He appears, in fact, from the references in other authors, which alone furnish us with knowledge of his work, in the light of a scientific traveller of a type rare in his time. Mathematical geography was carried a long step forward by Eratosthenes (_c._ 276–194 B.C.), a native of Cyrene, who became chief librarian at Alexandria under Ptolemy III Euergetes. He calculated the circumference of the earth. He considered Syene to be situated on the tropic (which it was not, precisely), because at noon on the day of the summer solstice the sun appeared to shine directly down a deep well there. He therefore observed the zenith distance of the sun at Alexandria at the same time, and obtained his result from this and the measured distance between Alexandria and Syene. His result was to make the earth’s circumference only about one-seventh greater than it actually is. He also estimated the size of the habitable earth (œcumene), and considered it, as a result, to be about double as long from west to east as it was broad from north to south. But his estimate of the distance from what is now the extremity of Brittany to the known eastern limit of India was about one-third too great. On a map of the world he drew seven parallels, using the few points of which the latitudes had been worked out, and also seven meridians at irregular distances apart. Hipparchus (middle and second half of the second century), an astronomer, native of Nicæa in Bithynia, who worked in Rhodes, drew an elaborate series of parallels, and made the division into 360 degrees; the spaces between the lines he called climata, or zones. The problem presented by meridians was more difficult, for there was no instrument for the calculation of longitude like the gnomon for that of latitude. A well-recognised line was that taken to lie from the mouth of the Danube to that of the Nile--Herodotus had used this--and southward up the latter river; but not only the line itself, but also the ideas of intermediate points lying on it, were rather far from the truth.