------------------------------------------------------------------------ [49] Greek _peri_ near, _apo_ away from, _ge_ Earth. ------------------------------------------------------------------------ [Illustration: Fig. 23. The Moveable Eccentric.] But, as the Greeks had discovered, Mars attains his greatest brilliance at different points of the zodiac, so P must be made moveable, and it always happens when he is opposite the sun, therefore P must keep pace with the sun’s apparent motion in the zodiac and P E always point towards him. This was accomplished by making P C A turn round upon the fixed point E, so that for instance when the sun had moved through a quarter of his circle (in three months) P A had moved to P′ A′, and the whole eccentric had moved into the new position shown in the diagram, its centre C being now at C′. In other words, the centre of the eccentric moves round Earth in the same time and in the same direction as the sun, that is in one year, and “with the signs” (from west to east). At the same time, Mars is moving in an opposite direction on the eccentric, and without entering into all the details of the problem, we may add that the Greek geometers found that by determining the proper relative sizes of the large and the small circle they could make the two motions neutralize one another when the planet reached its stationary points, and the retrograde motion prevail over the direct when it retrograded. A similar arrangement was made for Jupiter and Saturn. In this very ingenious way the varying brightness as well as the varying motions of these three planets were accounted for, without violating the principle of uniform circular motion, and without removing Earth from the centre of the Universe. She was also still the centre of planetary motion, in a certain sense; but to place the true centres of these planets’ spheres _outside Earth and in the direction of the sun_ was a very suggestive step, and may well have helped Aristarchus to his bold hypothesis. For he had only to put the sun, not at some indefinite point along the line E A, but exactly at the point C, and it became the centre of motion for Mars, Jupiter, and Saturn, just as in the “Egyptian theory” it was the centre of motion for Venus and Mercury. In this way he would arrive at the conception of the sun circling round Earth and carrying all the planets with him, (a theory which was held by the great astronomer Tycho Brahé in the sixteenth century A.D.). Then a flash of insight may have revealed to him the fact that this motion of the sun is apparent only, being but the reflection of Earth’s own motion; for she is circling round the sun like all the other planets.