# The Infinite in the Finite

By Alistair Macintosh Wilson | Go to book overview

14
APOLLONIUS THE GREAT GEOMETER

APOLLONIUS

Apollonius was born at Perga in Pamphylia, near Antalya in present-day Turkey, around 262 BC. He is believed to have studied at Alexandria, under the famous astronomer Aristarchus of Samos. Whilst studying with Aristarchus, Apollonius was given the nickname 'Epsilon', because of his interest in the theory of the Moon, whose crescent looks like that Greek letter.

One of the major problems of Greek astronomy was why the planets sometimes appear to move backwards in the sky. For example, Fig. 14.1 shows the backward, or retrograde, motion of the planet Mars.

Aristarchus, a strange anomalous figure in the history of science, suggested in around 250 BC that this problem could be solved if the Earth and all the planets revolve around the Sun, which remains at rest. If this were so, then a planet would appear to go backward when it was overtaken by the Earth. Aristarchus' views, which we now know to be true, were rejected by all the other Greek astronomers. Why? Simply because they were in complete disagreement with Aristotle's physics.

The argument ran like this. According to Aristotle, all bodies seek the centre of the universe. But we know that all bodies fall towards the centre of the Earth. Logically therefore, the centre of the Earth must be the centre of the universe. This means the Sun cannot be the centre of the universe. Therefore Aristarchus' suggestion is wrong.

Apollonius was later himself to suggest a way of explaining the retrograde motion of the planets which allowed the Earth to remain at the centre of the universe. The Greeks demanded that a planet must move around the Earth in a motion which is a combination of perfect circles. At the same time, at certain periods of the year, the planet must appear to perform retrograde motion in the sky. Apollonius' solution to this dilemma is shown in Fig. 14.2.

The planet moves on a small circle, the epicycle, whose centre moves on a larger circle, the deferent. If we now want the planet to move backwards at certain times, we simply set both circles revolving in the same direction,

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The Infinite in the Finite

• Title Page iii
• Preface vii
• Contents xi
• 1 - Symphonies of Stone 1
• 2 - The Pyramid Builders 19
• 3 - The Theban Mysteries 42
• 4 - Babylon 53
• 5 - The Middle Kingdom 72
• 6 - The Achaeans 105
• 7 - A World Made of Numbers 112
• 8 - The Thoughts of Zeus 132
• 9 - The Philosopher's Criticism 163
• 10 - The Elements of Euclid 206
• 11 - An Island Interlude 239
• 12 - Proportion 252
• 13 - The Divine Archimedes 278
• 14 - Apollonius the Great Geometer 324
• 15 - The Science of Numbers 366
• 16 - The School of Alexandria 388
• 17 - The Dark Sub­ Continent of India 426
• 18 - The Contribution of Islam 461
• Bibliography 509
• Index 515
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