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Eratosthenes: Ptolemaic Alexandria
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At the time when the new library at Alexandria opened its gates, the first comprehensive monograph on the head librarian of the old library at Alexandria between 246 and c.196 BC, Eratosthenes of Cyrene, came out. This rich book is the somewhat revised version of Geus' Habilitationsschrift (post-doctoral thesis) at Bamberg University. Due to the universal interests of this Alexandrian scholar that comprised such diverse fields as philosophy, poetry, grammar, musical theory, history, chronography, mathematics, astronomy, and geography, nobody has tried to deal with life and the complete oeuvre of Eratosthenes in one book before. Geus' ambitious aim is to shape a full picture of this outstanding Hellenistic scholar and his "intellectual profile", including his significance for Hellenistic cultural history. He succeeds well and has produced a fine book, full of references, arguments and engaging details.
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Eratosthenes knew that on the summer solstice at local noon on the Tropic of Cancer, the Sun would appear at the zenith, directly overhead - though Syene was in fact slightly north of the tropic. He ... knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7° south of the zenith at the same time. Assuming that Alexandria was due north of Syene - Alexandria is in fact on a more westerly longitude - he concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of the Earth. The distance between the cities was known from caravan travellings to be about 5,000 stadia (1 stadion=148.5 m). He established a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is no longer known (the common Attic stadion was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 km and 46,620 km. The circumference of the Earth around the poles is now measured at around 40,008 km. Eratosthenes result is not bad at all.
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Eratosthenes, a Greek geographer (about 276 to 194 B.C.), made a surprisingly accurate estimate of the earth's circumference. In the great library in Alexandria he read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth (sorry Columbus) by making two assumptions - that the earth is round and that the sun's rays are essentially parallel.
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Eratosthenes achieved his greatest fame by using a most ingenious and simple method to measure the circumference of the Earth. He was aware that on a certain day the Sun at Syene (now Aswan) was exactly at its zenith (it was known to shine directly down a deep well on that day). He found that on the same day at Alexandria it was south of its zenith by an angle corresponding to 1/50 of a circle (7° 12′). He ... knew that the distance between Syene and Alexandria was 5000 stadia – a distance that he estimated from the time it took a camel train to make the journey. Therefore, 5000 stadia must be 1/50 of the circumference of the Earth; that is, 250,000 stadia. (Since the exact length of a stade is not known it is impossible to work out exactly how accurate his measurement was but it has been thought to be within 50 miles of the presently accepted value.) Eratosthenes also established an improved figure for the obliquity of the ecliptic (the tilt of the Earth's axis) of 23°51′20ʺ.
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While the idea that the Earth is round was not uncommon among ancient Greek philosophers, Eratosthenes was able to demonstrate this fact, and calculate the Earth's circumference accurately. The ancients noticed that, in the city of Syene (modern day Aswan), at noon on June 21, the sun is directly overhead. Shadows of vertical columns and sticks disappeared. A shaft of sunlight penetrated to the bottom of a well. This fact aroused Eratosthenes' curiosity, and he did an experiment to determine whether vertical sticks cast shadows in Alexandria at noon on the summer solstice. As it turned out, they do.
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Eratosthenes was able to measure the circumference of the Earth using very simple trigonometry and geometry. Eratosthenes knew that sunlight would shine directly down a well in Syene at noon on the summer solstice. On that same day, a building in Alexandria would cast a shadow which could be measured. By measuring the length of the shadow and the height of the building, the angle between Alexandria and Syene could be established. This angle was found to be approximately seven degrees. Since the distance between the two cities was known, the circumference of the Earth could be established.
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