up to the beginning of the last 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 rough 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 far the largest amount was gained, not by systematic
investigation for the purpose of geography, but by military expeditions
for the purpose of conquest. We must now retrace our steps, and
give a rough review of the various stages of conquest. We must now