<p>Here, I believe he is referring to the <a href="https://en.wikipedia.org/wiki/Horizontal_coordinate_system" rel="nofollow noreferrer">altitude</a> of the celestial poles at different latitudes on the Earth.</p>

<p><a href="https://i.sstatic.net/A41n3.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/A41n3.jpg" alt="The celestial poles"></a></p>

<p>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.</p>

<p><a href="https://i.sstatic.net/W4OA3.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/W4OA3.gif" alt="local coordinates"></a></p>

<p>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).</p>

<p>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.
<a href="https://i.sstatic.net/6F9Of.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6F9Of.jpg" alt="Star trails in Ecuador"></a></p>

CC BY-SA 3.0
2017-06-29T16:53:52.303Z
2017-06-29T16:53:52.303Z
Albatross
<p>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 </p>

<blockquote>
  <p>the elevations of the poles have the same ratio everywhere to the portions of the earth that have been traversed.</p>
</blockquote>

<p>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.</p>

CC BY-SA 3.0
2017-06-29T16:42:46.117Z
Sounds to me like the "distance of Earth that have been traversed" is referring to the distance from the equator, which in terms of latitude always equals the altitude of the pole in the sky. E.g. on the equator the North pole is at 0 degrees altitude, or at 30 degrees latitude it is 30 degrees above the horizon.
Dean
CC BY-SA 3.0
2017-06-29T16:56:01.517Z
@Dean On the equator, the north pole is *not* at 0 degrees altitude from the horizon. Due to the curvature of the Earth, it would be below the horizon and have a negative altitude.
zephyr
CC BY-SA 3.0
2017-06-29T17:03:19.283Z
@zephyr I think by definition the north pole is at 0 degrees altitude on the equator, regardless of if you can see it or not. Otherwise the opposite to this where the north pole is overhead at the north pole cannot hold true, mathematically speaking anyway.
Dean
CC BY-SA 3.0
2017-06-29T17:09:04.070Z
@Dean That's absolutely not right. Your horizon is defined based on how far you can see at your given location and height. For example the distance to your horizon (regardless of obstructing buildings, mountains, etc.) is given by $d=\sqrt{h^2+2R_Eh}$. The location of the north pole has nothing to do with what you can see from a particular location at a particular height. It makes no sense for the north pole to be on your horizon at the Equator. What if you grew two inches? Your statement about the opposite not being true then also makes no sense. I see no connection between the two ideas.
zephyr
CC BY-SA 3.0
2017-06-29T17:35:35.233Z
@Dean Don't get me wrong, the north pole will be very near the horizon while at the Equator, but it won't be *exactly* at the horizon. That's just the nature of the geometry you're looking at. We might call it zero for convenience, but my point is that it isn't exactly zero, mathematically.
zephyr
CC BY-SA 3.0
2017-06-29T21:22:28.830Z
@zephyr I can see what your saying but I think your over-complicating things, its a well known principle in astronomy that you can use your latitude to calculate the altitude of the pole in the celestial sphere http://cseligman.com/text/sky/motions.htm, using the example of the equator was just one extreme. I was neglecting local geography and height just for simplicity. Maybe we can just agree to disagree on this one, I think were both coming at it from different levels of precision.
Dean
<earth><history>
How are the elevations of the poles proportionate to distances of earth that have been traversed according to Copernicus
SultySultan
# How are the elevations of the poles proportionate to distances of earth that have been traversed according to Copernicus

(Asked by: username_0 on 2017-06-29)

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.

**Tags:** earth, history
> **Comments:**
> **username_1**: Sounds to me like the "distance of Earth that have been traversed" is referring to the distance from the equator, which in terms of latitude always equals the altitude of the pole in the sky. E.g. on the equator the North pole is at 0 degrees altitude, or at 30 degrees latitude it is 30 degrees above the horizon.  
> **username_2**: @Dean On the equator, the north pole is *not* at 0 degrees altitude from the horizon. Due to the curvature of the Earth, it would be below the horizon and have a negative altitude.  
> **username_1**: @zephyr I think by definition the north pole is at 0 degrees altitude on the equator, regardless of if you can see it or not. Otherwise the opposite to this where the north pole is overhead at the north pole cannot hold true, mathematically speaking anyway.  
> **username_2**: @Dean That's absolutely not right. Your horizon is defined based on how far you can see at your given location and height. For example the distance to your horizon (regardless of obstructing buildings, mountains, etc.) is given by $d=\sqrt{h^2+2R_Eh}$. The location of the north pole has nothing to do with what you can see from a particular location at a particular height. It makes no sense for the north pole to be on your horizon at the Equator. What if you grew two inches? Your statement about the opposite not being true then also makes no sense. I see no connection between the two ideas.  
> **username_2**: @Dean Don't get me wrong, the north pole will be very near the horizon while at the Equator, but it won't be *exactly* at the horizon. That's just the nature of the geometry you're looking at. We might call it zero for convenience, but my point is that it isn't exactly zero, mathematically.  
> **username_1**: @zephyr I can see what your saying but I think your over-complicating things, its a well known principle in astronomy that you can use your latitude to calculate the altitude of the pole in the celestial sphere http://cseligman.com/text/sky/motions.htm, using the example of the equator was just one extreme. I was neglecting local geography and height just for simplicity. Maybe we can just agree to disagree on this one, I think were both coming at it from different levels of precision.  

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## 1 answers

### Answer by username_3 on 2017-06-29. Score: 2

Here, I believe he is referring to the [altitude](https://en.wikipedia.org/wiki/Horizontal_coordinate_system) of the celestial poles at different latitudes on the Earth.

[![The celestial poles](https://i.sstatic.net/A41n3.jpg)](https://i.sstatic.net/A41n3.jpg)

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.

[![local coordinates](https://i.sstatic.net/W4OA3.gif)](https://i.sstatic.net/W4OA3.gif)

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.
[![Star trails in Ecuador](https://i.sstatic.net/6F9Of.jpg)](https://i.sstatic.net/6F9Of.jpg)


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