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In chapter 4 of "The Revolutions of the Heavenly Spheres" where Copernicus maintains that the objects in our solar system have circular orbits or orbits compounded of several circles, the Edward Rosen translation of the book states this

It stands to reason, therefore, that their uniform motions appear nonuniform to us. The cause may be either that their circles have poles different [from the earth's] or that the earth is not at the center of the circles on which they revolve.

To add context: Copernicus believes that features of orbit that are inconsistent to circular motion such as retrograde motion, apogee, perigee, fast/slow movement, etc... Don't actually occur in the orbits of the Sun, Moon, and the planets. Stating that the actual causes of the inconsistencies could either be that "their circles have poles different [from the earth's.]" Or that these objects don't revolve around the Earth.

I'm mainly concerned with what Copernicus is referring to when he states that the orbits of these objects "have poles different [from the earth's,]" and how (if true) it could produce these inconsistencies in orbits.

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Remember that Copernicus was espousing a heliocentric Solar System. What he means by "pole" is the object's axis of revolution and its axis of rotation. The Earth rotates around its poles: i.e. the North and South pole. A line between those poles is our axis of rotation. The axis of revolution would be the axis about which the Earth orbits. This would correspond to an imaginary line at the Sun. Copernicus is presenting the idea that the axis of rotation is not the axis of revolution.

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Quoting page 12 of https://books.google.com/books?id=LH4tWpJzzCcC (translator uncredited):

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and looking at the second sentence, we have "they do not revolve around the same poles [...] but follow the oblique ecliptic".

Assuming the use of poles later in the page is the same, he's pointing out the north ecliptic pole (which is in Draco) is not the same as the north celestial pole (which is in Ursa Minor and close to the star Polaris).

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