[Illustration: PTOLEMAEI ORBIS]

It was left to PTOLEMY of Alexandria to sum up for the ancient
world all the knowledge that had been accumulating from the time
of Eratosthenes to his own day, which we may fix at about 150 A.D.
He took all the information he could find in the writings of the
preceding four hundred years, and reduced it all to one uniform
scale; for it is to him that we owe the invention of the method
and the names of latitude and longitude. Previous writers had been
content to say that the distance between one point and another
was so many stadia, but he reduced all this rough reckoning to
so many degrees of latitude and longitude, from fixed lines as
starting-points. But, unfortunately, all these reckonings were
rough calculations, which are almost invariably beyond the truth;
and Ptolemy, though the greatest of ancient astronomers, still
further distorted his results by assuming that a degree was 500
stadia, or 50 geographical miles. Thus when he found in any of
his authorities that the distance between one port and another was
500 stadia, he assumed, in the first place, that this was accurate,
and, in the second, that the distance between the two places was
equal to a degree of latitude or longitude, as the case might be.
Accordingly he arrived at the result that the breadth of the habitable
globe was, as he put it, twelve hours of longitude (corresponding
to 180°)--nearly one-third as much again as the real dimensions
from Spain to China. The consequence of this was that the distance
from Spain to China _westward_ was correspondingly diminished by
sixty degrees (or nearly 4000 miles), and it was this error that
ultimately encouraged Columbus to attempt his epoch-making voyage.