How was the circumference of the earth measured?

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Eratosthenes was one of the first to come up with a means of measuring the circumference of the earth. Already by that time, and even earlier, the earth was considered to be a sphere, although it was thought of as an exact one.

Eratosthenes was the director of the famous library of Alexandria. Reportedly, it was in a papyrus in the library that he learned a remarkable fact: In Syene, what is now Aswan, for the summer solstice (≈20 June) perpendicular objects, such as a stick stuck in the ground for example, cast no shadow. The sun fell exactly on them at noon.

However, in Alexandria it did cast a slight shadow at the same time.

It is not known exactly how but he deduced that the shadow was 1/50 of a circle, that is, a fragment of a cake cut into 50 pieces. Knowing this, the arc of this piece multiplied by 50 would be the circumference of the earth.

According to Cleomedes, Eratosthenes made use of the scaphium or gnomon (a proto-solar quadrant) for the calculation of the angle and thus deduced the proportion.

For this, he needed to know the distance between Alexandria and Syene. Reportedly, he took the measurement thanks to a regiment of soldiers who would count his steps and give them equal throughout the journey. Perhaps he got the distance from some other papyrus in the library, actually. Anyway, the approximate distance he used was 5 thousand stadia, so the earth must have measured 250 thousand stadia in circumference.

Then, about 150 years later, Posidonius did the calculations again only to find that the earth was smaller. Ptolemy accepted this size as the correct one, disregarding the one obtained by Eratosthenes. Columbus based himself on this measurement to affirm that the trip through the west to Asia was possible, because it was not so big, and thus he convinced the queen. Although those who accepted Eratosthenes' measurement indicated that it was an impossible undertaking.

If the calculation according to Eratosthenes were redone with today's more accurate data and using updated reference points, we would see that he would only have been wrong by 66 km. According to his method the earth is 40 074 km and today's calculations say it is about 40 008 km. And his result deviates so little only because the earth is not a perfect sphere.

Translated with www.DeepL.com/Translator