Eratosthenes Measures Earth
Around 240 BCE, Eratosthenes of Cyrene, a Greek scholar working in Alexandria, Egypt, produced one of the first known scientific estimates of the size of the Earth. Using little more than shadows, geometry, and an estimate of the distance between two cities, he arrived at a circumference that, by some modern readings, came remarkably close to the true figure of about 40,000 kilometers. The achievement matters because it showed that the natural world could be measured through reasoning and observation, and it did so more than two thousand years before satellites.
Eratosthenes was born in Cyrene, in present-day Libya, and studied in Athens before being invited to Alexandria by the Ptolemaic king. There he became head of the great Library, a center of learning that drew mathematicians, astronomers, and poets. By this period, educated Greeks already accepted that the Earth was a sphere, an idea supported by the shape of its shadow during lunar eclipses and by the changing stars seen as travelers moved north or south. What remained unsettled was how large that sphere was.
According to later accounts, notably those of Cleomedes and Pliny, Eratosthenes learned that at midsummer noon in Syene (modern Aswan), the sun shone straight down a deep well, casting no shadow. In Alexandria, to the north, a vertical rod did cast a shadow at the same moment. He measured the angle of that shadow as roughly one-fiftieth of a full circle. If the sun's rays are effectively parallel, that angle should equal the arc between the two cities along the Earth's surface. Knowing the distance between them, he could multiply up to the whole circumference. The distance was reportedly about 5,000 stadia, giving a total of 250,000 stadia, a figure sometimes adjusted to 252,000.
How accurate he really was is debated. The stadion was not a single fixed unit, and the Greek world used several different lengths. Depending on which is assumed, his result falls within a couple of percent of the true value or errs by perhaps 15 percent. Syene is also not exactly on the same meridian as Alexandria, nor precisely on the Tropic, so the method contained small flaws. Even so, the principle was sound, and the result was impressively close either way.
Eratosthenes' original work, On the Measure of the Earth, has not survived, so we depend on later writers. His approach nonetheless became a model for geodesy. Later scholars such as Posidonius offered alternative figures, and Ptolemy adopted a smaller Earth that may have influenced later geographic thinking, including estimates of the distance westward to Asia. Eratosthenes also drew an early map of the known world and is credited with a prime-number sieve, making him one of antiquity's most versatile thinkers.