In the third century b.c.e., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made better (...) measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. (shrink)

In this article, I analyze the coincidence of the prediction of the Earth–Sun distance carried out by Ptolemy in his Almagest and the one he carried out, with another method, in the Planetary Hypotheses. In both cases, the values obtained for the Earth–Sun distance are very similar, so that the great majority of historians have suspected that Ptolemy altered or at least selected the data in order to obtain this agreement. In this article, I will provide a reconstruction of some (...) way in which Ptolemy could have altered or selected the data and subsequently will try to argue in favor of its historical plausibility. (shrink)

The eighth book of Martianus Capella’s famous De Nuptiis Philologiae et Mercurii deserves a prominent place in the history of astronomy because it is the oldest source that came down to us unambiguously postulating the heliocentrism of the inner planets. Just after the paragraph in which Capella asserts that Mercury and Venus revolve around the Sun, he describes 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. It is possible to find some descriptions of the argument in general histories of astronomy or in books dedicated to Capella’s work, but usually they do not try to make sense of the argument. Rather, they limit themselves to describe or paraphrase what Capella says. As far as I know, there is no single study of the argument itself. The explanation for this absence is simple: the calculation offers many difficulties in its interpretation, for it shows obvious inconsistencies in the steps of the argument and apparent arbitrariness in the selection of the data used. In this article, I offer an interpretation that tries to discover, behind Capella’s confusing presentation, a well-sound argument for calculating the Moon’s absolute size. Interestingly, we have no records of this argument in other sources, at least in the form described by Capella. (shrink)