History of Western Philosophy - Bertrand Russell [123]
The four terrestrial elements are not eternal, but are generated out of each other—fire is absolutely light, in the sense that its natural motion is upward; earth is absolutely heavy. Air is relatively light, and water is relatively heavy.
This theory provided many difficulties for later ages. Comets, which were recognized as destructible, had to be assigned to the sublunary sphere, but in the seventeenth century it was found that they describe orbits round the sun, and are very seldom as near as the moon. Since the natural motion of terrestrial bodies is rectilinear, it was held that a projectile fired horizontally will move horizontally for a time, and then suddenly begin to fall vertically. Galileo's discovery that a projectile moves in a parabola shocked his Aristotelian colleagues. Copernicus, Kepler, and Galileo had to combat Aristotle as well as the Bible in establishing the view that the earth is not the centre of the universe, but rotates once a day and goes round the sun once a year.
To come to a more general matter: Aristotelian physics is incompatible with Newton's 'First Law of Motion', originally enunciated by Galileo. This law states that every body, left to itself, will, if already in motion, continue to move in a straight line with uniform velocity. Thus outside causes are required, not to account for motion, but to account for change of motion, either in velocity or in direction. Circular motion, which Aristotle thought 'natural' for the heavenly bodies, involves a continual change in the direction of motion, and therefore requires a force directed towards the centre of the circle, as in Newton's law of gravitation.
Finally: The view that the heavenly bodies are eternal and incorruptible has had to be abandoned. The sun and stars have long lives, but do not live for ever. They are born from a nebula, and in the end they either explode or die of cold. Nothing in the visible world is exempt from change and decay; the Aristotelian belief to the contrary, though accepted by medieval Christians, is a product of the pagan worship of sun and moon and planets.
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EARLY GREEK MATHEMATICS AND ASTRONOMY
I am concerned in this chapter with mathematics, not on its own account, but as it was related to Greek philosophy—a relation which, especially in Plato, was very close. The pre-eminence of the Greeks appears more clearly in mathematics and astronomy than in anything else. What they did in art, in literature, and in philosophy, may be judged better or worse according to taste, but what they accomplished in geometry is wholly beyond question. They derived something from Egypt, and rather less from Babylonia; but what they obtained from these sources was, in mathematics, mainly simple rules, and in astronomy records of observations extended over very long periods. The art of mathematical demonstration was, almost wholly, Greek in origin.
There are many pleasant stories, probably unhistorical, showing what practical problems stimulated mathematical investigations. The earliest and simplest relates to Thales, who, when in Egypt was asked by the king to find out the height of a pyramid. He waited for the time of day when his shadow was as long as he was tall; he then measured the shadow of the pyramid, which was of course equal to its height. It is said that the laws of perspective were first studied by the geometer Agatharcus, in order to paint scenery for the plays of Aeschylus. The problem of finding the distance of a ship at sea, which was said to have been studied by Thales, was correctly solved at an early stage. One of the great problems that occupied Greek geometers, that of the duplication of the cube, originated, we are told, with the priests of a certain temple, who were informed by the oracle that the god wanted a statue twice as large as the one they had. At first they thought simply of doubling all the dimensions of the statue, but then they realized that the result would be