Heath T. A History of Greek Mathematics. Volume 1. From Thales to Euclid

Oxford: Clarendon press, 1921. — 460 p.The idea may seem quixotic, but it is nevertheless the authors 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 masterpieces 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 universe 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; άγξωμέτρητο$ μηβζις ϊΐσίτω, 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, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry.Introductory
Greek numerical notation and arithmetical operations
Pythagorean arithmetic
The earliest Greek geometry. Thales
Pythagorean geometry
Progress in the elements down to Plato's time
Special problems
Zeno of Elea
Plato
From Plato to Euclid
Euclid