Sacrobosco via Morgan Mar

I recently discovered David Morgan Mar’s fun blog 100 Proofs that the Earth is a Globe. He’s adding things over time, so he’s only up to 42 proofs so far.

I browsed the site looking for a proof that I know from Copernicus. It figures in debates about underdetermination, and it’s a stock example I give to students to illustrate the Duhem-Quine problem.1

I couldn’t find it among the proofs he’s discussed, but he uses an image which clearly illustrates Copernicus’ proof. It’s a nice old woodcut, which I might have used— had I known about it— rather than making my own illustrations. I wrote him, and he responded to say that he just hasn’t gotten to it yet.

I did a reverse image lookup and found it attributed (via Wikipedia) to a sixteenth-century edition of a thirteenth-century astronomy text. Other internet sources corroborate this. So the argument was well known among pre-Copernican astronomers. Here’s the argument first, then the image.

SURFACE OF THE SEA SPHERICAL. — That the water has a bulge and is approximately round is shown thus: Let a signal be set up on the seacoast and a ship leave port and sail away so far that the eye of a person standing at the foot of the mast can no longer discern the signal. Yet if the ship is stopped, the eye of the same person, if he has climbed to the top of the mast, will see the signal clearly. Yet the eye of a person at the bottom of the mast ought to see the signal better than he who is at the top, as is shown by drawing straight lines from both to the signal. And there is no other explanation of this thing than the bulge of the water. For all other impediments are excluded, such as clouds and rising vapors.

Iohannes de Sacrobosco2
One can see land from the mast of the ship, but from the deck the view is occulted by the curve of the ocean.
I cleaned up the image a bit, with an eye toward eventually making a vector version.
  1. See my paper ‘Background Theories and Total Science’, which recapitulates section 3.3 of my dissertation.
  2. translation by Lynn Thorndike via Esoteric Archives

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