<p>In chapter 3 of "The Revolutions of the Heavenly Spheres" where Copernicus defines "how the Earth forms a single sphere with water", the Edward Rosen translation of the book states this.</p>

<blockquote>
  <p>For they do not realize that the water cannot be even seven times greater and still leave any part of the land dry, unless earth as a whole vacated the center of gravity and yielded that position to water, as if the latter were heavier than itself For, spheres are to each other as the cubes of their diameters. Therefore, if Earth were the eighth part to seven parts of water, earth's diameter could not be greater than the distance from [their joint] center to the circumference of the waters.</p>
</blockquote>

<p>For context, "they" is referring to Aristotelians which according to Copernicus, believe that there is ten times more water than land.</p>

<p>My main lack of understanding comes from how Copernicus uses the statement "spheres are to each other as the cubes of their diameters." To prove that "if Earth were the eighth part to seven parts of water, earth's diameter could not be greater than the distance from [their joint] center to the circumference of the waters." Thereby showing that a 1:7 ratio of land to water is the threshold where water submerges the entire Earth.</p>

CC BY-SA 3.0
2017-07-09T12:27:45.013Z
After all this, I'm afraid this question might be better suited for [HSM.SE](http://hsm.stackexchange.com); I think the argument is a philosophical/mathematical one and not really connected to science.
Spencer
CC BY-SA 3.0
2017-07-09T15:55:16.910Z
re: "...cubes of their diameters". Copernicus most likely used a volumetric comparison.
Fred
<history-of-science>
How Copernicus figured out that it took 7 parts of water and 1 part earth until the entire Earth was submersed in water
SultySultan
# How Copernicus figured out that it took 7 parts of water and 1 part earth until the entire Earth was submersed in water

(Asked by: username_0 on 2017-07-08)

In chapter 3 of "The Revolutions of the Heavenly Spheres" where Copernicus defines "how the Earth forms a single sphere with water", the Edward Rosen translation of the book states this.

> For they do not realize that the water cannot be even seven times greater and still leave any part of the land dry, unless earth as a whole vacated the center of gravity and yielded that position to water, as if the latter were heavier than itself For, spheres are to each other as the cubes of their diameters. Therefore, if Earth were the eighth part to seven parts of water, earth's diameter could not be greater than the distance from [their joint] center to the circumference of the waters.

For context, "they" is referring to Aristotelians which according to Copernicus, believe that there is ten times more water than land.

My main lack of understanding comes from how Copernicus uses the statement "spheres are to each other as the cubes of their diameters." To prove that "if Earth were the eighth part to seven parts of water, earth's diameter could not be greater than the distance from [their joint] center to the circumference of the waters." Thereby showing that a 1:7 ratio of land to water is the threshold where water submerges the entire Earth.

**Tags:** history-of-science

> **Comments:**
> **username_1**: After all this, I'm afraid this question might be better suited for [HSM.SE](http://hsm.stackexchange.com); I think the argument is a philosophical/mathematical one and not really connected to science.  
> **username_2**: re: "...cubes of their diameters". Copernicus most likely used a volumetric comparison.  

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## 0 answers

