Eratosthenes of Cyrene (c. 276–194 BCE), head of the Library of Alexandria, estimated the Earth's circumference from noon shadows and a measured distance, and founded a geography that placed the known world on a grid of parallels and meridians.
Seeing moreover in you, as I say, an earnest student, a man of considerable eminence in philosophy, and an admirer [of mathematical inquiry], I thought fit to write out for you and explain in detail in the same book the peculiarity of a certain method ...
—— Archimedes, The Method, prefatory letter to Eratosthenes, trans. T. L. Heath (1912)
History
Born at Cyrene around 276 BCE and educated in Athens, Eratosthenes was summoned to Alexandria by Ptolemy III around 245 BCE as tutor to the heir, later succeeded Apollonius of Rhodes as head of the Library, and lived into the reign of Ptolemy V. His measurement of the Earth survives in the account of Cleomedes. At the summer solstice the noon sun cast no shadow at Syene (Aswan), while at Alexandria the shadow in a bowl-shaped sundial marked 1/50 of a circle; taking the two cities to lie on one meridian 5,000 stades apart, the circumference came to 250,000 stades. Strabo, Pliny and others give 252,000, or 700 stades to a degree. How good this was depends on the length of his stade, which is still disputed: at about 157.5 metres the result is some 39,000 km, within 2 percent of the true 40,000; with the Attic stade of about 185 metres it is some 16 percent too large. His Geographika in three books arranged the known world on a grid of parallels and meridians, and he probably coined the word geographia itself. He also devised the sieve for finding prime numbers and a chronology counted from the fall of Troy. The tenth-century Suda says that because he came second in every field to its leading figure, he was nicknamed "Beta", and also "Pentathlos".
Connections
Causes1
- The Library of AlexandriainspiresHe became its head librarian; its holdings were his data for measuring and mapping the earth
Consequences1
- Claudius PtolemyinspiresHe began the tradition of a gridded geography that Ptolemy's Geography brought to completion
Echoes2
- al-Ma'munechoesTwo measurements of the earth: shadows at Alexandria, survey lines on the plain of Sinjar
- ArchimedesechoesArchimedes addressed The Method to Eratosthenes
Sources
- Duane W. Roller, Eratosthenes' Geography: Fragments Collected and Translated (2010)
- Alan C. Bowen and Robert B. Todd, Cleomedes' Lectures on Astronomy: A Translation of The Heavens (2004)
- Jacques Dutka, Eratosthenes' measurement of the Earth reconsidered (Archive for History of Exact Sciences 46) (1993)
- Malcolm Heath (trans.), Suda On Line, s.v. Eratosthenes (ε 2898) (2001)
Open questionspartly uncertain
- His method of measuring the Earth is known only from later accounts such as that of Cleomedes, which may have simplified it.
- The length of the stade is uncertain, so judgements of his accuracy vary with it.
- Whether his original figure was 250,000 or 252,000 stades is disputed.
- The years of his summons and of his appointment as head of the Library are both inferred.
- He may have coined the word "geography", but this is only a possibility.
Why it matters
The measurement is often told as one man with a stick outwitting the planet, which hides what it rested on. The 5,000 stades probably came from royal surveyors or travellers' itineraries, the shadow angle from a good sundial, the geometry from the Euclidean tradition, and the gathering of all three from a royal library. Some of the famous accuracy may come from errors cancelling one another. The method itself was new: reading off in the sky an angle that converts into a distance no one could walk end to end. The same move returned a thousand years later when al-Ma'mun sent surveyors onto the plain of Sinjar, and modern geodesy follows it still. The nickname "Beta" mocked a man who was second at everything; measuring the Earth called for exactly such a man, able to draw on astronomy, geometry, geography and books at once.