N° 439
The Circumference of the Earth and Ptolemy’s World Map
Download pdf

The interlink between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography (c. 150 AD) is discussed. As Ptolemy himself stated, he used the value of 180,000 stades for the circumference of the Earth which is in stark contrast to the famous result of Eratosthenes, i.e. 252,000 stades. Many scholars see these different values as a result of the diverse definitions of a stade used by both ancient authors. Such a view cannot, nevertheless, explain the excessive distortion of Ptolemy's world map along the east-west direction. We have treated the problem with the methods of spherical trigonometry and have shown that many features of Ptolemy’s map can be easily explained and corrected under the presupposition that the length of the stade used by Ptolemy coincides with that of Eratosthenes. The latitudinal distortion in Ptolemaic map is caused by his underestimating of the size of the Earth in combination with his efforts to keep the known latitudes of the localities. Another mathematical consequence is a significant longitudinal displacement of the localities lying approximately on the same meridian (so-called antikemenoi poleis), as in the case Carthage in relation to Rome. It is shown that a simple transformation of the Ptolemaic coordinates to the circumference of the Earth measured by Eratosthenes drastically improves the positions of the locations given in Ptolemy´s catalogue. The comparison of the recalculated positions of the identified localities with their actual positions confirmed a very high precision of Eratosthenes' result for the circumference of the Earth.