principles (e.g. Ptolemy's set of touching spheres) to determine just where the planets are. However, Copernicus could not dispense with epicycles altogether, because his heliocentric structure did not explain the variation of the planets' speeds in their orbits - the so-called first anomaly.

In On the Revolutions, the planetary theories are modified versions of those used in the Commentariolus, based on the theories of Ibn al-Shatir. Copernicus began with the superior planets and the geometrical scheme he used is illustrated in Figure 5.5. The planet P rotates once per sidereal period around an epicycle centred at C. The centre of the epicycle rotates in the same sense and at the same rate around a deferent circle centred at O. This point is not the Sun, but is close to it. In fact, Copernicus did not use the actual Sun in the planetary theory, but rather the mean sun that is labelled S in Figure 5.5 and which corresponds to the point O in Figure 5.4. The Earth E moves in a circular orbit around S. The motion is arranged so that /PCO = ┬┐COA, SOA being the apsidal line of the planet's orbit.

From a geometrical viewpoint, it is unimportant whether the Earth E or the Sun S is stationary, and Copernicus' model with the Earth stationary is shown in

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