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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 \(33^{\circ}\)!”

MSC:

01A20 History of Greek and Roman mathematics
85-03 History of astronomy and astrophysics

Biographic References:

Capella, Martianus
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References:

[1] Bowen, A., and R. Todd. 2004. Cleomedes’ lectures on astronomy. A translation of the heavens with an introduction and commentary. Los Angeles: University of California Press.
[2] Carman, C., and J. Evans. 2015. The two earths of Eratosthenes. Isis 106(1): 1-16. · Zbl 1326.01015
[3] Delambre, J.B.J. 1817. Histoire de l’astronomie ancienne. Paris: Ve Courcier.
[4] Dicks, A. 1925. Martianus Capella. Leipzig: Teubner.
[5] Dreyer, J.L. 1953. A history of astronomy from Thales to Kepler, 2nd edition, originally published as History of the planetary systems from Thales to Kepler. 1905. New York: Dover.
[6] Eastwood, B. 2007. Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance. History of Science and Medicine Library, 4; Medieval and Early Modern Science, vol. 8. Leiden: Brill.
[7] Evans, J., and J.L. Berggren. 2006. Geminus’s introduction to the phenomena: A translation and study of a Hellenistic survey of astronomy. Princeton: Princeton University Press.
[8] Heath, Th. 1913. Aristarchus of Samos. The ancient Copernicus. A history of greek astronomy to aristarchus together with Aristarchus’ treatise on the sizes and distances of the sun and moon. A new Greek text with translation and notes by Sir Thomas Heath. Oxford: Oxford University Press. · JFM 44.0056.04
[9] Jones, H.L. 1960. The geography of Strabo, vol. 1. Cambridge: Harvard University Press.
[10] Neugebauer, O. 1975. A history of ancient mathematical astronomy. Studies in the history of mathematics and physical sciences 1. 3 vols. Berlin: Springer. · Zbl 0323.01002
[11] Pedersen, O. and A. Jones (1974-2010) A survey of the Almagest. Acta Historica Scientirarum Naturalium et medicinalium. Vol. 30. Odense: Odense University Press. With Annotation and New Commentary by Alexander Jones. New York: Springer.
[12] Ramelli, I. 2001. Le nozze di Filologia e Mercurio. Milano: Bompiani.
[13] Rosen, Edward. 1992. Nicholas Copernicus on the Revolutions. Baltimore: The John Hopkins University Press.
[14] Stahl, W. 1971. The quadrivium of Martianus Capella. Latin traditions in the mathematical sciences, 50 B.C.-A.D. 1250, vol. 1. New York: Columbia University Press.
[15] Stahl, W., and R. Johnson. 1977. Martianus Capella and the Seven Liberal arts, vol. 2. New York: Columbia University Press.
[16] Swerdlow, Noel. 1969. Hipparchus on the distance of the sun. Centaurus 14 1: 287-305. · Zbl 0195.00701
[17] Todd, R. 1990. Cleomedis Caelestia (Meteōra). Leipzig: Teubner.
[18] Toomer, G.J. 1974. Hipparchus on the distances of the sun and moon. Archive for History of Exact Sciences 14: 126-142. · Zbl 0339.01004
[19] Toomer, G.J. 1998. Ptolemy’s Almagest. (Primera edición: London: Durkworth, 1984) Princeton: Princeton University Press. · Zbl 0339.01004
[20] Willis, J. 1983. Martianus Capella. Leipzig: Teubner.
[21] Zekl, H.G. 2005. Martianus Capella: Die Hochzeit der Philologia mit Merkur (De nuptiis Philologiae et Mercurii). Würzburg: Verlag Königshausen & Neumann.
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