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 32 the Old World it remained the basis of geographical knowledgfe up to the beginning of the eighteenth century, just as his astronomical work was only finally abolished by the work of Newton. Ptolemy has thus the rare distinction of being the greatest authority on two important departments of human knowledge—astronomy and geography—for over fifteen hundred years. Into the details of his description of the world it is unnecessary to go. The map will indicate how near he came to the main outlines of the Mediterranean, of Northwest Europe, of Arabia, and of the Black Sea. Beyond these regions he could only depend upon the rough indications and guesses of untutored merchants. But it is worth while referring to his method of determining latitude, as it was followed up by most succeeding geographers. Between the equator and the most northerly point known to him, he divides up the earth into horizontal strips, called by him "climates," and determined by the average length of the longest day in each. This is a very ropgh method of determining latitude, but it was probably, in most cases, all that Ptolemy had to depend upon, since the measurement of angles would be a rare accomplishment even in modern times, and would only exist among a few mathematicians and astronomers in Ptolemy's days. With him the history of geographical knowledge and discovery in the ancient world closes.

In this chapter I have roughly given the names and exploits of the Greek men of science, who summed up in a series of systematic records the knowledge obtained by merchants, by soldiers, and by travellers of the extent of the world known to the ancients. Of this knowledge, by