The Museum was not only a home for poets and editors. For about two centuries it was also one of the great centers of science in the ancient world, where mathematicians, astronomers, engineers and doctors worked side by side.

Euclid

Very little is known about the life of Euclid, except that he taught in Alexandria around 300 BCE. His Elements organized the geometry of his day into a single chain of reasoning: start from a few definitions and assumptions, then prove each result from those already established. The Elements became one of the most widely used textbooks in history, studied for more than two thousand years, and its method of proof shaped how mathematics and even philosophy present arguments.

Eratosthenes measures the Earth

Educated Greeks already knew the Earth was round. Eratosthenes, head of the library in the third century BCE, set out to measure how big it was. He had heard that at Syene, modern Aswan, far to the south, the noon sun at the summer solstice shone straight down a deep well, casting no shadow. At the same moment in Alexandria, a vertical pointer did cast a short shadow. He measured the angle of the sun's rays there and found it was about one fiftieth of a full circle.

His reasoning was simple. If the sun's rays arrive parallel, the difference in angle between two places equals the fraction of the Earth's circumference between them. The distance from Syene to Alexandria was reckoned at about 5,000 stadia, so the whole Earth must measure about 50 times that, or 250,000 stadia. How accurate this was depends on which length of the stadion he used, which is uncertain. On common estimates his answer was within a few percent to about fifteen percent of the true figure, a remarkable result from a shadow and a well.

Eratosthenes also drew one of the first maps of the known world with lines of latitude and longitude, and devised a method for finding prime numbers still taught as the “sieve of Eratosthenes.”

A network of letters

Scientists outside the city stayed in touch with the Museum. The great mathematician Archimedes of Syracuse, in Sicily, is thought to have studied in Alexandria as a young man, and he later sent his work to scholars there. One of his treatises, known as The Method, is addressed to Eratosthenes. Rediscovered in 1906 beneath the text of a medieval prayer book, whose maker had scraped and reused the old parchment, it shows how the leading thinkers of the age shared their results by letter across the Mediterranean.

Engineering

Ctesibius, working in Alexandria in the third century BCE, is credited with inventing a force pump and an improved water clock, and with early work on devices driven by air and water pressure. Centuries later, Hero of Alexandria described a spinning steam-powered sphere and many automatic machines. Hero's steam device was a curiosity rather than an engine; no one turned it to work. Historians still debate why ancient societies, with abundant slave labor among other factors, did not develop such inventions further.

Medicine and the human body

In the early third century BCE, the physicians Herophilus and Erasistratus carried out systematic dissection of human bodies, something long forbidden in Greek lands for religious reasons. Herophilus distinguished nerves from tendons, described parts of the brain and eye, and studied the pulse. Their discoveries advanced anatomy for centuries.

They also raise a grave ethical question. The Roman writer Celsus, two centuries later, reports that they performed vivisection on condemned criminals supplied by the king, cutting open living people. Some historians doubt the report; others find it plausible. Either way, the claim forces a question that runs through this whole course's commitment to human dignity: can knowledge gained by treating people merely as means ever be justified? Modern medical ethics, shaped by the Nuremberg Code of 1947 after Nazi experiments, answers firmly that research on human beings requires their informed consent.

Later science

Alexandria remained a scientific center under Roman rule. In the second century CE Claudius Ptolemy, no relation to the kings, wrote the Almagest, a mathematical model of the heavens with the Earth at the center that dominated astronomy for some fourteen centuries. The great doctor Galen studied there too.

Worked example: repeating Eratosthenes

Students around the world still repeat Eratosthenes' measurement. Here is how it works in words.

1. Two places, one moment. Two schools far apart on roughly the same north to south line each stand a straight stick upright at local noon on the same day.
2. Measure the shadows. Each school measures the length of its stick's shadow and works out the angle of the sun's rays from it. The school nearer the equator usually gets the smaller angle.
3. Find the difference. Suppose the angles differ by one fiftieth of a circle, just as Eratosthenes found.
4. Scale up. If the schools are 800 kilometers apart, the Earth's circumference is about 50 times 800, or 40,000 kilometers. The true figure is about 40,075.

The lesson is not only about geometry. Eratosthenes trusted careful observation and reasoning over authority, and anyone with a stick, a ruler and a partner can check his work. That openness to checking is what makes knowledge scientific, and what makes it belong to everyone.