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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.

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closed as off-topic by Spencer, Tactopoda, Fred, farrenthorpe, arkaia Jul 10 '17 at 1:30

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about earth science, within the scope defined in the help center." – Spencer, Tactopoda, Fred, farrenthorpe, arkaia
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ After all this, I'm afraid this question might be better suited for HSM.SE; I think the argument is a philosophical/mathematical one and not really connected to science. $\endgroup$ – Spencer Jul 9 '17 at 12:27
  • $\begingroup$ re: "...cubes of their diameters". Copernicus most likely used a volumetric comparison. $\endgroup$ – Fred Jul 9 '17 at 15:55