PREFACE 
The idea may seem quixotic, but it is nevertheless the 
author’s confident hope that this book will give a fresh interest 
to the story of Greek mathematics in the eyes both of 
mathematicians and of classical scholars. 
For the mathematician the important consideration is that 
the foundations of mathematics and a great portion of its 
content are Greek. The Greeks laid down the first principles, 
invented the methods ah initio, and fixed the terminology. 
Mathematics in short is a Greek science, whatever new 
developments modern analysis has brought or may bring. 
The interest of the subject for the classical scholar is no 
doubt of a different kind. Greek mathematics reveals an 
important aspect of the Greek genius of which the student of 
Greek culture is apt to lose sight. Most people, when they 
think of the Greek genius, naturally call to mind its master 
pieces in literature and art with their notes of beauty, truth, 
freedom and humanism. But the Greek, with his insatiable 
desire to know the true meaning of everything in the uni 
verse and to be able to give a rational explanation of it, was 
just as irresistibly driven to natural science, mathematics, and 
exact reasoning in general or logic. This austere side of the 
Greek genius found perhaps its most complete expression in 
Aristotle. Aristotle would, however, by no means admit that 
mathematics was divorced from aesthetic; he could conceive, 
he said, of nothing more beautiful than the objects of mathe 
matics. Plato delighted in geometry and in the wonders of 
numbers; dyeco/j.eTpr)Tos prjSels danco, said the inscription 
over the door of the Academy. Euclid was a no less typical 
Greek. Indeed, seeing that so much of Greek is mathematics,