Measuring the Size of the Earth in Antiquity
Uwe Topper
Berlin · June 2001

Eratosthenes supposedly determined the size of the earth, and his calculations were not surpassed until 1800 years later. Even worse: According to historiographers Ptolemy's erroneous tablets and maps were imposed on the medieval world and only laid aside in the 16th century. Yet evidence suggests that these are fairytales just like other stories that are presented as history. Maps showing the real face of the earth always existed. They might be pre-catastrophic.

Part I: Measures  

There exists a prehistorical pattern for geodetic purposes covering the land on a great scale, as Walther Machalett and Hermann Zschweigert found out during many years of research. The result of the trigonometric works of the ancients has been preserved in many megalithic structures, from the dolmens and cairns of France through Central European megaliths down to Egyptian pyramids. Their measurements confirm the use of unified lengths that are fractions of the earth's diameter or circumference.
This grand-scale geodetic system works with trigonometric points on hilltops similar to the one employed today. Toponymics as well as ruins testify to a pattern that covered great areas of the north German plain.
It is obvious that mountainous landscapes cannot be used this way, nor can islands or countries with a rugged coastline. Apart from the northern plain, desert regions like the North African Sahara or vast river valleys like Mesopotamia are appropriate for large-scale geodetic work.

To calculate the diameter or the circumference of the globe two basic measurements are needed: The distance between two localities - A and B - on a meridian (same longitude), and the parallel (degree of latitude) of the two localities.
The latitude of a place is easily obtainable with reasonable accuracy by measuring the angle to the Polar Point or measuring the shadow at equinox noon. The distance between two localities should be chosen as long as possible for best results.
This works if the earth is supposed to be a perfect globe, which we know it is not. Yet an ideal globe may be assumed.
I think primitive people have no interest in determining the size of the earth. It is rather higher cultures like the megalith builders who needed this information, and I believe they needed it for more specific reasons such as calculations of the movements of the moon and the planets and especially the distance of the sun. Their fear of deviations in the motion of celestial bodies was not without reason.
Where could these measurements and calculations have been obtained first ?

In school we learned that Eratosthenes (276-194 B.C.), director of the great library at Alexandria, was the first to determine the size of the earth. Yet his alleged method does not convince me at all.
The following procedure is described: He assumed that Alexandria and Syene (now Assuan on the Nile before the first cataract) are situated on the same meridian and are exactly 5000 stades distant from each other. The latitudinal difference is given as 7°12' which is accurate. But these towns don't lie on the same meridian - Alexandria is 30° eastern longitude and Syene is 33°. The difference of 3° amounts to more than 300 km. We don't know how Eratosthenes determined these towns are 5000 stades distant (which is close enough). From these data Eratosthenes calculated the circumference of our planet to be 252,000 stades, which is astonishingly correct. The stade used in Egypt is 157,5 m, and thus the earth's circumference 39,690 km which is fairly correct (today a bit more than 40,000 km). It means roundabout 110 km distance between two parallels (today 111 km).

The latitudinal difference between Alexandria and Syene, 7°12', is exactly a 50th part of the whole circumference. If this had been applied correctly in the calculation, the circumference would have come to 250,000 stades, or 2000 stades short of what Eratosthenes assumed. This suggests he knew the outcome in advance and only looked for measures that led to the right result.
My doubts are reinforced if we consider the length of the stade: 40,000 stades make the radius of the earth, and 1° of the earth's circumference equals exactly 700 stades. Thus I conclude the stade is a measure deducted from the size of the earth. If Eratosthenes applied it to measure and calculate the earth, he used the knowledge that people had used before him. And he had to twist his mathematical elaboration a bit to arrive at the same result.

Part II: Greek science  

One of the great German scholars at the end of the 19th century, Konrad Miller, worked on the ancient geographers in Greek and Latin texts, and especially on Eratosthenes. He says that "in the whole antiquity there is only one single measurement of the earth worthy of that name, the one made by Eratosthenes" (published 1919, p.16; my translation as in all quotes that follow). According to Miller all other ancient geographers such as Posidonius, Ptolemy etc. copied or misunderstood Eratosthenes' calculation.
The first Greek to talk about the size and form of the earth explicitly was Aristotle. He insisted the earth was a globe and reported that mathematicians had given its circumference as 400.000 stades. Clearly the basic dimension was known, although not yet precisely correct. Presumably Aristotle did not know what linear measure was employed, and if we put his "stade" down to 100 m (an old megalithic measure), the circumference is given precisely. Miller says (p.4) that there is no indication that some highly developed Asian culture such as the Chaldaeans furnished these dates.
Next in line was Archimedes a century later, but his assertion is enigmatic. He writes that his predecessors mentioned the circumference of the earth as 300,000 stades. This would be near the actual size in Egyptian stades, but I do not accept it seriously because the way Aristotle describes how this value was obtained is too shaky. The towns Lysimachos and Syene are supposed to differ 24° at 20,000 stades distance. Both data are wrong. The Greek town lies beyond the Mediterranean, which means the distance between cannot be measured. In fact it is much shorter than indicated, and the arc between the two towns is only 16.5°. So if Aristotle arrived at a close value he must have used earlier data and guessed at the way the ancients arrived at the result without knowing anything certain.
Then came Eratosthenes. His books are not preserved, only some contents of the "Book of Dimensions" are quoted in Galen, and other parts mentioned in the "Geographica" of Strabo. Although Eratosthenes divides the circumference into 60 parts, he does not use this calculation, but transforms his measures into stades (see also Harley and Woodward, vol.I, p.155). One 60th of the circumference amounts to exactly 4200 stades, 42 being the typical sacred number of the Egyptians. The tropic given by Eratosthenes is situated 16,800 stades from the equator, that is 4/60th of the circle, which we would today describe as 24° northern latitude.
In order to get more exact results, Eratosthenes applied two more manipulations.
First, a group of royal geodesists measured the distance from Syene to Meroe in the Sudan (today: Dar Shendy on the Nile), which came to 5000 stades. In this case the longitudinal difference is only 2°, but it is not negligible. And how could they really measure this great distance (about 800 km) over very rough mountainous surface? Only trigonometry would have served the job, but its use is denied by Miller (p.24). He talks about measuring by steps or with a rod or a rope, always reducing the outcome to the meridian. Let us assume that this might be probable. This suggests Syene is the center of Egyptian geodetics.
The third improvement need not be taken seriously: Sailors told him that the distance between Rhodes and Alexandria is about 4000 to 5000 stades. That was not an improvement at all. We know that it is nearly impossible to determine the distance a ship has sailed. Eratosthenes neglected the longitudinal difference of 2° and probably used measurements of latitude when he implied a distance of 3750 stades, as Miller says (p.27). Posidonius, who died about 150 years later, chose 4000 stades and arrived at a similarly exact result.
Again, this tells me the result was there first, and the way of obtaining it was a pure guess.
According to Miller (p.16) recent scholars take this view. They speak of Eratosthenes as "unconsciously" arriving at his results, or borrowing them from another learned culture.
For me the question remains: where did Eratosthenes get his knowledge? That he himself was not learned is highlighted by other data given in his texts (Miller p.5): the diameter of the sun is three times that of the earth, its distance is 51 diameters of the earth, and the moon is 19,5 earth-radii away. All figures are far wrong.
So if he could not estimate himself, not even nearly, how did he arrive at an exact result for the earth's circumference?
The problem of the incorrect data used by Eratosthenes, especially the 3° difference in longitude, is brushed aside by Miller's remarks (p.6 and p.25), that they are corrected by giving the latitudinal difference between Alexandria and Syene as 7° 1/7 . This is not said in the Greek text, but only surmised by Miller defending Eratosthenes. Miller says Eratosthenes was able to correct his wrong longitudes by the inexact difference of the latitudes and thus find the real circumference of the earth. Committing two mistakes and arriving at the correct result means that he knew the result in advance.
We can elaborate on this point a bit more.

Part III: Maps  

The oecumene, that is: the great landmass from the straits of Gibraltar (the Pillars of Hercules, as they were known) to the end of southeast Asia (probably Korea), was one of the important measures for ancient geographers. As it is extremely difficult to determine the meridian (longitude) of a place, these measures even in Renaissance time had been grossly wrong. According to Miller, Eratosthenes gave 120° as the size of the oecumene, Posidonius 180° . Harley and Woodward (p.156) allot 138° referring to the fragments of Eratosthenes' Geographica transmitted in Strabo, a figure quite exact.
Posidonius gave the distance between the Pillars of Hercules westward across the Atlantic Ocean to India amounting to 70.000 stades, which is 11.000 km less than the actual distance. He doesn't mention America at all, and the incorrect distance results from the error in estimating the circumference of the globe which he gave far too long. Posidonius obviously did not understand the issue and had learnt nothing from Eratosthenes.
This can also be seen from his way of calculating the size of the earth: The bright star Canopus rises at Rhodes only just above the horizon, he says (according to Cleomedes), whereas in Alexandria it culminates at 7.5°. As the distance between the two places is given as 5000 stades, he gets 240,000 stades as circumference of the earth. But neither the arc is correct - it is only around 5° - nor is the distance, because that was guessed by sailors. Thus the two mistakes cancel and the result is reasonably accurate, as Miller (p.10) writes: "because he (P.) wanted the result that way."
Another important measure is the size of the sun and its distance from the earth. Miller (p.10f) tells us that they were obtained as follows: Around Syene at summer solstice there is a circle of 300 stades diameter where there is no shadow.
This can hardly be verified, because the assertion "no shadow" depends on very personal criteria, depending on who makes the observation. And Syene is not situated on the tropic of Cancer but on 24° 4.5' northern latitude, which nowadays is about half a degree north of the tropic. Miller acknowledges this and admits great variation is possible (p.28), so that I can only conclude: The diameter of 300 stades was retrocalculated after the circumference of the earth was known. Anyhow, the objective was to calculate the diameter of the sun from this basic measure. Eratosthenes - or rather Posidonius - now multiplies the diameter of the shadowless circle, 300 stades, by ten thousand (10.000) and arrives at 3 million stades, which would be 4.7 million km, more than three times the real diameter of the sun.
For the distance of the sun from the earth he multiplies the radius of the earth by ten thousand and gets 63 million kilometers, which is between one half and one third of the average distance of 150 million km. The reason for multiplying by ten thousand is not explained. Both results are far from reality, but still within a reasonable range which makes me believe the correct measures were known.
Miller states "it was a lucky coincidence that he came closer to the truth than any other astronomer of antiquity." (1919, p. 11). Of course this is a type of chance, and Miller calls Posidonius a "mathematical rope-dancer" (p.11).
Archimedes does the same trick, multiplying the earth diameter by ten thousand. But since his basic measure for the earth is ten times the real value, he arrives at a nonsense result. This suggests the ten thousand factor was a common trick of the time.

Part IV: Arab tradition and Ptolemy  

Miller writes (chapter 3), that Eratosthenes' measurements were passed on to the Arabs, although they don't credit him but mention Hermes or Indians as authorities. Moreover the length of the measure used, the parasang, is never uniform. By different ways of transforming Arab data Miller arrives at the same results Eratosthenes had laid down, i.e., 252.000 stades for the circumference of the earth. Miller states that the Arabs did not understand their own writings although they measured from one latitudinal degree to the next in the Syrian desert. There are several reports of attempts to measure the distance of one latitudinal degree, especially from Alfraganus, but "unluckily none is authentic" (Miller, p. 33).

Mas'udi describes three different measurements of the degree and affirms that the result agrees with that of Ptolemy, but Miller claims it is incorrect. Ibn Yunis (officially died 1008, probably lived in the 14th century) also reports very exact measuring work and the correct results, but says they were not taken into account by contemporaries, because the ancient results were generally used and could not be changed. Arab results for 1° are only 1.5% to 2% wrong. Thus the circumference is between 39,168 and 39,400 km, very near to our data today. The deviation is again due to not taking into account the exact meridian, a difficult task not resolved until around 1600.
The Arabs did not heed their own measurements but followed Ptolemy's incorrect results, yet Christians like Albertus Magnus and Roger Bacon in the 13th century used Arab calculations. I find this absurd, pointing out to intentionally distorted historiography.

Another point on which we are badly informed is the assertion that in those times clerics thought that the earth is a disk. It is unclear why this rumor was invented, but all the dispute about the real size of the earth proves that at least everybody concerned knew the earth is a globe.

Next, Miller looks at the world map of Ptolemy and realizes that the alleged measuring of the coordinates of 330 localities - the "famous cities" - had not been measured at all. Based on very few ancient dates Ptolemy built up a system that was completely wrong and gave a distorted picture of the earth.
His latitudes - which could have easily been observed by simple means - are 2.5° to 5° off to the North, and the Canary Islands deviate by as much as 18° to the South. Only Cádiz in Spain, lying in the center, is exactly placed at 36°. I conclude that only from Cádiz, the famous place of classic learning and knowledge, a real observation was recorded.
For the meridians the data are even worse than might be expected. In this case the center is Alexandria in Egypt. Ptolemy suggests a rational method to obtain clear results by following the progress of an eclipse, but he never used this method. Instead he estimates distances in the east-western direction from reports of sailors and travelers, and distorts them more by attempting to smooth them out. It is clear he had no knowledge about the size of the Mediterranean Sea.

Miller goes on to say that Ptolemy's great map was decisive all through medieval times in an authoritarian way to such an extent that superior knowledge as contained in itineraries and portolans (coastal maps for sailing) was not acknowledged. A look at this model map reveals that coastlines and towns and rivers and mountains are drawn at random and render it worthless. The Mediterranean is stretched far too much; in reality it should only measure two thirds the length Ptolemy gives. Rivers and landmarks in Northern Africa reflect Roman standards of discoveries, which means they represent only those parts of Morocco and Libya-Egypt that had been explored before that time.
A great deal of the distortions, says Miller, are the result of the wrong measure Ptolemy was applying, and of his zeal to improve it. Because of this the mistakes are chaotic and cannot be repaired. "Ptolemy could have easily recognized his main error that disfigures his whole work; if he had put one single place to the test, he would have doubted and then with more tests discovered his error." (p.48)
There remain only three big and one small map attributed to Ptolemy and also the written tables that go along with them. This is not much. From the 14th century on portolans show correct distances and exact coastlines. These probably go back to antiquity, asserts Miller (p. 49, following H. Wagner). Can we assume from this that antiquity finished somewhere around 1300?
And how can we explain the deterioration of map drawing from 1300 to 1500?

Part V: Renaissance  

Gregor Reisch (1503) and Glareanus (1527) realized that Ptolemy's map was worthless but they didn't know the reason. Only the Spaniard Jaime Ferrier explained the mistakes as wrong renderings of the length of the stade when he handed his note to Columbus in 1495 (printed in 1545; Miller p. 14)
I recently looked at the famous "Erdapfel" (apple of the earth) of Martin Behaim in Nuremberg, a world map in form of a globe, produced in 1492 and corrected several times until 1510. It is distorted and unusable. Not even Sicily is presented in an approximate form, let alone the tip of Africa or Ceylon.
This is really astonishing, because at the same time we have splendid maps of the Atlantic Ocean, of South America and the Antarctic which was not discovered until centuries later. These are the Turkish maps of Piri Reis, and I read that others exist. The Germans Finaeus in 1531 and Mercator in 1569 produced similar maps (Hertel, p.59 and 67). The center of the projection of the first Piri Reis map (of 1513) lies exactly at Syene. This might indicate the ancient settlement of Syene housed a school of cartographers whose knowledge is reflected in Eratosthenes and in Renaissance maps.
As the discoveries of the new world and the Pacific Ocean progressed, the quality of these maps deteriorated, because cartographers added new finds to the old information and thus distorted them. The other map of Piri Reis (of 1528) is a mere shadow of the first one. It seems to me that prior to the Renaissance a stock of good maps had survived and been copied and used, but slowly those were supplanted by modern maps which needed another century or two until their quality improved. Abbé Piccard in 1669 used trigonometry to find the exact value of the earth's circumference, and Perrier in 1875 tackled the problem of measuring the width of the Mediterranean between the Sierra Nevada in Spain and the opposite mountain range in Algeria by means of light signals and angle measurements (see Bachmann, Abb. 71). As their utensils were not sophisticated, it is thinkable that sometime in Prehistory people had made exact measurements, which are reflected in Eratosthenes but were not improved throughout the Middle Ages.

The radius and circumference of the earth were known to megalith builders, and still available to Eratosthenes who did not fully grasp the way they were attained but transmitted them correctly, whereas later no scientist, not even the Arabs, made use of these exact measurements. I can only imagine some obscure power that has changed our knowledge of the past. We were told in school that Christian medieval scholars believed in a disk-like earth although it is clear from all this discussion that they knew shape and size of the globe very well. Who gained by dumbfounding his people? And is he still at work?

Bachmann, Emil (1965): Wer hat Himmel und Erde gemessen? (Thun/Schweiz)
Bagrow, L. (1951): Die Geschichte der Kartographie (Berlin)
Bunbury, E.H. (1883): A History of Ancient Geography among the Greeks and Romans (2 vol.; New York; reprint 1959)
Eratosthenes (Fragm.): Die geographischen Fragmente. Neu gesammelt, geordnet und besprochen von Hugo Berger (Leipzig 1880/reprint Amsterdam 1964)
Harley, J.B. and Woodward, David (ed.) (1987): Cartography in Prehistoric, Ancient, and Medieval Europe and the Mediterranean (Chicago and London, 3 vol.)
Hertel, Gisa and Peter (1984): Ungelöste Rätsel alter Erdkarten (Gotha and Cologne)
Machalett, Walther (1970): Die Externsteine - Das Zentrum des Abendlandes (4 vol.; Hallonen Verlag, Maschen)
Miller, Konrad (1919): Die Erdmessung im Altertum und ihr Schicksal (Stuttgart) 66 pp.
Zschweigert, Hermann; Meier, Gert et al. (1997): Die Hochkultur der Megalithzeit (Tübingen)

Addenda: I would like to add that I no longer believe in the authenticity and usefulness of the map of Piri Reis
of 1513, it might even be a falsification. (Topper 2017)

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