# Bits of Map Projection History

#### Contents

Earth's Size and Shape in Time and Space

### EARTH'S SIZE AND SHAPE IN TIME AND SPACE, by Lance Nelson

#### (The following are notes were prepared by Lance Nelson for the seminar in map projections.)

World maps, per se, don't exist in the most ancient times. Both ancient Egypt and Mesopotamia develop some kind of cadastral mapping, but they do not attempt to represent the earth beyond their realms except to diagram their relationship to a cosmos of some sort.

In western history we have records of some of the first speculations about the shape of a world in 7th century BC Greece.

• Thales (625-547 BC) - proposes a disc on the ocean.
• Anaximander (611-554 BC) - proposes a cylinder, with the land on its curving surface.
• Pythagoras (6th century BC) - propose sphere due to its geometrical perfection. Aristotle also proposes sphere and develops a proof by observation. At about the same time a Phoenician, Hanno, circumnavigates Africa from the East. Aristotle and Archimedes propose without explanation a circumference of 64K and 48K kilometers, respectively.
• Eratosthenes (276 - 196 BC) - Librarian at Alexandria makes the first attempt to measure the circumference of the globe. Uses triangulation and solar observation to measure the distance along a meridian. Calculates a circumference of 250K stadia, which translates to about 46K. (stay tuned this figure may be incorrect) This is only 16% too large. Eratosthenes also used the idea of meridians and parallels to locate places in relationship to each other in the known world. Others, using the gnomon, also determine latitudes with accuracy.
• Ptolemy (2nd century BC) - Compiles astronomical data of the time using a geocentric model of the cosmos in the Algamest. Compiles his Geography, creating the first known projection of the known, spherical world, onto a plane.

As Europe enters the dark ages, these ideas about the world are gradually lost. Europe's view of the world is increasingly shaped by theological concerns and lack of contact with other places. Generally the map of the world became a theological rather than geographic statement. In Europe this was expressed in the development of the so-called T-O map, which had some recognizable geographic informations in all of its forms, but was heavily influenced by dogmas and theology. These were the main world maps for centuries in Europe, but the concept of maps as tools did not disappear. All through this period Itineraries and other kinds of route maps were published for crusaders and pilgrims. On the seas portolan charts were in constant use.

Meanwhile...

All through Asia and parts of Africa seafaring and overland trade is taking place. The ideas of the Greeks and Ptolemy are preserved in Arabic translation. Eventually due to trade and contacts these works start to re-enter Europe. The Book of Roger, commissioned by a Norman king in Sicily in the 12 century, had maps and a geography based on Ptolemy. Additional information, probably based on trade in the East was used to update the Ptolemaic maps.

China has had a bureaucratic mapping tradition for administering its realm since the 3rd century BC. A graticule was developed, but was not related to the idea of the earth as a globe. There was always a certain amount of knowledge about the wider world available in China, but world maps do not seem to have been of much interest to scholars or rulers. The only ones that are available seem to be similar to the European T-O in their focus on religious or philosophical ideas.

For various reasons Europe starts to look at the world in a different way. In addition to a willingness to accept some of the Classical ideas now becoming available, there is heightened interest in the seafaring trade to Asia.

In the 15th and 16th century Portugal circumnavigates Africa, Columbus uses Ptolemy and others to underestimate the size of the globe and sails for Asia, Magellan more or less circumnavigates the globe.

In 1525 Pernel tries to measure a degree of latitude in France.

In the 17th century there is the development of surveying equipment and triangulation methods, including the logarithms, theodolite, pendulum clock, and barometric level. In 1669 Picard develops a triangulation line near Paris and measures a degree of latitude. Newton develops the theory of gravity and proposes that the globe is actually an oblate spheroid due to angular momentum.

In the 1690's Cassini, father and son, propose triangulation to further verify the degree of latitude. Their southern routes gives a shorter degree than Picard, the son goes on to measure a northern route and finds this degree is longer. He propose a prolate spheroid as the correct shape for the earth.

1735 - 1743 - Expeditions are mounted to Lapland and Peru by the French to measure the length of a degree of latitude and determine the correct shape of the earth. The Northern expedition measure a longer degree, thus proving Newton's proposal of the oblate spheroid based on the theory of gravity.

In the 18th century there is a great race to accurately determine the longitude. John Harrison's chronometer No 4 is successful at sea in 1761.

In the 20th century the two major developments are the use of the geoid and other models for the earth's surface and the ability to use space to make measurements of the earth.

Over-all the history of the shape of the earth can be divided into three major eras, if one ignores the flat earth theory which still captures some adherents in moderns times. These three are the time of the spherical earth from ancient ideas, the ellipsoidal earth, where the major perturbations of gravity are included in the modeled shape of the earth and finally the geoid which includes many local perturbations in the general shape of the earth.

### Claudius Ptolemy (90-170 AD) Dr. K. C. Clarke

#### (The following are notes were prepared by Dr. Clarke for the seminar in map projections.)

• Born Greece.
• Active Scholar, 127-151 AD in Alexandria.
• Published in Biography, Music, Math, Optics & CARTOGRAPHY.

### Major Works

ALMAGEST (From the Arabic translation "the greatest")

• 13 books on Math and Astronomy.
• Important work on the circle, including use of 360 degrees, and division into minutes (partes minutae primae) and seconds (partes minutae secundae).
• Gave long-standing support to earth-centered universe.
• Advanced basic "principles of science", e.g. that the best explanation of a phenomenon is the simplest hypothesis advanced which does not contradict results. Also encouraged checking and rechecking of results.

GEOGRAPHY Meaning: Cartography: Mapping of all the world and the phenomena it contains.

• Practical treatise on world mapping.
• One world map, 26 regional maps (all lost). Eight books in all.
• Rejected Eratosthanes estimate of size of earth, used instead Poseidonius, 3/4 of actual size. Assumed "known world" stretched 180 degrees of longitude (Ecumene).
• Supported corrections of scale distortions in other maps, i.e. introduced map projections.
• Mentions use of gnomon and astrolabe for pole star & sun.
• Discounts travel stories.
• Included a gazeteer of know places with lat. & long. By 1740, only 116 places known.

### ONE

• Used for world map in the first edition (Bologna, 1477) Regional maps used same projec- tion.
• Straight converging meridians, converge to north of north pole.
• Curved, circular arcs as par- allels.
• Southern hemisphere only partly covered.

### TWO

• Pseudoconic. "much greater resemblance to the known world in our map."
• Used in Germanus copy of Ptolemy, 1470, and Ulm, 1482. Inspired later conic projections.
• Curved, parallel circlular parallels. Curved meridians, converging at pole.

### THREE

• Azimuthal-like (book 7)
• Modified perpective view.
• True scale along straight central meridian, taped scale along Syene parallel (straight), and other lines concave and curved.
• Unused or lost.

### PTOLEMY's PARALLELS

• Used length of day variations of 1/4 hour on longest day (summer solstice).
• First parallel at 4 15'N, tenth at 36 N, 21st is Thule.

### PTOLEMY's MERIDIANS

• Used 1/3rd part of equinoctial hour (5 degrees) of longitude., i.e. 36 meridians for 180 degrees.

last updated 7/14/97