I 
INTRODUCTORY 
The Greeks and mathematics. 
It is an encouraging sign of the times that more and more 
effort is being directed to promoting a due appreciation and 
a clear understanding of the gifts of the Greeks to mankind. 
What we owe to Greece, what the Greeks have done for 
civilization, aspects of the Greek genius : such are the themes 
of many careful studies which have made a wide appeal and 
will surely produce their effect. In truth all nations, in the 
West at all events, have been to school to the Greeks, in art, 
literature, philosophy, and science, the things which are essen 
tial to the rational use and enjoyment of human powers and 
activities, the things which make life worth living to a rational 
human being. ‘ Of all peoples the Greeks have dreamed the 
dream of life the best.’ And the Greeks were not merely the 
pioneers in the branches of knowledge which they invented 
and to which they gave names. What they began they carried 
to a height of perfection which has not since been surpassed; 
if there are exceptions, it is only where a few crowded centuries 
were not enough to provide the accumulation of experience 
required, whether .for the purpose of correcting hypotheses 
which at first could only be of the nature of guesswork, or of 
suggesting new methods and machinery. 
Of all the manifestations of the Greek genius none is more 
impressive and even awe-inspiring than that which is revealed 
by the history of Greek mathematics. Not only are the range 
and the sum of what the Greek mathematicians actually 
accomplished wonderful in themselves; it is necessary to bear 
in mind that this mass of original work'was done in an almost 
incredibly short space of time, and in spite of the comparative 
inadequacy (as it would seem to us) of the only methods at 
their disposal, namely those of pure geometry, supplemented, 
where necessary, by the ordinary arithmetical operations.