Solar Epicycle: An epicycle is a circle whose center is fixed on and revolves around the periphery of another circle at a uniform speed. The epicycle itself will rotate at its own uniform speed. Manuscript Diagrams for this topic are recognizably related to each other, but the details of the epicyclic circles vary and suggest some difficulty in the understanding by early medieval scholars of these combinations of circular motions. Calcidius states that the motions of the circles are uniform, although his description omits some potentially useful elements, such as the division of the epicycle into four equal quadrants; he does this explicitly only for the deferent circle. His definition of an epicycle is extremely general. The geometrical framework is simple. The same zodiacal circle ABΓΔ, ordered anti-clockwise, as used in the explanation by an eccentric circle appears again here. The earth is at the center Θ. Concentric with the zodiacal circle is the deferent circle MONΞ (anti-clockwise). The epicyclic circle has its center initially at M. The periphery of the epicycle is labelled anti-clockwise EZHK. The rotation of each of these three circles is specified. ABΓΔ rotates daily in a clockwise direction. MONΞ rotates with the planetary orbital speed --- once a year in the case of the Sun --- anti-clockwise. The epicycle EZHK rotates at a speed specific to the planet, in this case, for the Sun, once a year clockwise.With the motion of the epicycle's center on the deferent from M to O, the epicyclic circle is oriented so that E remains outermost and towards the zodiacal point B. The Sun, located on the epicycle initially at E, rotates 90° to the point K, which is the uppermost point on the epicycle when its center is at O. This combination of motions continues from quadrant to quadrant through the year, at the end of which the solar epicycle will return to M and the Sun on the periphery of the epicycle will return to point E. But as the annual motion of the Sun occurs, the appearance from the earth, at the center of the deferent and zodiacal circles, is that the Sun moves faster from K to H and H to Z than it moves from E to K and Z to E. This appearance of varying speed can be understood by noticing that from E to K and from Z to E the Sun seems to move slower than the center of the solar epicycle from M to O and from Ξ to M; conversely from K to H and from H to Z the Sun seems to move faster than the center of the epicycle from nO to N and from N to Ξ. And the Sun at H is closest to the earth and at E is farthest from the earth during the annual motion. All this is as seen from the earth, and the motions of the circles remain uniform.

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