In his thesis The origins of antipodal theory (see below for details), Schiöth gives a useful summary of the history of measuring the earth's size.

Calculating the size of the earth

The first known calculation in the extant literature of the circumference of the earth might be derived from Eudoxus. In On the Heavens (298b), Aristotle attributes the figure of 400,000 stades for the circumference of the earth, to unknown 'mathematicians.' Due to Eudoxus’s known influence on Aristotle’s astronomy, some scholars have pointed out that in this passage Aristotle might be referring to Eudoxus.

Value of the stade: The stade (στάδιον or stadion) was an ancient Greek unit of measurement, ‘in origin the distance covered by a plow in a single draft, consisted of 600 Greek feet; but the length of a foot was subject to some local variation in the Greek world’ (Harley & Woodard, 1987, p. 148n). It was variously counted as 7½ to 8⅓ stades to the Roman mile (Roller, 2010, p. 272). There is a great scholarly controversy over the actual value of the stade, it has been variously defined as anywhere between 157.5 to 185 metres (Thomson, 1948, p. 161), or 177.7 to 197.3 metres (Roller, 2014, p. 33). See the discussions of the stade in Thomson (1948, pp. 161-62); Dicks (1960, pp. 40-46); Harley & Woodard (1987, p. 148n) and Roller (2010, pp. 271-73).

(FP note) Bunbury takes the stade to be 185m and Berggren & Jones the same.

It was Eratosthenes himself who initiated a scientific revolution in the fields of geography and geodesy (earth measurement), with his accurate calculation of the earth’s circumference at 250,000 stades (according to Cleomedes), or 252,000 stades (according to Strabo and others). This opened the gate for the scientific mapping of the known world. The issue of measuring ‘the size and location of the inhabited world was of intense and continuing interest to the Greeks’ (Harley & Woodward, 1987, p.155), even more so than the proportions of the whole earth. But now that Eratosthenes had a figure of the whole earth’s dimension to work with, the task of measuring the size of the inhabited world (the oikoumene) could be realized. Eratoshenes undertook the task and reported his findings in a book called Geographica, the first such work to bear that name. It is from this treatise that the term ‘geography’ originates (Roller, 2015, p. 3). But this work is now lost, almost everything we know about it is what is reported by Strabo. From the available evidence, we understand that it was the first attempt to make a map projection of the globular surface of the earth (instead of the usual flat plane), and it was also the first to use parallels and meridians, which Eratosthenes was able to calculate because of his figure for the entire earth’s circumference (Harley & Woodward, 1987, p. 154). In his map of the oikoumene, ‘Eratosthenes located the inhabited world completely in the Northern Hemisphere, occupying the northern half of the distance between the Tropic of Cancer and the equator, and the entire distance between that tropic and the polar circle’ (Harley & Woodward, 1987, p. 155-56).

He calculated the breadth of the oikoumene from the ‘Cinnamon country’ [poss. Somalia] to Thule at 38,000 stades, and its length from Iberia to India at 78,000 stades. … His oikoumene stretched 8400 stades beyond the Tropic of Cancer, exactly halfway (according to his calculations) between the tropic and the equator. These calculations indeed showed that the oikoumene occupied only a very small portion of the entire globe.

(FP note) The identity of Thule is contested. It was apparently observed by Pytheas on his northern voyage, and was probably Shetland, according to Bunbury. Others argue that it was Iceland.

As regards his poem Hermes, which is our earliest attestation of the antipodal theory, Romm (1992, p. 128) asserts that Eratosthenes was “strongly influenced” by Plato, pointing to the same literary technique of imagining a character (in Eratosthenes’s case, the god Hermes) flying high above the earth to see its whole shape from above. Romm argues that Plato makes Socrates employ this approach in the Phaedo 110b, and also the character Er in Book 10 of the Republic. The Myth of Er, in turn, inspired Cicero’s Dream of Scipio in the De res publica, that was subsequently the subject of Macrobius’s Commentary, which became highly influential in the Middle Ages. Romm (1992) also argues that Eratosthenes’s poem was the main inspiration for the passage in Virgil’s Georgics which describes the climatic zones and the antipodes (1.233-38).

This belief [in antipodeans] seems to have followed from the ancients’ understanding that the earth was a globe, and that they were living on a landmass situated in the northern hemisphere (which they called the oikoumene or οἰκουμένη, meaning ‘inhabited world’ – corresponding to Eurasia and North Africa). From this observation they used logical deduction to hypothesize that there could be an unexplored landmass on the opposite side of the globe, which was most often thought to be in the southern hemisphere, and sometimes in the northern hemisphere (or both). From this, it followed that these unexplored landmasses could potentially be inhabited by an uncontacted race of people referred to as the antipodes. Hence the term ‘antipodes’ derives from the Greek ἀντίποδες, meaning ‘with feet opposite of ours.’

Then there is the most advanced form of the antipodal theory, the so-called Cratesian model, which was based on a fourfold (quadripartite) division of the globe, with a total of four inhabited continents that were situated in each quarter of the four opposite sides of the earth. According to this model, there were, in addition to the oikoumene, two inhabited continents in the temperate zone of the southern hemisphere, and another in the northern hemisphere, which shared the same temperate zone as our oikoumene. The Cratesian model appears on quite a few medieval maps and is illustrated in medieval manuscripts, the so-called zonal maps (Wright, 1925, p. 66; Harley & Woodward, pp. 296-300). This was largely due to the influence of Macrobius’ Commentary on the Dream of Scipio (ca. 410 CE) which was a quite popular text during the Middle Ages (Stahl, 1952). This commentary was based on Cicero’s (106 – 43 BCE) Somnium Scipionis, an extant chapter from his De re publica, written in Latin, where one of the most vivid descriptions of the Cratesian model is to be found.

Sources

• Schiöth, Tjörvi, The origins of antipodal theory in ancient Greek science and philosophy. MA Thesis (Univ. Iceland, 2022)

For the Greek geographic tradition:

• Aubrey Diller, Tradition of the Minor Greek Geographers.

The major ones were Strabo, Ptolemy and perhaps Pausanias.

• Bunbury, History of Ancient Geography 1879 – seems to still be the only major reference.

• J Oliver Thomson, similar title, 1948, much less use – time periods all mixed up, no chronological approach