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The geographers of Miletus: 6th century BC

Nothing is known of the map of the world supposedly produced in Miletus by Anaximander in the mid-6th century BC. But by the end of the century, also in Miletus, another geographer writes a book of which sufficient details survive for his ideas to be reconstructed. He is Hecataeus.

Like most early mapmakers, Hecataeus puts the most important place at the centre of the world. For medieval Christian cartographers this is Jerusalem. For Hecataeus it is the Aegean Sea, on the east coast of which stands Miletus.

The shape of the world according to Hecataeus has a geometrical simplicity. It is a flat circle, with a continuous ocean forming the rim. The circular land mass is divided into two parts by an almost unbroken stretch of water linked with the ocean on the west at the straits of Gibraltar, then running east the length of the Mediterranean, through the Black Sea and (after a short land bridge) into the Caspian Sea, which joins the ocean on the east.

The semicircle of land above this belt of water is Europe, while the semicircle below is Asia. The part west of the Nile has the subsidiary name of Libya, standing in for Africa.

The coast of northwest Europe: c.310 BC

Pytheas, an explorer from the Greek city of Massilia (now Marseilles), voyages past Gibraltar and turns north up the European coast. Off Brittany he veers west to visit Cornwall, where he describes the trade in tin. He then sails up the west coast of Britain and continues beyond it for six days to reach a land which he calls Thule. It is inhabited but uncomfortable and strange. At midsummer the sun never sets, and beyond here the sea is frozen.

As a result of this report Thule (presumably Norway) becomes for all Greek and Roman geographers the most northerly place in the world.

The circumference of the earth: calculated c. 220 BC

Eratosthenes, the librarian of the museum at Alexandria, has more on his mind than just looking after the scrolls. He is making a map of the stars (he will eventually catalogue nearly 700), and he is busy with his search for prime numbers; he does this by an infinitely laborious process now known as the Sieve of Eratosthenes.

But his most significant project is working out the circumference of the earth.

Eratosthenes hears that in noon at midsummer the sun shines straight down a well at Aswan, in the south of Egypt. He finds that on the same day of the year in Alexandria it casts a shadow 7.2 degrees from the vertical. If he can calculate the distance between Aswan and Alexandria, he will know the circumference of the earth (360 degrees instead of 7.2 degrees, or 50 times greater).

He discovers that camels take 50 days to make the journey from Aswan, and he measures an average day's walk by this fairly predictable beast of burden. It gives him a figure of about 46,000 km for the circumference of the earth. This is, amazingly, only 15% out (40,000 km is closer to the truth).

A grid before its time: 2nd century BC

One of the most rigorous of Greek scientists, the astronomer Hipparchus, foresees in the 2nd century BC the requirements of a modern map. He is critical of mapmaking efforts by his Greek contemporaries, based on measurements taken on the ground. Instead he proposes a grid of 360° of latitude and of longitude (a number relating back to Babylonian systems), on which places will be plotted according to astronomical readings taken on location.

The necessary instruments of measurement (in particular for the accurate recording of time) are not available to Hipparchus. But his bold idea prefigures the principle of scientific cartography.

The influential errors of Ptolemy: 2nd century AD

Ptolemy, working in Alexandria in the 2nd century AD, is one of the great synthesizers of history. In several important fields (cosmology, astronomy, geography) he brings together in encyclopedic form an account of the received wisdom of his time.

His influence derives from the accident that his predecessors' works are lost while his have survived. Their achievements are known only through him, and when he disagrees with them it is usually he who is wrong. Just as in astronomy he wrongly adjusts the degree of precession of Hipparchus, so in geography he rejects Eratosthenes, whose calculation of the circumference of the earth is very close, and prefers instead another estimate which is 30% too small.

In geography Ptolemy seems to offer what Hipparchus had proposed - the location of the world's natural and man-made features on a grid of 360° of latitude and longitude. He lists and places some 8000 towns, islands, rivers and mountains. But he is no more capable of providing accurate data, astronomically based, than Hipparchus was. The relative positions of his named features are calculated by collating travellers' accounts of the number of days taken on their journeys.

The results are wildly inaccurate. But the great prestige of Ptolemy means that with the revival of classical learning, in the Renaissance, his errors become enshrined in the earliest printed maps.

The medieval world: 5th - 15th century

The temperate belt of the northern hemisphere, from Britain to China, is reasonably familiar from trade and travel by the time of the late Roman empire. From the 7th century the spread of Islam provides further detail, as subsequently do travellers such as Marco Polo or Ibn Batuta. Much information is forgotten or becomes confused; the mysterious regions of northern Asia and southern Africa remain full of monsters; and the medieval love of a marvellous tale will cloud many issues. But the known world is seen as a rectangular chunk of continuous land, like a belt round most of the earth, with a single ocean dividing western Europe from eastern Asia.

This view of geography prevails until the decade of exploration - the 1490s.

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