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What are epicycles?

What are epicycles? Here are some definitions.

Noun
  1. plural of epicycle
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Examples
But Copernicus kept the old astronomy by retaining the system of spheres and epicycles.
Waves come in like epicycles rippling through the larger cycles of tides, and the moon's revolution around the Earth, and the Earth's revolution around the sun.
This is not strictly true since the theory of epicycles certainly predates Apollonius.
For example, each planet was said to move in its own small curve called an epicycle, while all the epicycles moved around the earth in larger circles called deferents.
The historically older concept of epicycles has not found use in the geological literature.
Other threads appeared out of nowhere, forming, with epicycles and Celtic knotting, a mesh bag that pulled him irresistibly toward the bleak globe that was the Inquisitor.

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