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**Martianus Capella’s calculation of the size of the Moon.**
*(English)*
Zbl 1367.01004

One of the few that Copernicus recognizes as an influence, Martianus Capella’s De nuptiis Philologiae et Mercurii contains, in its eighth book the assertion that Mercury and Venus revolve around the Sun, followed by a method for calculating the size of the Moon, as well as the proportion between the size of its orbit and the size of the Earth.

After presenting the manner in which historians have commented this passage, and after presenting the obscurities and contradictions inherent in it, the author offers “an interpretation that tries to discover, behind Capella’s confusing presentation, a sound argument for calculating the Moon’s absolute size”. There are “no records of this argument in other sources, at least in the form described by Capella”.

The presentation starts with a look at total solar eclipses, concludes that Capella’s argument was likely not based on observations, but was probably constructed post hoc, then assumes that the argument put forward by Capella for calculating the absolute size of the Moon is sound but “badly explained”. From these hypotheses the author infers “a nice method of calculation not previously attested, which asserts that the size of the penumbra of a total solar eclipse at the zenith is equal to two lunar diameters”.

Under that assumption, “the input error in Capella’s argument is not in the cities used, but on the size of the circumference of the Earth, which gives \(20^{\circ}\) for \(\Delta\)lat instead of the correct \(33^{\circ}\). Had he used the correct Eratosthenes’ value, he would have found a much better value for the lunar diameter. Actually, with a circumference of \(252,000\) stadia and a distance between the cities of \(23,100\) stadia, \(\Delta\)lat would be exactly \(33^{\circ}\)!”

After presenting the manner in which historians have commented this passage, and after presenting the obscurities and contradictions inherent in it, the author offers “an interpretation that tries to discover, behind Capella’s confusing presentation, a sound argument for calculating the Moon’s absolute size”. There are “no records of this argument in other sources, at least in the form described by Capella”.

The presentation starts with a look at total solar eclipses, concludes that Capella’s argument was likely not based on observations, but was probably constructed post hoc, then assumes that the argument put forward by Capella for calculating the absolute size of the Moon is sound but “badly explained”. From these hypotheses the author infers “a nice method of calculation not previously attested, which asserts that the size of the penumbra of a total solar eclipse at the zenith is equal to two lunar diameters”.

Under that assumption, “the input error in Capella’s argument is not in the cities used, but on the size of the circumference of the Earth, which gives \(20^{\circ}\) for \(\Delta\)lat instead of the correct \(33^{\circ}\). Had he used the correct Eratosthenes’ value, he would have found a much better value for the lunar diameter. Actually, with a circumference of \(252,000\) stadia and a distance between the cities of \(23,100\) stadia, \(\Delta\)lat would be exactly \(33^{\circ}\)!”

Reviewer: Victor V. Pambuccian (Phoenix)

### Keywords:

size of the Moon### Biographic References:

Capella, Martianus
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\textit{C. C. Carman}, Arch. Hist. Exact Sci. 71, No. 2, 193--210 (2017; Zbl 1367.01004)

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### References:

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