it is made clear in the extract from Archimedes which follows later.

The application of mathematical reasoning to physics and astronomy, a method which has led to such tremendous results in modern times, is first seen in Aristarchus. The proofs, cast in geometrical form, are unsuited for our present purpose, but we illustrate the method by recording his hypotheses and his propositions.

ARISTARCHUS ON THE SIZES AND DISTANCES OF THE SUN AND MOON

(From Aristarchus of Samos, by Sir Thomas Heath.)

HYPOTHESES

1. That the moon receives its light from the sun.

2. That the earth is in the relation of a point and centre to the sphere in which the moon moves.

3. That, when the moon appears to us halved, the great

circle which divides the dark and the bright portions of the moon is in the direction of our eye.

4. That, when the moon appears to us halved, its distance from the sun is then less than a quadrant by one-thirtieth of a quadrant. 5. That the breadth of the (earth's) shadow is (that) of two

moons.

6. That the moon subtends one-fifteenth part of a sign of the zodiac.

We are now in a position to prove the following propositions:

1. The distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon (from the earth); this follows from the hypothesis about the halved moon.

2. The diameter of the sun has the same ratio (as aforesaid) to the diameter of the moon.

3. The diameter of the sun has to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6; this follows from the ratio thus discovered between the distances, the hypothesis about the shadow, and the hypothesis that the moon subtends one-fifteenth part of a sign of the zodiac.

ARCHIMEDES. THE SAND-RECKONER

(From The Works of Archimedes, Edited by Sir Thomas Heath.) THERE are some, king Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and hollows of the earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognising that any number could be expressed which exceeded the multitude of the sand so taken. But

I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe. Now you are aware that "universe" is the name given by most astronomers to the sphere whose centre is the centre of the earth and whose radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account as you have heard from astronomers. But Aristarchus of Samos brought out a book consisting of some hypotheses, in which the premisses lead to the result that the universe is many times greater than that now so called. 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, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface. Now it is easy to see that this is impossible; for, since the centre of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere. We must however take Aristarchus to mean this: since we conceive the earth to be, as it were, the centre of the universe, the ratio which the earth bears to what we describe as the "universe" is the same as the ratio which the sphere containing the circle in which he supposes the earth to revolve bears to the sphere of the fixed stars. For he adapts the proofs of his results to a hypothesis of this kind, and in particular he appears to suppose the magnitude of the sphere in which he represents the earth as moving to be equal to what we call the "universe."

I say then that, even if a sphere were made up of the sand, as great as Aristarchus supposes the sphere of the fixed stars to be, I shall still prove that, of the numbers named in the Principles, some exceed in multitude the number of the sand which is equal in magnitude to the sphere referred to....

COPERNICUS

THE solar theory of Aristarchus did not commend itself to the astronomers who followed him. It is far more obvious to take the solid earth beneath us as the centre of the universe. Round it the celestial globe of the fixed stars is seen to revolve, and among those stars the sun and planets wander. This view was developed mathematically about 130 B.C. by Hipparchus, the inventor of trigonometry. Hipparchus showed that the apparent motions could be explained by the supposition that the sun and planets moved round central points in orbits or epicycles, while these orbits were themselves carried round in larger orbits or cycles. Hipparchus' theory was expounded and recorded for us by Ptolemy of Alexandria, about 127–151 A.D., and held the field till the 15th century.

Rome never contributed much to original scientific thought, and, with the fall of Rome and the ruin of the Roman Empire, Alexandria remained the latest effective school of the ancient world. From Alexandria, as well as from the East, Arabian scholars helped to bring fragments of Greek learning to Western Europe after the Dark Ages, throughout which a few Latin commentaries formed the only direct link of knowledge.

In the revival of learning, a landmark was the recovery between 1210 and 1225 of the complete works of Aristotle, first rendered into Latin from imperfect Arabian versions, and then by direct translation from the Greek. The philosophy of Aristotle was welded into one with Christian dogma by Thomas Aquinas, and thus, when in the 15th and 16th centuries observation and experiment threw doubt on much of Aristotle's physical science, it was thought that religion was assailed also, and some ecclesiastical opposition was encountered.

Especially was this so, when Copernicus (1473-1543) revived the theory of astronomy which held the sun to be the centre of our system. Though published with the consent of Pope Clement VII, Copernicus' book was suspended in 1616 by the Vatican till it should be corrected by the omission of the heliocentric theory, which was declared "false and altogether opposed to Holy Scripture.'

Nicolaus Koppernigk, who Latinized his name as Copernicus, was a Polish mathematician and astronomer. After a visit to Italy where the Pythagorean speculations were known, Copernicus began observations which led him to form a definite theory of the universe, taking the sun for its centre as in the scheme of Aristarchus. Copernicus showed that this theory explained the facts more simply than the cycles and epicycles of Hipparchus and Ptolemy. The first printed copy of his book reached him on his deathbed in 1543.

DE REVOLUTIONIBUS ORBIUM CELESTIUM

LIB. I. CAP. VIII.

THE ancient philosophers affirm the earth to be at rest at the centre of the universe, and doubtless to maintain itself there. But, if anyone holds that the earth revolves, he affirms at any rate that the motion is natural and not forced. Which things indeed are according to nature, for motions which are forced produce different effects. It is true that things to which force or impact is applied necessarily disintegrate, and cannot hold together for long; but those which have a natural motion maintain themselves steadily, and are preserved in coherence. It is without reason, therefore, that Ptolemy fears lest the earth if it move should disintegrate and all terrestrial things be thrown into confusion by the power of nature, so far beyond that of art, or anything possible to human ingenuity. But why, on his view of a fixed earth and a moving sky, does he not fear it even more for the sky, whose motion is so much the more swift, as the heaven is greater than the earth? Is the sky perhaps an immense structure, which by the power of an ineffable motion is separated from its centre, and on the other hand falls in ruin if it stand still? Surely, if this be so, the magnitude of the heaven will increase to infinity. For by how much the further from the centre the motion is carried by its own impetus, by so much the motion will be swifter, on account of the ever-growing circumference which it must describe in order to traverse space in 24 hours: and, in turn, the immensity of the heaven grows greater by reason of this increasing motion. Thus the velocity increases the magnitude and the magnitude the velocity to infinity. And next comes the physical axiom: That which is infinite is unable to travel forwards, nor can it move through any cause. The heaven, therefore, necessarily stands still. But, they say, beyond the sky is neither body, nor space, nor vacuum—in a word nothing, and therefore no means exist of breaking out through the sky; then indeed it is wonderful, if from nothing anything is able to hold together. And if the heaven were infinite, and only bounded by its inner concavity, all the more can it be proved, perhaps, that there is nothing beyond the sky;