Ptolemy's maps: the father of modern Geography

The basic principles of Ptolemy’s map projections remain in use to this day – even Google’s ‘Earth’ application uses a projection first invented by him – and yet his life as well as his methods remain a mystery. What little we know about him is based on later Byzantine sources. He was a native of Ptolemaic Egypt, which, during his lifetime, was already under the control of the Roman empire. Taking the name ‘Ptolemaeus’ suggests he had Greek ancestors, and ‘Claudius’ indicates he possessed Roman citizenship.

What is known is that Ptolemy worked at the Alexandria Library, founded in c300 BC, the repository of all written knowledge, which held thousands of manuscripts from across the Greco-Roman world. Some of the greatest classical scholars worked there, including the mathematicians Euclid (c325–265 BC) and Archimedes (c287–212 BC), the poet Callimachus (c310–240 BC) and the astronomer – and one of the earliest librarians at Alexandria – Eratosthenes (c275–194 BC). By Ptolemy’s time the library, like the Hellenic culture it represented, was in decline, ravaged by warfare, neglect and looting. For Ptolemy this decline represented a unique opportunity to summarise nearly a millennia of Greek geography. By drawing on what remained of the library’s resources, Ptolemy compiled his Geography, to “show the known world as a single and continuous entity” and to “investigate the Earth’s shape, size, and position with respect to its surroundings”.

The Greeks had been drawing maps – onto a physical medium, such as wood, stone or bronze, called pinax – for centuries, and writing about them in works usually entitled periodos ge¯s (literally a ‘circuit of the Earth’). Homer describes a circular, flat Earth encircled by water in his Odyssey, but by the fifth century BC Pythagoras and Parmenides concluded that if the universe was spherical, then so was the Earth.

In Phaedo (c380 BC), Plato described the Earth as “round and in the centre of the heavens”, “marvellous for its beauty” and circular perfection. Aristotle agreed, adding climatic zones, which led his disciples to introduce rudimentary lines of latitude and longitude. Using astronomy and geometry, they pieced together a map of the known world which they called the ecumene – an inhabited ‘dwelling space’. Although none of these maps survive, a reconstruction of the world map of Aristotle’s pupil Dicaearchus of Messina, who worked between c326–296 BC, shows how the Greeks began to understand the size and shape of a world centred on Rhodes.

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Ptolemy was also able to draw on some remarkably accurate calculations of the size of the Earth, including those of Eratosthenes. Using a sundial, Eratosthenes measured the angle cast at midday on the summer solstice at both Aswan and Alexandria, which he believed were on the same meridian, 5,000 stades apart (a Greek stadion measured between 148 and 185 metres). He calculated the angle between the two places as one-fiftieth of a circle. This led him to conclude that the globe had a circumference of 250,000 stades (between 37,000 and 46,000km). Considering the Earth’s circumference at the equator is 40,075km, his calculations were remarkably accurate.

When Ptolemy came to write his Geography, he synthesised this mass of Greek learning, and drew a geometrical net of latitude and longitude over the world, preferring the consistency of mathematics over the unreliable gossip of travellers’ tales (what the Greeks called akoe, or ‘hearsay’). He began by defining geography as “an imitation through drawing of the entire known part of the world”. He then divided the globe’s circumference into 360° (based on the Babylonian sexagesimal system), with the known world stretching from west to east through an arc of 177°, from the Canary Islands to Cattigara in modern-day Vietnam.

The known world’s breadth was estimated at just over half its length, from Thule (Iceland), 63° north of the equator, to the region of ‘Agisymba’ (modern-day Chad), 16° south of the equator, a latitudinal range of just over 79°.

Yet expanding the world in this way made it difficult to project the globe onto a flat surface. Ptolemy knew that no map projection could ever represent the globe without distortions, so he used Euclidean geometry to offer two different methods of making a world map. On the first cone-like projection the meridians were drawn as straight lines converging at an imaginary point beyond the north pole, with the parallels shown as curved arcs of different lengths, centred on the same point. Ptolemy explained that anyone could draw such a map by using a swinging ruler and referring to his tables of latitude and longitude in the later books of the Geography.

He conceded that this projection had its drawbacks: on a globe, parallel lines diminish south of the equator, but on Ptolemy’s projection they actually increase in length. His compromise was to propose meridians forming acute angles at the equator. This was fine for the Greeks, who regarded the habitable world as ending somewhere in the Sahara, but it would prove a problem for 15th-century pilots when they tried to sail down the African coast.

He therefore offered a second projection that was “similarly proportioned” to the globe by drawing curved parallels and meridians. The trigonometry was more complex, and Ptolemy confessed that it was harder to construct a map on this projection, as the curved meridians could not be drawn with the aid of a swinging ruler.

However Ptolemy cheerfully advised readers to “hold on to descriptions of both methods, for the sake of those who will be attracted to the handier one of them because it is easy”. He was, in effect, offering subsequent generations a mapping tool-kit, and a gazetteer of places to which they could expand almost indefinitely, building up an ever-changing map of the world as new data became available.

Mapping the future

But there was also another astonishing reason for the success of Ptolemy’s projections. The earliest surviving manuscripts of the Geography with maps come from late 12th-century Byzantium. There is no concrete evidence that Ptolemy ever drew his own maps. Instead, he transmitted geographical data in digital form, using a series of numbers and diagrams that allowed later map-makers to adapt it. Perhaps we should therefore regard Ptolemy as the first digital geographer.

When Columbus and Magellan planned their epic voyages to the east by sailing west, they both turned to Ptolemy to support their expeditions, and for good reason. Ignoring Eratosthenes’s calculations, Ptolemy had estimated the length of a degree as 500 stades, underestimating the global circumference by as much as 10,000km, or more than 18 per cent of the Earth’s actual circumference.

Looking at a world map based on Ptolemy’s calculations, it is no wonder that Columbus and Magellan believed it was possible to sail west to get to the east. Without Ptolemy’s mistaken calculations they would probably have never set off on such daunting voyages, and the shape of the age of discovery might have looked very different.

Jerry Brotton is professor of renaissance studies at Queen Mary, University of London. He is the author of A History of the World in Twelve Maps (Allen Lane, September 2012)

This article was first published in the September 2012 issue of BBC History Magazine