How are the elevations of the poles proportionate to distances of earth that have been traversed according to Copernicus In chapter 2 of "The Revolutions of the Heavenly Spheres" where Copernicus maintains that the Earth is spherical, the Edward Rosen translation of the book states that 


  the elevations of the poles have the same ratio everywhere to the portions of the earth that have been traversed.


I'd like to know what Copernicus is referring to in the aforementioned piece of text and how it provides evidence for the spherical shape of the Earth.
Here, I believe he is referring to the altitude of the celestial poles at different latitudes on the Earth.



If the Earth is indeed a sphere then the altitude of the celestial poles above the horizon should be the same as your latitude on the Earth. That is, as you travel along a line of latitude, the altitude of the pole should change accordingly.



So Copernicus was noting that this is indeed what we observe. At the North pole the North celestial pole is directly overhead, and on the equator it is on the horizon. This observation, therefore, is direct evidence that the Earth is spherical (or at least spheroidal).

You can see the evidence of this in star trail photographs. The stars will always appear to rotate about the celestial poles. This image shows the star trails above Ecuador, at a latitude of about 1$^{\circ}$. You can clearly see that the stars are rolling directly over head; with the North and South celestial poles located on the horizon to the right and left, respectively.